Imported Upstream version 1.71.0upstream/1.71.0

author: DongHun Kwak <dh0128.kwak@samsung.com> 2019-12-05 15:24:45 +0900
committer: DongHun Kwak <dh0128.kwak@samsung.com> 2019-12-05 15:24:45 +0900
commit: 5ce1cfc2525b06c0a9e38531813781de0281c96d (patch)
tree: 19cc66c6cf6396db288813b2558cc350f1deede2 /libs/math
parent: 3c1df2168531ad5580076ae08d529054689aeedd (diff)
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504 files changed, 14823 insertions, 2921 deletions
diff --git a/libs/math/doc/Jamfile.v2 b/libs/math/doc/Jamfile.v2
index f0874c0784..66e7378a1f 100644
--- a/libs/math/doc/Jamfile.v2
+++ b/libs/math/doc/Jamfile.v2
@@ -65,6 +65,7 @@ boostbook standalone
         # default pnd graphics are awful in PDF form,
         # better use SVG's instead:
         <format>pdf:<xsl:param>admon.graphics.extension=".svg"
+        <format>pdf:<xsl:param>admon.graphics.path=$(here)/../../../doc/src/images/
         <format>pdf:<xsl:param>use.role.for.mediaobject=1 
         <format>pdf:<xsl:param>preferred.mediaobject.role=print
         <format>pdf:<xsl:param>img.src.path=$(images_location)/
diff --git a/libs/math/doc/concepts/concepts.qbk b/libs/math/doc/concepts/concepts.qbk
index 2723f071bd..845b67a292 100644
--- a/libs/math/doc/concepts/concepts.qbk
+++ b/libs/math/doc/concepts/concepts.qbk
@@ -8,7 +8,8 @@ can be used with a number of high-precision libraries, including:
 * __NTL
 * __GMP
 * __MPFR
-* __float128
+* __gcc_quad_type
+* Intel _Quad type
 
 The last four have some license restrictions;
 only __multiprecision when using the `cpp_float` backend
@@ -42,7 +43,8 @@ Some reasons why one would want to use a higher precision:
 * Using an extended-precision type implemented in software as
 [@http://en.wikipedia.org/wiki/Double-double_(arithmetic)#Double-double_arithmetic double-double]
 ([@http://en.wikipedia.org/wiki/Darwin_(operating_system) Darwin]) is sometimes unpredictably inaccurate.
-* Loss of precision or inaccuracy caused by extreme arguments or cancellation error.
+* Loss of precision or inaccuracy caused by extreme arguments or
+[@http://en.wikipedia.org/wiki/Loss_of_significance cancellation errors].
 * An accuracy as good as possible for a chosen built-in floating-point type is required.
 * As a reference value, for example, to determine the inaccuracy
 of a value computed with a built-in floating point type,
@@ -65,7 +67,10 @@ often caused by [@http://en.wikipedia.org/wiki/Loss_of_significance cancellation
 can be avoided by using __complements: see __why_complements).
 
 If you require a value which is as accurate as can be represented in the floating-point type,
-and is thus the closest representable value and has an error less than 1/2 a
+and is thus the 
+[@https://en.wikipedia.org/wiki/Floating-point_arithmetic#Representable_numbers,_conversion_and_rounding closest representable value]
+correctly rounded to nearest,
+and has an error less than 1/2 a
 [@http://en.wikipedia.org/wiki/Least_significant_bit least significant bit] or
 [@http://en.wikipedia.org/wiki/Unit_in_the_last_place ulp]
 it may be useful to use a higher-precision type,
@@ -93,10 +98,15 @@ is a practical way of generating (almost always) correctly rounded values.
 [import ../../example/big_seventh.cpp]
 
 [big_seventh_example_1]
+[big_seventh_example_2]
+The full source of this example is at [@../../example/big_seventh.cpp big_seventh.cpp]
 
 [import ../../example/fft_sines_table.cpp]
 
 [fft_sines_table_example_1]
+[fft_sines_table_example_2]
+[fft_sines_table_example_3
+]
 
 The table output is:
 
@@ -104,6 +114,7 @@ The table output is:
 
 [fft_sines_table_example_check]
 
+The full source of this example is at [@../../example/fft_sines_table.cpp fft_sines_table.cpp]
 
 [/TODO another example needed here]
 
@@ -123,8 +134,9 @@ At present support for GCC's native `__float128` datatype is extremely limited:
 will all work with that type, and that's about it.  If you want to use the distributions or special
 functions then you will need to provide your own wrapper header that:
 
-* Provides std::numeric_limits<__float128> support.
-* Provides overloads of the standard library math function for type `__float128`and which forward to the libquadmath equivalents.
+* Provides `std::numeric_limits<__float128>` support.
+* Provides overloads of the standard library math functions for type `__float128` 
+and which forward to the libquadmath equivalents.
 
 Ultimately these facilities should be provided by GCC and `libstdc++`.
 
diff --git a/libs/math/doc/constants/constants.qbk b/libs/math/doc/constants/constants.qbk
index 34ccaa984d..4811f6caaa 100644
--- a/libs/math/doc/constants/constants.qbk
+++ b/libs/math/doc/constants/constants.qbk
@@ -498,7 +498,7 @@ The result of an expanded macro for Pi is shown below.
 
 [endsect] [/section:new_const Defining New Constants]
 
-[section:constants_faq FAQs]
+[section:constants_faq Math Constants FAQs]
 
 [h4 Why are ['these] Constants Chosen?]
 It is, of course, impossible to please everyone with a list like this.
diff --git a/libs/math/doc/cstdfloat/cstdfloat.qbk b/libs/math/doc/cstdfloat/cstdfloat.qbk
index 0c90e61986..b49af3a841 100644
--- a/libs/math/doc/cstdfloat/cstdfloat.qbk
+++ b/libs/math/doc/cstdfloat/cstdfloat.qbk
@@ -153,28 +153,28 @@ The definition (or not) of a
 [link math_toolkit.macros floating-point constant macro]
 is a way to test if a [*specific width floating-point] is available on a platform.
 
-	#if defined(BOOST_FLOAT16_C)
-	// Can use boost::float16_t, perhaps a proposed __short_float.
-	// P0192R1, Adding Fundamental Type for Short Float,
-	// Boris Fomitchev, Sergei Nikolaev, Olivier Giroux, Lawrence Crowl, 2016 Feb14
-	// http://www.open-std.org/jtc1/sc22/wg14/www/docs/n2016.pdf
-	#endif
+  #if defined(BOOST_FLOAT16_C)
+  // Can use boost::float16_t, perhaps a proposed __short_float.
+  // P0192R1, Adding Fundamental Type for Short Float,
+  // Boris Fomitchev, Sergei Nikolaev, Olivier Giroux, Lawrence Crowl, 2016 Feb14
+  // http://www.open-std.org/jtc1/sc22/wg14/www/docs/n2016.pdf
+  #endif
 
-	#if defined(BOOST_FLOAT32_C)
-	// Can use boost::float32_t, usually type `float`.
-	#endif
+  #if defined(BOOST_FLOAT32_C)
+  // Can use boost::float32_t, usually type `float`.
+  #endif
 
-	#if defined(BOOST_FLOAT64_C)
-	// Can use boost::float64_t, usually type `double`, and sometimes also type `long double`.
-	#endif
+  #if defined(BOOST_FLOAT64_C)
+  // Can use boost::float64_t, usually type `double`, and sometimes also type `long double`.
+  #endif
 
-	#if defined(BOOST_FLOAT80_C)
-	// Can use boost::float80_t, sometimes type `long double`.
-	#endif
+  #if defined(BOOST_FLOAT80_C)
+  // Can use boost::float80_t, sometimes type `long double`.
+  #endif
 
-	#if defined(BOOST_FLOAT128_C)
-	// Can use boost::float128_t. Sometimes type `__float128` or `_Quad`.
-	#endif
+  #if defined(BOOST_FLOAT128_C)
+  // Can use boost::float128_t. Sometimes type `__float128` or `_Quad`.
+  #endif
 
 This can be used to write code which will compile and run (albeit differently) on several platforms.
 Without these tests, if a width, say `float128_t` is not supported, then compilation would fail.
@@ -407,13 +407,13 @@ Intel on Windows you need to compile with `-Qoption,cpp,--extended_float_type -D
 activate 128-bit floating point support.]
 
 The `__float128` type is provided by the [@http://gcc.gnu.org/onlinedocs/libquadmath/ libquadmath library] on GCC or
-by Intel's FORTRAN library with Intel C++. THey also provide a full set of `<cmath>` functions in `namespace std`.
+by Intel's FORTRAN library with Intel C++. They also provide a full set of `<cmath>` functions in `namespace std`.
 
 [h4 Using C __float128 quadmath type]
 
-[quadmath_snprintf_1]
+[/quadmath_snprintf_1]
 
-The source code is at [@../../example/quadmath_snprintf.c quadmath_snprintf.c].
+The source code is at [@https://gcc.gnu.org/onlinedocs/gcc-9.1.0/libquadmath/quadmath_005fsnprintf.html#quadmath_005fsnprintf quadmath_snprintf.c].
 
 [h4 Using C++ `float128` quadmath type]
 
diff --git a/libs/math/doc/differentiation/autodiff.pdf b/libs/math/doc/differentiation/autodiff.pdf
new file mode 100644
index 0000000000..46da5d644b
--- /dev/null
+++ b/libs/math/doc/differentiation/autodiff.pdf
diff --git a/libs/math/doc/differentiation/autodiff.qbk b/libs/math/doc/differentiation/autodiff.qbk
new file mode 100644
index 0000000000..522502d800
--- /dev/null
+++ b/libs/math/doc/differentiation/autodiff.qbk
@@ -0,0 +1,313 @@
+[/          Copyright Matthew Pulver 2018 - 2019.
+// Distributed under the Boost Software License, Version 1.0.
+//    (See accompanying file LICENSE_1_0.txt or copy at
+//          https://www.boost.org/LICENSE_1_0.txt)]
+
+[section:autodiff Automatic Differentiation]
+[template autodiff_equation[name]  '''<inlinemediaobject><imageobject><imagedata fileref="../equations/autodiff/'''[name]'''"></imagedata></imageobject></inlinemediaobject>''']
+
+[h1:synopsis Synopsis]
+
+    #include <boost/math/differentiation/autodiff.hpp>
+    
+    namespace boost {
+    namespace math {
+    namespace differentiation {
+    
+    // Function returning a single variable of differentiation. Recommended: Use auto for type.
+    template <typename RealType, size_t Order, size_t... Orders>
+    autodiff_fvar<RealType, Order, Orders...> make_fvar(RealType const& ca);
+    
+    // Function returning multiple independent variables of differentiation in a std::tuple.
+    template<typename RealType, size_t... Orders, typename... RealTypes>
+    auto make_ftuple(RealTypes const&... ca);
+    
+    // Type of combined autodiff types. Recommended: Use auto for return type (C++14).
+    template <typename RealType, typename... RealTypes>
+    using promote = typename detail::promote_args_n<RealType, RealTypes...>::type;
+    
+    namespace detail {
+    
+    // Single autodiff variable. Use make_fvar() or make_ftuple() to instantiate.
+    template <typename RealType, size_t Order>
+    class fvar {
+     public:
+      // Query return value of function to get the derivatives.
+      template <typename... Orders>
+      get_type_at<RealType, sizeof...(Orders) - 1> derivative(Orders... orders) const;
+    
+      // All of the arithmetic and comparison operators are overloaded.
+      template <typename RealType2, size_t Order2>
+      fvar& operator+=(fvar<RealType2, Order2> const&);
+    
+      fvar& operator+=(root_type const&);
+    
+      // ...
+    };
+    
+    // Standard math functions are overloaded and called via argument-dependent lookup (ADL).
+    template <typename RealType, size_t Order>
+    fvar<RealType, Order> floor(fvar<RealType, Order> const&);
+    
+    template <typename RealType, size_t Order>
+    fvar<RealType, Order> exp(fvar<RealType, Order> const&);
+    
+    // ...
+    
+    }  // namespace detail
+    
+    }  // namespace differentiation
+    }  // namespace math
+    }  // namespace boost
+
+[h1:description Description]
+
+Autodiff is a header-only C++ library that facilitates the [@https://en.wikipedia.org/wiki/Automatic_differentiation
+automatic differentiation] (forward mode) of mathematical functions of single and multiple variables.
+
+This implementation is based upon the [@https://en.wikipedia.org/wiki/Taylor_series Taylor series] expansion of
+an analytic function /f/ at the point ['x[sub 0]]:
+
+[/ Thanks to http://www.tlhiv.org/ltxpreview/ for LaTeX-to-SVG conversions. ]
+[/ \Large\begin{align*}
+f(x_0+\varepsilon) &= f(x_0) + f'(x_0)\varepsilon + \frac{f''(x_0)}{2!}\varepsilon^2 + \frac{f'''(x_0)}{3!}\varepsilon^3 + \cdots \\
+  &= \sum_{n=0}^N\frac{f^{(n)}(x_0)}{n!}\varepsilon^n + O\left(\varepsilon^{N+1}\right).
+\end{align*} ]
+[:[:[autodiff_equation taylor_series.svg]]]
+
+The essential idea of autodiff is the substitution of numbers with polynomials in the evaluation of ['f(x[sub 0])].
+By substituting the number ['x[sub 0]] with the first-order polynomial ['x[sub 0]+\u03b5], and using the same
+algorithm to compute ['f(x[sub 0]+\u03b5)], the resulting polynomial in ['\u03b5] contains the function's derivatives
+['f'(x[sub 0])], ['f''(x[sub 0])], ['f\'\'\'(x[sub 0])], ... within the coefficients. Each coefficient is equal to the
+derivative of its respective order, divided by the factorial of the order.
+
+In greater detail, assume one is interested in calculating the first /N/ derivatives of /f/ at ['x[sub 0]]. Without
+loss of precision to the calculation of the derivatives, all terms ['O(\u03b5[super N+1])] that include powers
+of ['\u03b5] greater than /N/ can be discarded. (This is due to the fact that each term in a polynomial depends
+only upon equal and lower-order terms under arithmetic operations.) Under these truncation rules, /f/ provides a
+polynomial-to-polynomial transformation:
+
+[/ \Large$$f \qquad : \qquad x_0+\varepsilon \qquad \mapsto \qquad
+    \sum_{n=0}^Ny_n\varepsilon^n=\sum_{n=0}^N\frac{f^{(n)}(x_0)}{n!}\varepsilon^n.$$ ]
+[:[:[autodiff_equation polynomial_transform.svg]]]
+
+C++'s ability to overload operators and functions allows for the creation of a class `fvar` ([_f]orward-mode autodiff
+[_var]iable) that represents polynomials in ['\u03b5]. Thus the same algorithm /f/ that calculates the numeric value
+of ['y[sub 0]=f(x[sub 0])], when written to accept and return variables of a generic (template) type, is also used
+to calculate the polynomial ['\u03a3[sub n]y[sub n]\u03b5[super n]=f(x[sub 0]+\u03b5)].  The derivatives
+['f[super (n)](x[sub 0])] are then found from the product of the respective factorial ['n!] and coefficient
+['y[sub n]]:
+
+[/ \Large$$\frac{d^nf}{dx^n}(x_0)=n!y_n.$$ ]
+[:[:[autodiff_equation derivative_formula.svg]]]
+
+
+[h1:examples Examples]
+
+[h2:example-single-variable Example 1: Single-variable derivatives]
+
+[h3 Calculate derivatives of ['f(x)=x[super 4]] at /x/=2.]
+
+In this example, `make_fvar<double, Order>(2.0)` instantiates the polynomial 2+['\u03b5]. The `Order=5`
+means that enough space is allocated (on the stack) to hold a polynomial of up to degree 5 during the proceeding
+computation.
+
+Internally, this is modeled by a `std::array<double,6>` whose elements `{2, 1, 0, 0, 0, 0}` correspond
+to the 6 coefficients of the polynomial upon initialization. Its fourth power, at the end of the computation, is
+a polynomial with coefficients `y = {16, 32, 24, 8, 1, 0}`.  The derivatives are obtained using the formula
+['f[super (n)](2)=n!*y[n]].
+
+    #include <boost/math/differentiation/autodiff.hpp>
+    #include <iostream>
+    
+    template <typename T>
+    T fourth_power(T const& x) {
+      T x4 = x * x;  // retval in operator*() uses x4's memory via NRVO.
+      x4 *= x4;      // No copies of x4 are made within operator*=() even when squaring.
+      return x4;     // x4 uses y's memory in main() via NRVO.
+    }
+    
+    int main() {
+      using namespace boost::math::differentiation;
+    
+      constexpr unsigned Order = 5;                  // Highest order derivative to be calculated.
+      auto const x = make_fvar<double, Order>(2.0);  // Find derivatives at x=2.
+      auto const y = fourth_power(x);
+      for (unsigned i = 0; i <= Order; ++i)
+        std::cout << "y.derivative(" << i << ") = " << y.derivative(i) << std::endl;
+      return 0;
+    }
+    /*
+    Output:
+    y.derivative(0) = 16
+    y.derivative(1) = 32
+    y.derivative(2) = 48
+    y.derivative(3) = 48
+    y.derivative(4) = 24
+    y.derivative(5) = 0
+    */
+
+The above calculates
+
+[/ \Large\begin{alignat*}{3}
+{\tt y.derivative(0)} &=& f(2) =&& \left.x^4\right|_{x=2} &= 16\\
+{\tt y.derivative(1)} &=& f'(2) =&& \left.4\cdot x^3\right|_{x=2} &= 32\\
+{\tt y.derivative(2)} &=& f''(2) =&& \left.4\cdot 3\cdot x^2\right|_{x=2} &= 48\\
+{\tt y.derivative(3)} &=& f'''(2) =&& \left.4\cdot 3\cdot2\cdot x\right|_{x=2} &= 48\\
+{\tt y.derivative(4)} &=& f^{(4)}(2) =&& 4\cdot 3\cdot2\cdot1 &= 24\\
+{\tt y.derivative(5)} &=& f^{(5)}(2) =&& 0 &
+\end{alignat*} ]
+[:[:[autodiff_equation example1.svg]]]
+
+[h2:example-multiprecision
+Example 2: Multi-variable mixed partial derivatives with multi-precision data type]
+
+[/ \Large$\frac{\partial^{12}f}{\partial w^{3}\partial x^{2}\partial y^{4}\partial z^{3}}(11,12,13,14)$]
+[/ \Large$f(w,x,y,z)=\exp\left(w\sin\left(\frac{x\log(y)}{z}\right)+\sqrt{\frac{wz}{xy}}\right)+\frac{w^2}{\tan(z)}$]
+[h3 Calculate [autodiff_equation mixed12.svg] with a precision of about 50 decimal digits,
+where [autodiff_equation example2f.svg].]
+
+In this example, `make_ftuple<float50, Nw, Nx, Ny, Nz>(11, 12, 13, 14)` returns a `std::tuple` of 4
+independent `fvar` variables, with values of 11, 12, 13, and 14, for which the maximum order derivative to
+be calculated for each are 3, 2, 4, 3, respectively. The order of the variables is important, as it is the same
+order used when calling `v.derivative(Nw, Nx, Ny, Nz)` in the example below.
+
+    #include <boost/math/differentiation/autodiff.hpp>
+    #include <boost/multiprecision/cpp_bin_float.hpp>
+    #include <iostream>
+    
+    using namespace boost::math::differentiation;
+    
+    template <typename W, typename X, typename Y, typename Z>
+    promote<W, X, Y, Z> f(const W& w, const X& x, const Y& y, const Z& z) {
+      using namespace std;
+      return exp(w * sin(x * log(y) / z) + sqrt(w * z / (x * y))) + w * w / tan(z);
+    }
+    
+    int main() {
+      using float50 = boost::multiprecision::cpp_bin_float_50;
+    
+      constexpr unsigned Nw = 3;  // Max order of derivative to calculate for w
+      constexpr unsigned Nx = 2;  // Max order of derivative to calculate for x
+      constexpr unsigned Ny = 4;  // Max order of derivative to calculate for y
+      constexpr unsigned Nz = 3;  // Max order of derivative to calculate for z
+      // Declare 4 independent variables together into a std::tuple.
+      auto const variables = make_ftuple<float50, Nw, Nx, Ny, Nz>(11, 12, 13, 14);
+      auto const& w = std::get<0>(variables);  // Up to Nw derivatives at w=11
+      auto const& x = std::get<1>(variables);  // Up to Nx derivatives at x=12
+      auto const& y = std::get<2>(variables);  // Up to Ny derivatives at y=13
+      auto const& z = std::get<3>(variables);  // Up to Nz derivatives at z=14
+      auto const v = f(w, x, y, z);
+      // Calculated from Mathematica symbolic differentiation.
+      float50 const answer("1976.319600747797717779881875290418720908121189218755");
+      std::cout << std::setprecision(std::numeric_limits<float50>::digits10)
+                << "mathematica   : " << answer << '\n'
+                << "autodiff      : " << v.derivative(Nw, Nx, Ny, Nz) << '\n'
+                << std::setprecision(3)
+                << "relative error: " << (v.derivative(Nw, Nx, Ny, Nz) / answer - 1) << '\n';
+      return 0;
+    }
+    /*
+    Output:
+    mathematica   : 1976.3196007477977177798818752904187209081211892188
+    autodiff      : 1976.3196007477977177798818752904187209081211892188
+    relative error: 2.67e-50
+    */
+
+[h2:example-black_scholes
+Example 3: Black-Scholes Option Pricing with Greeks Automatically Calculated]
+[h3 Calculate greeks directly from the Black-Scholes pricing function.]
+
+Below is the standard Black-Scholes pricing function written as a function template, where the price, volatility
+(sigma), time to expiration (tau) and interest rate are template parameters. This means that any greek based on
+these 4 variables can be calculated using autodiff. The below example calculates delta and gamma where the variable
+of differentiation is only the price. For examples of more exotic greeks, see `example/black_scholes.cpp`.
+
+```
+#include <boost/math/differentiation/autodiff.hpp>
+#include <iostream>
+
+using namespace boost::math::constants;
+using namespace boost::math::differentiation;
+
+// Equations and function/variable names are from
+// https://en.wikipedia.org/wiki/Greeks_(finance)#Formulas_for_European_option_Greeks
+
+// Standard normal cumulative distribution function
+template <typename X>
+X Phi(X const& x) {
+  return 0.5 * erfc(-one_div_root_two<X>() * x);
+}
+
+enum class CP { call, put };
+
+// Assume zero annual dividend yield (q=0).
+template <typename Price, typename Sigma, typename Tau, typename Rate>
+promote<Price, Sigma, Tau, Rate> black_scholes_option_price(CP cp,
+                                                            double K,
+                                                            Price const& S,
+                                                            Sigma const& sigma,
+                                                            Tau const& tau,
+                                                            Rate const& r) {
+  using namespace std;
+  auto const d1 = (log(S / K) + (r + sigma * sigma / 2) * tau) / (sigma * sqrt(tau));
+  auto const d2 = (log(S / K) + (r - sigma * sigma / 2) * tau) / (sigma * sqrt(tau));
+  switch (cp) {
+    case CP::call:
+      return S * Phi(d1) - exp(-r * tau) * K * Phi(d2);
+    case CP::put:
+      return exp(-r * tau) * K * Phi(-d2) - S * Phi(-d1);
+  }
+}
+
+int main() {
+  double const K = 100.0;                    // Strike price.
+  auto const S = make_fvar<double, 2>(105);  // Stock price.
+  double const sigma = 5;                    // Volatility.
+  double const tau = 30.0 / 365;             // Time to expiration in years. (30 days).
+  double const r = 1.25 / 100;               // Interest rate.
+  auto const call_price = black_scholes_option_price(CP::call, K, S, sigma, tau, r);
+  auto const put_price = black_scholes_option_price(CP::put, K, S, sigma, tau, r);
+
+  std::cout << "black-scholes call price = " << call_price.derivative(0) << '\n'
+            << "black-scholes put  price = " << put_price.derivative(0) << '\n'
+            << "call delta = " << call_price.derivative(1) << '\n'
+            << "put  delta = " << put_price.derivative(1) << '\n'
+            << "call gamma = " << call_price.derivative(2) << '\n'
+            << "put  gamma = " << put_price.derivative(2) << '\n';
+  return 0;
+}
+/*
+Output:
+black-scholes call price = 56.5136
+black-scholes put  price = 51.4109
+call delta = 0.773818
+put  delta = -0.226182
+call gamma = 0.00199852
+put  gamma = 0.00199852
+*/
+```
+
+[h1 Advantages of Automatic Differentiation]
+The above examples illustrate some of the advantages of using autodiff:
+
+* Elimination of code redundancy. The existence of /N/ separate functions to calculate derivatives is a form
+  of code redundancy, with all the liabilities that come with it:
+    * Changes to one function require /N/ additional changes to other functions. In the 3rd example above,
+      consider how much larger and inter-dependent the above code base would be if a separate function were
+      written for [@https://en.wikipedia.org/wiki/Greeks_(finance)#Formulas_for_European_option_Greeks
+      each Greek] value.
+    * Dependencies upon a derivative function for a different purpose will break when changes are made to
+      the original function. What doesn't need to exist cannot break.
+    * Code bloat, reducing conceptual integrity. Control over the evolution of code is easier/safer when
+      the code base is smaller and able to be intuitively grasped.
+* Accuracy of derivatives over finite difference methods. Single-iteration finite difference methods always include
+  a ['\u0394x] free variable that must be carefully chosen for each application. If ['\u0394x] is too small, then
+  numerical errors become large. If ['\u0394x] is too large, then mathematical errors become large.  With autodiff,
+  there are no free variables to set and the accuracy of the answer is generally superior to finite difference
+  methods even with the best choice of ['\u0394x].
+
+[h1 Manual]
+Additional details are in the [@../differentiation/autodiff.pdf autodiff manual].
+
+[endsect]
diff --git a/libs/math/doc/differentiation/autodiff.tex b/libs/math/doc/differentiation/autodiff.tex
new file mode 100644
index 0000000000..e71876a81d
--- /dev/null
+++ b/libs/math/doc/differentiation/autodiff.tex
@@ -0,0 +1,1054 @@
+%           Copyright Matthew Pulver 2018 - 2019.
+% Distributed under the Boost Software License, Version 1.0.
+%     (See accompanying file LICENSE_1_0.txt or copy at
+%           https://www.boost.org/LICENSE_1_0.txt)
+
+\documentclass{article}
+\usepackage{amsmath} %\usepackage{mathtools}
+\usepackage{amssymb} %\mathbb
+\usepackage{array} % m{} column in tabular
+\usepackage{csquotes} % displayquote
+\usepackage{fancyhdr}
+\usepackage{fancyvrb}
+\usepackage[margin=0.75in]{geometry}
+\usepackage{graphicx}
+\usepackage{hyperref}
+%\usepackage{listings}
+\usepackage{multirow}
+\usepackage[super]{nth}
+\usepackage{wrapfig}
+\usepackage{xcolor}
+
+\hypersetup{%
+  colorlinks=false,% hyperlinks will be black
+  linkbordercolor=blue,% hyperlink borders will be red
+  urlbordercolor=blue,%
+  pdfborderstyle={/S/U/W 1}% border style will be underline of width 1pt
+}
+
+\pagestyle{fancyplain}
+\fancyhf{}
+\renewcommand{\headrulewidth}{0pt}
+\cfoot[]{\thepage\\
+\scriptsize\color{gray} Copyright \textcopyright\/ Matthew Pulver 2018--2019.
+Distributed under the Boost Software License, Version 1.0.\\
+(See accompanying file LICENSE\_1\_0.txt or copy at
+\url{https://www.boost.org/LICENSE\_1\_0.txt})}
+
+\DeclareMathOperator{\sinc}{sinc}
+
+\begin{document}
+
+\title{Autodiff\\
+\large Automatic Differentiation C++ Library}
+\author{Matthew Pulver}
+\maketitle
+
+%\date{}
+
+%\begin{abstract}
+%\end{abstract}
+
+\tableofcontents
+
+%\section{Synopsis}
+%\begingroup
+%\fontsize{10pt}{10pt}\selectfont
+%\begin{verbatim}
+% example/synopsis.cpp
+%\end{verbatim}
+%\endgroup
+
+\newpage
+
+\section{Description}
+
+Autodiff is a header-only C++ library that facilitates the
+\href{https://en.wikipedia.org/wiki/Automatic_differentiation}{automatic differentiation} (forward mode) of
+mathematical functions of single and multiple variables.
+
+This implementation is based upon the \href{https://en.wikipedia.org/wiki/Taylor_series}{Taylor series} expansion of
+an analytic function $f$ at the point $x_0$:
+
+\begin{align*}
+f(x_0+\varepsilon) &= f(x_0) + f'(x_0)\varepsilon + \frac{f''(x_0)}{2!}\varepsilon^2 + \frac{f'''(x_0)}{3!}\varepsilon^3 + \cdots \\
+  &= \sum_{n=0}^N\frac{f^{(n)}(x_0)}{n!}\varepsilon^n + O\left(\varepsilon^{N+1}\right).
+\end{align*}
+The essential idea of autodiff is the substitution of numbers with polynomials in the evaluation of $f(x_0)$. By
+substituting the number $x_0$ with the first-order polynomial $x_0+\varepsilon$, and using the same algorithm
+to compute $f(x_0+\varepsilon)$, the resulting polynomial in $\varepsilon$ contains the function's derivatives
+$f'(x_0)$, $f''(x_0)$, $f'''(x_0)$, ...  within the coefficients. Each coefficient is equal to the derivative of
+its respective order, divided by the factorial of the order.
+
+In greater detail, assume one is interested in calculating the first $N$ derivatives of $f$ at $x_0$. Without loss
+of precision to the calculation of the derivatives, all terms $O\left(\varepsilon^{N+1}\right)$ that include powers
+of $\varepsilon$ greater than $N$ can be discarded. (This is due to the fact that each term in a polynomial depends
+only upon equal and lower-order terms under arithmetic operations.) Under these truncation rules, $f$ provides a
+polynomial-to-polynomial transformation:
+
+\[
+f \qquad : \qquad x_0+\varepsilon \qquad \mapsto \qquad
+    \sum_{n=0}^Ny_n\varepsilon^n=\sum_{n=0}^N\frac{f^{(n)}(x_0)}{n!}\varepsilon^n.
+\]
+C++'s ability to overload operators and functions allows for the creation of a class {\tt fvar}
+(\underline{f}orward-mode autodiff \underline{var}iable) that represents polynomials in $\varepsilon$. Thus
+the same algorithm $f$ that calculates the numeric value of $y_0=f(x_0)$, when
+written to accept and return variables of a generic (template) type, is also used to calculate the polynomial
+$\sum_{n=0}^Ny_n\varepsilon^n=f(x_0+\varepsilon)$. The derivatives $f^{(n)}(x_0)$ are then found from the
+product of the respective factorial $n!$ and coefficient $y_n$:
+
+\[ \frac{d^nf}{dx^n}(x_0)=n!y_n. \]
+
+\section{Examples}
+
+\subsection{Example 1: Single-variable derivatives}
+
+\subsubsection{Calculate derivatives of $f(x)=x^4$ at $x=2$.}
+
+In this example, {\tt make\_fvar<double, Order>(2.0)} instantiates the polynomial $2+\varepsilon$. The {\tt Order=5}
+means that enough space is allocated (on the stack) to hold a polynomial of up to degree 5 during the proceeding
+computation.
+
+Internally, this is modeled by a {\tt std::array<double,6>} whose elements {\tt \{2, 1, 0, 0, 0, 0\}} correspond
+to the 6 coefficients of the polynomial upon initialization. Its fourth power, at the end of the computation, is
+a polynomial with coefficients {\tt y = \{16, 32, 24, 8, 1, 0\}}.  The derivatives are obtained using the formula
+$f^{(n)}(2)=n!*{\tt y[n]}$.
+
+\begin{verbatim}
+#include <boost/math/differentiation/autodiff.hpp>
+#include <iostream>
+
+template <typename T>
+T fourth_power(T const& x) {
+  T x4 = x * x;  // retval in operator*() uses x4's memory via NRVO.
+  x4 *= x4;      // No copies of x4 are made within operator*=() even when squaring.
+  return x4;     // x4 uses y's memory in main() via NRVO.
+}
+
+int main() {
+  using namespace boost::math::differentiation;
+
+  constexpr unsigned Order = 5;                  // Highest order derivative to be calculated.
+  auto const x = make_fvar<double, Order>(2.0);  // Find derivatives at x=2.
+  auto const y = fourth_power(x);
+  for (unsigned i = 0; i <= Order; ++i)
+    std::cout << "y.derivative(" << i << ") = " << y.derivative(i) << std::endl;
+  return 0;
+}
+/*
+Output:
+y.derivative(0) = 16
+y.derivative(1) = 32
+y.derivative(2) = 48
+y.derivative(3) = 48
+y.derivative(4) = 24
+y.derivative(5) = 0
+*/
+\end{verbatim}
+The above calculates
+
+\begin{alignat*}{3}
+{\tt y.derivative(0)} &=& f(2) =&& \left.x^4\right|_{x=2} &= 16\\
+{\tt y.derivative(1)} &=& f'(2) =&& \left.4\cdot x^3\right|_{x=2} &= 32\\
+{\tt y.derivative(2)} &=& f''(2) =&& \left.4\cdot 3\cdot x^2\right|_{x=2} &= 48\\
+{\tt y.derivative(3)} &=& f'''(2) =&& \left.4\cdot 3\cdot2\cdot x\right|_{x=2} &= 48\\
+{\tt y.derivative(4)} &=& f^{(4)}(2) =&& 4\cdot 3\cdot2\cdot1 &= 24\\
+{\tt y.derivative(5)} &=& f^{(5)}(2) =&& 0 &
+\end{alignat*}
+
+\subsection{Example 2: Multi-variable mixed partial derivatives with multi-precision data type}\label{multivar}
+\subsubsection{Calculate $\frac{\partial^{12}f}{\partial w^{3}\partial x^{2}\partial y^{4}\partial z^{3}}(11,12,13,14)$
+with a precision of about 50 decimal digits,\\
+where $f(w,x,y,z)=\exp\left(w\sin\left(\frac{x\log(y)}{z}\right)+\sqrt{\frac{wz}{xy}}\right)+\frac{w^2}{\tan(z)}$.}
+
+In this example, {\tt make\_ftuple<float50, Nw, Nx, Ny, Nz>(11, 12, 13, 14)} returns a {\tt std::tuple} of 4
+independent {\tt fvar} variables, with values of 11, 12, 13, and 14, for which the maximum order derivative to
+be calculated for each are 3, 2, 4, 3, respectively. The order of the variables is important, as it is the same
+order used when calling {\tt v.derivative(Nw, Nx, Ny, Nz)} in the example below.
+
+\begin{verbatim}
+#include <boost/math/differentiation/autodiff.hpp>
+#include <boost/multiprecision/cpp_bin_float.hpp>
+#include <iostream>
+
+using namespace boost::math::differentiation;
+
+template <typename W, typename X, typename Y, typename Z>
+promote<W, X, Y, Z> f(const W& w, const X& x, const Y& y, const Z& z) {
+  using namespace std;
+  return exp(w * sin(x * log(y) / z) + sqrt(w * z / (x * y))) + w * w / tan(z);
+}
+
+int main() {
+  using float50 = boost::multiprecision::cpp_bin_float_50;
+
+  constexpr unsigned Nw = 3;  // Max order of derivative to calculate for w
+  constexpr unsigned Nx = 2;  // Max order of derivative to calculate for x
+  constexpr unsigned Ny = 4;  // Max order of derivative to calculate for y
+  constexpr unsigned Nz = 3;  // Max order of derivative to calculate for z
+  // Declare 4 independent variables together into a std::tuple.
+  auto const variables = make_ftuple<float50, Nw, Nx, Ny, Nz>(11, 12, 13, 14);
+  auto const& w = std::get<0>(variables);  // Up to Nw derivatives at w=11
+  auto const& x = std::get<1>(variables);  // Up to Nx derivatives at x=12
+  auto const& y = std::get<2>(variables);  // Up to Ny derivatives at y=13
+  auto const& z = std::get<3>(variables);  // Up to Nz derivatives at z=14
+  auto const v = f(w, x, y, z);
+  // Calculated from Mathematica symbolic differentiation.
+  float50 const answer("1976.319600747797717779881875290418720908121189218755");
+  std::cout << std::setprecision(std::numeric_limits<float50>::digits10)
+            << "mathematica   : " << answer << '\n'
+            << "autodiff      : " << v.derivative(Nw, Nx, Ny, Nz) << '\n'
+            << std::setprecision(3)
+            << "relative error: " << (v.derivative(Nw, Nx, Ny, Nz) / answer - 1) << '\n';
+  return 0;
+}
+/*
+Output:
+mathematica   : 1976.3196007477977177798818752904187209081211892188
+autodiff      : 1976.3196007477977177798818752904187209081211892188
+relative error: 2.67e-50
+*/
+\end{verbatim}
+
+\subsection{Example 3: Black-Scholes Option Pricing with Greeks Automatically Calculated}
+\subsubsection{Calculate greeks directly from the Black-Scholes pricing function.}
+
+Below is the standard Black-Scholes pricing function written as a function template, where the price, volatility
+(sigma), time to expiration (tau) and interest rate are template parameters. This means that any Greek based on
+these 4 variables can be calculated using autodiff. The below example calculates delta and gamma where the variable
+of differentiation is only the price. For examples of more exotic greeks, see {\tt example/black\_scholes.cpp}.
+
+\begin{verbatim}
+#include <boost/math/differentiation/autodiff.hpp>
+#include <iostream>
+
+using namespace boost::math::constants;
+using namespace boost::math::differentiation;
+
+// Equations and function/variable names are from
+// https://en.wikipedia.org/wiki/Greeks_(finance)#Formulas_for_European_option_Greeks
+
+// Standard normal cumulative distribution function
+template <typename X>
+X Phi(X const& x) {
+  return 0.5 * erfc(-one_div_root_two<X>() * x);
+}
+
+enum class CP { call, put };
+
+// Assume zero annual dividend yield (q=0).
+template <typename Price, typename Sigma, typename Tau, typename Rate>
+promote<Price, Sigma, Tau, Rate> black_scholes_option_price(CP cp,
+                                                            double K,
+                                                            Price const& S,
+                                                            Sigma const& sigma,
+                                                            Tau const& tau,
+                                                            Rate const& r) {
+  using namespace std;
+  auto const d1 = (log(S / K) + (r + sigma * sigma / 2) * tau) / (sigma * sqrt(tau));
+  auto const d2 = (log(S / K) + (r - sigma * sigma / 2) * tau) / (sigma * sqrt(tau));
+  switch (cp) {
+    case CP::call:
+      return S * Phi(d1) - exp(-r * tau) * K * Phi(d2);
+    case CP::put:
+      return exp(-r * tau) * K * Phi(-d2) - S * Phi(-d1);
+  }
+}
+
+int main() {
+  double const K = 100.0;                    // Strike price.
+  auto const S = make_fvar<double, 2>(105);  // Stock price.
+  double const sigma = 5;                    // Volatility.
+  double const tau = 30.0 / 365;             // Time to expiration in years. (30 days).
+  double const r = 1.25 / 100;               // Interest rate.
+  auto const call_price = black_scholes_option_price(CP::call, K, S, sigma, tau, r);
+  auto const put_price = black_scholes_option_price(CP::put, K, S, sigma, tau, r);
+
+  std::cout << "black-scholes call price = " << call_price.derivative(0) << '\n'
+            << "black-scholes put  price = " << put_price.derivative(0) << '\n'
+            << "call delta = " << call_price.derivative(1) << '\n'
+            << "put  delta = " << put_price.derivative(1) << '\n'
+            << "call gamma = " << call_price.derivative(2) << '\n'
+            << "put  gamma = " << put_price.derivative(2) << '\n';
+  return 0;
+}
+/*
+Output:
+black-scholes call price = 56.5136
+black-scholes put  price = 51.4109
+call delta = 0.773818
+put  delta = -0.226182
+call gamma = 0.00199852
+put  gamma = 0.00199852
+*/
+\end{verbatim}
+
+\section{Advantages of Automatic Differentiation}
+The above examples illustrate some of the advantages of using autodiff:
+\begin{itemize}
+\item Elimination of code redundancy. The existence of $N$ separate functions to calculate derivatives is a form
+  of code redundancy, with all the liabilities that come with it:
+  \begin{itemize}
+    \item Changes to one function require $N$ additional changes to other functions. In the \nth{3} example above,
+        consider how much larger and inter-dependent the above code base would be if a separate function were
+        written for \href{https://en.wikipedia.org/wiki/Greeks\_(finance)#Formulas\_for\_European\_option\_Greeks}
+        {each Greek} value.
+    \item Dependencies upon a derivative function for a different purpose will break when changes are made to
+        the original function. What doesn't need to exist cannot break.
+    \item Code bloat, reducing conceptual integrity. Control over the evolution of code is easier/safer when
+        the code base is smaller and able to be intuitively grasped.
+  \end{itemize}
+\item Accuracy of derivatives over finite difference methods. Single-iteration finite difference methods always
+   include a $\Delta x$ free variable that must be carefully chosen for each application. If $\Delta x$ is too
+   small, then numerical errors become large. If $\Delta x$ is too large, then mathematical errors become large.
+   With autodiff, there are no free variables to set and the accuracy of the answer is generally superior to finite
+   difference methods even with the best choice of $\Delta x$.
+\end{itemize}
+
+\section{Mathematics}
+
+In order for the usage of the autodiff library to make sense, a basic understanding of the mathematics will help.
+
+\subsection{Truncated Taylor Series}
+
+Basic calculus courses teach that a real \href{https://en.wikipedia.org/wiki/Analytic_function}{analytic function}
+$f : D\rightarrow\mathbb{R}$ is one which can be expressed as a Taylor series at a point
+$x_0\in D\subseteq\mathbb{R}$:
+
+\[
+f(x) = f(x_0) + f'(x_0)(x-x_0) + \frac{f''(x_0)}{2!}(x-x_0)^2 + \frac{f'''(x_0)}{3!}(x-x_0)^3 + \cdots
+\]
+One way of thinking about this form is that given the value of an analytic function $f(x_0)$ and its derivatives
+$f'(x_0), f''(x_0), f'''(x_0), ...$ evaluated at a point $x_0$, then the value of the function
+$f(x)$ can be obtained at any other point $x\in D$ using the above formula.
+
+Let us make the substitution $x=x_0+\varepsilon$ and rewrite the above equation to get:
+
+\[
+f(x_0+\varepsilon) = f(x_0) + f'(x_0)\varepsilon + \frac{f''(x_0)}{2!}\varepsilon^2 + \frac{f'''(x_0)}{3!}\varepsilon^3 + \cdots
+\]
+Now consider $\varepsilon$ as {\it an abstract algebraic entity that never acquires a numeric value}, much like
+one does in basic algebra with variables like $x$ or $y$. For example, we can still manipulate entities
+like $xy$ and $(1+2x+3x^2)$ without having to assign specific numbers to them.
+
+Using this formula, autodiff goes in the other direction. Given a general formula/algorithm for calculating
+$f(x_0+\varepsilon)$, the derivatives are obtained from the coefficients of the powers of $\varepsilon$
+in the resulting computation. The general coefficient for $\varepsilon^n$ is
+
+\[\frac{f^{(n)}(x_0)}{n!}.\]
+Thus to obtain $f^{(n)}(x_0)$, the coefficient of $\varepsilon^n$ is multiplied by $n!$.
+
+\subsubsection{Example}
+
+Apply the above technique to calculate the derivatives of $f(x)=x^4$ at $x_0=2$.
+
+The first step is to evaluate $f(x_0+\varepsilon)$ and simply go through the calculation/algorithm, treating
+$\varepsilon$ as an abstract algebraic entity:
+
+\begin{align*}
+f(x_0+\varepsilon) &= f(2+\varepsilon) \\
+ &= (2+\varepsilon)^4 \\
+ &= \left(4+4\varepsilon+\varepsilon^2\right)^2 \\
+ &= 16+32\varepsilon+24\varepsilon^2+8\varepsilon^3+\varepsilon^4.
+\end{align*}
+Equating the powers of $\varepsilon$ from this result with the above $\varepsilon$-taylor expansion
+yields the following equalities:
+
+\[
+f(2) = 16, \qquad
+f'(2) = 32, \qquad
+\frac{f''(2)}{2!} = 24, \qquad
+\frac{f'''(2)}{3!} = 8, \qquad
+\frac{f^{(4)}(2)}{4!} = 1, \qquad
+\frac{f^{(5)}(2)}{5!} = 0.
+\]
+Multiplying both sides by the respective factorials gives
+
+\[
+f(2) = 16, \qquad
+f'(2) = 32, \qquad
+f''(2) = 48, \qquad
+f'''(2) = 48, \qquad
+f^{(4)}(2) = 24, \qquad
+f^{(5)}(2) = 0.
+\]
+These values can be directly confirmed by the \href{https://en.wikipedia.org/wiki/Power_rule}{power rule}
+applied to $f(x)=x^4$.
+
+\subsection{Arithmetic}
+
+What was essentially done above was to take a formula/algorithm for calculating $f(x_0)$ from a number $x_0$,
+and instead apply the same formula/algorithm to a polynomial $x_0+\varepsilon$. Intermediate steps operate on
+values of the form
+
+\[
+{\bf x} = x_0 + x_1\varepsilon + x_2\varepsilon^2 +\cdots+ x_N\varepsilon^N
+\]
+and the final return value is of this polynomial form as well. In other words, the normal arithmetic operators
+$+,-,\times,\div$ applied to numbers $x$ are instead applied to polynomials $\bf x$. Through the overloading of C++
+operators and functions, floating point data types are replaced with data types that represent these polynomials. More
+specifically, C++ types such as {\tt double} are replaced with {\tt std::array<double,N+1>}, which hold the above
+$N+1$ coefficients $x_i$, and are wrapped in a {\tt class} that overloads all of the arithmetic operators.
+
+The logic of these arithmetic operators simply mirror that which is applied to polynomials. We'll look at
+each of the 4 arithmetic operators in detail.
+
+\subsubsection{Addition}
+
+The addition of polynomials $\bf x$ and $\bf y$ is done component-wise:
+
+\begin{align*}
+{\bf z} &= {\bf x} + {\bf y} \\
+ &= \left(\sum_{i=0}^Nx_i\varepsilon^i\right) + \left(\sum_{i=0}^Ny_i\varepsilon^i\right) \\
+ &= \sum_{i=0}^N(x_i+y_i)\varepsilon^i \\
+z_i &= x_i + y_i \qquad \text{for}\; i\in\{0,1,2,...,N\}.
+\end{align*}
+
+\subsubsection{Subtraction}
+
+Subtraction follows the same form as addition:
+
+\begin{align*}
+{\bf z} &= {\bf x} - {\bf y} \\
+ &= \left(\sum_{i=0}^Nx_i\varepsilon^i\right) - \left(\sum_{i=0}^Ny_i\varepsilon^i\right) \\
+ &= \sum_{i=0}^N(x_i-y_i)\varepsilon^i \\
+z_i &= x_i - y_i \qquad \text{for}\; i\in\{0,1,2,...,N\}.
+\end{align*}
+
+\subsubsection{Multiplication}
+
+Multiplication produces higher-order terms:
+
+\begin{align*}
+{\bf z} &= {\bf x} \times {\bf y} \\
+ &= \left(\sum_{i=0}^Nx_i\varepsilon^i\right) \left(\sum_{i=0}^Ny_i\varepsilon^i\right) \\
+ &= x_0y_0 + (x_0y_1+x_1y_0)\varepsilon + (x_0y_2+x_1y_1+x_2y_0)\varepsilon^2 + \cdots +
+    \left(\sum_{j=0}^Nx_jy_{N-j}\right)\varepsilon^N + O\left(\varepsilon^{N+1}\right) \\
+ &= \sum_{i=0}^N\sum_{j=0}^ix_jy_{i-j}\varepsilon^i + O\left(\varepsilon^{N+1}\right) \\
+z_i &= \sum_{j=0}^ix_jy_{i-j} \qquad \text{for}\; i\in\{0,1,2,...,N\}.
+\end{align*}
+In the case of multiplication, terms involving powers of $\varepsilon$ greater than $N$, collectively denoted
+by $O\left(\varepsilon^{N+1}\right)$, are simply discarded. Fortunately, the values of $z_i$ for $i\le N$ do not
+depend on any of these discarded terms, so there is no loss of precision in the final answer. The only information
+that is lost are the values of higher order derivatives, which we are not interested in anyway. If we were, then
+we would have simply chosen a larger value of $N$ to begin with.
+
+\subsubsection{Division}
+
+Division is not directly calculated as are the others. Instead, to find the components of
+${\bf z}={\bf x}\div{\bf y}$ we require that ${\bf x}={\bf y}\times{\bf z}$. This yields
+a recursive formula for the components $z_i$:
+
+\begin{align*}
+x_i &= \sum_{j=0}^iy_jz_{i-j} \\
+ &= y_0z_i + \sum_{j=1}^iy_jz_{i-j} \\
+z_i &= \frac{1}{y_0}\left(x_i - \sum_{j=1}^iy_jz_{i-j}\right) \qquad \text{for}\; i\in\{0,1,2,...,N\}.
+\end{align*}
+In the case of division, the values for $z_i$ must be calculated sequentially, since $z_i$
+depends on the previously calculated values $z_0, z_1, ..., z_{i-1}$.
+
+\subsection{General Functions}
+
+Calling standard mathematical functions such as {\tt log()}, {\tt cos()}, etc. should return accurate higher
+order derivatives. For example, {\tt exp(x)} may be written internally as a specific \nth{14}-degree polynomial to
+approximate $e^x$ when $0<x<1$. This would mean that the \nth{15} derivative, and all higher order derivatives, would
+be 0, however we know that $\frac{d^{15}}{dx^{15}}e^x=e^x$.  How should such functions whose derivatives are known
+be written to provide accurate higher order derivatives? The answer again comes back to the function's Taylor series.
+
+To simplify notation, for a given polynomial ${\bf x} = x_0 + x_1\varepsilon + x_2\varepsilon^2 +\cdots+
+x_N\varepsilon^N$ define
+
+\[
+{\bf x}_\varepsilon = x_1\varepsilon + x_2\varepsilon^2 +\cdots+ x_N\varepsilon^N = \sum_{i=1}^Nx_i\varepsilon^i.
+\]
+This allows for a concise expression of a general function $f$ of $\bf x$:
+
+\begin{align*}
+f({\bf x}) &= f(x_0 + {\bf x}_\varepsilon) \\
+ & = f(x_0) + f'(x_0){\bf x}_\varepsilon + \frac{f''(x_0)}{2!}{\bf x}_\varepsilon^2 + \frac{f'''(x_0)}{3!}{\bf x}_\varepsilon^3 + \cdots + \frac{f^{(N)}(x_0)}{N!}{\bf x}_\varepsilon^N + O\left(\varepsilon^{N+1}\right) \\
+ & = \sum_{i=0}^N\frac{f^{(i)}(x_0)}{i!}{\bf x}_\varepsilon^i + O\left(\varepsilon^{N+1}\right)
+\end{align*}
+where $\varepsilon$ has been substituted with ${\bf x}_\varepsilon$ in the $\varepsilon$-taylor series
+for $f(x)$. This form gives a recipe for calculating $f({\bf x})$ in general from regular numeric calculations
+$f(x_0)$, $f'(x_0)$, $f''(x_0)$, ... and successive powers of the epsilon terms ${\bf x}_\varepsilon$.
+
+For an application in which we are interested in up to $N$ derivatives in $x$ the data structure to hold
+this information is an $(N+1)$-element array {\tt v} whose general element is
+
+\[ {\tt v[i]} = \frac{f^{(i)}(x_0)}{i!} \qquad \text{for}\; i\in\{0,1,2,...,N\}. \]
+
+\subsection{Multiple Variables}
+
+In C++, the generalization to mixed partial derivatives with multiple independent variables is conveniently achieved
+with recursion. To begin to see the recursive pattern, consider a two-variable function $f(x,y)$. Since $x$
+and $y$ are independent, they require their own independent epsilons $\varepsilon_x$ and $\varepsilon_y$,
+respectively.
+
+Expand $f(x,y)$ for $x=x_0+\varepsilon_x$:
+\begin{align*}
+f(x_0+\varepsilon_x,y) &= f(x_0,y)
++ \frac{\partial f}{\partial x}(x_0,y)\varepsilon_x
++ \frac{1}{2!}\frac{\partial^2 f}{\partial x^2}(x_0,y)\varepsilon_x^2
++ \frac{1}{3!}\frac{\partial^3 f}{\partial x^3}(x_0,y)\varepsilon_x^3
++ \cdots
++ \frac{1}{M!}\frac{\partial^M f}{\partial x^M}(x_0,y)\varepsilon_x^M
++ O\left(\varepsilon_x^{M+1}\right) \\
+&= \sum_{i=0}^M\frac{1}{i!}\frac{\partial^i f}{\partial x^i}(x_0,y)\varepsilon_x^i + O\left(\varepsilon_x^{M+1}\right).
+\end{align*}
+Next, expand $f(x_0+\varepsilon_x,y)$ for $y=y_0+\varepsilon_y$:
+
+\begin{align*}
+f(x_0+\varepsilon_x,y_0+\varepsilon_y) &= \sum_{j=0}^N\frac{1}{j!}\frac{\partial^j}{\partial y^j}
+    \left(\sum_{i=0}^M\varepsilon_x^i\frac{1}{i!}\frac{\partial^if}{\partial x^i}\right)(x_0,y_0)\varepsilon_y^j
+    + O\left(\varepsilon_x^{M+1}\right) + O\left(\varepsilon_y^{N+1}\right) \\
+&= \sum_{i=0}^M\sum_{j=0}^N\frac{1}{i!j!}\frac{\partial^{i+j}f}{\partial x^i\partial y^j}(x_0,y_0)
+   \varepsilon_x^i\varepsilon_y^j + O\left(\varepsilon_x^{M+1}\right) + O\left(\varepsilon_y^{N+1}\right).
+\end{align*}
+
+Similar to the single-variable case, for an application in which we are interested in up to $M$ derivatives in
+$x$ and $N$ derivatives in $y$, the data structure to hold this information is an $(M+1)\times(N+1)$
+array {\tt v} whose element at $(i,j)$ is
+
+\[
+{\tt v[i][j]} = \frac{1}{i!j!}\frac{\partial^{i+j}f}{\partial x^i\partial y^j}(x_0,y_0)
+    \qquad \text{for}\; (i,j)\in\{0,1,2,...,M\}\times\{0,1,2,...,N\}.
+\]
+The generalization to additional independent variables follows the same pattern.
+
+\subsubsection{Declaring Multiple Variables}
+
+Internally, independent variables are represented by vectors within orthogonal vector spaces. Because of this,
+one must be careful when declaring more than one independent variable so that they do not end up in
+parallel vector spaces. This can easily be achieved by following one rule:
+\begin{itemize}
+\item When declaring more than one independent variable, call {\tt make\_ftuple<>()} once and only once.
+\end{itemize}
+The tuple of values returned are independent. Though it is possible to achieve the same result with multiple calls
+to {\tt make\_fvar}, this is an easier and less error-prone method. See Section~\ref{multivar} for example usage.
+
+%\section{Usage}
+%
+%\subsection{Single Variable}
+%
+%To calculate derivatives of a single variable $x$, at a particular value $x_0$, the following must be
+%specified at compile-time:
+%
+%\begin{enumerate}
+%\item The numeric data type {\tt T} of $x_0$. Examples: {\tt double},
+%    {\tt boost::multiprecision::cpp\_bin\_float\_50}, etc.
+%\item The maximum derivative order $M$ that is to be calculated with respect to $x$.
+%\end{enumerate}
+%Note that both of these requirements are entirely analogous to declaring and using a {\tt std::array<T,N>}. {\tt T}
+%and {\tt N} must be set as compile-time, but which elements in the array are accessed can be determined at run-time,
+%just as the choice of what derivatives to query in autodiff can be made during run-time.
+%
+%To declare and initialize $x$:
+%
+%\begin{verbatim}
+%    using namespace boost::math::differentiation;
+%    autodiff_fvar<T,M> x = make_fvar<T,M>(x0);
+%\end{verbatim}
+%where {\tt x0} is a run-time value of type {\tt T}. Assuming {\tt 0 < M}, this represents the polynomial $x_0 +
+%\varepsilon$. Internally, the member variable of type {\tt std::array<T,M>} is {\tt v = \{ x0, 1, 0, 0, ... \}},
+%consistent with the above mathematical treatise.
+%
+%To find the derivatives $f^{(n)}(x_0)$ for $0\le n\le M$ of a function
+%$f : \mathbb{R}\rightarrow\mathbb{R}$, the function can be represented as a template
+%
+%\begin{verbatim}
+%    template<typename T>
+%    T f(T x);
+%\end{verbatim}
+%Using a generic type {\tt T} allows for {\tt x} to be of a regular type such as {\tt double}, but also allows for\\
+%{\tt boost::math::differentiation::autodiff\_fvar<>} types.
+%
+%Internal calls to mathematical functions must allow for
+%\href{https://en.cppreference.com/w/cpp/language/adl}{argument-dependent lookup} (ADL). Many standard library functions
+%are overloaded in the {\tt boost::math::differentiation} namespace. For example, instead of calling {\tt std::cos(x)}
+%from within {\tt f}, include the line {\tt using std::cos;} and call {\tt cos(x)} without a namespace prefix.
+%
+%Calling $f$ and retrieving the calculated value and derivatives:
+%
+%\begin{verbatim}
+%    using namespace boost::math::differentiation;
+%    autodiff_fvar<T,M> x = make_fvar<T,M>(x0);
+%    autodiff_fvar<T,M> y = f(x);
+%    for (int n=0 ; n<=M ; ++n)
+%        std::cout << "y.derivative("<<n<<") == " << y.derivative(n) << std::endl;
+%\end{verbatim}
+%{\tt y.derivative(0)} returns the undifferentiated value $f(x_0)$, and {\tt y.derivative(n)} returns $f^{(n)}(x_0)$.
+%Casting {\tt y} to type {\tt T} also gives the undifferentiated value. In other words, the following 3 values
+%are equal:
+%
+%\begin{enumerate}
+%\item {\tt f(x0)}
+%\item {\tt y.derivative(0)}
+%\item {\tt static\_cast<T>(y)}
+%\end{enumerate}
+%
+%\subsection{Multiple Variables}
+%
+%Independent variables are represented in autodiff as independent dimensions within a multi-dimensional array.
+%This is perhaps best illustrated with examples. The {\tt namespace boost::math::differentiation} is assumed.
+%
+%The following instantiates a variable of $x=13$ with up to 3 orders of derivatives:
+%
+%\begin{verbatim}
+%    autodiff_fvar<double,3> x = make_fvar<double,3>(13);
+%\end{verbatim}
+%This instantiates {\bf an independent} value of $y=14$ with up to 4 orders of derivatives:
+%
+%\begin{verbatim}
+%    autodiff_fvar<double,0,4> y = make_fvar<double,0,4>(14);
+%\end{verbatim}
+%Combining them together {\bf promotes} their data type automatically to the smallest multidimensional array that
+%accommodates both.
+%
+%\begin{verbatim}
+%    // z is promoted to autodiff_fvar<double,3,4>
+%    auto z = 10*x*x + 50*x*y + 100*y*y;
+%\end{verbatim}
+%The object {\tt z} holds a 2-dimensional array, thus {\tt derivative(...)} is a 2-parameter method:
+%
+%\[
+%{\tt z.derivative(i,j)} = \frac{\partial^{i+j}f}{\partial x^i\partial y^j}(13,14)
+%    \qquad \text{for}\; (i,j)\in\{0,1,2,3\}\times\{0,1,2,3,4\}.
+%\]
+%A few values of the result can be confirmed through inspection:
+%
+%\begin{verbatim}
+%    z.derivative(2,0) == 20
+%    z.derivative(1,1) == 50
+%    z.derivative(0,2) == 200
+%\end{verbatim}
+%Note how the position of the parameters in {\tt derivative(...)} match how {\tt x} and {\tt y} were declared.
+%This will be clarified next.
+%
+%\subsubsection{Two Rules of Variable Initialization}
+%
+%In general, there are two rules to keep in mind when dealing with multiple variables:
+%
+%\begin{enumerate}
+%\item Independent variables correspond to parameter position, in both the initialization {\tt make\_fvar<T,...>}
+%    and calls to {\tt derivative(...)}.
+%\item The last template position in {\tt make\_fvar<T,...>} determines which variable a derivative will be
+%   taken with respect to.
+%\end{enumerate}
+%Both rules are illustrated with an example in which there are 3 independent variables $x,y,z$ and 1 dependent
+%variable $w=f(x,y,z)$, though the following code readily generalizes to any number of independent variables, limited
+%only by the C++ compiler/memory/platform. The maximum derivative order of each variable is {\tt Nx}, {\tt Ny}, and
+%{\tt Nz}, respectively. Then the type for {\tt w} is {\tt boost::math::differentiation::autodiff\_fvar<T,Nx,Ny,Nz>}
+%and all possible mixed partial derivatives are available via
+%
+%\[
+%{\tt w.derivative(nx,ny,nz)} =
+%    \frac{\partial^{n_x+n_y+n_z}f}{\partial x^{n_x}\partial y^{n_y}\partial z^{n_z} }(x_0,y_0,z_0)
+%\]
+%for $(n_x,n_y,n_z)\in\{0,1,2,...,N_x\}\times\{0,1,2,...,N_y\}\times\{0,1,2,...,N_z\}$ where $x_0, y_0, z_0$ are
+%the numerical values at which the function $f$ and its derivatives are evaluated.
+%
+%In code:
+%\begin{verbatim}
+%    using namespace boost::math::differentiation;
+%
+%    using var = autodiff_fvar<double,Nx,Ny,Nz>; // Nx, Ny, Nz are constexpr size_t.
+%
+%    var x = make_fvar<double,Nx>(x0);       // x0 is of type double
+%    var y = make_fvar<double,Nx,Ny>(y0);    // y0 is of type double
+%    var z = make_fvar<double,Nx,Ny,Nz>(z0); // z0 is of type double
+%
+%    var w = f(x,y,z);
+%
+%    for (size_t nx=0 ; nx<=Nx ; ++nx)
+%        for (size_t ny=0 ; ny<=Ny ; ++ny)
+%            for (size_t nz=0 ; nz<=Nz ; ++nz)
+%                std::cout << "w.derivative("<<nx<<','<<ny<<','<<nz<<") == "
+%                    << w.derivative(nx,ny,nz) << std::endl;
+%\end{verbatim}
+%Note how {\tt x}, {\tt y}, and {\tt z} are initialized: the last template parameter determines which variable
+%$x, y,$ or $z$ a derivative is taken with respect to. In terms of the $\varepsilon$-polynomials
+%above, this determines whether to add $\varepsilon_x, \varepsilon_y,$ or $\varepsilon_z$ to
+%$x_0, y_0,$ or $z_0$, respectively.
+%
+%In contrast, the following initialization of {\tt x} would be INCORRECT:
+%
+%\begin{verbatim}
+%    var x = make_fvar<T,Nx,0>(x0); // WRONG
+%\end{verbatim}
+%Mathematically, this represents $x_0+\varepsilon_y$, since the last template parameter corresponds to the
+%$y$ variable, and thus the resulting value will be invalid.
+%
+%\subsubsection{Type Promotion}
+%
+%The previous example can be optimized to save some unnecessary computation, by declaring smaller arrays,
+%and relying on autodiff's automatic type-promotion:
+%
+%\begin{verbatim}
+%    using namespace boost::math::differentiation;
+%
+%    autodiff_fvar<double,Nx> x = make_fvar<double,Nx>(x0);
+%    autodiff_fvar<double,0,Ny> y = make_fvar<double,0,Ny>(y0);
+%    autodiff_fvar<double,0,0,Nz> z = make_fvar<double,0,0,Nz>(z0);
+%
+%    autodiff_fvar<double,Nx,Ny,Nz> w = f(x,y,z);
+%
+%    for (size_t nx=0 ; nx<=Nx ; ++nx)
+%        for (size_t ny=0 ; ny<=Ny ; ++ny)
+%            for (size_t nz=0 ; nz<=Nz ; ++nz)
+%                std::cout << "w.derivative("<<nx<<','<<ny<<','<<nz<<") == "
+%                    << w.derivative(nx,ny,nz) << std::endl;
+%\end{verbatim}
+%For example, if one of the first steps in the computation of $f$ was {\tt z*z}, then a significantly less number of
+%multiplications and additions may occur if {\tt z} is declared as {\tt autodiff\_fvar<double,0,0,Nz>} as opposed to \\
+%{\tt autodiff\_fvar<double,Nx,Ny,Nz>}. There is no loss of precision with the former, since the extra dimensions
+%represent 0 values. Once {\tt z} is combined with {\tt x} and {\tt y} during the computation, the types will be
+%promoted as necessary.  This is the recommended way to initialize variables in autodiff.
+
+\section{Writing Functions for Autodiff Compatibility}\label{compatibility}
+
+In this section, a general procedure is given for writing new, and transforming existing, C++ mathematical
+functions for compatibility with autodiff.
+
+There are 3 categories of functions that require different strategies:
+\begin{enumerate}
+\item Piecewise-rational functions. These are simply piecewise quotients of polynomials. All that is needed is to
+    turn the function parameters and return value into generic (template) types. This will then allow the function
+    to accept and return autodiff's {\tt fvar} types, thereby using autodiff's overloaded arithmetic operators
+    which calculate the derivatives automatically.
+\item Functions that call existing autodiff functions. This is the same as the previous, but may also include
+    calls to functions that are in the autodiff library. Examples: {\tt exp()}, {\tt log()}, {\tt tgamma()}, etc.
+\item New functions for which the derivatives can be calculated. This is the most general technique, as it
+    allows for the development of a function which do not fall into the previous two categories.
+\end{enumerate}
+Functions written in any of these ways may then be added to the autodiff library.
+
+\subsection{Piecewise-Rational Functions}
+\[
+f(x) = \frac{1}{1+x^2}
+\]
+By simply writing this as a template function, autodiff can calculate derivatives for it:
+\begin{Verbatim}[xleftmargin=2em]
+#include <boost/math/differentiation/autodiff.hpp>
+#include <iostream>
+
+template <typename T>
+T rational(T const& x) {
+  return 1 / (1 + x * x);
+}
+
+int main() {
+  using namespace boost::math::differentiation;
+  auto const x = make_fvar<double, 10>(0);
+  auto const y = rational(x);
+  std::cout << std::setprecision(std::numeric_limits<double>::digits10)
+            << "y.derivative(10) = " << y.derivative(10) << std::endl;
+  return 0;
+}
+/*
+Output:
+y.derivative(10) = -3628800
+*/
+\end{Verbatim}
+As simple as $f(x)$ may seem, the derivatives can get increasingly complex as derivatives are taken.
+For example, the \nth{10} derivative has the form
+\[
+f^{(10)}(x) = -3628800\frac{1 - 55x^2 + 330x^4 - 462x^6 + 165x^8 - 11x^{10}}{(1 + x^2)^{11}}.
+\]
+Derivatives of $f(x)$ are useful, and in fact used, in calculating higher order derivatives for $\arctan(x)$
+for instance, since
+\[
+\arctan^{(n)}(x) = \left(\frac{d}{dx}\right)^{n-1} \frac{1}{1+x^2}\qquad\text{for}\quad 1\le n.
+\]
+
+\subsection{Functions That Call Existing Autodiff Functions}
+
+Many of the standard library math function are overloaded in autodiff. It is recommended to use
+\href{https://en.cppreference.com/w/cpp/language/adl}{argument-dependent lookup} (ADL) in order for functions to
+be written in a way that is general enough to accommodate standard types ({\tt double}) as well as autodiff types
+({\tt fvar}).
+\\
+Example:
+\begin{Verbatim}[xleftmargin=2em]
+#include <boost/math/constants/constants.hpp>
+#include <cmath>
+
+using namespace boost::math::constants;
+
+// Standard normal cumulative distribution function
+template <typename T>
+T Phi(T const& x)
+{
+  return 0.5 * std::erfc(-one_div_root_two<T>() * x);
+}
+\end{Verbatim}
+Though {\tt Phi(x)} is general enough to handle the various fundamental floating point types, this will
+not work if {\tt x} is an autodiff {\tt fvar} variable, since {\tt std::erfc} does not include a specialization
+for {\tt fvar}. The recommended solution is to remove the namespace prefix {\tt std::} from {\tt erfc}:
+\begin{Verbatim}[xleftmargin=2em]
+#include <boost/math/constants/constants.hpp>
+#include <boost/math/differentiation/autodiff.hpp>
+#include <cmath>
+
+using namespace boost::math::constants;
+
+// Standard normal cumulative distribution function
+template <typename T>
+T Phi(T const& x)
+{
+  using std::erfc;
+  return 0.5 * erfc(-one_div_root_two<T>() * x);
+}
+\end{Verbatim}
+In this form, when {\tt x} is of type {\tt fvar}, the C++ compiler will search for and find a function {\tt erfc}
+within the same namespace as {\tt fvar}, which is in the autodiff library, via ADL. Because of the using-declaration,
+it will also call {\tt std::erfc} when {\tt x} is a fundamental type such as {\tt double}.
+
+\subsection{New Functions For Which The Derivatives Can Be Calculated}\label{new_functions}
+
+Mathematical functions which do not fall into the previous two categories can be constructed using autodiff helper
+functions. This requires a separate function for calculating the derivatives. In case you are asking yourself what
+good is an autodiff library if one needs to supply the derivatives, the answer is that the new function will fit
+in with the rest of the autodiff library, thereby allowing for the creation of additional functions via all of
+the arithmetic operators, plus function composition, which was not readily available without the library.
+
+The example given here is for {\tt cos}:
+\begin{Verbatim}[xleftmargin=2em]
+template <typename RealType, size_t Order>
+fvar<RealType, Order> cos(fvar<RealType, Order> const& cr) {
+  using std::cos;
+  using std::sin;
+  using root_type = typename fvar<RealType, Order>::root_type;
+  constexpr size_t order = fvar<RealType, Order>::order_sum;
+  root_type const d0 = cos(static_cast<root_type>(cr));
+  if constexpr (order == 0)
+    return fvar<RealType, Order>(d0);
+  else {
+    root_type const d1 = -sin(static_cast<root_type>(cr));
+    root_type const derivatives[4]{d0, d1, -d0, -d1};
+    return cr.apply_derivatives(order,
+                                [&derivatives](size_t i) { return derivatives[i & 3]; });
+  }
+}
+\end{Verbatim}
+This uses the helper function {\tt fvar::apply\_derivatives} which takes two parameters:
+\begin{enumerate}
+\item The highest order derivative to be calculated.
+\item A function that maps derivative order to derivative value.
+\end{enumerate}
+The highest order derivative necessary to be calculated is generally equal to {\tt fvar::order\_sum}.  In the case
+of {\tt sin} and {\tt cos}, the derivatives are cyclical with period 4. Thus it is sufficient to store only these
+4 values into an array, and take the derivative order modulo 4 as the index into this array.
+
+A second helper function, not shown here, is {\tt apply\_coefficients}. This is used the same as
+{\tt apply\_derivatives} except that the supplied function calculates coefficients instead of derivatives.
+The relationship between a coefficient $C_n$ and derivative $D_n$ for derivative order $n$ is
+\[
+C_n = \frac{D_n}{n!}.
+\]
+Internally, {\tt fvar} holds coefficients rather than derivatives, so in case the coefficient values are more readily
+available than the derivatives, it can save some unnecessary computation to use {\tt apply\_coefficients}.
+See the definition of {\tt atan} for an example.
+
+Both of these helper functions use Horner's method when calculating the resulting polynomial {\tt fvar}. This works
+well when the derivatives are finite, but in cases where derivatives are infinite, this can quickly result in NaN
+values as the computation progresses. In these cases, one can call non-Horner versions of both function which
+better ``isolate'' infinite values so that they are less likely to evolve into NaN values.
+
+The four helper functions available for constructing new autodiff functions from known coefficients/derivatives are:
+\begin{enumerate}
+\item {\tt fvar::apply\_coefficients}
+\item {\tt fvar::apply\_coefficients\_nonhorner}
+\item {\tt fvar::apply\_derivatives}
+\item {\tt fvar::apply\_derivatives\_nonhorner}
+\end{enumerate}
+
+\section{Function Writing Guidelines}
+
+At a high level there is one fairly simple principle, loosely and intuitively speaking, to writing functions for
+which autodiff can effectively calculate derivatives: \\
+
+{\bf Autodiff Function Principle (AFP)}
+\begin{displayquote}
+A function whose branches in logic correspond to piecewise analytic calculations over non-singleton intervals,
+with smooth transitions between the intervals, and is free of indeterminate forms in the calculated value and
+higher order derivatives, will work fine with autodiff.
+\end{displayquote}
+Stating this with greater mathematical rigor can be done. However what seems to be more practical, in this
+case, is to give examples and categories of examples of what works, what doesn't, and how to remedy some of the
+common problems that may be encountered. That is the approach taken here.
+
+\subsection{Example 1: $f(x)=\max(0,x)$}
+
+One potential implementation of $f(x)=\max(0,x)$ is:
+
+\begin{verbatim}
+    template<typename T>
+    T f(const T& x)
+    {
+        return 0 < x ? x : 0;
+    }
+\end{verbatim}
+Though this is consistent with Section~\ref{compatibility}, there are two problems with it:
+
+\begin{enumerate}
+\item {\tt f(nan) = 0}. This problem is independent of autodiff, but is worth addressing anyway. If there is
+    an indeterminate form that arises within a calculation and is input into $f$, then it gets ``covered up'' by
+    this implementation leading to an unknowingly incorrect result. Better for functions in general to propagate
+    NaN values, so that the user knows something went wrong and doesn't rely on an incorrect result, and likewise
+    the developer can track down where the NaN originated from and remedy it.
+\item $f'(0) = 0$ when autodiff is applied. This is because {\tt f} returns 0 as a constant when {\tt x==0}, wiping
+    out any of the derivatives (or sensitivities) that {\tt x} was holding as an autodiff variable. Instead, let us
+    apply the AFP and identify the two intervals over which $f$ is defined: $(-\infty,0]\cup(0,\infty)$.
+    Though the function itself is not analytic at $x=0$, we can attempt somewhat to smooth out this transition
+    point by averaging the calculation of $f(x)$ at $x=0$ from each interval. If $x<0$ then the result is simply
+    0, and if $0<x$ then the result is $x$. The average is $\frac{1}{2}(0 + x)$ which will allow autodiff to
+    calculate $f'(0)=\frac{1}{2}$. This is a more reasonable answer.
+\end{enumerate}
+A better implementation that resolves both issues is:
+\begin{verbatim}
+    template<typename T>
+    T f(const T& x)
+    {
+        if (x < 0)
+            return 0;
+        else if (x == 0)
+            return 0.5*x;
+        else
+            return x;
+    }
+\end{verbatim}
+
+\subsection{Example 2: $f(x)=\sinc(x)$}
+
+The definition of $\sinc:\mathbb{R}\rightarrow\mathbb{R}$ is
+
+\[
+\sinc(x) = \begin{cases}
+    1 &\text{if}\; x = 0 \\
+    \frac{\sin(x)}{x} &\text{otherwise.}\end{cases}
+\]
+A potential implementation is:
+
+\begin{verbatim}
+    template<typename T>
+    T sinc(const T& x)
+    {
+        using std::sin;
+        return x == 0 ? 1 : sin(x) / x;
+    }
+\end{verbatim}
+Though this is again consistent with Section~\ref{compatibility}, and returns correct non-derivative values,
+it returns a constant when {\tt x==0} thereby losing all derivative information contained in {\tt x} and
+contributions from $\sinc$. For example, $\sinc''(0)=-\frac{1}{3}$, however {\tt y.derivative(2) == 0} when
+{\tt y = sinc(make\_fvar<double,2>(0))} using the above incorrect implementation. Applying the AFP, the intervals
+upon which separate branches of logic are applied are $(-\infty,0)\cup[0,0]\cup(0,\infty)$. The violation occurs
+due to the singleton interval $[0,0]$, even though a constant function of 1 is technically analytic. The remedy
+is to define a custom $\sinc$ overload and add it to the autodiff library. This has been done. Mathematically, it
+is well-defined and free of indeterminate forms, as is the \nth{3} expression in the equalities
+\[
+\frac{1}{x}\sin(x) = \frac{1}{x}\sum_{n=0}^\infty\frac{(-1)^n}{(2n+1)!}x^{2n+1}
+    = \sum_{n=0}^\infty\frac{(-1)^n}{(2n+1)!}x^{2n}.
+\]
+The autodiff library contains helper functions to help write function overloads when the derivatives of a function
+are known. This is an advanced feature and documentation for this may be added at a later time.
+
+For now, it is worth understanding the ways in which indeterminate forms can occur within a mathematical calculation,
+and avoid them when possible by rewriting the function. Table~\ref{3nans} compares 3 types of indeterminate
+forms. Assume the product {\tt a*b} is a positive finite value.
+
+\begin{table}[h]
+\centering\begin{tabular}{m{7em}||c|c|c}
+ & $\displaystyle f(x)=\left(\frac{a}{x}\right)\times(bx^2)$
+ & $\displaystyle g(x)=\left(\frac{a}{x}\right)\times(bx)$
+ & $\displaystyle h(x)=\left(\frac{a}{x^2}\right)\times(bx)$ \\[0.618em]
+\hline\hline
+Mathematical\newline Limit
+ & $\displaystyle\lim_{x\rightarrow0}f(x) = 0$
+ & $\displaystyle\lim_{x\rightarrow0}g(x) = ab$
+ & $\displaystyle\lim_{x\rightarrow0}h(x) = \infty$ \\
+\hline
+Floating Point\newline Arithmetic
+ & {\tt f(0) = inf*0 = nan} & {\tt g(0) = inf*0 = nan} & {\tt h(0) = inf*0 = nan}
+\end{tabular}
+\caption{Automatic differentiation does not compute limits.
+Indeterminate forms must be simplified manually. (These cases are not meant to be exhaustive.)}\label{3nans}
+\end{table}
+
+Indeterminate forms result in NaN values within a calculation. Mathematically, if they occur at locally isolated
+points, then we generally prefer the mathematical limit as the result, even if it is infinite. As demonstrated in
+Table~\ref{3nans}, depending upon the nature of the indeterminate form, the mathematical limit can be 0 (no matter
+the values of $a$ or $b$), or $ab$, or $\infty$, but these 3 cases cannot be distinguished by the floating point
+result of nan. Floating point arithmetic does not perform limits (directly), and neither does the autodiff library.
+Thus it is up to the diligence of the developer to keep a watchful eye over where indeterminate forms can arise.
+
+\subsection{Example 3: $f(x)=\sqrt x$ and $f'(0)=\infty$}
+
+When working with functions that have infinite higher order derivatives, this can very quickly result in nans in
+higher order derivatives as the computation progresses, as {\tt inf-inf}, {\tt inf/inf}, and {\tt 0*inf} result
+in {\tt nan}. See Table~\ref{sqrtnan} for an example.
+
+\begin{table}[h]
+\centering\begin{tabular}{c||c|c|c|c}
+$f(x)$ & $f(0)$ & $f'(0)$ & $f''(0)$ & $f'''(0)$ \\
+\hline\hline
+{\tt sqrt(x)} & {\tt 0} & {\tt inf} & {\tt -inf} & {\tt inf} \\
+\hline
+{\tt sqr(sqrt(x)+1)} & {\tt 1} & {\tt inf} & {\tt nan} & {\tt nan} \\
+\hline
+{\tt x+2*sqrt(x)+1} & {\tt 1} & {\tt inf} & {\tt -inf}& {\tt inf}
+\end{tabular}
+\caption{Indeterminate forms in higher order derivatives. {\tt sqr(x) == x*x}.}\label{sqrtnan}
+\end{table}
+
+Calling the autodiff-overloaded implementation of $f(x)=\sqrt x$ at the value {\tt x==0} results in the
+\nth{1} row (after the header row) of Table~\ref{sqrtnan}, as is mathematically correct. The \nth{2} row shows
+$f(x)=(\sqrt{x}+1)^2$ resulting in {\tt nan} values for $f''(0)$ and all higher order derivatives. This is due to
+the internal arithmetic in which {\tt inf} is added to {\tt -inf} during the squaring, resulting in a {\tt nan}
+value for $f''(0)$ and all higher orders. This is typical of {\tt inf} values in autodiff. Where they show up,
+they are correct, however they can quickly introduce {\tt nan} values into the computation upon the addition of
+oppositely signed {\tt inf} values, division by {\tt inf}, or multiplication by {\tt 0}. It is worth noting that
+the infection of {\tt nan} only spreads upward in the order of derivatives, since lower orders do not depend upon
+higher orders (which is also why dropping higher order terms in an autodiff computation does not result in any
+loss of precision for lower order terms.)
+
+The resolution in this case is to manually perform the squaring in the computation, replacing the \nth{2} row
+with the \nth{3}: $f(x)=x+2\sqrt{x}+1$. Though mathematically equivalent, it allows autodiff to avoid {\tt nan}
+values since $\sqrt x$ is more ``isolated'' in the computation. That is, the {\tt inf} values that unavoidably
+show up in the derivatives of {\tt sqrt(x)} for {\tt x==0} do not have the chance to interact with other {\tt inf}
+values as with the squaring.
+
+\subsection{Summary}
+
+The AFP gives a high-level unified guiding principle for writing C++ template functions that autodiff can
+effectively evaluate derivatives for.
+
+Examples have been given to illustrate some common items to avoid doing:
+
+\begin{enumerate}
+\item It is not enough for functions to be piecewise continuous. On boundary points between intervals, consider
+    returning the average expression of both intervals, rather than just one of them. Example: $\max(0,x)$ at $x=0$.
+    In cases where the limits from both sides must match, and they do not, then {\tt nan} may be a more appropriate
+    value depending on the application.
+\item Avoid returning individual constant values (e.g. $\sinc(0)=1$.) Values must be computed uniformly along
+    with other values in its local interval. If that is not possible, then the function must be overloaded to
+    compute the derivatives precisely using the helper functions from Section~\ref{new_functions}.
+\item Avoid intermediate indeterminate values in both the value ($\sinc(x)$ at $x=0$) and derivatives
+    ($(\sqrt{x}+1)^2$ at $x=0$). Try to isolate expressions that may contain infinite values/derivatives so
+    that they do not introduce NaN values into the computation.
+\end{enumerate}
+
+\section{Acknowledgments}
+
+\begin{itemize}
+\item Kedar Bhat --- C++11 compatibility, Boost Special Functions compatibility testing, codecov integration,
+    and feedback.
+\item Nick Thompson --- Initial feedback and help with Boost integration.
+\item John Maddock --- Initial feedback and help with Boost integration.
+\end{itemize}
+
+\begin{thebibliography}{1}
+\bibitem{ad} \url{https://en.wikipedia.org/wiki/Automatic\_differentiation}
+\bibitem{ed} Andreas Griewank, Andrea Walther. \textit{Evaluating Derivatives}. SIAM, 2nd ed. 2008.
+\end{thebibliography}
+
+\end{document}
diff --git a/libs/math/doc/distributions/binomial.qbk b/libs/math/doc/distributions/binomial.qbk
index eae3e83104..bb9c4bfd8d 100644
--- a/libs/math/doc/distributions/binomial.qbk
+++ b/libs/math/doc/distributions/binomial.qbk
@@ -311,19 +311,17 @@ the context of this distribution:
 
 `cdf(complement(binomial(n, p), k))`]]
 [[__quantile]
-   [The [*greatest] number of successes that may be observed from n trials
-   with success fraction p, at probability P.  Note that the value returned
-   is a real-number, and not an integer.  Depending on the use case you may
-   want to take either the floor or ceiling of the result.  For example:
-
-`quantile(binomial(n, p), P)`]]
+   [Given a binomial distribution with ['n] trials, success fraction ['p] and probability ['P], 
+   finds the largest number of successes ['k] whose CDF is less than ['P].
+   It is strongly recommended that you read the tutorial 
+   [link math_toolkit.pol_tutorial.understand_dis_quant Understanding Quantiles of Discrete Distributions] before
+   using the quantile function.]]
 [[__quantile_c]
-   [The [*smallest] number of successes that may be observed from n trials
-   with success fraction p, at probability P.  Note that the value returned
-   is a real-number, and not an integer.  Depending on the use case you may
-   want to take either the floor or ceiling of the result. For example:
-
-`quantile(complement(binomial(n, p), P))`]]
+   [Given a binomial distribution with ['n] trials, success fraction ['p] and probability ['Q], 
+   finds the smallest number of successes ['k] whose CDF is greater than ['1-Q].
+   It is strongly recommended that you read the tutorial 
+   [link math_toolkit.pol_tutorial.understand_dis_quant Understanding Quantiles of Discrete Distributions] before
+   using the quantile function.]]
 ]
 
 [h4 Examples]
diff --git a/libs/math/doc/equations/autodiff/derivative_formula.svg b/libs/math/doc/equations/autodiff/derivative_formula.svg
new file mode 100644
index 0000000000..7aefac09a7
--- /dev/null
+++ b/libs/math/doc/equations/autodiff/derivative_formula.svg
@@ -0,0 +1,94 @@
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diff --git a/libs/math/doc/html/backgrounders.html b/libs/math/doc/html/backgrounders.html
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--- a/libs/math/doc/html/backgrounders.html
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-<link rel="home" href="index.html" title="Math Toolkit 2.9.0">
-<link rel="up" href="index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="index.html" title="Math Toolkit 2.10.0">
+<link rel="up" href="index.html" title="Math Toolkit 2.10.0">
 <link rel="prev" href="math_toolkit/perf_test_app.html" title="The Performance Test Applications">
 <link rel="next" href="math_toolkit/sf_implementation.html" title="Additional Implementation Notes">
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@@ -52,11 +52,11 @@
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 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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diff --git a/libs/math/doc/html/constants.html b/libs/math/doc/html/constants.html
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--- a/libs/math/doc/html/constants.html
+++ b/libs/math/doc/html/constants.html
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-<link rel="home" href="index.html" title="Math Toolkit 2.9.0">
-<link rel="up" href="index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="index.html" title="Math Toolkit 2.10.0">
+<link rel="up" href="index.html" title="Math Toolkit 2.10.0">
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 </head>
@@ -39,17 +39,17 @@
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-<dt><span class="section"><a href="math_toolkit/constants_faq.html">FAQs</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/constants_faq.html">Math Constants FAQs</a></span></dt>
 </dl>
 </div>
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/cstdfloat.html b/libs/math/doc/html/cstdfloat.html
index 816e8ab5ae..2f193b57f0 100644
--- a/libs/math/doc/html/cstdfloat.html
+++ b/libs/math/doc/html/cstdfloat.html
@@ -4,8 +4,8 @@
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-<link rel="home" href="index.html" title="Math Toolkit 2.9.0">
-<link rel="up" href="index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="index.html" title="Math Toolkit 2.10.0">
+<link rel="up" href="index.html" title="Math Toolkit 2.10.0">
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@@ -53,11 +53,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/dist.html b/libs/math/doc/html/dist.html
index 2b8e927dbd..8cac8c0190 100644
--- a/libs/math/doc/html/dist.html
+++ b/libs/math/doc/html/dist.html
@@ -4,9 +4,9 @@
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-<link rel="home" href="index.html" title="Math Toolkit 2.9.0">
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-<link rel="prev" href="math_toolkit/constants_faq.html" title="FAQs">
+<link rel="home" href="index.html" title="Math Toolkit 2.10.0">
+<link rel="up" href="index.html" title="Math Toolkit 2.10.0">
+<link rel="prev" href="math_toolkit/constants_faq.html" title="Math Constants FAQs">
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@@ -203,11 +203,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/extern_c.html b/libs/math/doc/html/extern_c.html
index 1dce7910d6..c901baf143 100644
--- a/libs/math/doc/html/extern_c.html
+++ b/libs/math/doc/html/extern_c.html
@@ -4,8 +4,8 @@
 <title>Chapter&#160;8.&#160;TR1 and C99 external "C" Functions</title>
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-<link rel="home" href="index.html" title="Math Toolkit 2.9.0">
-<link rel="up" href="index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="index.html" title="Math Toolkit 2.10.0">
+<link rel="up" href="index.html" title="Math Toolkit 2.10.0">
 <link rel="prev" href="math_toolkit/owens_t.html" title="Owen's T function">
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@@ -36,11 +36,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/gcd_lcm.html b/libs/math/doc/html/gcd_lcm.html
index 2ee7992b34..37893acd4d 100644
--- a/libs/math/doc/html/gcd_lcm.html
+++ b/libs/math/doc/html/gcd_lcm.html
@@ -4,8 +4,8 @@
 <title>Chapter&#160;16.&#160;Integer Utilities (Greatest Common Divisor and Least Common Multiple)</title>
 <link rel="stylesheet" href="math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="index.html" title="Math Toolkit 2.9.0">
-<link rel="up" href="index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="index.html" title="Math Toolkit 2.10.0">
+<link rel="up" href="index.html" title="Math Toolkit 2.10.0">
 <link rel="prev" href="math_toolkit/oct_todo.html" title="To Do">
 <link rel="next" href="internals.html" title="Chapter&#160;17.&#160;Internal Details: Series, Rationals and Continued Fractions, Testing, and Development Tools">
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@@ -37,11 +37,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/index.html b/libs/math/doc/html/index.html
index 062d081b18..b41e83d86f 100644
--- a/libs/math/doc/html/index.html
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@@ -1,10 +1,10 @@
 <html>
 <head>
 <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
-<title>Math Toolkit 2.9.0</title>
+<title>Math Toolkit 2.10.0</title>
 <link rel="stylesheet" href="math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="index.html" title="Math Toolkit 2.10.0">
 <link rel="next" href="overview.html" title="Chapter&#160;1.&#160;Overview">
 </head>
 <body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
@@ -22,7 +22,7 @@
 <div class="titlepage">
 <div>
 <div><h1 class="title">
-<a name="math_toolkit"></a>Math Toolkit 2.9.0</h1></div>
+<a name="math_toolkit"></a>Math Toolkit 2.10.0</h1></div>
 <div><div class="authorgroup">
 <div class="author"><h3 class="author">
 <span class="firstname">Nikhar</span> <span class="surname">Agrawal</span>
@@ -52,6 +52,9 @@
 <span class="firstname">Jeremy W.</span> <span class="surname">Murphy</span>
 </h3></div>
 <div class="author"><h3 class="author">
+<span class="firstname">Matthew</span> <span class="surname">Pulver</span>
+</h3></div>
+<div class="author"><h3 class="author">
 <span class="firstname">Johan</span> <span class="surname">R&#229;de</span>
 </h3></div>
 <div class="author"><h3 class="author">
@@ -77,11 +80,11 @@
 This manual is also available in <a href="http://sourceforge.net/projects/boost/files/boost-docs/" target="_top">printer
   friendly PDF format</a>, and as a CD ISBN 0-9504833-2-X 978-0-9504833-2-0,
   Classification 519.2-dc22. </p></div>
-<div><p class="copyright">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<div><p class="copyright">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang</p></div>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang</p></div>
 <div><div class="legalnotice">
 <a name="math_toolkit.legal"></a><p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
@@ -123,7 +126,7 @@ This manual is also available in <a href="http://sourceforge.net/projects/boost/
 </div>
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
-<td align="left"><p><small>Last revised: April 09, 2019 at 19:39:01 GMT</small></p></td>
+<td align="left"><p><small>Last revised: August 14, 2019 at 12:06:01 GMT</small></p></td>
 <td align="right"><div class="copyright-footer"></div></td>
 </tr></table>
 <hr>
diff --git a/libs/math/doc/html/indexes.html b/libs/math/doc/html/indexes.html
index 009aac23c4..93d152b457 100644
--- a/libs/math/doc/html/indexes.html
+++ b/libs/math/doc/html/indexes.html
@@ -4,8 +4,8 @@
 <title>Chapter&#160;23.&#160;Indexes</title>
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-<link rel="home" href="index.html" title="Math Toolkit 2.9.0">
-<link rel="up" href="index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="index.html" title="Math Toolkit 2.10.0">
+<link rel="up" href="index.html" title="Math Toolkit 2.10.0">
 <link rel="prev" href="math_toolkit/credits.html" title="Credits and Acknowledgements">
 <link rel="next" href="indexes/s01.html" title="Function Index">
 </head>
@@ -38,11 +38,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/indexes/s01.html b/libs/math/doc/html/indexes/s01.html
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 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../indexes.html" title="Chapter&#160;23.&#160;Indexes">
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-<a name="idm45603834793984"></a>Function Index</h2></div></div></div>
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+<a name="idm45274473484352"></a>Function Index</h2></div></div></div>
+<p><a class="link" href="s01.html#idx_id_0">1</a> <a class="link" href="s01.html#idx_id_1">2</a> <a class="link" href="s01.html#idx_id_2">4</a> <a class="link" href="s01.html#idx_id_5">A</a> <a class="link" href="s01.html#idx_id_6">B</a> <a class="link" href="s01.html#idx_id_7">C</a> <a class="link" href="s01.html#idx_id_8">D</a> <a class="link" href="s01.html#idx_id_9">E</a> <a class="link" href="s01.html#idx_id_10">F</a> <a class="link" href="s01.html#idx_id_11">G</a> <a class="link" href="s01.html#idx_id_12">H</a> <a class="link" href="s01.html#idx_id_13">I</a> <a class="link" href="s01.html#idx_id_14">J</a> <a class="link" href="s01.html#idx_id_15">K</a> <a class="link" href="s01.html#idx_id_16">L</a> <a class="link" href="s01.html#idx_id_17">M</a> <a class="link" href="s01.html#idx_id_18">N</a> <a class="link" href="s01.html#idx_id_19">O</a> <a class="link" href="s01.html#idx_id_20">P</a> <a class="link" href="s01.html#idx_id_21">Q</a> <a class="link" href="s01.html#idx_id_22">R</a> <a class="link" href="s01.html#idx_id_23">S</a> <a class="link" href="s01.html#idx_id_24">T</a> <a class="link" href="s01.html#idx_id_25">U</a> <a class="link" href="s01.html#idx_id_26">V</a> <a class="link" href="s01.html#idx_id_27">W</a> <a class="link" href="s01.html#idx_id_28">X</a> <a class="link" href="s01.html#idx_id_29">Y</a> <a class="link" href="s01.html#idx_id_30">Z</a></p>
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@@ -47,7 +47,10 @@
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+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/ellint/ellint_d.html" title="Elliptic Integral D - Legendre Form"><span class="index-entry-level-1">Elliptic Integral D - Legendre Form</span></a></p></li>
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+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/ellint/ellint_1.html" title="Elliptic Integrals of the First Kind - Legendre Form"><span class="index-entry-level-1">Elliptic Integrals of the First Kind - Legendre Form</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/ellint/ellint_2.html" title="Elliptic Integrals of the Second Kind - Legendre Form"><span class="index-entry-level-1">Elliptic Integrals of the Second Kind - Legendre Form</span></a></p></li>
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+<a name="idx_id_5"></a><span class="term">A</span>
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+<p><span class="index-entry-level-0">at</span></p>
+<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/sf_implementation.html" title="Additional Implementation Notes"><span class="index-entry-level-1">Additional Implementation Notes</span></a></p></li></ul></div>
+</li>
+<li class="listitem" style="list-style-type: none">
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+<a name="idx_id_6"></a><span class="term">B</span>
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+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/vector_barycentric.html" title="Vector-valued Barycentric Rational Interpolation"><span class="index-entry-level-1">Vector-valued Barycentric Rational Interpolation</span></a></p></li>
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+<a name="idx_id_7"></a><span class="term">C</span>
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+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/constants_faq.html" title="Math Constants FAQs"><span class="index-entry-level-1">Math Constants FAQs</span></a></p></li>
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+<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">derivative</span></p>
+<div class="index"><ul class="index" style="list-style-type: none; ">
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/autodiff.html" title="Automatic Differentiation"><span class="index-entry-level-1">Automatic Differentiation</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/root_finding_examples/cbrt_eg.html" title="Finding the Cubed Root With and Without Derivatives"><span class="index-entry-level-1">Finding the Cubed Root With and Without Derivatives</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/history1.html" title="History and What's New"><span class="index-entry-level-1">History and What's New</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/roots_deriv.html" title="Root Finding With Derivatives: Newton-Raphson, Halley &amp; Schr&#246;der"><span class="index-entry-level-1">Root Finding With Derivatives: Newton-Raphson, Halley &amp; Schr&#246;der</span></a></p></li>
+</ul></div>
+</li>
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+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/main_faq.html" title="Boost.Math Frequently Asked Questions (FAQs)"><span class="index-entry-level-1">Boost.Math Frequently Asked Questions (FAQs)</span></a></p></li>
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+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/autodiff.html" title="Automatic Differentiation"><span class="index-entry-level-1">Automatic Differentiation</span></a></p></li>
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 </ul></div>
 </li>
+<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">fvar</span></p>
+<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/autodiff.html" title="Automatic Differentiation"><span class="index-entry-level-1">Automatic Differentiation</span></a></p></li></ul></div>
+</li>
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 <dt>
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+<a name="idx_id_11"></a><span class="term">G</span>
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@@ -1447,7 +1469,7 @@
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@@ -1551,7 +1573,7 @@
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@@ -1666,6 +1688,7 @@
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 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/sf_poly/chebyshev.html" title="Chebyshev Polynomials"><span class="index-entry-level-1">Chebyshev Polynomials</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/double_exponential/de_exp_sinh.html" title="exp_sinh"><span class="index-entry-level-1">exp_sinh</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/fourier_integrals.html" title="Fourier Integrals"><span class="index-entry-level-1">Fourier Integrals</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/gauss_kronrod.html" title="Gauss-Kronrod Quadrature"><span class="index-entry-level-1">Gauss-Kronrod Quadrature</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/gauss.html" title="Gauss-Legendre quadrature"><span class="index-entry-level-1">Gauss-Legendre quadrature</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/naive_monte_carlo.html" title="Naive Monte Carlo Integration"><span class="index-entry-level-1">Naive Monte Carlo Integration</span></a></p></li>
@@ -1721,7 +1744,7 @@
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 <dt>
-<a name="idx_id_12"></a><span class="term">J</span>
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@@ -1790,7 +1813,7 @@
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@@ -1825,7 +1848,7 @@
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+<div class="index"><ul class="index" style="list-style-type: none; ">
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/autodiff.html" title="Automatic Differentiation"><span class="index-entry-level-1">Automatic Differentiation</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/number_series/bernoulli_numbers.html" title="Bernoulli Numbers"><span class="index-entry-level-1">Bernoulli Numbers</span></a></p></li>
+</ul></div>
 </li>
 <li class="listitem" style="list-style-type: none">
 <p><span class="index-entry-level-0">lp_distance</span></p>
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@@ -2202,6 +2228,14 @@
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 </li>
 <li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">make_ftuple</span></p>
+<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/autodiff.html" title="Automatic Differentiation"><span class="index-entry-level-1">Automatic Differentiation</span></a></p></li></ul></div>
+</li>
+<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">make_fvar</span></p>
+<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/autodiff.html" title="Automatic Differentiation"><span class="index-entry-level-1">Automatic Differentiation</span></a></p></li></ul></div>
+</li>
+<li class="listitem" style="list-style-type: none">
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@@ -2263,7 +2297,7 @@
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@@ -2397,12 +2431,13 @@
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 <p><span class="index-entry-level-0">O</span></p>
 <div class="index"><ul class="index" style="list-style-type: none; ">
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/autodiff.html" title="Automatic Differentiation"><span class="index-entry-level-1">Automatic Differentiation</span></a></p></li>
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 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/diff0.html" title="Lanczos Smoothing Derivatives"><span class="index-entry-level-1">Lanczos Smoothing Derivatives</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/bessel/mbessel.html" title="Modified Bessel Functions of the First and Second Kinds"><span class="index-entry-level-1">Modified Bessel Functions of the First and Second Kinds</span></a></p></li>
@@ -2422,6 +2457,7 @@
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+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/cardinal_quadratic_b.html" title="Cardinal Quadratic B-spline interpolation"><span class="index-entry-level-1">Cardinal Quadratic B-spline interpolation</span></a></p></li>
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 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/sf_poly/chebyshev.html" title="Chebyshev Polynomials"><span class="index-entry-level-1">Chebyshev Polynomials</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/root_finding_examples/5th_root_eg.html" title="Computing the Fifth Root"><span class="index-entry-level-1">Computing the Fifth Root</span></a></p></li>
@@ -2437,6 +2473,8 @@
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 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/roots_noderiv/root_termination.html" title="Termination Condition Functors"><span class="index-entry-level-1">Termination Condition Functors</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/vector_barycentric.html" title="Vector-valued Barycentric Rational Interpolation"><span class="index-entry-level-1">Vector-valued Barycentric Rational Interpolation</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/whittaker_shannon.html" title="Whittaker-Shannon interpolation"><span class="index-entry-level-1">Whittaker-Shannon interpolation</span></a></p></li>
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 </li>
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@@ -2453,12 +2491,13 @@
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 <dt>
-<a name="idx_id_18"></a><span class="term">P</span>
+<a name="idx_id_20"></a><span class="term">P</span>
 </dt>
 <dd><div class="index"><ul class="index" style="list-style-type: none; ">
 <li class="listitem" style="list-style-type: none">
 <p><span class="index-entry-level-0">P</span></p>
 <div class="index"><ul class="index" style="list-style-type: none; ">
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/main_faq.html" title="Boost.Math Frequently Asked Questions (FAQs)"><span class="index-entry-level-1">Boost.Math Frequently Asked Questions (FAQs)</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/catmull_rom.html" title="Catmull-Rom Splines"><span class="index-entry-level-1">Catmull-Rom Splines</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/cubic_b.html" title="Cubic B-spline interpolation"><span class="index-entry-level-1">Cubic B-spline interpolation</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/sf_gamma/digamma.html" title="Digamma"><span class="index-entry-level-1">Digamma</span></a></p></li>
@@ -2466,7 +2505,6 @@
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 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/stat_tut/weg/find_eg/find_mean_and_sd_eg.html" title="Find mean and standard deviation example"><span class="index-entry-level-1">Find mean and standard deviation example</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/stat_tut/weg/find_eg/find_scale_eg.html" title="Find Scale (Standard Deviation) Example"><span class="index-entry-level-1">Find Scale (Standard Deviation) Example</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/main_faq.html" title="Frequently Asked Questions FAQ"><span class="index-entry-level-1">Frequently Asked Questions FAQ</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/stat_tut/overview/generic.html" title="Generic operations common to all distributions are non-member functions"><span class="index-entry-level-1">Generic operations common to all distributions are non-member functions</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution"><span class="index-entry-level-1">Negative Binomial Distribution</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/stat_tut/variates.html" title="Random Variates and Distribution Parameters"><span class="index-entry-level-1">Random Variates and Distribution Parameters</span></a></p></li>
@@ -2475,6 +2513,10 @@
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 <li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">p1</span></p>
+<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/catmull_rom.html" title="Catmull-Rom Splines"><span class="index-entry-level-1">Catmull-Rom Splines</span></a></p></li></ul></div>
+</li>
+<li class="listitem" style="list-style-type: none">
 <p><span class="index-entry-level-0">pdf</span></p>
 <div class="index"><ul class="index" style="list-style-type: none; ">
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist_ref/dists/arcine_dist.html" title="Arcsine Distribution"><span class="index-entry-level-1">Arcsine Distribution</span></a></p></li>
@@ -2502,17 +2544,20 @@
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+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/cardinal_quadratic_b.html" title="Cardinal Quadratic B-spline interpolation"><span class="index-entry-level-1">Cardinal Quadratic B-spline interpolation</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/catmull_rom.html" title="Catmull-Rom Splines"><span class="index-entry-level-1">Catmull-Rom Splines</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/sf_poly/chebyshev.html" title="Chebyshev Polynomials"><span class="index-entry-level-1">Chebyshev Polynomials</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/cubic_b.html" title="Cubic B-spline interpolation"><span class="index-entry-level-1">Cubic B-spline interpolation</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/sf_poly/legendre_stieltjes.html" title="Legendre-Stieltjes Polynomials"><span class="index-entry-level-1">Legendre-Stieltjes Polynomials</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/polynomials.html" title="Polynomials"><span class="index-entry-level-1">Polynomials</span></a></p></li>
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+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/vector_barycentric.html" title="Vector-valued Barycentric Rational Interpolation"><span class="index-entry-level-1">Vector-valued Barycentric Rational Interpolation</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/whittaker_shannon.html" title="Whittaker-Shannon interpolation"><span class="index-entry-level-1">Whittaker-Shannon interpolation</span></a></p></li>
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 <dt>
-<a name="idx_id_19"></a><span class="term">Q</span>
+<a name="idx_id_21"></a><span class="term">Q</span>
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@@ -2549,7 +2594,7 @@
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-<a name="idx_id_20"></a><span class="term">R</span>
+<a name="idx_id_22"></a><span class="term">R</span>
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@@ -2714,7 +2759,7 @@
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-<a name="idx_id_21"></a><span class="term">S</span>
+<a name="idx_id_23"></a><span class="term">S</span>
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@@ -3014,7 +3059,7 @@
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-<a name="idx_id_22"></a><span class="term">T</span>
+<a name="idx_id_24"></a><span class="term">T</span>
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@@ -3028,6 +3073,7 @@
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+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/vector_barycentric.html" title="Vector-valued Barycentric Rational Interpolation"><span class="index-entry-level-1">Vector-valued Barycentric Rational Interpolation</span></a></p></li>
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-<a name="idx_id_23"></a><span class="term">U</span>
+<a name="idx_id_25"></a><span class="term">U</span>
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@@ -3251,7 +3297,7 @@
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-<a name="idx_id_24"></a><span class="term">V</span>
+<a name="idx_id_26"></a><span class="term">V</span>
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@@ -3264,6 +3310,7 @@
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 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist_ref/dists/nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution"><span class="index-entry-level-1">Noncentral Chi-Squared Distribution</span></a></p></li>
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+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/whittaker_shannon.html" title="Whittaker-Shannon interpolation"><span class="index-entry-level-1">Whittaker-Shannon interpolation</span></a></p></li>
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@@ -3293,7 +3340,7 @@
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-<a name="idx_id_25"></a><span class="term">W</span>
+<a name="idx_id_27"></a><span class="term">W</span>
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@@ -3309,7 +3356,7 @@
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-<a name="idx_id_26"></a><span class="term">X</span>
+<a name="idx_id_28"></a><span class="term">X</span>
 </dt>
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 <p><span class="index-entry-level-0">x</span></p>
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+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/vector_barycentric.html" title="Vector-valued Barycentric Rational Interpolation"><span class="index-entry-level-1">Vector-valued Barycentric Rational Interpolation</span></a></p></li>
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@@ -3365,11 +3413,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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diff --git a/libs/math/doc/html/indexes/s02.html b/libs/math/doc/html/indexes/s02.html
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+++ b/libs/math/doc/html/indexes/s02.html
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-<link rel="home" href="../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../indexes.html" title="Chapter&#160;23.&#160;Indexes">
 <link rel="prev" href="s01.html" title="Function Index">
 <link rel="next" href="s03.html" title="Typedef Index">
@@ -24,15 +24,15 @@
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+<a name="idm45274470839136"></a>Class Index</h2></div></div></div>
+<p><a class="link" href="s02.html#idx_id_36">A</a> <a class="link" href="s02.html#idx_id_37">B</a> <a class="link" href="s02.html#idx_id_38">C</a> <a class="link" href="s02.html#idx_id_39">D</a> <a class="link" href="s02.html#idx_id_40">E</a> <a class="link" href="s02.html#idx_id_41">F</a> <a class="link" href="s02.html#idx_id_42">G</a> <a class="link" href="s02.html#idx_id_43">H</a> <a class="link" href="s02.html#idx_id_44">I</a> <a class="link" href="s02.html#idx_id_47">L</a> <a class="link" href="s02.html#idx_id_48">M</a> <a class="link" href="s02.html#idx_id_49">N</a> <a class="link" href="s02.html#idx_id_50">O</a> <a class="link" href="s02.html#idx_id_51">P</a> <a class="link" href="s02.html#idx_id_52">Q</a> <a class="link" href="s02.html#idx_id_53">R</a> <a class="link" href="s02.html#idx_id_54">S</a> <a class="link" href="s02.html#idx_id_55">T</a> <a class="link" href="s02.html#idx_id_56">U</a> <a class="link" href="s02.html#idx_id_57">V</a> <a class="link" href="s02.html#idx_id_58">W</a></p>
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 <dt>
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+<a name="idx_id_38"></a><span class="term">C</span>
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 <dd><div class="index"><ul class="index" style="list-style-type: none; ">
 <li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">cardinal_quadratic_b_spline</span></p>
+<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/cardinal_quadratic_b.html" title="Cardinal Quadratic B-spline interpolation"><span class="index-entry-level-1">Cardinal Quadratic B-spline interpolation</span></a></p></li></ul></div>
+</li>
+<li class="listitem" style="list-style-type: none">
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 <div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/catmull_rom.html" title="Catmull-Rom Splines"><span class="index-entry-level-1">Catmull-Rom Splines</span></a></p></li></ul></div>
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-<a name="idx_id_35"></a><span class="term">D</span>
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 <dt>
-<a name="idx_id_36"></a><span class="term">E</span>
+<a name="idx_id_40"></a><span class="term">E</span>
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@@ -124,14 +128,20 @@
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 </ul></div></dd>
 <dt>
-<a name="idx_id_37"></a><span class="term">F</span>
+<a name="idx_id_41"></a><span class="term">F</span>
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-<dd><div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none">
+<dd><div class="index"><ul class="index" style="list-style-type: none; ">
+<li class="listitem" style="list-style-type: none">
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-</li></ul></div></dd>
+</li>
+<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">fvar</span></p>
+<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/autodiff.html" title="Automatic Differentiation"><span class="index-entry-level-1">Automatic Differentiation</span></a></p></li></ul></div>
+</li>
+</ul></div></dd>
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 <dt>
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+<a name="idx_id_49"></a><span class="term">N</span>
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-<a name="idx_id_46"></a><span class="term">O</span>
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-<dd><div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none">
+<dd><div class="index"><ul class="index" style="list-style-type: none; ">
+<li class="listitem" style="list-style-type: none">
 <p><span class="index-entry-level-0">octonion</span></p>
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 </ul></div>
-</li></ul></div></dd>
+</li>
+<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">ooura_fourier_cos</span></p>
+<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/fourier_integrals.html" title="Fourier Integrals"><span class="index-entry-level-1">Fourier Integrals</span></a></p></li></ul></div>
+</li>
+<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">ooura_fourier_sin</span></p>
+<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/fourier_integrals.html" title="Fourier Integrals"><span class="index-entry-level-1">Fourier Integrals</span></a></p></li></ul></div>
+</li>
+</ul></div></dd>
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+<a name="idx_id_57"></a><span class="term">V</span>
+</dt>
+<dd><div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">vector_barycentric_rational</span></p>
+<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/vector_barycentric.html" title="Vector-valued Barycentric Rational Interpolation"><span class="index-entry-level-1">Vector-valued Barycentric Rational Interpolation</span></a></p></li></ul></div>
+</li></ul></div></dd>
+<dt>
+<a name="idx_id_58"></a><span class="term">W</span>
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+<dd><div class="index"><ul class="index" style="list-style-type: none; ">
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist_ref/dists/weibull_dist.html" title="Weibull Distribution"><span class="index-entry-level-0">weibull_distribution</span></a></p></li>
+<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">whittaker_shannon</span></p>
+<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/whittaker_shannon.html" title="Whittaker-Shannon interpolation"><span class="index-entry-level-1">Whittaker-Shannon interpolation</span></a></p></li></ul></div>
+</li>
+</ul></div></dd>
 </dl></div>
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
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@@ -4,7 +4,7 @@
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-<link rel="home" href="../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../index.html" title="Math Toolkit 2.10.0">
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
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-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
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+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
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-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
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+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
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+<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">11th root(28) for float, double, long double and cpp_bin_float_50 types, using _X64_SSE2</span></p>
+<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/root_comparison/root_n_comparison.html#math_toolkit.root_comparison.root_n_comparison.root_11_1" title="Table&#160;9.11.&#160;11th root(28) for float, double, long double and cpp_bin_float_50 types, using _X64_SSE2"><span class="index-entry-level-1">cpp_bin_float</span></a></p></li></ul></div>
+</li>
+<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">11th root(28) for float, double, long double and cpp_bin_float_50 types, using _X86_SSE2</span></p>
+<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/root_comparison/root_n_comparison.html#math_toolkit.root_comparison.root_n_comparison.root_11" title="Table&#160;9.5.&#160;11th root(28) for float, double, long double and cpp_bin_float_50 types, using _X86_SSE2"><span class="index-entry-level-1">cpp_bin_float</span></a></p></li></ul></div>
+</li>
+</ul></div></dd>
 <dt>
-<a name="idx_id_117"></a><span class="term">2</span>
+<a name="idx_id_125"></a><span class="term">2</span>
 </dt>
 <dd><div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none">
 <p><span class="index-entry-level-0">2</span></p>
@@ -46,7 +60,10 @@
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist_ref/dists/arcine_dist.html" title="Arcsine Distribution"><span class="index-entry-level-1">Arcsine Distribution</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/bessel/bessel_first.html" title="Bessel Functions of the First and Second Kinds"><span class="index-entry-level-1">Bessel Functions of the First and Second Kinds</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist_ref/dists/beta_dist.html" title="Beta Distribution"><span class="index-entry-level-1">Beta Distribution</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/ellint/ellint_d.html" title="Elliptic Integral D - Legendre Form"><span class="index-entry-level-1">Elliptic Integral D - Legendre Form</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/ellint/ellint_intro.html" title="Elliptic Integral Overview"><span class="index-entry-level-1">Elliptic Integral Overview</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/ellint/ellint_1.html" title="Elliptic Integrals of the First Kind - Legendre Form"><span class="index-entry-level-1">Elliptic Integrals of the First Kind - Legendre Form</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/ellint/ellint_2.html" title="Elliptic Integrals of the Second Kind - Legendre Form"><span class="index-entry-level-1">Elliptic Integrals of the Second Kind - Legendre Form</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/ellint/ellint_3.html" title="Elliptic Integrals of the Third Kind - Legendre Form"><span class="index-entry-level-1">Elliptic Integrals of the Third Kind - Legendre Form</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/bessel/bessel_root.html" title="Finding Zeros of Bessel Functions of the First and Second Kinds"><span class="index-entry-level-1">Finding Zeros of Bessel Functions of the First and Second Kinds</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/history1.html" title="History and What's New"><span class="index-entry-level-1">History and What's New</span></a></p></li>
@@ -58,14 +75,48 @@
 </ul></div>
 </li></ul></div></dd>
 <dt>
-<a name="idx_id_118"></a><span class="term">4</span>
+<a name="idx_id_126"></a><span class="term">4</span>
 </dt>
 <dd><div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none">
 <p><span class="index-entry-level-0">41</span></p>
 <div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses"><span class="index-entry-level-1">The Incomplete Beta Function Inverses</span></a></p></li></ul></div>
 </li></ul></div></dd>
 <dt>
-<a name="idx_id_119"></a><span class="term">A</span>
+<a name="idx_id_127"></a><span class="term">5</span>
+</dt>
+<dd><div class="index"><ul class="index" style="list-style-type: none; ">
+<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">5th root(28) for float, double, long double and cpp_bin_float_50 types, using _X64_AVX</span></p>
+<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/root_comparison/root_n_comparison.html#math_toolkit.root_comparison.root_n_comparison.root_5_0" title="Table&#160;9.6.&#160;5th root(28) for float, double, long double and cpp_bin_float_50 types, using _X64_AVX"><span class="index-entry-level-1">cpp_bin_float</span></a></p></li></ul></div>
+</li>
+<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">5th root(28) for float, double, long double and cpp_bin_float_50 types, using _X64_SSE2</span></p>
+<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/root_comparison/root_n_comparison.html#math_toolkit.root_comparison.root_n_comparison.root_5_1" title="Table&#160;9.9.&#160;5th root(28) for float, double, long double and cpp_bin_float_50 types, using _X64_SSE2"><span class="index-entry-level-1">cpp_bin_float</span></a></p></li></ul></div>
+</li>
+<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">5th root(28) for float, double, long double and cpp_bin_float_50 types, using _X86_SSE2</span></p>
+<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/root_comparison/root_n_comparison.html#math_toolkit.root_comparison.root_n_comparison.root_5" title="Table&#160;9.3.&#160;5th root(28) for float, double, long double and cpp_bin_float_50 types, using _X86_SSE2"><span class="index-entry-level-1">cpp_bin_float</span></a></p></li></ul></div>
+</li>
+</ul></div></dd>
+<dt>
+<a name="idx_id_128"></a><span class="term">7</span>
+</dt>
+<dd><div class="index"><ul class="index" style="list-style-type: none; ">
+<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">7th root(28) for float, double, long double and cpp_bin_float_50 types, using _X64_AVX</span></p>
+<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/root_comparison/root_n_comparison.html#math_toolkit.root_comparison.root_n_comparison.root_7_0" title="Table&#160;9.7.&#160;7th root(28) for float, double, long double and cpp_bin_float_50 types, using _X64_AVX"><span class="index-entry-level-1">cpp_bin_float</span></a></p></li></ul></div>
+</li>
+<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">7th root(28) for float, double, long double and cpp_bin_float_50 types, using _X64_SSE2</span></p>
+<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/root_comparison/root_n_comparison.html#math_toolkit.root_comparison.root_n_comparison.root_7_1" title="Table&#160;9.10.&#160;7th root(28) for float, double, long double and cpp_bin_float_50 types, using _X64_SSE2"><span class="index-entry-level-1">cpp_bin_float</span></a></p></li></ul></div>
+</li>
+<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">7th root(28) for float, double, long double and cpp_bin_float_50 types, using _X86_SSE2</span></p>
+<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/root_comparison/root_n_comparison.html#math_toolkit.root_comparison.root_n_comparison.root_7" title="Table&#160;9.4.&#160;7th root(28) for float, double, long double and cpp_bin_float_50 types, using _X86_SSE2"><span class="index-entry-level-1">cpp_bin_float</span></a></p></li></ul></div>
+</li>
+</ul></div></dd>
+<dt>
+<a name="idx_id_129"></a><span class="term">A</span>
 </dt>
 <dd><div class="index"><ul class="index" style="list-style-type: none; ">
 <li class="listitem" style="list-style-type: none">
@@ -73,6 +124,7 @@
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 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/main_intro.html" title="About the Math Toolkit"><span class="index-entry-level-1">constants</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/main_intro.html" title="About the Math Toolkit"><span class="index-entry-level-1">functions</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/main_intro.html" title="About the Math Toolkit"><span class="index-entry-level-1">multiprecision</span></a></p></li>
 </ul></div>
 </li>
 <li class="listitem" style="list-style-type: none">
@@ -100,6 +152,7 @@
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 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/inv_hyper/asinh.html" title="asinh"><span class="index-entry-level-1">asinh</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/inv_hyper/atanh.html" title="atanh"><span class="index-entry-level-1">atanh</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/autodiff.html" title="Automatic Differentiation"><span class="index-entry-level-1">Automatic Differentiation</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/barycentric.html" title="Barycentric Rational Interpolation"><span class="index-entry-level-1">Barycentric Rational Interpolation</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist_ref/dists/bernoulli_dist.html" title="Bernoulli Distribution"><span class="index-entry-level-1">Bernoulli Distribution</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/number_series/bernoulli_numbers.html" title="Bernoulli Numbers"><span class="index-entry-level-1">Bernoulli Numbers</span></a></p></li>
@@ -108,6 +161,7 @@
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist_ref/dists/beta_dist.html" title="Beta Distribution"><span class="index-entry-level-1">Beta Distribution</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/factorials/sf_binomial.html" title="Binomial Coefficients"><span class="index-entry-level-1">Binomial Coefficients</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist_ref/dists/binomial_dist.html" title="Binomial Distribution"><span class="index-entry-level-1">Binomial Distribution</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/main_faq.html" title="Boost.Math Frequently Asked Questions (FAQs)"><span class="index-entry-level-1">Boost.Math Frequently Asked Questions (FAQs)</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist_ref/dists/cauchy_dist.html" title="Cauchy-Lorentz Distribution"><span class="index-entry-level-1">Cauchy-Lorentz Distribution</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/double_exponential/de_caveats.html" title="Caveats"><span class="index-entry-level-1">Caveats</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/powers/cbrt.html" title="cbrt"><span class="index-entry-level-1">cbrt</span></a></p></li>
@@ -145,11 +199,9 @@
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 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/factorials/sf_factorial.html" title="Factorial"><span class="index-entry-level-1">Factorial</span></a></p></li>
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-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/constants_faq.html" title="FAQs"><span class="index-entry-level-1">FAQs</span></a></p></li>
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 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/root_finding_examples/cbrt_eg.html" title="Finding the Cubed Root With and Without Derivatives"><span class="index-entry-level-1">Finding the Cubed Root With and Without Derivatives</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/next_float.html" title="Floating-Point Representation Distance (ULP), and Finding Adjacent Floating-Point Values"><span class="index-entry-level-1">Floating-Point Representation Distance (ULP), and Finding Adjacent Floating-Point Values</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/main_faq.html" title="Frequently Asked Questions FAQ"><span class="index-entry-level-1">Frequently Asked Questions FAQ</span></a></p></li>
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 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution"><span class="index-entry-level-1">Gamma (and Erlang) Distribution</span></a></p></li>
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@@ -182,6 +234,7 @@
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 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist_ref/dists/logistic_dist.html" title="Logistic Distribution"><span class="index-entry-level-1">Logistic Distribution</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/constants_faq.html" title="Math Constants FAQs"><span class="index-entry-level-1">Math Constants FAQs</span></a></p></li>
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 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist_ref/dists/nc_beta_dist.html" title="Noncentral Beta Distribution"><span class="index-entry-level-1">Noncentral Beta Distribution</span></a></p></li>
@@ -234,6 +287,7 @@
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 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist_ref/dists/weibull_dist.html" title="Weibull Distribution"><span class="index-entry-level-1">Weibull Distribution</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/whittaker_shannon.html" title="Whittaker-Shannon interpolation"><span class="index-entry-level-1">Whittaker-Shannon interpolation</span></a></p></li>
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 </ul></div>
 </li>
@@ -456,6 +510,10 @@
 </ul></div>
 </li>
 <li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">at</span></p>
+<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/sf_implementation.html" title="Additional Implementation Notes"><span class="index-entry-level-1">Additional Implementation Notes</span></a></p></li></ul></div>
+</li>
+<li class="listitem" style="list-style-type: none">
 <p><span class="index-entry-level-0">atanh</span></p>
 <div class="index"><ul class="index" style="list-style-type: none; ">
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/inv_hyper/atanh.html" title="atanh"><span class="index-entry-level-1">accuracy</span></a></p></li>
@@ -481,9 +539,25 @@
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 </ul></div>
 </li>
+<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">Automatic Differentiation</span></p>
+<div class="index"><ul class="index" style="list-style-type: none; ">
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/autodiff.html" title="Automatic Differentiation"><span class="index-entry-level-1">accuracy</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/autodiff.html" title="Automatic Differentiation"><span class="index-entry-level-1">constants</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/autodiff.html" title="Automatic Differentiation"><span class="index-entry-level-1">cpp_bin_float</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/autodiff.html" title="Automatic Differentiation"><span class="index-entry-level-1">derivative</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/autodiff.html" title="Automatic Differentiation"><span class="index-entry-level-1">erfc</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/autodiff.html" title="Automatic Differentiation"><span class="index-entry-level-1">fvar</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/autodiff.html" title="Automatic Differentiation"><span class="index-entry-level-1">lookup</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/autodiff.html" title="Automatic Differentiation"><span class="index-entry-level-1">make_ftuple</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/autodiff.html" title="Automatic Differentiation"><span class="index-entry-level-1">make_fvar</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/autodiff.html" title="Automatic Differentiation"><span class="index-entry-level-1">multiprecision</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/autodiff.html" title="Automatic Differentiation"><span class="index-entry-level-1">O</span></a></p></li>
+</ul></div>
+</li>
 </ul></div></dd>
 <dt>
-<a name="idx_id_120"></a><span class="term">B</span>
+<a name="idx_id_130"></a><span class="term">B</span>
 </dt>
 <dd><div class="index"><ul class="index" style="list-style-type: none; ">
 <li class="listitem" style="list-style-type: none">
@@ -528,8 +602,10 @@
 <div class="index"><ul class="index" style="list-style-type: none; ">
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/number_series/bernoulli_numbers.html" title="Bernoulli Numbers"><span class="index-entry-level-1">accuracy</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/number_series/bernoulli_numbers.html" title="Bernoulli Numbers"><span class="index-entry-level-1">bernoulli_b2n</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/number_series/bernoulli_numbers.html" title="Bernoulli Numbers"><span class="index-entry-level-1">cpp_dec_float</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/number_series/bernoulli_numbers.html" title="Bernoulli Numbers"><span class="index-entry-level-1">lookup</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/number_series/bernoulli_numbers.html" title="Bernoulli Numbers"><span class="index-entry-level-1">message</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/number_series/bernoulli_numbers.html" title="Bernoulli Numbers"><span class="index-entry-level-1">multiprecision</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/number_series/bernoulli_numbers.html" title="Bernoulli Numbers"><span class="index-entry-level-1">performance</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/number_series/bernoulli_numbers.html" title="Bernoulli Numbers"><span class="index-entry-level-1">unchecked_bernoulli_b2n</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/number_series/bernoulli_numbers.html" title="Bernoulli Numbers"><span class="index-entry-level-1">zero</span></a></p></li>
@@ -700,6 +776,20 @@
 <div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/polynomials.html" title="Polynomials"><span class="index-entry-level-1">Polynomials</span></a></p></li></ul></div>
 </li>
 <li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">Boost.Math Frequently Asked Questions (FAQs)</span></p>
+<div class="index"><ul class="index" style="list-style-type: none; ">
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/main_faq.html" title="Boost.Math Frequently Asked Questions (FAQs)"><span class="index-entry-level-1">accuracy</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/main_faq.html" title="Boost.Math Frequently Asked Questions (FAQs)"><span class="index-entry-level-1">Cephes</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/main_faq.html" title="Boost.Math Frequently Asked Questions (FAQs)"><span class="index-entry-level-1">cpp_bin_float</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/main_faq.html" title="Boost.Math Frequently Asked Questions (FAQs)"><span class="index-entry-level-1">cpp_dec_float</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/main_faq.html" title="Boost.Math Frequently Asked Questions (FAQs)"><span class="index-entry-level-1">distribution</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/main_faq.html" title="Boost.Math Frequently Asked Questions (FAQs)"><span class="index-entry-level-1">FAQ</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/main_faq.html" title="Boost.Math Frequently Asked Questions (FAQs)"><span class="index-entry-level-1">multiprecision</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/main_faq.html" title="Boost.Math Frequently Asked Questions (FAQs)"><span class="index-entry-level-1">P</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/main_faq.html" title="Boost.Math Frequently Asked Questions (FAQs)"><span class="index-entry-level-1">performance</span></a></p></li>
+</ul></div>
+</li>
+<li class="listitem" style="list-style-type: none">
 <p><span class="index-entry-level-0">Boost.Math Macros</span></p>
 <div class="index"><ul class="index" style="list-style-type: none; ">
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/config_macros.html#math_toolkit.config_macros.boost_math_macros" title="Table&#160;1.11.&#160;Boost.Math Macros"><span class="index-entry-level-1">BOOST_FPU_EXCEPTION_GUARD</span></a></p></li>
@@ -736,7 +826,7 @@
 <div class="index"><ul class="index" style="list-style-type: none; ">
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/sf_implementation.html" title="Additional Implementation Notes"><span class="index-entry-level-1">Additional Implementation Notes</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/new_const.html" title="Defining New Constants"><span class="index-entry-level-1">Defining New Constants</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/constants_faq.html" title="FAQs"><span class="index-entry-level-1">FAQs</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/constants_faq.html" title="Math Constants FAQs"><span class="index-entry-level-1">Math Constants FAQs</span></a></p></li>
 </ul></div>
 </li>
 <li class="listitem" style="list-style-type: none">
@@ -1037,11 +1127,12 @@
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/airy/airy_root.html" title="Finding Zeros of Airy Functions"><span class="index-entry-level-1">Finding Zeros of Airy Functions</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/sf_gamma/igamma.html" title="Incomplete Gamma Functions"><span class="index-entry-level-1">Incomplete Gamma Functions</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/issues.html" title="Known Issues, and TODO List"><span class="index-entry-level-1">Known Issues, and TODO List</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/vector_barycentric.html" title="Vector-valued Barycentric Rational Interpolation"><span class="index-entry-level-1">Vector-valued Barycentric Rational Interpolation</span></a></p></li>
 </ul></div>
 </li>
 </ul></div></dd>
 <dt>
-<a name="idx_id_121"></a><span class="term">C</span>
+<a name="idx_id_131"></a><span class="term">C</span>
 </dt>
 <dd><div class="index"><ul class="index" style="list-style-type: none; ">
 <li class="listitem" style="list-style-type: none">
@@ -1506,11 +1597,23 @@
 <div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/naive_monte_carlo.html" title="Naive Monte Carlo Integration"><span class="index-entry-level-1">Naive Monte Carlo Integration</span></a></p></li></ul></div>
 </li>
 <li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">Cardinal Quadratic B-spline interpolation</span></p>
+<div class="index"><ul class="index" style="list-style-type: none; ">
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/cardinal_quadratic_b.html" title="Cardinal Quadratic B-spline interpolation"><span class="index-entry-level-1">cardinal_quadratic_b_spline</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/cardinal_quadratic_b.html" title="Cardinal Quadratic B-spline interpolation"><span class="index-entry-level-1">operator</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/cardinal_quadratic_b.html" title="Cardinal Quadratic B-spline interpolation"><span class="index-entry-level-1">prime</span></a></p></li>
+</ul></div>
+</li>
+<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">cardinal_quadratic_b_spline</span></p>
+<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/cardinal_quadratic_b.html" title="Cardinal Quadratic B-spline interpolation"><span class="index-entry-level-1">Cardinal Quadratic B-spline interpolation</span></a></p></li></ul></div>
+</li>
+<li class="listitem" style="list-style-type: none">
 <p><span class="index-entry-level-0">case</span></p>
 <div class="index"><ul class="index" style="list-style-type: none; ">
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist_ref/dists/extreme_dist.html" title="Extreme Value Distribution"><span class="index-entry-level-1">Extreme Value Distribution</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/constants_faq.html" title="FAQs"><span class="index-entry-level-1">FAQs</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/fp_facets/facets_intro.html" title="Introduction"><span class="index-entry-level-1">Introduction</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/constants_faq.html" title="Math Constants FAQs"><span class="index-entry-level-1">Math Constants FAQs</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/relative_error.html" title="Relative Error"><span class="index-entry-level-1">Relative Error</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses"><span class="index-entry-level-1">The Incomplete Beta Function Inverses</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/univariate_statistics.html" title="Univariate Statistics"><span class="index-entry-level-1">Univariate Statistics</span></a></p></li>
@@ -1524,6 +1627,7 @@
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/catmull_rom.html" title="Catmull-Rom Splines"><span class="index-entry-level-1">K</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/catmull_rom.html" title="Catmull-Rom Splines"><span class="index-entry-level-1">operator</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/catmull_rom.html" title="Catmull-Rom Splines"><span class="index-entry-level-1">P</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/catmull_rom.html" title="Catmull-Rom Splines"><span class="index-entry-level-1">p1</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/catmull_rom.html" title="Catmull-Rom Splines"><span class="index-entry-level-1">performance</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/catmull_rom.html" title="Catmull-Rom Splines"><span class="index-entry-level-1">prime</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/catmull_rom.html" title="Catmull-Rom Splines"><span class="index-entry-level-1">resize</span></a></p></li>
@@ -1619,11 +1723,11 @@
 <div class="index"><ul class="index" style="list-style-type: none; ">
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/bessel/bessel_first.html" title="Bessel Functions of the First and Second Kinds"><span class="index-entry-level-1">Bessel Functions of the First and Second Kinds</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/sf_beta/beta_function.html" title="Beta"><span class="index-entry-level-1">Beta</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/main_faq.html" title="Boost.Math Frequently Asked Questions (FAQs)"><span class="index-entry-level-1">Boost.Math Frequently Asked Questions (FAQs)</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/sf_erf/error_function.html" title="Error Functions"><span class="index-entry-level-1">Error Functions</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/constants_faq.html" title="FAQs"><span class="index-entry-level-1">FAQs</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/main_faq.html" title="Frequently Asked Questions FAQ"><span class="index-entry-level-1">Frequently Asked Questions FAQ</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/sf_beta/ibeta_function.html" title="Incomplete Beta Functions"><span class="index-entry-level-1">Incomplete Beta Functions</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/sf_gamma/igamma.html" title="Incomplete Gamma Functions"><span class="index-entry-level-1">Incomplete Gamma Functions</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/constants_faq.html" title="Math Constants FAQs"><span class="index-entry-level-1">Math Constants FAQs</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/refs.html" title="References"><span class="index-entry-level-1">References</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/zetas/zeta.html" title="Riemann Zeta Function"><span class="index-entry-level-1">Riemann Zeta Function</span></a></p></li>
 </ul></div>
@@ -1725,17 +1829,27 @@
 <li class="listitem" style="list-style-type: none">
 <p><span class="index-entry-level-0">Comparison of Cube Root Finding Algorithms</span></p>
 <div class="index"><ul class="index" style="list-style-type: none; ">
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/root_comparison/cbrt_comparison.html" title="Comparison of Cube Root Finding Algorithms"><span class="index-entry-level-1">cpp_bin_float</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/root_comparison/cbrt_comparison.html" title="Comparison of Cube Root Finding Algorithms"><span class="index-entry-level-1">double</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/root_comparison/cbrt_comparison.html" title="Comparison of Cube Root Finding Algorithms"><span class="index-entry-level-1">multiprecision</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/root_comparison/cbrt_comparison.html" title="Comparison of Cube Root Finding Algorithms"><span class="index-entry-level-1">performance</span></a></p></li>
 </ul></div>
 </li>
 <li class="listitem" style="list-style-type: none">
 <p><span class="index-entry-level-0">Comparison of Elliptic Integral Root Finding Algoritghms</span></p>
-<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/root_comparison/elliptic_comparison.html" title="Comparison of Elliptic Integral Root Finding Algoritghms"><span class="index-entry-level-1">accuracy</span></a></p></li></ul></div>
+<div class="index"><ul class="index" style="list-style-type: none; ">
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/root_comparison/elliptic_comparison.html" title="Comparison of Elliptic Integral Root Finding Algoritghms"><span class="index-entry-level-1">accuracy</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/root_comparison/elliptic_comparison.html" title="Comparison of Elliptic Integral Root Finding Algoritghms"><span class="index-entry-level-1">cpp_bin_float</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/root_comparison/elliptic_comparison.html" title="Comparison of Elliptic Integral Root Finding Algoritghms"><span class="index-entry-level-1">multiprecision</span></a></p></li>
+</ul></div>
 </li>
 <li class="listitem" style="list-style-type: none">
 <p><span class="index-entry-level-0">Comparison of Nth-root Finding Algorithms</span></p>
-<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/root_comparison/root_n_comparison.html" title="Comparison of Nth-root Finding Algorithms"><span class="index-entry-level-1">accuracy</span></a></p></li></ul></div>
+<div class="index"><ul class="index" style="list-style-type: none; ">
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/root_comparison/root_n_comparison.html" title="Comparison of Nth-root Finding Algorithms"><span class="index-entry-level-1">accuracy</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/root_comparison/root_n_comparison.html" title="Comparison of Nth-root Finding Algorithms"><span class="index-entry-level-1">cpp_bin_float</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/root_comparison/root_n_comparison.html" title="Comparison of Nth-root Finding Algorithms"><span class="index-entry-level-1">multiprecision</span></a></p></li>
+</ul></div>
 </li>
 <li class="listitem" style="list-style-type: none">
 <p><span class="index-entry-level-0">Comparison with C, R, FORTRAN-style Free Functions</span></p>
@@ -1809,6 +1923,7 @@
 <p><span class="index-entry-level-0">Computing the Fifth Root</span></p>
 <div class="index"><ul class="index" style="list-style-type: none; ">
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/root_finding_examples/5th_root_eg.html" title="Computing the Fifth Root"><span class="index-entry-level-1">expression</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/root_finding_examples/5th_root_eg.html" title="Computing the Fifth Root"><span class="index-entry-level-1">multiprecision</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/root_finding_examples/5th_root_eg.html" title="Computing the Fifth Root"><span class="index-entry-level-1">operator</span></a></p></li>
 </ul></div>
 </li>
@@ -1896,11 +2011,14 @@
 <div class="index"><ul class="index" style="list-style-type: none; ">
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/real_concepts.html" title="Conceptual Requirements for Real Number Types"><span class="index-entry-level-1">accuracy</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/real_concepts.html" title="Conceptual Requirements for Real Number Types"><span class="index-entry-level-1">constants</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/real_concepts.html" title="Conceptual Requirements for Real Number Types"><span class="index-entry-level-1">cpp_bin_float</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/real_concepts.html" title="Conceptual Requirements for Real Number Types"><span class="index-entry-level-1">cpp_dec_float</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/real_concepts.html" title="Conceptual Requirements for Real Number Types"><span class="index-entry-level-1">expression</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/real_concepts.html" title="Conceptual Requirements for Real Number Types"><span class="index-entry-level-1">iround</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/real_concepts.html" title="Conceptual Requirements for Real Number Types"><span class="index-entry-level-1">itrunc</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/real_concepts.html" title="Conceptual Requirements for Real Number Types"><span class="index-entry-level-1">Lanczos approximation</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/real_concepts.html" title="Conceptual Requirements for Real Number Types"><span class="index-entry-level-1">ldexp</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/real_concepts.html" title="Conceptual Requirements for Real Number Types"><span class="index-entry-level-1">multiprecision</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/real_concepts.html" title="Conceptual Requirements for Real Number Types"><span class="index-entry-level-1">round</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/real_concepts.html" title="Conceptual Requirements for Real Number Types"><span class="index-entry-level-1">trunc</span></a></p></li>
 </ul></div>
@@ -1966,6 +2084,7 @@
 <div class="index"><ul class="index" style="list-style-type: none; ">
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/main_intro.html" title="About the Math Toolkit"><span class="index-entry-level-1">About the Math Toolkit</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/sf_implementation.html" title="Additional Implementation Notes"><span class="index-entry-level-1">Additional Implementation Notes</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/autodiff.html" title="Automatic Differentiation"><span class="index-entry-level-1">Automatic Differentiation</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/barycentric.html" title="Barycentric Rational Interpolation"><span class="index-entry-level-1">Barycentric Rational Interpolation</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist_ref/dists/binomial_dist.html" title="Binomial Distribution"><span class="index-entry-level-1">Binomial Distribution</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/stat_tut/weg/binom_eg/binomial_quiz_example.html" title="Binomial Quiz Example"><span class="index-entry-level-1">Binomial Quiz Example</span></a></p></li>
@@ -1989,7 +2108,6 @@
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 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist_ref/dists/extreme_dist.html" title="Extreme Value Distribution"><span class="index-entry-level-1">Extreme Value Distribution</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/factorials/sf_factorial.html" title="Factorial"><span class="index-entry-level-1">Factorial</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/constants_faq.html" title="FAQs"><span class="index-entry-level-1">FAQs</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/macros.html" title="Floating-Point Constant Macros"><span class="index-entry-level-1">Floating-Point Constant Macros</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/gauss_kronrod.html" title="Gauss-Kronrod Quadrature"><span class="index-entry-level-1">Gauss-Kronrod Quadrature</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/gauss.html" title="Gauss-Legendre quadrature"><span class="index-entry-level-1">Gauss-Legendre quadrature</span></a></p></li>
@@ -2003,6 +2121,7 @@
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/constants_intro.html" title="Introduction"><span class="index-entry-level-1">Introduction</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/lambert_w.html" title="Lambert W function"><span class="index-entry-level-1">Lambert W function</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/sf_gamma/lgamma.html" title="Log Gamma"><span class="index-entry-level-1">Log Gamma</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/constants_faq.html" title="Math Constants FAQs"><span class="index-entry-level-1">Math Constants FAQs</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../constants.html" title="Chapter&#160;4.&#160;Mathematical Constants"><span class="index-entry-level-1">Mathematical Constants</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/internals/minimax.html" title="Minimax Approximations and the Remez Algorithm"><span class="index-entry-level-1">Minimax Approximations and the Remez Algorithm</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/diff.html" title="Numerical Differentiation"><span class="index-entry-level-1">Numerical Differentiation</span></a></p></li>
@@ -2115,20 +2234,86 @@
 <p><span class="index-entry-level-0">Cost of Finite-Difference Numerical Differentiation</span></p>
 <div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/diff.html#math_toolkit.diff.id" title="Table&#160;12.1.&#160;Cost of Finite-Difference Numerical Differentiation"><span class="index-entry-level-1">accuracy</span></a></p></li></ul></div>
 </li>
+<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">Cost of High-Precision Non-built-in Floating-point</span></p>
+<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/multiprecision.html" title="Cost of High-Precision Non-built-in Floating-point"><span class="index-entry-level-1">multiprecision</span></a></p></li></ul></div>
+</li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/powers/cos_pi.html" title="cos_pi"><span class="index-entry-level-0">cos_pi</span></a></p></li>
 <li class="listitem" style="list-style-type: none">
 <p><span class="index-entry-level-0">covariance</span></p>
 <div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/bivariate_statistics.html" title="Bivariate Statistics"><span class="index-entry-level-1">Bivariate Statistics</span></a></p></li></ul></div>
 </li>
 <li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">cpp_bin_float</span></p>
+<div class="index"><ul class="index" style="list-style-type: none; ">
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/root_comparison/root_n_comparison.html#math_toolkit.root_comparison.root_n_comparison.root_11_0" title="Table&#160;9.8.&#160;11th root(28) for float, double, long double and cpp_bin_float_50 types, using _X64_AVX"><span class="index-entry-level-1">11th root(28) for float, double, long double and cpp_bin_float_50 types, using _X64_AVX</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/root_comparison/root_n_comparison.html#math_toolkit.root_comparison.root_n_comparison.root_11_1" title="Table&#160;9.11.&#160;11th root(28) for float, double, long double and cpp_bin_float_50 types, using _X64_SSE2"><span class="index-entry-level-1">11th root(28) for float, double, long double and cpp_bin_float_50 types, using _X64_SSE2</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/root_comparison/root_n_comparison.html#math_toolkit.root_comparison.root_n_comparison.root_11" title="Table&#160;9.5.&#160;11th root(28) for float, double, long double and cpp_bin_float_50 types, using _X86_SSE2"><span class="index-entry-level-1">11th root(28) for float, double, long double and cpp_bin_float_50 types, using _X86_SSE2</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/root_comparison/root_n_comparison.html#math_toolkit.root_comparison.root_n_comparison.root_5_0" title="Table&#160;9.6.&#160;5th root(28) for float, double, long double and cpp_bin_float_50 types, using _X64_AVX"><span class="index-entry-level-1">5th root(28) for float, double, long double and cpp_bin_float_50 types, using _X64_AVX</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/root_comparison/root_n_comparison.html#math_toolkit.root_comparison.root_n_comparison.root_5_1" title="Table&#160;9.9.&#160;5th root(28) for float, double, long double and cpp_bin_float_50 types, using _X64_SSE2"><span class="index-entry-level-1">5th root(28) for float, double, long double and cpp_bin_float_50 types, using _X64_SSE2</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/root_comparison/root_n_comparison.html#math_toolkit.root_comparison.root_n_comparison.root_5" title="Table&#160;9.3.&#160;5th root(28) for float, double, long double and cpp_bin_float_50 types, using _X86_SSE2"><span class="index-entry-level-1">5th root(28) for float, double, long double and cpp_bin_float_50 types, using _X86_SSE2</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/root_comparison/root_n_comparison.html#math_toolkit.root_comparison.root_n_comparison.root_7_0" title="Table&#160;9.7.&#160;7th root(28) for float, double, long double and cpp_bin_float_50 types, using _X64_AVX"><span class="index-entry-level-1">7th root(28) for float, double, long double and cpp_bin_float_50 types, using _X64_AVX</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/root_comparison/root_n_comparison.html#math_toolkit.root_comparison.root_n_comparison.root_7_1" title="Table&#160;9.10.&#160;7th root(28) for float, double, long double and cpp_bin_float_50 types, using _X64_SSE2"><span class="index-entry-level-1">7th root(28) for float, double, long double and cpp_bin_float_50 types, using _X64_SSE2</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/root_comparison/root_n_comparison.html#math_toolkit.root_comparison.root_n_comparison.root_7" title="Table&#160;9.4.&#160;7th root(28) for float, double, long double and cpp_bin_float_50 types, using _X86_SSE2"><span class="index-entry-level-1">7th root(28) for float, double, long double and cpp_bin_float_50 types, using _X86_SSE2</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/autodiff.html" title="Automatic Differentiation"><span class="index-entry-level-1">Automatic Differentiation</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/main_faq.html" title="Boost.Math Frequently Asked Questions (FAQs)"><span class="index-entry-level-1">Boost.Math Frequently Asked Questions (FAQs)</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/root_comparison/cbrt_comparison.html" title="Comparison of Cube Root Finding Algorithms"><span class="index-entry-level-1">Comparison of Cube Root Finding Algorithms</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/root_comparison/elliptic_comparison.html" title="Comparison of Elliptic Integral Root Finding Algoritghms"><span class="index-entry-level-1">Comparison of Elliptic Integral Root Finding Algoritghms</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/root_comparison/root_n_comparison.html" title="Comparison of Nth-root Finding Algorithms"><span class="index-entry-level-1">Comparison of Nth-root Finding Algorithms</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/real_concepts.html" title="Conceptual Requirements for Real Number Types"><span class="index-entry-level-1">Conceptual Requirements for Real Number Types</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/root_comparison/cbrt_comparison.html#math_toolkit.root_comparison.cbrt_comparison.cbrt_4" title="Table&#160;9.1.&#160;Cube root(28) for float, double, long double and cpp_bin_float_50"><span class="index-entry-level-1">Cube root(28) for float, double, long double and cpp_bin_float_50</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/stat_tut/weg/dist_construct_eg.html" title="Distribution Construction Examples"><span class="index-entry-level-1">Distribution Construction Examples</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/next_float.html" title="Floating-Point Representation Distance (ULP), and Finding Adjacent Floating-Point Values"><span class="index-entry-level-1">Floating-Point Representation Distance (ULP), and Finding Adjacent Floating-Point Values</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/gauss.html" title="Gauss-Legendre quadrature"><span class="index-entry-level-1">Gauss-Legendre quadrature</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/root_finding_examples/nth_root.html" title="Generalizing to Compute the nth root"><span class="index-entry-level-1">Generalizing to Compute the nth root</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/lambert_w.html" title="Lambert W function"><span class="index-entry-level-1">Lambert W function</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/multiprecision.html#math_toolkit.multiprecision.linpack_time" title="Table&#160;20.2.&#160;Linpack Benchmark"><span class="index-entry-level-1">Linpack Benchmark</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/brent_minima.html" title="Locating Function Minima using Brent's algorithm"><span class="index-entry-level-1">Locating Function Minima using Brent's algorithm</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/root_comparison/elliptic_comparison.html#math_toolkit.root_comparison.elliptic_comparison.elliptic0" title="Table&#160;9.13.&#160;root with radius 28 and arc length 300) for float, double, long double and cpp_bin_float_50 types, using _X64_AVX"><span class="index-entry-level-1">root with radius 28 and arc length 300) for float, double, long double and cpp_bin_float_50 types, using _X64_AVX</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/root_comparison/elliptic_comparison.html#math_toolkit.root_comparison.elliptic_comparison.elliptic1" title="Table&#160;9.14.&#160;root with radius 28 and arc length 300) for float, double, long double and cpp_bin_float_50 types, using _X64_SSE2"><span class="index-entry-level-1">root with radius 28 and arc length 300) for float, double, long double and cpp_bin_float_50 types, using _X64_SSE2</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/root_comparison/elliptic_comparison.html#math_toolkit.root_comparison.elliptic_comparison.elliptic" title="Table&#160;9.12.&#160;root with radius 28 and arc length 300) for float, double, long double and cpp_bin_float_50 types, using _X86_SSE2"><span class="index-entry-level-1">root with radius 28 and arc length 300) for float, double, long double and cpp_bin_float_50 types, using _X86_SSE2</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/root_finding_examples/multiprecision_root.html" title="Root-finding using Boost.Multiprecision"><span class="index-entry-level-1">Root-finding using Boost.Multiprecision</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/high_precision/use_multiprecision.html" title="Using Boost.Multiprecision"><span class="index-entry-level-1">Using Boost.Multiprecision</span></a></p></li>
+</ul></div>
+</li>
+<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">cpp_dec_float</span></p>
+<div class="index"><ul class="index" style="list-style-type: none; ">
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/sf_implementation.html" title="Additional Implementation Notes"><span class="index-entry-level-1">Additional Implementation Notes</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/number_series/bernoulli_numbers.html" title="Bernoulli Numbers"><span class="index-entry-level-1">Bernoulli Numbers</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/main_faq.html" title="Boost.Math Frequently Asked Questions (FAQs)"><span class="index-entry-level-1">Boost.Math Frequently Asked Questions (FAQs)</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/real_concepts.html" title="Conceptual Requirements for Real Number Types"><span class="index-entry-level-1">Conceptual Requirements for Real Number Types</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/stat_tut/weg/dist_construct_eg.html" title="Distribution Construction Examples"><span class="index-entry-level-1">Distribution Construction Examples</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/airy/airy_root.html" title="Finding Zeros of Airy Functions"><span class="index-entry-level-1">Finding Zeros of Airy Functions</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/bessel/bessel_root.html" title="Finding Zeros of Bessel Functions of the First and Second Kinds"><span class="index-entry-level-1">Finding Zeros of Bessel Functions of the First and Second Kinds</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/next_float.html" title="Floating-Point Representation Distance (ULP), and Finding Adjacent Floating-Point Values"><span class="index-entry-level-1">Floating-Point Representation Distance (ULP), and Finding Adjacent Floating-Point Values</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/root_finding_examples/nth_root.html" title="Generalizing to Compute the nth root"><span class="index-entry-level-1">Generalizing to Compute the nth root</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/history1.html" title="History and What's New"><span class="index-entry-level-1">History and What's New</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/lambert_w.html" title="Lambert W function"><span class="index-entry-level-1">Lambert W function</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/brent_minima.html" title="Locating Function Minima using Brent's algorithm"><span class="index-entry-level-1">Locating Function Minima using Brent's algorithm</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/root_finding_examples/multiprecision_root.html" title="Root-finding using Boost.Multiprecision"><span class="index-entry-level-1">Root-finding using Boost.Multiprecision</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/special_tut/special_tut_test.html" title="Testing"><span class="index-entry-level-1">Testing</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/tutorial/user_def.html" title="Use With User-Defined Types"><span class="index-entry-level-1">Use With User-Defined Types</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/high_precision.html" title="Using Boost.Math with High-Precision Floating-Point Libraries"><span class="index-entry-level-1">Using Boost.Math with High-Precision Floating-Point Libraries</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/high_precision/use_multiprecision.html" title="Using Boost.Multiprecision"><span class="index-entry-level-1">Using Boost.Multiprecision</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/high_precision/using_test.html" title="Using without expression templates for Boost.Test and others"><span class="index-entry-level-1">Using without expression templates for Boost.Test and others</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/high_precision/why_high_precision.html" title="Why use a high-precision library rather than built-in floating-point types?"><span class="index-entry-level-1">Why use a high-precision library rather than built-in floating-point types?</span></a></p></li>
+</ul></div>
+</li>
+<li class="listitem" style="list-style-type: none">
 <p><span class="index-entry-level-0">Credits and Acknowledgements</span></p>
 <div class="index"><ul class="index" style="list-style-type: none; ">
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/credits.html" title="Credits and Acknowledgements"><span class="index-entry-level-1">accuracy</span></a></p></li>
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 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/credits.html" title="Credits and Acknowledgements"><span class="index-entry-level-1">expression</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/credits.html" title="Credits and Acknowledgements"><span class="index-entry-level-1">multiprecision</span></a></p></li>
 </ul></div>
 </li>
 <li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">Cube root(28) for float, double, long double and cpp_bin_float_50</span></p>
+<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/root_comparison/cbrt_comparison.html#math_toolkit.root_comparison.cbrt_comparison.cbrt_4" title="Table&#160;9.1.&#160;Cube root(28) for float, double, long double and cpp_bin_float_50"><span class="index-entry-level-1">cpp_bin_float</span></a></p></li></ul></div>
+</li>
+<li class="listitem" style="list-style-type: none">
 <p><span class="index-entry-level-0">Cubic B-spline interpolation</span></p>
 <div class="index"><ul class="index" style="list-style-type: none; ">
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/cubic_b.html" title="Cubic B-spline interpolation"><span class="index-entry-level-1">accuracy</span></a></p></li>
@@ -2309,7 +2494,7 @@
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 <dt>
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 <li class="listitem" style="list-style-type: none">
@@ -2364,6 +2549,7 @@
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/new_const.html" title="Defining New Constants"><span class="index-entry-level-1">function</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/new_const.html" title="Defining New Constants"><span class="index-entry-level-1">get</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/new_const.html" title="Defining New Constants"><span class="index-entry-level-1">get_from_string</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/new_const.html" title="Defining New Constants"><span class="index-entry-level-1">multiprecision</span></a></p></li>
 </ul></div>
 </li>
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@@ -2371,6 +2557,15 @@
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 </li>
 <li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">derivative</span></p>
+<div class="index"><ul class="index" style="list-style-type: none; ">
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/autodiff.html" title="Automatic Differentiation"><span class="index-entry-level-1">Automatic Differentiation</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/root_finding_examples/cbrt_eg.html" title="Finding the Cubed Root With and Without Derivatives"><span class="index-entry-level-1">Finding the Cubed Root With and Without Derivatives</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/history1.html" title="History and What's New"><span class="index-entry-level-1">History and What's New</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/roots_deriv.html" title="Root Finding With Derivatives: Newton-Raphson, Halley &amp; Schr&#246;der"><span class="index-entry-level-1">Root Finding With Derivatives: Newton-Raphson, Halley &amp; Schr&#246;der</span></a></p></li>
+</ul></div>
+</li>
+<li class="listitem" style="list-style-type: none">
 <p><span class="index-entry-level-0">Derivative of the Incomplete Beta Function</span></p>
 <div class="index"><ul class="index" style="list-style-type: none; ">
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/sf_beta/beta_derivative.html" title="Derivative of the Incomplete Beta Function"><span class="index-entry-level-1">accuracy</span></a></p></li>
@@ -2436,6 +2631,7 @@
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 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist_ref/dists/bernoulli_dist.html" title="Bernoulli Distribution"><span class="index-entry-level-1">Bernoulli Distribution</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/main_faq.html" title="Boost.Math Frequently Asked Questions (FAQs)"><span class="index-entry-level-1">Boost.Math Frequently Asked Questions (FAQs)</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/stat_tut/weg/neg_binom_eg/neg_binom_conf.html" title="Calculating Confidence Limits on the Frequency of Occurrence for the Negative Binomial Distribution"><span class="index-entry-level-1">Calculating Confidence Limits on the Frequency of Occurrence for the Negative Binomial Distribution</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist_ref/dists/cauchy_dist.html" title="Cauchy-Lorentz Distribution"><span class="index-entry-level-1">Cauchy-Lorentz Distribution</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/pol_tutorial/changing_policy_defaults.html" title="Changing the Policy Defaults"><span class="index-entry-level-1">Changing the Policy Defaults</span></a></p></li>
@@ -2443,7 +2639,6 @@
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 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/stat_tut/weg/binom_eg/binom_size_eg.html" title="Estimating Sample Sizes for a Binomial Distribution."><span class="index-entry-level-1">Estimating Sample Sizes for a Binomial Distribution.</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/stat_tut/weg/neg_binom_eg/neg_binom_size_eg.html" title="Estimating Sample Sizes for the Negative Binomial."><span class="index-entry-level-1">Estimating Sample Sizes for the Negative Binomial.</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/main_faq.html" title="Frequently Asked Questions FAQ"><span class="index-entry-level-1">Frequently Asked Questions FAQ</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/stat_tut/overview/generic.html" title="Generic operations common to all distributions are non-member functions"><span class="index-entry-level-1">Generic operations common to all distributions are non-member functions</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/history1.html" title="History and What's New"><span class="index-entry-level-1">History and What's New</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist_ref/dists/hyperexponential_dist.html" title="Hyperexponential Distribution"><span class="index-entry-level-1">Hyperexponential Distribution</span></a></p></li>
@@ -2463,9 +2658,12 @@
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 <p><span class="index-entry-level-0">Distribution Construction Examples</span></p>
 <div class="index"><ul class="index" style="list-style-type: none; ">
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/stat_tut/weg/dist_construct_eg.html" title="Distribution Construction Examples"><span class="index-entry-level-1">cpp_bin_float</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/stat_tut/weg/dist_construct_eg.html" title="Distribution Construction Examples"><span class="index-entry-level-1">cpp_dec_float</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/stat_tut/weg/dist_construct_eg.html" title="Distribution Construction Examples"><span class="index-entry-level-1">distribution</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/stat_tut/weg/dist_construct_eg.html" title="Distribution Construction Examples"><span class="index-entry-level-1">function</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/stat_tut/weg/dist_construct_eg.html" title="Distribution Construction Examples"><span class="index-entry-level-1">mean</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/stat_tut/weg/dist_construct_eg.html" title="Distribution Construction Examples"><span class="index-entry-level-1">multiprecision</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/stat_tut/weg/dist_construct_eg.html" title="Distribution Construction Examples"><span class="index-entry-level-1">negative_binomial</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/stat_tut/weg/dist_construct_eg.html" title="Distribution Construction Examples"><span class="index-entry-level-1">x</span></a></p></li>
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@@ -2509,7 +2707,7 @@
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 <dt>
-<a name="idx_id_123"></a><span class="term">E</span>
+<a name="idx_id_133"></a><span class="term">E</span>
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 <li class="listitem" style="list-style-type: none">
@@ -2623,6 +2821,7 @@
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 <p><span class="index-entry-level-0">Elliptic Integral D - Legendre Form</span></p>
 <div class="index"><ul class="index" style="list-style-type: none; ">
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/ellint/ellint_d.html" title="Elliptic Integral D - Legendre Form"><span class="index-entry-level-1">2</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/ellint/ellint_d.html" title="Elliptic Integral D - Legendre Form"><span class="index-entry-level-1">accuracy</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/ellint/ellint_d.html" title="Elliptic Integral D - Legendre Form"><span class="index-entry-level-1">D</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/ellint/ellint_d.html" title="Elliptic Integral D - Legendre Form"><span class="index-entry-level-1">ellint_3</span></a></p></li>
@@ -2655,6 +2854,7 @@
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 <p><span class="index-entry-level-0">Elliptic Integrals of the First Kind - Legendre Form</span></p>
 <div class="index"><ul class="index" style="list-style-type: none; ">
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/ellint/ellint_1.html" title="Elliptic Integrals of the First Kind - Legendre Form"><span class="index-entry-level-1">2</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/ellint/ellint_1.html" title="Elliptic Integrals of the First Kind - Legendre Form"><span class="index-entry-level-1">accuracy</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/ellint/ellint_1.html" title="Elliptic Integrals of the First Kind - Legendre Form"><span class="index-entry-level-1">ellint_1</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/ellint/ellint_1.html" title="Elliptic Integrals of the First Kind - Legendre Form"><span class="index-entry-level-1">K</span></a></p></li>
@@ -2663,6 +2863,7 @@
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 <p><span class="index-entry-level-0">Elliptic Integrals of the Second Kind - Legendre Form</span></p>
 <div class="index"><ul class="index" style="list-style-type: none; ">
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/ellint/ellint_2.html" title="Elliptic Integrals of the Second Kind - Legendre Form"><span class="index-entry-level-1">2</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/ellint/ellint_2.html" title="Elliptic Integrals of the Second Kind - Legendre Form"><span class="index-entry-level-1">accuracy</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/ellint/ellint_2.html" title="Elliptic Integrals of the Second Kind - Legendre Form"><span class="index-entry-level-1">ellint_2</span></a></p></li>
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@@ -2712,6 +2913,7 @@
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 <p><span class="index-entry-level-0">erfc</span></p>
 <div class="index"><ul class="index" style="list-style-type: none; ">
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/autodiff.html" title="Automatic Differentiation"><span class="index-entry-level-1">Automatic Differentiation</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/overview_tr1.html" title="C99 and C++ TR1 C-style Functions"><span class="index-entry-level-1">C99 and C++ TR1 C-style Functions</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/main_tr1.html" title="C99 and TR1 C Functions Overview"><span class="index-entry-level-1">C99 and TR1 C Functions Overview</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/c99.html" title="C99 C Functions"><span class="index-entry-level-1">C99 C Functions</span></a></p></li>
@@ -3413,7 +3615,6 @@
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 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist_ref/dists/f_dist.html" title="F Distribution"><span class="index-entry-level-1">F Distribution</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/factorials/sf_factorial.html" title="Factorial"><span class="index-entry-level-1">Factorial</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/constants_faq.html" title="FAQs"><span class="index-entry-level-1">FAQs</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/stat_tut/weg/find_eg/find_scale_eg.html" title="Find Scale (Standard Deviation) Example"><span class="index-entry-level-1">Find Scale (Standard Deviation) Example</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/bessel/bessel_root.html" title="Finding Zeros of Bessel Functions of the First and Second Kinds"><span class="index-entry-level-1">Finding Zeros of Bessel Functions of the First and Second Kinds</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution"><span class="index-entry-level-1">Gamma (and Erlang) Distribution</span></a></p></li>
@@ -3428,6 +3629,7 @@
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 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/lambert_w.html" title="Lambert W function"><span class="index-entry-level-1">Lambert W function</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/brent_minima.html" title="Locating Function Minima using Brent's algorithm"><span class="index-entry-level-1">Locating Function Minima using Brent's algorithm</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/constants_faq.html" title="Math Constants FAQs"><span class="index-entry-level-1">Math Constants FAQs</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/pol_ref/assert_undefined.html" title="Mathematically Undefined Function Policies"><span class="index-entry-level-1">Mathematically Undefined Function Policies</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/stat_tut/weg/neg_binom_eg/negative_binomial_example1.html" title="Negative Binomial Sales Quota Example."><span class="index-entry-level-1">Negative Binomial Sales Quota Example.</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist_ref/nmp.html" title="Non-Member Properties"><span class="index-entry-level-1">Non-Member Properties</span></a></p></li>
@@ -3485,7 +3687,7 @@
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 </ul></div></dd>
 <dt>
-<a name="idx_id_124"></a><span class="term">F</span>
+<a name="idx_id_134"></a><span class="term">F</span>
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 <dd><div class="index"><ul class="index" style="list-style-type: none; ">
 <li class="listitem" style="list-style-type: none">
@@ -3527,14 +3729,11 @@
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 <li class="listitem" style="list-style-type: none">
-<p><span class="index-entry-level-0">FAQs</span></p>
+<p><span class="index-entry-level-0">FAQ</span></p>
 <div class="index"><ul class="index" style="list-style-type: none; ">
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/constants_faq.html" title="FAQs"><span class="index-entry-level-1">accuracy</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/constants_faq.html" title="FAQs"><span class="index-entry-level-1">BOOST_DEFINE_MATH_CONSTANT</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/constants_faq.html" title="FAQs"><span class="index-entry-level-1">case</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/constants_faq.html" title="FAQs"><span class="index-entry-level-1">Cephes</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/constants_faq.html" title="FAQs"><span class="index-entry-level-1">constants</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/constants_faq.html" title="FAQs"><span class="index-entry-level-1">expression</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/main_faq.html" title="Boost.Math Frequently Asked Questions (FAQs)"><span class="index-entry-level-1">Boost.Math Frequently Asked Questions (FAQs)</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/history1.html" title="History and What's New"><span class="index-entry-level-1">History and What's New</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/constants_faq.html" title="Math Constants FAQs"><span class="index-entry-level-1">Math Constants FAQs</span></a></p></li>
 </ul></div>
 </li>
 <li class="listitem" style="list-style-type: none">
@@ -3593,6 +3792,7 @@
 <div class="index"><ul class="index" style="list-style-type: none; ">
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/root_finding_examples/cbrt_eg.html" title="Finding the Cubed Root With and Without Derivatives"><span class="index-entry-level-1">accuracy</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/root_finding_examples/cbrt_eg.html" title="Finding the Cubed Root With and Without Derivatives"><span class="index-entry-level-1">bracket_and_solve_root</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/root_finding_examples/cbrt_eg.html" title="Finding the Cubed Root With and Without Derivatives"><span class="index-entry-level-1">derivative</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/root_finding_examples/cbrt_eg.html" title="Finding the Cubed Root With and Without Derivatives"><span class="index-entry-level-1">float_distance</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/root_finding_examples/cbrt_eg.html" title="Finding the Cubed Root With and Without Derivatives"><span class="index-entry-level-1">n</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/root_finding_examples/cbrt_eg.html" title="Finding the Cubed Root With and Without Derivatives"><span class="index-entry-level-1">operator</span></a></p></li>
@@ -3620,8 +3820,10 @@
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 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/airy/airy_root.html" title="Finding Zeros of Airy Functions"><span class="index-entry-level-1">airy_bi_zero</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/airy/airy_root.html" title="Finding Zeros of Airy Functions"><span class="index-entry-level-1">by</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/airy/airy_root.html" title="Finding Zeros of Airy Functions"><span class="index-entry-level-1">cpp_dec_float</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/airy/airy_root.html" title="Finding Zeros of Airy Functions"><span class="index-entry-level-1">float_type</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/airy/airy_root.html" title="Finding Zeros of Airy Functions"><span class="index-entry-level-1">function</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/airy/airy_root.html" title="Finding Zeros of Airy Functions"><span class="index-entry-level-1">multiprecision</span></a></p></li>
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@@ -3629,10 +3831,12 @@
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 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/bessel/bessel_root.html" title="Finding Zeros of Bessel Functions of the First and Second Kinds"><span class="index-entry-level-1">Ai</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/bessel/bessel_root.html" title="Finding Zeros of Bessel Functions of the First and Second Kinds"><span class="index-entry-level-1">cpp_dec_float</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/bessel/bessel_root.html" title="Finding Zeros of Bessel Functions of the First and Second Kinds"><span class="index-entry-level-1">cyl_bessel_j_zero</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/bessel/bessel_root.html" title="Finding Zeros of Bessel Functions of the First and Second Kinds"><span class="index-entry-level-1">cyl_neumann_zero</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/bessel/bessel_root.html" title="Finding Zeros of Bessel Functions of the First and Second Kinds"><span class="index-entry-level-1">expression</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/bessel/bessel_root.html" title="Finding Zeros of Bessel Functions of the First and Second Kinds"><span class="index-entry-level-1">float_type</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/bessel/bessel_root.html" title="Finding Zeros of Bessel Functions of the First and Second Kinds"><span class="index-entry-level-1">multiprecision</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/bessel/bessel_root.html" title="Finding Zeros of Bessel Functions of the First and Second Kinds"><span class="index-entry-level-1">x</span></a></p></li>
 </ul></div>
 </li>
@@ -3735,7 +3939,12 @@
 </li>
 <li class="listitem" style="list-style-type: none">
 <p><span class="index-entry-level-0">Floating-Point Representation Distance (ULP), and Finding Adjacent Floating-Point Values</span></p>
-<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/next_float.html" title="Floating-Point Representation Distance (ULP), and Finding Adjacent Floating-Point Values"><span class="index-entry-level-1">accuracy</span></a></p></li></ul></div>
+<div class="index"><ul class="index" style="list-style-type: none; ">
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/next_float.html" title="Floating-Point Representation Distance (ULP), and Finding Adjacent Floating-Point Values"><span class="index-entry-level-1">accuracy</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/next_float.html" title="Floating-Point Representation Distance (ULP), and Finding Adjacent Floating-Point Values"><span class="index-entry-level-1">cpp_bin_float</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/next_float.html" title="Floating-Point Representation Distance (ULP), and Finding Adjacent Floating-Point Values"><span class="index-entry-level-1">cpp_dec_float</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/next_float.html" title="Floating-Point Representation Distance (ULP), and Finding Adjacent Floating-Point Values"><span class="index-entry-level-1">multiprecision</span></a></p></li>
+</ul></div>
 </li>
 <li class="listitem" style="list-style-type: none">
 <p><span class="index-entry-level-0">float_advance</span></p>
@@ -3846,6 +4055,16 @@
 <div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/special_tut/special_tut_impl.html" title="Implementation"><span class="index-entry-level-1">Implementation</span></a></p></li></ul></div>
 </li>
 <li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">Fourier Integrals</span></p>
+<div class="index"><ul class="index" style="list-style-type: none; ">
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/fourier_integrals.html" title="Fourier Integrals"><span class="index-entry-level-1">integrate</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/fourier_integrals.html" title="Fourier Integrals"><span class="index-entry-level-1">multiprecision</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/fourier_integrals.html" title="Fourier Integrals"><span class="index-entry-level-1">ooura_fourier_cos</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/fourier_integrals.html" title="Fourier Integrals"><span class="index-entry-level-1">ooura_fourier_sin</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/fourier_integrals.html" title="Fourier Integrals"><span class="index-entry-level-1">performance</span></a></p></li>
+</ul></div>
+</li>
+<li class="listitem" style="list-style-type: none">
 <p><span class="index-entry-level-0">fpclassify</span></p>
 <div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/fpclass.html" title="Floating-Point Classification: Infinities and NaNs"><span class="index-entry-level-1">Floating-Point Classification: Infinities and NaNs</span></a></p></li></ul></div>
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@@ -3878,16 +4097,6 @@
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-<p><span class="index-entry-level-0">Frequently Asked Questions FAQ</span></p>
-<div class="index"><ul class="index" style="list-style-type: none; ">
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/main_faq.html" title="Frequently Asked Questions FAQ"><span class="index-entry-level-1">accuracy</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/main_faq.html" title="Frequently Asked Questions FAQ"><span class="index-entry-level-1">Cephes</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/main_faq.html" title="Frequently Asked Questions FAQ"><span class="index-entry-level-1">distribution</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/main_faq.html" title="Frequently Asked Questions FAQ"><span class="index-entry-level-1">P</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/main_faq.html" title="Frequently Asked Questions FAQ"><span class="index-entry-level-1">performance</span></a></p></li>
-</ul></div>
-</li>
-<li class="listitem" style="list-style-type: none">
 <p><span class="index-entry-level-0">function</span></p>
 <div class="index"><ul class="index" style="list-style-type: none; ">
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/stat_tut/weg/binom_eg/binomial_quiz_example.html" title="Binomial Quiz Example"><span class="index-entry-level-1">Binomial Quiz Example</span></a></p></li>
@@ -3925,9 +4134,13 @@
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 </ul></div>
 </li>
+<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">fvar</span></p>
+<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/autodiff.html" title="Automatic Differentiation"><span class="index-entry-level-1">Automatic Differentiation</span></a></p></li></ul></div>
+</li>
 </ul></div></dd>
 <dt>
-<a name="idx_id_125"></a><span class="term">G</span>
+<a name="idx_id_135"></a><span class="term">G</span>
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 <dd><div class="index"><ul class="index" style="list-style-type: none; ">
 <li class="listitem" style="list-style-type: none">
@@ -4019,6 +4232,7 @@
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 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/gauss_kronrod.html" title="Gauss-Kronrod Quadrature"><span class="index-entry-level-1">gauss_kronrod</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/gauss_kronrod.html" title="Gauss-Kronrod Quadrature"><span class="index-entry-level-1">integrate</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/gauss_kronrod.html" title="Gauss-Kronrod Quadrature"><span class="index-entry-level-1">multiprecision</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/gauss_kronrod.html" title="Gauss-Kronrod Quadrature"><span class="index-entry-level-1">range</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/gauss_kronrod.html" title="Gauss-Kronrod Quadrature"><span class="index-entry-level-1">weights</span></a></p></li>
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@@ -4028,9 +4242,11 @@
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 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/gauss.html" title="Gauss-Legendre quadrature"><span class="index-entry-level-1">constants</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/gauss.html" title="Gauss-Legendre quadrature"><span class="index-entry-level-1">cpp_bin_float</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/gauss.html" title="Gauss-Legendre quadrature"><span class="index-entry-level-1">expression</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/gauss.html" title="Gauss-Legendre quadrature"><span class="index-entry-level-1">gauss</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/gauss.html" title="Gauss-Legendre quadrature"><span class="index-entry-level-1">integrate</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/gauss.html" title="Gauss-Legendre quadrature"><span class="index-entry-level-1">multiprecision</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/gauss.html" title="Gauss-Legendre quadrature"><span class="index-entry-level-1">weights</span></a></p></li>
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 </li>
@@ -4043,6 +4259,9 @@
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 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/root_finding_examples/nth_root.html" title="Generalizing to Compute the nth root"><span class="index-entry-level-1">constants</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/root_finding_examples/nth_root.html" title="Generalizing to Compute the nth root"><span class="index-entry-level-1">cpp_bin_float</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/root_finding_examples/nth_root.html" title="Generalizing to Compute the nth root"><span class="index-entry-level-1">cpp_dec_float</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/root_finding_examples/nth_root.html" title="Generalizing to Compute the nth root"><span class="index-entry-level-1">multiprecision</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/root_finding_examples/nth_root.html" title="Generalizing to Compute the nth root"><span class="index-entry-level-1">operator</span></a></p></li>
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 </li>
@@ -4196,7 +4415,7 @@
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 </ul></div></dd>
 <dt>
-<a name="idx_id_126"></a><span class="term">H</span>
+<a name="idx_id_136"></a><span class="term">H</span>
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 <dd><div class="index"><ul class="index" style="list-style-type: none; ">
 <li class="listitem" style="list-style-type: none">
@@ -4279,13 +4498,17 @@
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 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/history1.html" title="History and What's New"><span class="index-entry-level-1">airy_bi_zero</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/history1.html" title="History and What's New"><span class="index-entry-level-1">constants</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/history1.html" title="History and What's New"><span class="index-entry-level-1">cpp_dec_float</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/history1.html" title="History and What's New"><span class="index-entry-level-1">derivative</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/history1.html" title="History and What's New"><span class="index-entry-level-1">distribution</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/history1.html" title="History and What's New"><span class="index-entry-level-1">erf</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/history1.html" title="History and What's New"><span class="index-entry-level-1">expression</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/history1.html" title="History and What's New"><span class="index-entry-level-1">FAQ</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/history1.html" title="History and What's New"><span class="index-entry-level-1">freedom</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/history1.html" title="History and What's New"><span class="index-entry-level-1">functions</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/history1.html" title="History and What's New"><span class="index-entry-level-1">Lanczos approximation</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/history1.html" title="History and What's New"><span class="index-entry-level-1">mode</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/history1.html" title="History and What's New"><span class="index-entry-level-1">multiprecision</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/history1.html" title="History and What's New"><span class="index-entry-level-1">n</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/history1.html" title="History and What's New"><span class="index-entry-level-1">nextafter</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/history1.html" title="History and What's New"><span class="index-entry-level-1">performance</span></a></p></li>
@@ -4387,7 +4610,7 @@
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 </ul></div></dd>
 <dt>
-<a name="idx_id_127"></a><span class="term">I</span>
+<a name="idx_id_137"></a><span class="term">I</span>
 </dt>
 <dd><div class="index"><ul class="index" style="list-style-type: none; ">
 <li class="listitem" style="list-style-type: none">
@@ -4497,6 +4720,7 @@
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/special_tut/special_tut_impl.html" title="Implementation"><span class="index-entry-level-1">constants</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/special_tut/special_tut_impl.html" title="Implementation"><span class="index-entry-level-1">forwarding_policy</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/special_tut/special_tut_impl.html" title="Implementation"><span class="index-entry-level-1">function</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/special_tut/special_tut_impl.html" title="Implementation"><span class="index-entry-level-1">multiprecision</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/special_tut/special_tut_impl.html" title="Implementation"><span class="index-entry-level-1">promote_args</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/special_tut/special_tut_impl.html" title="Implementation"><span class="index-entry-level-1">T</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/special_tut/special_tut_impl.html" title="Implementation"><span class="index-entry-level-1">value_type</span></a></p></li>
@@ -4510,14 +4734,17 @@
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 <div class="index"><ul class="index" style="list-style-type: none; ">
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/sf_implementation.html" title="Additional Implementation Notes"><span class="index-entry-level-1">accuracy</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/sf_implementation.html" title="Additional Implementation Notes"><span class="index-entry-level-1">at</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/sf_implementation.html" title="Additional Implementation Notes"><span class="index-entry-level-1">BOOST_DEFINE_MATH_CONSTANT</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/sf_implementation.html" title="Additional Implementation Notes"><span class="index-entry-level-1">BOOST_MATH_DOMAIN_ERROR_POLICY</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/sf_implementation.html" title="Additional Implementation Notes"><span class="index-entry-level-1">cdf</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/sf_implementation.html" title="Additional Implementation Notes"><span class="index-entry-level-1">constants</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/sf_implementation.html" title="Additional Implementation Notes"><span class="index-entry-level-1">cpp_dec_float</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/sf_implementation.html" title="Additional Implementation Notes"><span class="index-entry-level-1">data</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/sf_implementation.html" title="Additional Implementation Notes"><span class="index-entry-level-1">defined</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/sf_implementation.html" title="Additional Implementation Notes"><span class="index-entry-level-1">infinity</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/sf_implementation.html" title="Additional Implementation Notes"><span class="index-entry-level-1">median</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/sf_implementation.html" title="Additional Implementation Notes"><span class="index-entry-level-1">multiprecision</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/sf_implementation.html" title="Additional Implementation Notes"><span class="index-entry-level-1">scale</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/sf_implementation.html" title="Additional Implementation Notes"><span class="index-entry-level-1">size</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/sf_implementation.html" title="Additional Implementation Notes"><span class="index-entry-level-1">support</span></a></p></li>
@@ -4525,6 +4752,10 @@
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 </li>
 <li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">Implementation of Float128 type</span></p>
+<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/float128.html" title="Implementation of Float128 type"><span class="index-entry-level-1">multiprecision</span></a></p></li></ul></div>
+</li>
+<li class="listitem" style="list-style-type: none">
 <p><span class="index-entry-level-0">Incomplete Beta Function Inverses</span></p>
 <div class="index"><ul class="index" style="list-style-type: none; ">
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses"><span class="index-entry-level-1">41</span></a></p></li>
@@ -4600,6 +4831,7 @@
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 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/double_exponential/de_exp_sinh.html" title="exp_sinh"><span class="index-entry-level-1">exp_sinh</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/fourier_integrals.html" title="Fourier Integrals"><span class="index-entry-level-1">Fourier Integrals</span></a></p></li>
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+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/constants_intro.html" title="Introduction"><span class="index-entry-level-1">multiprecision</span></a></p></li>
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+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/lambert_w.html" title="Lambert W function"><span class="index-entry-level-1">cpp_bin_float</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/lambert_w.html" title="Lambert W function"><span class="index-entry-level-1">cpp_dec_float</span></a></p></li>
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@@ -5026,6 +5261,7 @@
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/lambert_w.html" title="Lambert W function"><span class="index-entry-level-1">lambert_wm1</span></a></p></li>
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+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/lambert_w.html" title="Lambert W function"><span class="index-entry-level-1">multiprecision</span></a></p></li>
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 </li>
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+<p><span class="index-entry-level-0">Linpack Benchmark</span></p>
+<div class="index"><ul class="index" style="list-style-type: none; ">
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/multiprecision.html#math_toolkit.multiprecision.linpack_time" title="Table&#160;20.2.&#160;Linpack Benchmark"><span class="index-entry-level-1">cpp_bin_float</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/multiprecision.html#math_toolkit.multiprecision.linpack_time" title="Table&#160;20.2.&#160;Linpack Benchmark"><span class="index-entry-level-1">multiprecision</span></a></p></li>
+</ul></div>
+</li>
+<li class="listitem" style="list-style-type: none">
 <p><span class="index-entry-level-0">llrint</span></p>
 <div class="index"><ul class="index" style="list-style-type: none; ">
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/overview_tr1.html" title="C99 and C++ TR1 C-style Functions"><span class="index-entry-level-1">C99 and C++ TR1 C-style Functions</span></a></p></li>
@@ -5268,9 +5511,12 @@
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 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/brent_minima.html" title="Locating Function Minima using Brent's algorithm"><span class="index-entry-level-1">accuracy</span></a></p></li>
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+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/brent_minima.html" title="Locating Function Minima using Brent's algorithm"><span class="index-entry-level-1">cpp_bin_float</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/brent_minima.html" title="Locating Function Minima using Brent's algorithm"><span class="index-entry-level-1">cpp_dec_float</span></a></p></li>
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+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/brent_minima.html" title="Locating Function Minima using Brent's algorithm"><span class="index-entry-level-1">multiprecision</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/brent_minima.html" title="Locating Function Minima using Brent's algorithm"><span class="index-entry-level-1">operator</span></a></p></li>
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+<div class="index"><ul class="index" style="list-style-type: none; ">
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/autodiff.html" title="Automatic Differentiation"><span class="index-entry-level-1">Automatic Differentiation</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/number_series/bernoulli_numbers.html" title="Bernoulli Numbers"><span class="index-entry-level-1">Bernoulli Numbers</span></a></p></li>
+</ul></div>
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 <li class="listitem" style="list-style-type: none">
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 <li class="listitem" style="list-style-type: none">
@@ -5499,6 +5748,27 @@
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 </li>
 <li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">make_ftuple</span></p>
+<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/autodiff.html" title="Automatic Differentiation"><span class="index-entry-level-1">Automatic Differentiation</span></a></p></li></ul></div>
+</li>
+<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">make_fvar</span></p>
+<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/autodiff.html" title="Automatic Differentiation"><span class="index-entry-level-1">Automatic Differentiation</span></a></p></li></ul></div>
+</li>
+<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">Math Constants FAQs</span></p>
+<div class="index"><ul class="index" style="list-style-type: none; ">
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/constants_faq.html" title="Math Constants FAQs"><span class="index-entry-level-1">accuracy</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/constants_faq.html" title="Math Constants FAQs"><span class="index-entry-level-1">BOOST_DEFINE_MATH_CONSTANT</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/constants_faq.html" title="Math Constants FAQs"><span class="index-entry-level-1">case</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/constants_faq.html" title="Math Constants FAQs"><span class="index-entry-level-1">Cephes</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/constants_faq.html" title="Math Constants FAQs"><span class="index-entry-level-1">constants</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/constants_faq.html" title="Math Constants FAQs"><span class="index-entry-level-1">expression</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/constants_faq.html" title="Math Constants FAQs"><span class="index-entry-level-1">FAQ</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/constants_faq.html" title="Math Constants FAQs"><span class="index-entry-level-1">multiprecision</span></a></p></li>
+</ul></div>
+</li>
+<li class="listitem" style="list-style-type: none">
 <p><span class="index-entry-level-0">Mathematical Constants</span></p>
 <div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../constants.html" title="Chapter&#160;4.&#160;Mathematical Constants"><span class="index-entry-level-1">constants</span></a></p></li></ul></div>
 </li>
@@ -5603,9 +5873,58 @@
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 </ul></div>
 </li>
+<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">multiprecision</span></p>
+<div class="index"><ul class="index" style="list-style-type: none; ">
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/main_intro.html" title="About the Math Toolkit"><span class="index-entry-level-1">About the Math Toolkit</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/sf_implementation.html" title="Additional Implementation Notes"><span class="index-entry-level-1">Additional Implementation Notes</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/autodiff.html" title="Automatic Differentiation"><span class="index-entry-level-1">Automatic Differentiation</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/number_series/bernoulli_numbers.html" title="Bernoulli Numbers"><span class="index-entry-level-1">Bernoulli Numbers</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/main_faq.html" title="Boost.Math Frequently Asked Questions (FAQs)"><span class="index-entry-level-1">Boost.Math Frequently Asked Questions (FAQs)</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/root_comparison/cbrt_comparison.html" title="Comparison of Cube Root Finding Algorithms"><span class="index-entry-level-1">Comparison of Cube Root Finding Algorithms</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/root_comparison/elliptic_comparison.html" title="Comparison of Elliptic Integral Root Finding Algoritghms"><span class="index-entry-level-1">Comparison of Elliptic Integral Root Finding Algoritghms</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/root_comparison/root_n_comparison.html" title="Comparison of Nth-root Finding Algorithms"><span class="index-entry-level-1">Comparison of Nth-root Finding Algorithms</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/root_finding_examples/5th_root_eg.html" title="Computing the Fifth Root"><span class="index-entry-level-1">Computing the Fifth Root</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/real_concepts.html" title="Conceptual Requirements for Real Number Types"><span class="index-entry-level-1">Conceptual Requirements for Real Number Types</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/multiprecision.html" title="Cost of High-Precision Non-built-in Floating-point"><span class="index-entry-level-1">Cost of High-Precision Non-built-in Floating-point</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/credits.html" title="Credits and Acknowledgements"><span class="index-entry-level-1">Credits and Acknowledgements</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/new_const.html" title="Defining New Constants"><span class="index-entry-level-1">Defining New Constants</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/stat_tut/weg/dist_construct_eg.html" title="Distribution Construction Examples"><span class="index-entry-level-1">Distribution Construction Examples</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/airy/airy_root.html" title="Finding Zeros of Airy Functions"><span class="index-entry-level-1">Finding Zeros of Airy Functions</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/bessel/bessel_root.html" title="Finding Zeros of Bessel Functions of the First and Second Kinds"><span class="index-entry-level-1">Finding Zeros of Bessel Functions of the First and Second Kinds</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/next_float.html" title="Floating-Point Representation Distance (ULP), and Finding Adjacent Floating-Point Values"><span class="index-entry-level-1">Floating-Point Representation Distance (ULP), and Finding Adjacent Floating-Point Values</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/fourier_integrals.html" title="Fourier Integrals"><span class="index-entry-level-1">Fourier Integrals</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/gauss_kronrod.html" title="Gauss-Kronrod Quadrature"><span class="index-entry-level-1">Gauss-Kronrod Quadrature</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/gauss.html" title="Gauss-Legendre quadrature"><span class="index-entry-level-1">Gauss-Legendre quadrature</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/root_finding_examples/nth_root.html" title="Generalizing to Compute the nth root"><span class="index-entry-level-1">Generalizing to Compute the nth root</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/history1.html" title="History and What's New"><span class="index-entry-level-1">History and What's New</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/special_tut/special_tut_impl.html" title="Implementation"><span class="index-entry-level-1">Implementation</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/float128.html" title="Implementation of Float128 type"><span class="index-entry-level-1">Implementation of Float128 type</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/constants_intro.html" title="Introduction"><span class="index-entry-level-1">Introduction</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/lambert_w.html" title="Lambert W function"><span class="index-entry-level-1">Lambert W function</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/multiprecision.html#math_toolkit.multiprecision.linpack_time" title="Table&#160;20.2.&#160;Linpack Benchmark"><span class="index-entry-level-1">Linpack Benchmark</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/brent_minima.html" title="Locating Function Minima using Brent's algorithm"><span class="index-entry-level-1">Locating Function Minima using Brent's algorithm</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/constants_faq.html" title="Math Constants FAQs"><span class="index-entry-level-1">Math Constants FAQs</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/norms.html" title="Norms"><span class="index-entry-level-1">Norms</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/specified_typedefs.html" title="Overview"><span class="index-entry-level-1">Overview</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/root_finding_examples/multiprecision_root.html" title="Root-finding using Boost.Multiprecision"><span class="index-entry-level-1">Root-finding using Boost.Multiprecision</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/signal_statistics.html" title="Signal Statistics"><span class="index-entry-level-1">Signal Statistics</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/special_tut/special_tut_test.html" title="Testing"><span class="index-entry-level-1">Testing</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/sf_gamma/trigamma.html" title="Trigamma"><span class="index-entry-level-1">Trigamma</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/univariate_statistics.html" title="Univariate Statistics"><span class="index-entry-level-1">Univariate Statistics</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../using_udt.html" title="Chapter&#160;18.&#160;Use with User-Defined Floating-Point Types - Boost.Multiprecision and others"><span class="index-entry-level-1">Use with User-Defined Floating-Point Types - Boost.Multiprecision and others</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/tutorial/user_def.html" title="Use With User-Defined Types"><span class="index-entry-level-1">Use With User-Defined Types</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/high_precision.html" title="Using Boost.Math with High-Precision Floating-Point Libraries"><span class="index-entry-level-1">Using Boost.Math with High-Precision Floating-Point Libraries</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/high_precision/use_multiprecision.html" title="Using Boost.Multiprecision"><span class="index-entry-level-1">Using Boost.Multiprecision</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/high_precision/e_float.html" title="Using e_float Library"><span class="index-entry-level-1">Using e_float Library</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/high_precision/use_ntl.html" title="Using NTL Library"><span class="index-entry-level-1">Using NTL Library</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/high_precision/use_mpfr.html" title="Using With MPFR or GMP - High-Precision Floating-Point Library"><span class="index-entry-level-1">Using With MPFR or GMP - High-Precision Floating-Point Library</span></a></p></li>
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+</li>
+<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">ooura_fourier_sin</span></p>
+<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/fourier_integrals.html" title="Fourier Integrals"><span class="index-entry-level-1">Fourier Integrals</span></a></p></li></ul></div>
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+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/vector_barycentric.html" title="Vector-valued Barycentric Rational Interpolation"><span class="index-entry-level-1">Vector-valued Barycentric Rational Interpolation</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/whittaker_shannon.html" title="Whittaker-Shannon interpolation"><span class="index-entry-level-1">Whittaker-Shannon interpolation</span></a></p></li>
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+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/specified_typedefs.html" title="Overview"><span class="index-entry-level-1">multiprecision</span></a></p></li>
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+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/main_faq.html" title="Boost.Math Frequently Asked Questions (FAQs)"><span class="index-entry-level-1">Boost.Math Frequently Asked Questions (FAQs)</span></a></p></li>
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+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/whittaker_shannon.html" title="Whittaker-Shannon interpolation"><span class="index-entry-level-1">Whittaker-Shannon interpolation</span></a></p></li>
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+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/whittaker_shannon.html" title="Whittaker-Shannon interpolation"><span class="index-entry-level-1">Whittaker-Shannon interpolation</span></a></p></li>
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@@ -6395,7 +6738,7 @@
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+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/high_precision/using_test.html" title="Using without expression templates for Boost.Test and others"><span class="index-entry-level-1">cpp_dec_float</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/high_precision/using_test.html" title="Using without expression templates for Boost.Test and others"><span class="index-entry-level-1">expression</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/high_precision/using_test.html" title="Using without expression templates for Boost.Test and others"><span class="index-entry-level-1">multiprecision</span></a></p></li>
+</ul></div>
 </li>
 </ul></div></dd>
 <dt>
-<a name="idx_id_140"></a><span class="term">V</span>
+<a name="idx_id_150"></a><span class="term">V</span>
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+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/whittaker_shannon.html" title="Whittaker-Shannon interpolation"><span class="index-entry-level-1">Whittaker-Shannon interpolation</span></a></p></li>
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 </ul></div>
 </li>
+<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">Vector-valued Barycentric Rational Interpolation</span></p>
+<div class="index"><ul class="index" style="list-style-type: none; ">
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/vector_barycentric.html" title="Vector-valued Barycentric Rational Interpolation"><span class="index-entry-level-1">by</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/vector_barycentric.html" title="Vector-valued Barycentric Rational Interpolation"><span class="index-entry-level-1">operator</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/vector_barycentric.html" title="Vector-valued Barycentric Rational Interpolation"><span class="index-entry-level-1">performance</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/vector_barycentric.html" title="Vector-valued Barycentric Rational Interpolation"><span class="index-entry-level-1">prime</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/vector_barycentric.html" title="Vector-valued Barycentric Rational Interpolation"><span class="index-entry-level-1">t</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/vector_barycentric.html" title="Vector-valued Barycentric Rational Interpolation"><span class="index-entry-level-1">vector_barycentric_rational</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/vector_barycentric.html" title="Vector-valued Barycentric Rational Interpolation"><span class="index-entry-level-1">y</span></a></p></li>
+</ul></div>
+</li>
+<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">vector_barycentric_rational</span></p>
+<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/vector_barycentric.html" title="Vector-valued Barycentric Rational Interpolation"><span class="index-entry-level-1">Vector-valued Barycentric Rational Interpolation</span></a></p></li></ul></div>
+</li>
 </ul></div></dd>
 <dt>
-<a name="idx_id_141"></a><span class="term">W</span>
+<a name="idx_id_151"></a><span class="term">W</span>
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 <li class="listitem" style="list-style-type: none">
@@ -8041,15 +8447,31 @@
 </ul></div>
 </li>
 <li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">Whittaker-Shannon interpolation</span></p>
+<div class="index"><ul class="index" style="list-style-type: none; ">
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/whittaker_shannon.html" title="Whittaker-Shannon interpolation"><span class="index-entry-level-1">accuracy</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/whittaker_shannon.html" title="Whittaker-Shannon interpolation"><span class="index-entry-level-1">operator</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/whittaker_shannon.html" title="Whittaker-Shannon interpolation"><span class="index-entry-level-1">performance</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/whittaker_shannon.html" title="Whittaker-Shannon interpolation"><span class="index-entry-level-1">prime</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/whittaker_shannon.html" title="Whittaker-Shannon interpolation"><span class="index-entry-level-1">v</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/whittaker_shannon.html" title="Whittaker-Shannon interpolation"><span class="index-entry-level-1">whittaker_shannon</span></a></p></li>
+</ul></div>
+</li>
+<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">whittaker_shannon</span></p>
+<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/whittaker_shannon.html" title="Whittaker-Shannon interpolation"><span class="index-entry-level-1">Whittaker-Shannon interpolation</span></a></p></li></ul></div>
+</li>
+<li class="listitem" style="list-style-type: none">
 <p><span class="index-entry-level-0">Why use a high-precision library rather than built-in floating-point types?</span></p>
 <div class="index"><ul class="index" style="list-style-type: none; ">
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+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/high_precision/why_high_precision.html" title="Why use a high-precision library rather than built-in floating-point types?"><span class="index-entry-level-1">cpp_dec_float</span></a></p></li>
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+<a name="idx_id_152"></a><span class="term">X</span>
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@@ -8065,17 +8487,18 @@
 </ul></div>
 </li></ul></div></dd>
 <dt>
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+<a name="idx_id_153"></a><span class="term">Y</span>
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 <dd><div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none">
 <p><span class="index-entry-level-0">y</span></p>
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 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/barycentric.html" title="Barycentric Rational Interpolation"><span class="index-entry-level-1">Barycentric Rational Interpolation</span></a></p></li>
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+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/vector_barycentric.html" title="Vector-valued Barycentric Rational Interpolation"><span class="index-entry-level-1">Vector-valued Barycentric Rational Interpolation</span></a></p></li>
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 <dt>
-<a name="idx_id_144"></a><span class="term">Z</span>
+<a name="idx_id_154"></a><span class="term">Z</span>
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@@ -8105,11 +8528,11 @@
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 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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-<link rel="home" href="index.html" title="Math Toolkit 2.9.0">
-<link rel="up" href="index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="index.html" title="Math Toolkit 2.10.0">
+<link rel="up" href="index.html" title="Math Toolkit 2.10.0">
 <link rel="prev" href="gcd_lcm.html" title="Chapter&#160;16.&#160;Integer Utilities (Greatest Common Divisor and Least Common Multiple)">
 <link rel="next" href="math_toolkit/internals_overview.html" title="Overview">
 </head>
@@ -47,11 +47,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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diff --git a/libs/math/doc/html/interpolation.html b/libs/math/doc/html/interpolation.html
index fb5d999c72..5f4ad68119 100644
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-<link rel="home" href="index.html" title="Math Toolkit 2.9.0">
-<link rel="up" href="index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="index.html" title="Math Toolkit 2.10.0">
+<link rel="up" href="index.html" title="Math Toolkit 2.10.0">
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 <link rel="next" href="math_toolkit/cubic_b.html" title="Cubic B-spline interpolation">
 </head>
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 <p><b>Table of Contents</b></p>
 <dl class="toc">
 <dt><span class="section"><a href="math_toolkit/cubic_b.html">Cubic B-spline interpolation</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/cardinal_quadratic_b.html">Cardinal Quadratic B-spline
+    interpolation</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/whittaker_shannon.html">Whittaker-Shannon interpolation</a></span></dt>
 <dt><span class="section"><a href="math_toolkit/barycentric.html">Barycentric Rational Interpolation</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/vector_barycentric.html">Vector-valued Barycentric
+    Rational Interpolation</a></span></dt>
 <dt><span class="section"><a href="math_toolkit/catmull_rom.html">Catmull-Rom Splines</a></span></dt>
 </dl>
 </div>
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/inverse_complex.html b/libs/math/doc/html/inverse_complex.html
index 0bb7a3eb76..a9dbba35fa 100644
--- a/libs/math/doc/html/inverse_complex.html
+++ b/libs/math/doc/html/inverse_complex.html
@@ -4,8 +4,8 @@
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-<link rel="home" href="index.html" title="Math Toolkit 2.9.0">
-<link rel="up" href="index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="index.html" title="Math Toolkit 2.10.0">
+<link rel="up" href="index.html" title="Math Toolkit 2.10.0">
 <link rel="prev" href="math_toolkit/diff0.html" title="Lanczos Smoothing Derivatives">
 <link rel="next" href="math_toolkit/complex_implementation.html" title="Implementation and Accuracy">
 </head>
@@ -48,11 +48,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/acknowledgement.html b/libs/math/doc/html/math_toolkit/acknowledgement.html
index 74698f4e16..719aceda5a 100644
--- a/libs/math/doc/html/math_toolkit/acknowledgement.html
+++ b/libs/math/doc/html/math_toolkit/acknowledgement.html
@@ -4,7 +4,7 @@
 <title>Acknowledgements</title>
 <link rel="stylesheet" href="../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../quaternions.html" title="Chapter&#160;14.&#160;Quaternions">
 <link rel="prev" href="exp.html" title="The Quaternionic Exponential">
 <link rel="next" href="quat_history.html" title="History">
@@ -35,11 +35,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/acknowledgements.html b/libs/math/doc/html/math_toolkit/acknowledgements.html
index 945d0ddcc3..1604db7590 100644
--- a/libs/math/doc/html/math_toolkit/acknowledgements.html
+++ b/libs/math/doc/html/math_toolkit/acknowledgements.html
@@ -4,7 +4,7 @@
 <title>Acknowledgements</title>
 <link rel="stylesheet" href="../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../octonions.html" title="Chapter&#160;15.&#160;Octonions">
 <link rel="prev" href="oct_tests.html" title="Test Program">
 <link rel="next" href="oct_history.html" title="History">
@@ -35,11 +35,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/acos.html b/libs/math/doc/html/math_toolkit/acos.html
index 61e2b51ee6..98eae667d7 100644
--- a/libs/math/doc/html/math_toolkit/acos.html
+++ b/libs/math/doc/html/math_toolkit/acos.html
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-<link rel="home" href="../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../inverse_complex.html" title="Chapter&#160;13.&#160;Complex Number Functions">
 <link rel="prev" href="asin.html" title="asin">
 <link rel="next" href="atan.html" title="atan">
@@ -49,11 +49,11 @@
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
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+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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@@ -49,11 +49,11 @@
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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@@ -49,11 +49,11 @@
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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diff --git a/libs/math/doc/html/math_toolkit/atan.html b/libs/math/doc/html/math_toolkit/atan.html
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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diff --git a/libs/math/doc/html/math_toolkit/atanh.html b/libs/math/doc/html/math_toolkit/atanh.html
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 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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+<div class="titlepage"><div><div><h2 class="title" style="clear: both">
+<a name="math_toolkit.autodiff"></a><a class="link" href="autodiff.html" title="Automatic Differentiation">Automatic Differentiation</a>
+</h2></div></div></div>
+<h2>
+<a name="math_toolkit.autodiff.h0"></a>
+      <span class="phrase"><a name="math_toolkit.autodiff.synopsis"></a></span><a class="link" href="autodiff.html#math_toolkit.autodiff.synopsis">Synopsis</a>
+    </h2>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">differentiation</span><span class="special">/</span><span class="identifier">autodiff</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+
+<span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span>
+<span class="keyword">namespace</span> <span class="identifier">math</span> <span class="special">{</span>
+<span class="keyword">namespace</span> <span class="identifier">differentiation</span> <span class="special">{</span>
+
+<span class="comment">// Function returning a single variable of differentiation. Recommended: Use auto for type.</span>
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">RealType</span><span class="special">,</span> <span class="identifier">size_t</span> <span class="identifier">Order</span><span class="special">,</span> <span class="identifier">size_t</span><span class="special">...</span> <span class="identifier">Orders</span><span class="special">&gt;</span>
+<span class="identifier">autodiff_fvar</span><span class="special">&lt;</span><span class="identifier">RealType</span><span class="special">,</span> <span class="identifier">Order</span><span class="special">,</span> <span class="identifier">Orders</span><span class="special">...&gt;</span> <span class="identifier">make_fvar</span><span class="special">(</span><span class="identifier">RealType</span> <span class="keyword">const</span><span class="special">&amp;</span> <span class="identifier">ca</span><span class="special">);</span>
+
+<span class="comment">// Function returning multiple independent variables of differentiation in a std::tuple.</span>
+<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">RealType</span><span class="special">,</span> <span class="identifier">size_t</span><span class="special">...</span> <span class="identifier">Orders</span><span class="special">,</span> <span class="keyword">typename</span><span class="special">...</span> <span class="identifier">RealTypes</span><span class="special">&gt;</span>
+<span class="keyword">auto</span> <span class="identifier">make_ftuple</span><span class="special">(</span><span class="identifier">RealTypes</span> <span class="keyword">const</span><span class="special">&amp;...</span> <span class="identifier">ca</span><span class="special">);</span>
+
+<span class="comment">// Type of combined autodiff types. Recommended: Use auto for return type (C++14).</span>
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">RealType</span><span class="special">,</span> <span class="keyword">typename</span><span class="special">...</span> <span class="identifier">RealTypes</span><span class="special">&gt;</span>
+<span class="keyword">using</span> <span class="identifier">promote</span> <span class="special">=</span> <span class="keyword">typename</span> <span class="identifier">detail</span><span class="special">::</span><span class="identifier">promote_args_n</span><span class="special">&lt;</span><span class="identifier">RealType</span><span class="special">,</span> <span class="identifier">RealTypes</span><span class="special">...&gt;::</span><span class="identifier">type</span><span class="special">;</span>
+
+<span class="keyword">namespace</span> <span class="identifier">detail</span> <span class="special">{</span>
+
+<span class="comment">// Single autodiff variable. Use make_fvar() or make_ftuple() to instantiate.</span>
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">RealType</span><span class="special">,</span> <span class="identifier">size_t</span> <span class="identifier">Order</span><span class="special">&gt;</span>
+<span class="keyword">class</span> <span class="identifier">fvar</span> <span class="special">{</span>
+ <span class="keyword">public</span><span class="special">:</span>
+  <span class="comment">// Query return value of function to get the derivatives.</span>
+  <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">typename</span><span class="special">...</span> <span class="identifier">Orders</span><span class="special">&gt;</span>
+  <span class="identifier">get_type_at</span><span class="special">&lt;</span><span class="identifier">RealType</span><span class="special">,</span> <span class="keyword">sizeof</span><span class="special">...(</span><span class="identifier">Orders</span><span class="special">)</span> <span class="special">-</span> <span class="number">1</span><span class="special">&gt;</span> <span class="identifier">derivative</span><span class="special">(</span><span class="identifier">Orders</span><span class="special">...</span> <span class="identifier">orders</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span>
+
+  <span class="comment">// All of the arithmetic and comparison operators are overloaded.</span>
+  <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">RealType2</span><span class="special">,</span> <span class="identifier">size_t</span> <span class="identifier">Order2</span><span class="special">&gt;</span>
+  <span class="identifier">fvar</span><span class="special">&amp;</span> <span class="keyword">operator</span><span class="special">+=(</span><span class="identifier">fvar</span><span class="special">&lt;</span><span class="identifier">RealType2</span><span class="special">,</span> <span class="identifier">Order2</span><span class="special">&gt;</span> <span class="keyword">const</span><span class="special">&amp;);</span>
+
+  <span class="identifier">fvar</span><span class="special">&amp;</span> <span class="keyword">operator</span><span class="special">+=(</span><span class="identifier">root_type</span> <span class="keyword">const</span><span class="special">&amp;);</span>
+
+  <span class="comment">// ...</span>
+<span class="special">};</span>
+
+<span class="comment">// Standard math functions are overloaded and called via argument-dependent lookup (ADL).</span>
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">RealType</span><span class="special">,</span> <span class="identifier">size_t</span> <span class="identifier">Order</span><span class="special">&gt;</span>
+<span class="identifier">fvar</span><span class="special">&lt;</span><span class="identifier">RealType</span><span class="special">,</span> <span class="identifier">Order</span><span class="special">&gt;</span> <span class="identifier">floor</span><span class="special">(</span><span class="identifier">fvar</span><span class="special">&lt;</span><span class="identifier">RealType</span><span class="special">,</span> <span class="identifier">Order</span><span class="special">&gt;</span> <span class="keyword">const</span><span class="special">&amp;);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">RealType</span><span class="special">,</span> <span class="identifier">size_t</span> <span class="identifier">Order</span><span class="special">&gt;</span>
+<span class="identifier">fvar</span><span class="special">&lt;</span><span class="identifier">RealType</span><span class="special">,</span> <span class="identifier">Order</span><span class="special">&gt;</span> <span class="identifier">exp</span><span class="special">(</span><span class="identifier">fvar</span><span class="special">&lt;</span><span class="identifier">RealType</span><span class="special">,</span> <span class="identifier">Order</span><span class="special">&gt;</span> <span class="keyword">const</span><span class="special">&amp;);</span>
+
+<span class="comment">// ...</span>
+
+<span class="special">}</span>  <span class="comment">// namespace detail</span>
+
+<span class="special">}</span>  <span class="comment">// namespace differentiation</span>
+<span class="special">}</span>  <span class="comment">// namespace math</span>
+<span class="special">}</span>  <span class="comment">// namespace boost</span>
+</pre>
+<h2>
+<a name="math_toolkit.autodiff.h1"></a>
+      <span class="phrase"><a name="math_toolkit.autodiff.description"></a></span><a class="link" href="autodiff.html#math_toolkit.autodiff.description">Description</a>
+    </h2>
+<p>
+      Autodiff is a header-only C++ library that facilitates the <a href="https://en.wikipedia.org/wiki/Automatic_differentiation" target="_top">automatic
+      differentiation</a> (forward mode) of mathematical functions of single
+      and multiple variables.
+    </p>
+<p>
+      This implementation is based upon the <a href="https://en.wikipedia.org/wiki/Taylor_series" target="_top">Taylor
+      series</a> expansion of an analytic function <span class="emphasis"><em>f</em></span> at
+      the point <span class="emphasis"><em>x<sub>0</sub></em></span>:
+    </p>
+<div class="blockquote"><blockquote class="blockquote"><div class="blockquote"><blockquote class="blockquote"><p>
+          <span class="inlinemediaobject"><img src="../../equations/autodiff/taylor_series.svg"></span>
+        </p></blockquote></div></blockquote></div>
+<p>
+      The essential idea of autodiff is the substitution of numbers with polynomials
+      in the evaluation of <span class="emphasis"><em>f(x<sub>0</sub>)</em></span>. By substituting the number
+      <span class="emphasis"><em>x<sub>0</sub></em></span> with the first-order polynomial <span class="emphasis"><em>x<sub>0</sub>+&#949;</em></span>,
+      and using the same algorithm to compute <span class="emphasis"><em>f(x<sub>0</sub>+&#949;)</em></span>,
+      the resulting polynomial in <span class="emphasis"><em>&#949;</em></span> contains the function's
+      derivatives <span class="emphasis"><em>f'(x<sub>0</sub>)</em></span>, <span class="emphasis"><em>f''(x<sub>0</sub>)</em></span>, <span class="emphasis"><em>f'''(x<sub>0</sub>)</em></span>,
+      ... within the coefficients. Each coefficient is equal to the derivative of
+      its respective order, divided by the factorial of the order.
+    </p>
+<p>
+      In greater detail, assume one is interested in calculating the first <span class="emphasis"><em>N</em></span>
+      derivatives of <span class="emphasis"><em>f</em></span> at <span class="emphasis"><em>x<sub>0</sub></em></span>. Without loss
+      of precision to the calculation of the derivatives, all terms <span class="emphasis"><em>O(&#949;<sup>N+1</sup>)</em></span>
+      that include powers of <span class="emphasis"><em>&#949;</em></span> greater than <span class="emphasis"><em>N</em></span>
+      can be discarded. (This is due to the fact that each term in a polynomial depends
+      only upon equal and lower-order terms under arithmetic operations.) Under these
+      truncation rules, <span class="emphasis"><em>f</em></span> provides a polynomial-to-polynomial
+      transformation:
+    </p>
+<div class="blockquote"><blockquote class="blockquote"><div class="blockquote"><blockquote class="blockquote"><p>
+          <span class="inlinemediaobject"><img src="../../equations/autodiff/polynomial_transform.svg"></span>
+        </p></blockquote></div></blockquote></div>
+<p>
+      C++'s ability to overload operators and functions allows for the creation of
+      a class <code class="computeroutput"><span class="identifier">fvar</span></code> (<span class="underline">f</span>orward-mode
+      autodiff <span class="underline">var</span>iable) that represents polynomials
+      in <span class="emphasis"><em>&#949;</em></span>. Thus the same algorithm <span class="emphasis"><em>f</em></span>
+      that calculates the numeric value of <span class="emphasis"><em>y<sub>0</sub>=f(x<sub>0</sub>)</em></span>, when written
+      to accept and return variables of a generic (template) type, is also used to
+      calculate the polynomial <span class="emphasis"><em>&#931;<sub>n</sub>y<sub>n</sub>&#949;<sup>n</sup>=f(x<sub>0</sub>+&#949;)</em></span>.
+      The derivatives <span class="emphasis"><em>f<sup>(n)</sup>(x<sub>0</sub>)</em></span> are then found from the product
+      of the respective factorial <span class="emphasis"><em>n!</em></span> and coefficient <span class="emphasis"><em>y<sub>n</sub></em></span>:
+    </p>
+<div class="blockquote"><blockquote class="blockquote"><div class="blockquote"><blockquote class="blockquote"><p>
+          <span class="inlinemediaobject"><img src="../../equations/autodiff/derivative_formula.svg"></span>
+        </p></blockquote></div></blockquote></div>
+<h2>
+<a name="math_toolkit.autodiff.h2"></a>
+      <span class="phrase"><a name="math_toolkit.autodiff.examples"></a></span><a class="link" href="autodiff.html#math_toolkit.autodiff.examples">Examples</a>
+    </h2>
+<h3>
+<a name="math_toolkit.autodiff.h3"></a>
+      <span class="phrase"><a name="math_toolkit.autodiff.example-single-variable"></a></span><a class="link" href="autodiff.html#math_toolkit.autodiff.example-single-variable">Example
+      1: Single-variable derivatives</a>
+    </h3>
+<h4>
+<a name="math_toolkit.autodiff.h4"></a>
+      <span class="phrase"><a name="math_toolkit.autodiff.calculate_derivatives_of_f_x_x_s"></a></span><a class="link" href="autodiff.html#math_toolkit.autodiff.calculate_derivatives_of_f_x_x_s">Calculate
+      derivatives of <span class="emphasis"><em>f(x)=x<sup>4</sup></em></span> at <span class="emphasis"><em>x</em></span>=2.</a>
+    </h4>
+<p>
+      In this example, <code class="computeroutput"><span class="identifier">make_fvar</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">,</span>
+      <span class="identifier">Order</span><span class="special">&gt;(</span><span class="number">2.0</span><span class="special">)</span></code> instantiates
+      the polynomial 2+<span class="emphasis"><em>&#949;</em></span>. The <code class="computeroutput"><span class="identifier">Order</span><span class="special">=</span><span class="number">5</span></code> means that
+      enough space is allocated (on the stack) to hold a polynomial of up to degree
+      5 during the proceeding computation.
+    </p>
+<p>
+      Internally, this is modeled by a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">array</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">,</span><span class="number">6</span><span class="special">&gt;</span></code> whose elements <code class="computeroutput"><span class="special">{</span><span class="number">2</span><span class="special">,</span> <span class="number">1</span><span class="special">,</span> <span class="number">0</span><span class="special">,</span>
+      <span class="number">0</span><span class="special">,</span> <span class="number">0</span><span class="special">,</span> <span class="number">0</span><span class="special">}</span></code>
+      correspond to the 6 coefficients of the polynomial upon initialization. Its
+      fourth power, at the end of the computation, is a polynomial with coefficients
+      <code class="computeroutput"><span class="identifier">y</span> <span class="special">=</span>
+      <span class="special">{</span><span class="number">16</span><span class="special">,</span>
+      <span class="number">32</span><span class="special">,</span> <span class="number">24</span><span class="special">,</span> <span class="number">8</span><span class="special">,</span> <span class="number">1</span><span class="special">,</span>
+      <span class="number">0</span><span class="special">}</span></code>. The
+      derivatives are obtained using the formula <span class="emphasis"><em>f<sup>(n)</sup>(2)=n!*y[n]</em></span>.
+    </p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">differentiation</span><span class="special">/</span><span class="identifier">autodiff</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">iostream</span><span class="special">&gt;</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="identifier">T</span> <span class="identifier">fourth_power</span><span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span><span class="special">&amp;</span> <span class="identifier">x</span><span class="special">)</span> <span class="special">{</span>
+  <span class="identifier">T</span> <span class="identifier">x4</span> <span class="special">=</span> <span class="identifier">x</span> <span class="special">*</span> <span class="identifier">x</span><span class="special">;</span>  <span class="comment">// retval in operator*() uses x4's memory via NRVO.</span>
+  <span class="identifier">x4</span> <span class="special">*=</span> <span class="identifier">x4</span><span class="special">;</span>      <span class="comment">// No copies of x4 are made within operator*=() even when squaring.</span>
+  <span class="keyword">return</span> <span class="identifier">x4</span><span class="special">;</span>     <span class="comment">// x4 uses y's memory in main() via NRVO.</span>
+<span class="special">}</span>
+
+<span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span> <span class="special">{</span>
+  <span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">differentiation</span><span class="special">;</span>
+
+  <span class="keyword">constexpr</span> <span class="keyword">unsigned</span> <span class="identifier">Order</span> <span class="special">=</span> <span class="number">5</span><span class="special">;</span>                  <span class="comment">// Highest order derivative to be calculated.</span>
+  <span class="keyword">auto</span> <span class="keyword">const</span> <span class="identifier">x</span> <span class="special">=</span> <span class="identifier">make_fvar</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">,</span> <span class="identifier">Order</span><span class="special">&gt;(</span><span class="number">2.0</span><span class="special">);</span>  <span class="comment">// Find derivatives at x=2.</span>
+  <span class="keyword">auto</span> <span class="keyword">const</span> <span class="identifier">y</span> <span class="special">=</span> <span class="identifier">fourth_power</span><span class="special">(</span><span class="identifier">x</span><span class="special">);</span>
+  <span class="keyword">for</span> <span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">i</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span> <span class="identifier">i</span> <span class="special">&lt;=</span> <span class="identifier">Order</span><span class="special">;</span> <span class="special">++</span><span class="identifier">i</span><span class="special">)</span>
+    <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"y.derivative("</span> <span class="special">&lt;&lt;</span> <span class="identifier">i</span> <span class="special">&lt;&lt;</span> <span class="string">") = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">y</span><span class="special">.</span><span class="identifier">derivative</span><span class="special">(</span><span class="identifier">i</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+  <span class="keyword">return</span> <span class="number">0</span><span class="special">;</span>
+<span class="special">}</span>
+<span class="comment">/*
+Output:
+y.derivative(0) = 16
+y.derivative(1) = 32
+y.derivative(2) = 48
+y.derivative(3) = 48
+y.derivative(4) = 24
+y.derivative(5) = 0
+*/</span>
+</pre>
+<p>
+      The above calculates
+    </p>
+<div class="blockquote"><blockquote class="blockquote"><div class="blockquote"><blockquote class="blockquote"><p>
+          <span class="inlinemediaobject"><img src="../../equations/autodiff/example1.svg"></span>
+        </p></blockquote></div></blockquote></div>
+<h3>
+<a name="math_toolkit.autodiff.h5"></a>
+      <span class="phrase"><a name="math_toolkit.autodiff.example-multiprecision"></a></span><a class="link" href="autodiff.html#math_toolkit.autodiff.example-multiprecision">Example
+      2: Multi-variable mixed partial derivatives with multi-precision data type</a>
+    </h3>
+<h4>
+<a name="math_toolkit.autodiff.h6"></a>
+      <span class="phrase"><a name="math_toolkit.autodiff.calculate_autodiff_equation_mixe"></a></span><a class="link" href="autodiff.html#math_toolkit.autodiff.calculate_autodiff_equation_mixe">Calculate
+      <span class="inlinemediaobject"><img src="../../equations/autodiff/mixed12.svg"></span> with a precision of about 50 decimal digits, where <span class="inlinemediaobject"><img src="../../equations/autodiff/example2f.svg"></span>.</a>
+    </h4>
+<p>
+      In this example, <code class="computeroutput"><span class="identifier">make_ftuple</span><span class="special">&lt;</span><span class="identifier">float50</span><span class="special">,</span> <span class="identifier">Nw</span><span class="special">,</span>
+      <span class="identifier">Nx</span><span class="special">,</span> <span class="identifier">Ny</span><span class="special">,</span> <span class="identifier">Nz</span><span class="special">&gt;(</span><span class="number">11</span><span class="special">,</span>
+      <span class="number">12</span><span class="special">,</span> <span class="number">13</span><span class="special">,</span> <span class="number">14</span><span class="special">)</span></code> returns a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">tuple</span></code> of
+      4 independent <code class="computeroutput"><span class="identifier">fvar</span></code> variables,
+      with values of 11, 12, 13, and 14, for which the maximum order derivative to
+      be calculated for each are 3, 2, 4, 3, respectively. The order of the variables
+      is important, as it is the same order used when calling <code class="computeroutput"><span class="identifier">v</span><span class="special">.</span><span class="identifier">derivative</span><span class="special">(</span><span class="identifier">Nw</span><span class="special">,</span>
+      <span class="identifier">Nx</span><span class="special">,</span> <span class="identifier">Ny</span><span class="special">,</span> <span class="identifier">Nz</span><span class="special">)</span></code> in the example below.
+    </p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">differentiation</span><span class="special">/</span><span class="identifier">autodiff</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">cpp_bin_float</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">iostream</span><span class="special">&gt;</span>
+
+<span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">differentiation</span><span class="special">;</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">W</span><span class="special">,</span> <span class="keyword">typename</span> <span class="identifier">X</span><span class="special">,</span> <span class="keyword">typename</span> <span class="identifier">Y</span><span class="special">,</span> <span class="keyword">typename</span> <span class="identifier">Z</span><span class="special">&gt;</span>
+<span class="identifier">promote</span><span class="special">&lt;</span><span class="identifier">W</span><span class="special">,</span> <span class="identifier">X</span><span class="special">,</span> <span class="identifier">Y</span><span class="special">,</span> <span class="identifier">Z</span><span class="special">&gt;</span> <span class="identifier">f</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">W</span><span class="special">&amp;</span> <span class="identifier">w</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">X</span><span class="special">&amp;</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">Y</span><span class="special">&amp;</span> <span class="identifier">y</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">Z</span><span class="special">&amp;</span> <span class="identifier">z</span><span class="special">)</span> <span class="special">{</span>
+  <span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">std</span><span class="special">;</span>
+  <span class="keyword">return</span> <span class="identifier">exp</span><span class="special">(</span><span class="identifier">w</span> <span class="special">*</span> <span class="identifier">sin</span><span class="special">(</span><span class="identifier">x</span> <span class="special">*</span> <span class="identifier">log</span><span class="special">(</span><span class="identifier">y</span><span class="special">)</span> <span class="special">/</span> <span class="identifier">z</span><span class="special">)</span> <span class="special">+</span> <span class="identifier">sqrt</span><span class="special">(</span><span class="identifier">w</span> <span class="special">*</span> <span class="identifier">z</span> <span class="special">/</span> <span class="special">(</span><span class="identifier">x</span> <span class="special">*</span> <span class="identifier">y</span><span class="special">)))</span> <span class="special">+</span> <span class="identifier">w</span> <span class="special">*</span> <span class="identifier">w</span> <span class="special">/</span> <span class="identifier">tan</span><span class="special">(</span><span class="identifier">z</span><span class="special">);</span>
+<span class="special">}</span>
+
+<span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span> <span class="special">{</span>
+  <span class="keyword">using</span> <span class="identifier">float50</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">::</span><span class="identifier">cpp_bin_float_50</span><span class="special">;</span>
+
+  <span class="keyword">constexpr</span> <span class="keyword">unsigned</span> <span class="identifier">Nw</span> <span class="special">=</span> <span class="number">3</span><span class="special">;</span>  <span class="comment">// Max order of derivative to calculate for w</span>
+  <span class="keyword">constexpr</span> <span class="keyword">unsigned</span> <span class="identifier">Nx</span> <span class="special">=</span> <span class="number">2</span><span class="special">;</span>  <span class="comment">// Max order of derivative to calculate for x</span>
+  <span class="keyword">constexpr</span> <span class="keyword">unsigned</span> <span class="identifier">Ny</span> <span class="special">=</span> <span class="number">4</span><span class="special">;</span>  <span class="comment">// Max order of derivative to calculate for y</span>
+  <span class="keyword">constexpr</span> <span class="keyword">unsigned</span> <span class="identifier">Nz</span> <span class="special">=</span> <span class="number">3</span><span class="special">;</span>  <span class="comment">// Max order of derivative to calculate for z</span>
+  <span class="comment">// Declare 4 independent variables together into a std::tuple.</span>
+  <span class="keyword">auto</span> <span class="keyword">const</span> <span class="identifier">variables</span> <span class="special">=</span> <span class="identifier">make_ftuple</span><span class="special">&lt;</span><span class="identifier">float50</span><span class="special">,</span> <span class="identifier">Nw</span><span class="special">,</span> <span class="identifier">Nx</span><span class="special">,</span> <span class="identifier">Ny</span><span class="special">,</span> <span class="identifier">Nz</span><span class="special">&gt;(</span><span class="number">11</span><span class="special">,</span> <span class="number">12</span><span class="special">,</span> <span class="number">13</span><span class="special">,</span> <span class="number">14</span><span class="special">);</span>
+  <span class="keyword">auto</span> <span class="keyword">const</span><span class="special">&amp;</span> <span class="identifier">w</span> <span class="special">=</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">get</span><span class="special">&lt;</span><span class="number">0</span><span class="special">&gt;(</span><span class="identifier">variables</span><span class="special">);</span>  <span class="comment">// Up to Nw derivatives at w=11</span>
+  <span class="keyword">auto</span> <span class="keyword">const</span><span class="special">&amp;</span> <span class="identifier">x</span> <span class="special">=</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">get</span><span class="special">&lt;</span><span class="number">1</span><span class="special">&gt;(</span><span class="identifier">variables</span><span class="special">);</span>  <span class="comment">// Up to Nx derivatives at x=12</span>
+  <span class="keyword">auto</span> <span class="keyword">const</span><span class="special">&amp;</span> <span class="identifier">y</span> <span class="special">=</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">get</span><span class="special">&lt;</span><span class="number">2</span><span class="special">&gt;(</span><span class="identifier">variables</span><span class="special">);</span>  <span class="comment">// Up to Ny derivatives at y=13</span>
+  <span class="keyword">auto</span> <span class="keyword">const</span><span class="special">&amp;</span> <span class="identifier">z</span> <span class="special">=</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">get</span><span class="special">&lt;</span><span class="number">3</span><span class="special">&gt;(</span><span class="identifier">variables</span><span class="special">);</span>  <span class="comment">// Up to Nz derivatives at z=14</span>
+  <span class="keyword">auto</span> <span class="keyword">const</span> <span class="identifier">v</span> <span class="special">=</span> <span class="identifier">f</span><span class="special">(</span><span class="identifier">w</span><span class="special">,</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">y</span><span class="special">,</span> <span class="identifier">z</span><span class="special">);</span>
+  <span class="comment">// Calculated from Mathematica symbolic differentiation.</span>
+  <span class="identifier">float50</span> <span class="keyword">const</span> <span class="identifier">answer</span><span class="special">(</span><span class="string">"1976.319600747797717779881875290418720908121189218755"</span><span class="special">);</span>
+  <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setprecision</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">float50</span><span class="special">&gt;::</span><span class="identifier">digits10</span><span class="special">)</span>
+            <span class="special">&lt;&lt;</span> <span class="string">"mathematica   : "</span> <span class="special">&lt;&lt;</span> <span class="identifier">answer</span> <span class="special">&lt;&lt;</span> <span class="char">'\n'</span>
+            <span class="special">&lt;&lt;</span> <span class="string">"autodiff      : "</span> <span class="special">&lt;&lt;</span> <span class="identifier">v</span><span class="special">.</span><span class="identifier">derivative</span><span class="special">(</span><span class="identifier">Nw</span><span class="special">,</span> <span class="identifier">Nx</span><span class="special">,</span> <span class="identifier">Ny</span><span class="special">,</span> <span class="identifier">Nz</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="char">'\n'</span>
+            <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setprecision</span><span class="special">(</span><span class="number">3</span><span class="special">)</span>
+            <span class="special">&lt;&lt;</span> <span class="string">"relative error: "</span> <span class="special">&lt;&lt;</span> <span class="special">(</span><span class="identifier">v</span><span class="special">.</span><span class="identifier">derivative</span><span class="special">(</span><span class="identifier">Nw</span><span class="special">,</span> <span class="identifier">Nx</span><span class="special">,</span> <span class="identifier">Ny</span><span class="special">,</span> <span class="identifier">Nz</span><span class="special">)</span> <span class="special">/</span> <span class="identifier">answer</span> <span class="special">-</span> <span class="number">1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="char">'\n'</span><span class="special">;</span>
+  <span class="keyword">return</span> <span class="number">0</span><span class="special">;</span>
+<span class="special">}</span>
+<span class="comment">/*
+Output:
+mathematica   : 1976.3196007477977177798818752904187209081211892188
+autodiff      : 1976.3196007477977177798818752904187209081211892188
+relative error: 2.67e-50
+*/</span>
+</pre>
+<h3>
+<a name="math_toolkit.autodiff.h7"></a>
+      <span class="phrase"><a name="math_toolkit.autodiff.example-black_scholes"></a></span><a class="link" href="autodiff.html#math_toolkit.autodiff.example-black_scholes">Example
+      3: Black-Scholes Option Pricing with Greeks Automatically Calculated</a>
+    </h3>
+<h4>
+<a name="math_toolkit.autodiff.h8"></a>
+      <span class="phrase"><a name="math_toolkit.autodiff.calculate_greeks_directly_from_t"></a></span><a class="link" href="autodiff.html#math_toolkit.autodiff.calculate_greeks_directly_from_t">Calculate
+      greeks directly from the Black-Scholes pricing function.</a>
+    </h4>
+<p>
+      Below is the standard Black-Scholes pricing function written as a function
+      template, where the price, volatility (sigma), time to expiration (tau) and
+      interest rate are template parameters. This means that any greek based on these
+      4 variables can be calculated using autodiff. The below example calculates
+      delta and gamma where the variable of differentiation is only the price. For
+      examples of more exotic greeks, see <code class="computeroutput"><span class="identifier">example</span><span class="special">/</span><span class="identifier">black_scholes</span><span class="special">.</span><span class="identifier">cpp</span></code>.
+    </p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">differentiation</span><span class="special">/</span><span class="identifier">autodiff</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">iostream</span><span class="special">&gt;</span>
+
+<span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">constants</span><span class="special">;</span>
+<span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">differentiation</span><span class="special">;</span>
+
+<span class="comment">// Equations and function/variable names are from</span>
+<span class="comment">// https://en.wikipedia.org/wiki/Greeks_(finance)#Formulas_for_European_option_Greeks</span>
+
+<span class="comment">// Standard normal cumulative distribution function</span>
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">&gt;</span>
+<span class="identifier">X</span> <span class="identifier">Phi</span><span class="special">(</span><span class="identifier">X</span> <span class="keyword">const</span><span class="special">&amp;</span> <span class="identifier">x</span><span class="special">)</span> <span class="special">{</span>
+  <span class="keyword">return</span> <span class="number">0.5</span> <span class="special">*</span> <span class="identifier">erfc</span><span class="special">(-</span><span class="identifier">one_div_root_two</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;()</span> <span class="special">*</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="special">}</span>
+
+<span class="keyword">enum</span> <span class="keyword">class</span> <span class="identifier">CP</span> <span class="special">{</span> <span class="identifier">call</span><span class="special">,</span> <span class="identifier">put</span> <span class="special">};</span>
+
+<span class="comment">// Assume zero annual dividend yield (q=0).</span>
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">Price</span><span class="special">,</span> <span class="keyword">typename</span> <span class="identifier">Sigma</span><span class="special">,</span> <span class="keyword">typename</span> <span class="identifier">Tau</span><span class="special">,</span> <span class="keyword">typename</span> <span class="identifier">Rate</span><span class="special">&gt;</span>
+<span class="identifier">promote</span><span class="special">&lt;</span><span class="identifier">Price</span><span class="special">,</span> <span class="identifier">Sigma</span><span class="special">,</span> <span class="identifier">Tau</span><span class="special">,</span> <span class="identifier">Rate</span><span class="special">&gt;</span> <span class="identifier">black_scholes_option_price</span><span class="special">(</span><span class="identifier">CP</span> <span class="identifier">cp</span><span class="special">,</span>
+                                                            <span class="keyword">double</span> <span class="identifier">K</span><span class="special">,</span>
+                                                            <span class="identifier">Price</span> <span class="keyword">const</span><span class="special">&amp;</span> <span class="identifier">S</span><span class="special">,</span>
+                                                            <span class="identifier">Sigma</span> <span class="keyword">const</span><span class="special">&amp;</span> <span class="identifier">sigma</span><span class="special">,</span>
+                                                            <span class="identifier">Tau</span> <span class="keyword">const</span><span class="special">&amp;</span> <span class="identifier">tau</span><span class="special">,</span>
+                                                            <span class="identifier">Rate</span> <span class="keyword">const</span><span class="special">&amp;</span> <span class="identifier">r</span><span class="special">)</span> <span class="special">{</span>
+  <span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">std</span><span class="special">;</span>
+  <span class="keyword">auto</span> <span class="keyword">const</span> <span class="identifier">d1</span> <span class="special">=</span> <span class="special">(</span><span class="identifier">log</span><span class="special">(</span><span class="identifier">S</span> <span class="special">/</span> <span class="identifier">K</span><span class="special">)</span> <span class="special">+</span> <span class="special">(</span><span class="identifier">r</span> <span class="special">+</span> <span class="identifier">sigma</span> <span class="special">*</span> <span class="identifier">sigma</span> <span class="special">/</span> <span class="number">2</span><span class="special">)</span> <span class="special">*</span> <span class="identifier">tau</span><span class="special">)</span> <span class="special">/</span> <span class="special">(</span><span class="identifier">sigma</span> <span class="special">*</span> <span class="identifier">sqrt</span><span class="special">(</span><span class="identifier">tau</span><span class="special">));</span>
+  <span class="keyword">auto</span> <span class="keyword">const</span> <span class="identifier">d2</span> <span class="special">=</span> <span class="special">(</span><span class="identifier">log</span><span class="special">(</span><span class="identifier">S</span> <span class="special">/</span> <span class="identifier">K</span><span class="special">)</span> <span class="special">+</span> <span class="special">(</span><span class="identifier">r</span> <span class="special">-</span> <span class="identifier">sigma</span> <span class="special">*</span> <span class="identifier">sigma</span> <span class="special">/</span> <span class="number">2</span><span class="special">)</span> <span class="special">*</span> <span class="identifier">tau</span><span class="special">)</span> <span class="special">/</span> <span class="special">(</span><span class="identifier">sigma</span> <span class="special">*</span> <span class="identifier">sqrt</span><span class="special">(</span><span class="identifier">tau</span><span class="special">));</span>
+  <span class="keyword">switch</span> <span class="special">(</span><span class="identifier">cp</span><span class="special">)</span> <span class="special">{</span>
+    <span class="keyword">case</span> <span class="identifier">CP</span><span class="special">::</span><span class="identifier">call</span><span class="special">:</span>
+      <span class="keyword">return</span> <span class="identifier">S</span> <span class="special">*</span> <span class="identifier">Phi</span><span class="special">(</span><span class="identifier">d1</span><span class="special">)</span> <span class="special">-</span> <span class="identifier">exp</span><span class="special">(-</span><span class="identifier">r</span> <span class="special">*</span> <span class="identifier">tau</span><span class="special">)</span> <span class="special">*</span> <span class="identifier">K</span> <span class="special">*</span> <span class="identifier">Phi</span><span class="special">(</span><span class="identifier">d2</span><span class="special">);</span>
+    <span class="keyword">case</span> <span class="identifier">CP</span><span class="special">::</span><span class="identifier">put</span><span class="special">:</span>
+      <span class="keyword">return</span> <span class="identifier">exp</span><span class="special">(-</span><span class="identifier">r</span> <span class="special">*</span> <span class="identifier">tau</span><span class="special">)</span> <span class="special">*</span> <span class="identifier">K</span> <span class="special">*</span> <span class="identifier">Phi</span><span class="special">(-</span><span class="identifier">d2</span><span class="special">)</span> <span class="special">-</span> <span class="identifier">S</span> <span class="special">*</span> <span class="identifier">Phi</span><span class="special">(-</span><span class="identifier">d1</span><span class="special">);</span>
+  <span class="special">}</span>
+<span class="special">}</span>
+
+<span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span> <span class="special">{</span>
+  <span class="keyword">double</span> <span class="keyword">const</span> <span class="identifier">K</span> <span class="special">=</span> <span class="number">100.0</span><span class="special">;</span>                    <span class="comment">// Strike price.</span>
+  <span class="keyword">auto</span> <span class="keyword">const</span> <span class="identifier">S</span> <span class="special">=</span> <span class="identifier">make_fvar</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">,</span> <span class="number">2</span><span class="special">&gt;(</span><span class="number">105</span><span class="special">);</span>  <span class="comment">// Stock price.</span>
+  <span class="keyword">double</span> <span class="keyword">const</span> <span class="identifier">sigma</span> <span class="special">=</span> <span class="number">5</span><span class="special">;</span>                    <span class="comment">// Volatility.</span>
+  <span class="keyword">double</span> <span class="keyword">const</span> <span class="identifier">tau</span> <span class="special">=</span> <span class="number">30.0</span> <span class="special">/</span> <span class="number">365</span><span class="special">;</span>             <span class="comment">// Time to expiration in years. (30 days).</span>
+  <span class="keyword">double</span> <span class="keyword">const</span> <span class="identifier">r</span> <span class="special">=</span> <span class="number">1.25</span> <span class="special">/</span> <span class="number">100</span><span class="special">;</span>               <span class="comment">// Interest rate.</span>
+  <span class="keyword">auto</span> <span class="keyword">const</span> <span class="identifier">call_price</span> <span class="special">=</span> <span class="identifier">black_scholes_option_price</span><span class="special">(</span><span class="identifier">CP</span><span class="special">::</span><span class="identifier">call</span><span class="special">,</span> <span class="identifier">K</span><span class="special">,</span> <span class="identifier">S</span><span class="special">,</span> <span class="identifier">sigma</span><span class="special">,</span> <span class="identifier">tau</span><span class="special">,</span> <span class="identifier">r</span><span class="special">);</span>
+  <span class="keyword">auto</span> <span class="keyword">const</span> <span class="identifier">put_price</span> <span class="special">=</span> <span class="identifier">black_scholes_option_price</span><span class="special">(</span><span class="identifier">CP</span><span class="special">::</span><span class="identifier">put</span><span class="special">,</span> <span class="identifier">K</span><span class="special">,</span> <span class="identifier">S</span><span class="special">,</span> <span class="identifier">sigma</span><span class="special">,</span> <span class="identifier">tau</span><span class="special">,</span> <span class="identifier">r</span><span class="special">);</span>
+
+  <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"black-scholes call price = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">call_price</span><span class="special">.</span><span class="identifier">derivative</span><span class="special">(</span><span class="number">0</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="char">'\n'</span>
+            <span class="special">&lt;&lt;</span> <span class="string">"black-scholes put  price = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">put_price</span><span class="special">.</span><span class="identifier">derivative</span><span class="special">(</span><span class="number">0</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="char">'\n'</span>
+            <span class="special">&lt;&lt;</span> <span class="string">"call delta = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">call_price</span><span class="special">.</span><span class="identifier">derivative</span><span class="special">(</span><span class="number">1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="char">'\n'</span>
+            <span class="special">&lt;&lt;</span> <span class="string">"put  delta = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">put_price</span><span class="special">.</span><span class="identifier">derivative</span><span class="special">(</span><span class="number">1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="char">'\n'</span>
+            <span class="special">&lt;&lt;</span> <span class="string">"call gamma = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">call_price</span><span class="special">.</span><span class="identifier">derivative</span><span class="special">(</span><span class="number">2</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="char">'\n'</span>
+            <span class="special">&lt;&lt;</span> <span class="string">"put  gamma = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">put_price</span><span class="special">.</span><span class="identifier">derivative</span><span class="special">(</span><span class="number">2</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="char">'\n'</span><span class="special">;</span>
+  <span class="keyword">return</span> <span class="number">0</span><span class="special">;</span>
+<span class="special">}</span>
+<span class="comment">/*
+Output:
+black-scholes call price = 56.5136
+black-scholes put  price = 51.4109
+call delta = 0.773818
+put  delta = -0.226182
+call gamma = 0.00199852
+put  gamma = 0.00199852
+*/</span>
+</pre>
+<h2>
+<a name="math_toolkit.autodiff.h9"></a>
+      <span class="phrase"><a name="math_toolkit.autodiff.advantages_of_automatic_differen"></a></span><a class="link" href="autodiff.html#math_toolkit.autodiff.advantages_of_automatic_differen">Advantages
+      of Automatic Differentiation</a>
+    </h2>
+<p>
+      The above examples illustrate some of the advantages of using autodiff:
+    </p>
+<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
+<li class="listitem">
+          Elimination of code redundancy. The existence of <span class="emphasis"><em>N</em></span>
+          separate functions to calculate derivatives is a form of code redundancy,
+          with all the liabilities that come with it:
+          <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: circle; ">
+<li class="listitem">
+                Changes to one function require <span class="emphasis"><em>N</em></span> additional
+                changes to other functions. In the 3rd example above, consider how
+                much larger and inter-dependent the above code base would be if a
+                separate function were written for <a href="https://en.wikipedia.org/wiki/Greeks_(finance)#Formulas_for_European_option_Greeks" target="_top">each
+                Greek</a> value.
+              </li>
+<li class="listitem">
+                Dependencies upon a derivative function for a different purpose will
+                break when changes are made to the original function. What doesn't
+                need to exist cannot break.
+              </li>
+<li class="listitem">
+                Code bloat, reducing conceptual integrity. Control over the evolution
+                of code is easier/safer when the code base is smaller and able to
+                be intuitively grasped.
+              </li>
+</ul></div>
+        </li>
+<li class="listitem">
+          Accuracy of derivatives over finite difference methods. Single-iteration
+          finite difference methods always include a <span class="emphasis"><em>&#916;x</em></span>
+          free variable that must be carefully chosen for each application. If <span class="emphasis"><em>&#916;x</em></span>
+          is too small, then numerical errors become large. If <span class="emphasis"><em>&#916;x</em></span>
+          is too large, then mathematical errors become large. With autodiff, there
+          are no free variables to set and the accuracy of the answer is generally
+          superior to finite difference methods even with the best choice of <span class="emphasis"><em>&#916;x</em></span>.
+        </li>
+</ul></div>
+<h2>
+<a name="math_toolkit.autodiff.h10"></a>
+      <span class="phrase"><a name="math_toolkit.autodiff.manual"></a></span><a class="link" href="autodiff.html#math_toolkit.autodiff.manual">Manual</a>
+    </h2>
+<p>
+      Additional details are in the <a href="../../differentiation/autodiff.pdf" target="_top">autodiff
+      manual</a>.
+    </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
+      Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="diff.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../quadrature.html"><img src="../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="diff0.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>
diff --git a/libs/math/doc/html/math_toolkit/bad_guess.html b/libs/math/doc/html/math_toolkit/bad_guess.html
index 043561878b..63f5cb7efd 100644
--- a/libs/math/doc/html/math_toolkit/bad_guess.html
+++ b/libs/math/doc/html/math_toolkit/bad_guess.html
@@ -4,7 +4,7 @@
 <title>The Effect of a Poor Initial Guess</title>
 <link rel="stylesheet" href="../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../root_finding.html" title="Chapter&#160;9.&#160;Root Finding &amp; Minimization Algorithms">
 <link rel="prev" href="root_finding_examples/elliptic_eg.html" title="A More complex example - Inverting the Elliptic Integrals">
 <link rel="next" href="bad_roots.html" title="Examples Where Root Finding Goes Wrong">
@@ -759,11 +759,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/bad_roots.html b/libs/math/doc/html/math_toolkit/bad_roots.html
index 43f113e812..e11796c3bc 100644
--- a/libs/math/doc/html/math_toolkit/bad_roots.html
+++ b/libs/math/doc/html/math_toolkit/bad_roots.html
@@ -4,7 +4,7 @@
 <title>Examples Where Root Finding Goes Wrong</title>
 <link rel="stylesheet" href="../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../root_finding.html" title="Chapter&#160;9.&#160;Root Finding &amp; Minimization Algorithms">
 <link rel="prev" href="bad_guess.html" title="The Effect of a Poor Initial Guess">
 <link rel="next" href="brent_minima.html" title="Locating Function Minima using Brent's algorithm">
@@ -110,11 +110,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/barycentric.html b/libs/math/doc/html/math_toolkit/barycentric.html
index b0fc5d210c..340d22808a 100644
--- a/libs/math/doc/html/math_toolkit/barycentric.html
+++ b/libs/math/doc/html/math_toolkit/barycentric.html
@@ -4,10 +4,10 @@
 <title>Barycentric Rational Interpolation</title>
 <link rel="stylesheet" href="../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../interpolation.html" title="Chapter&#160;11.&#160;Interpolation">
-<link rel="prev" href="cubic_b.html" title="Cubic B-spline interpolation">
-<link rel="next" href="catmull_rom.html" title="Catmull-Rom Splines">
+<link rel="prev" href="whittaker_shannon.html" title="Whittaker-Shannon interpolation">
+<link rel="next" href="vector_barycentric.html" title="Vector-valued Barycentric Rational Interpolation">
 </head>
 <body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
 <table cellpadding="2" width="100%"><tr>
@@ -20,7 +20,7 @@
 </tr></table>
 <hr>
 <div class="spirit-nav">
-<a accesskey="p" href="cubic_b.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../interpolation.html"><img src="../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="catmull_rom.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a>
+<a accesskey="p" href="whittaker_shannon.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../interpolation.html"><img src="../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="vector_barycentric.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a>
 </div>
 <div class="section">
 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
@@ -268,11 +268,11 @@ Root was found in 10 iterations.
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
@@ -280,7 +280,7 @@ Root was found in 10 iterations.
 </tr></table>
 <hr>
 <div class="spirit-nav">
-<a accesskey="p" href="cubic_b.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../interpolation.html"><img src="../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="catmull_rom.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a>
+<a accesskey="p" href="whittaker_shannon.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../interpolation.html"><img src="../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="vector_barycentric.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a>
 </div>
 </body>
 </html>
diff --git a/libs/math/doc/html/math_toolkit/bessel.html b/libs/math/doc/html/math_toolkit/bessel.html
index 3b6da5231b..c47f20a607 100644
--- a/libs/math/doc/html/math_toolkit/bessel.html
+++ b/libs/math/doc/html/math_toolkit/bessel.html
@@ -4,7 +4,7 @@
 <title>Bessel Functions</title>
 <link rel="stylesheet" href="../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../special.html" title="Chapter&#160;7.&#160;Special Functions">
 <link rel="prev" href="sf_poly/sph_harm.html" title="Spherical Harmonics">
 <link rel="next" href="bessel/bessel_over.html" title="Bessel Function Overview">
@@ -42,11 +42,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/bessel/bessel_derivatives.html b/libs/math/doc/html/math_toolkit/bessel/bessel_derivatives.html
index 03296a0576..5ac83aa5fc 100644
--- a/libs/math/doc/html/math_toolkit/bessel/bessel_derivatives.html
+++ b/libs/math/doc/html/math_toolkit/bessel/bessel_derivatives.html
@@ -4,7 +4,7 @@
 <title>Derivatives of the Bessel Functions</title>
 <link rel="stylesheet" href="../../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../bessel.html" title="Bessel Functions">
 <link rel="prev" href="sph_bessel.html" title="Spherical Bessel Functions of the First and Second Kinds">
 <link rel="next" href="../hankel.html" title="Hankel Functions">
@@ -1435,11 +1435,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/bessel/bessel_first.html b/libs/math/doc/html/math_toolkit/bessel/bessel_first.html
index be719dbd11..39c8f12e8f 100644
--- a/libs/math/doc/html/math_toolkit/bessel/bessel_first.html
+++ b/libs/math/doc/html/math_toolkit/bessel/bessel_first.html
@@ -4,7 +4,7 @@
 <title>Bessel Functions of the First and Second Kinds</title>
 <link rel="stylesheet" href="../../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../bessel.html" title="Bessel Functions">
 <link rel="prev" href="bessel_over.html" title="Bessel Function Overview">
 <link rel="next" href="bessel_root.html" title="Finding Zeros of Bessel Functions of the First and Second Kinds">
@@ -1348,11 +1348,11 @@ are also computed by recursions (involving gamma functions), but
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/bessel/bessel_over.html b/libs/math/doc/html/math_toolkit/bessel/bessel_over.html
index 4700252570..1676408e75 100644
--- a/libs/math/doc/html/math_toolkit/bessel/bessel_over.html
+++ b/libs/math/doc/html/math_toolkit/bessel/bessel_over.html
@@ -4,7 +4,7 @@
 <title>Bessel Function Overview</title>
 <link rel="stylesheet" href="../../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../bessel.html" title="Bessel Functions">
 <link rel="prev" href="../bessel.html" title="Bessel Functions">
 <link rel="next" href="bessel_first.html" title="Bessel Functions of the First and Second Kinds">
@@ -195,11 +195,11 @@ is also known as the spherical
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/bessel/bessel_root.html b/libs/math/doc/html/math_toolkit/bessel/bessel_root.html
index d3af6227eb..b1848a627e 100644
--- a/libs/math/doc/html/math_toolkit/bessel/bessel_root.html
+++ b/libs/math/doc/html/math_toolkit/bessel/bessel_root.html
@@ -4,7 +4,7 @@
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 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../bessel.html" title="Bessel Functions">
 <link rel="prev" href="bessel_first.html" title="Bessel Functions of the First and Second Kinds">
 <link rel="next" href="mbessel.html" title="Modified Bessel Functions of the First and Second Kinds">
@@ -747,11 +747,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/bessel/mbessel.html b/libs/math/doc/html/math_toolkit/bessel/mbessel.html
index 43a5d407f0..8b81c72612 100644
--- a/libs/math/doc/html/math_toolkit/bessel/mbessel.html
+++ b/libs/math/doc/html/math_toolkit/bessel/mbessel.html
@@ -4,7 +4,7 @@
 <title>Modified Bessel Functions of the First and Second Kinds</title>
 <link rel="stylesheet" href="../../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../bessel.html" title="Bessel Functions">
 <link rel="prev" href="bessel_root.html" title="Finding Zeros of Bessel Functions of the First and Second Kinds">
 <link rel="next" href="sph_bessel.html" title="Spherical Bessel Functions of the First and Second Kinds">
@@ -1131,11 +1131,11 @@ are also computed by recursions (involving gamma functions), but
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/bessel/sph_bessel.html b/libs/math/doc/html/math_toolkit/bessel/sph_bessel.html
index 34dbab80a0..f1eb72e915 100644
--- a/libs/math/doc/html/math_toolkit/bessel/sph_bessel.html
+++ b/libs/math/doc/html/math_toolkit/bessel/sph_bessel.html
@@ -4,7 +4,7 @@
 <title>Spherical Bessel Functions of the First and Second Kinds</title>
 <link rel="stylesheet" href="../../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../bessel.html" title="Bessel Functions">
 <link rel="prev" href="mbessel.html" title="Modified Bessel Functions of the First and Second Kinds">
 <link rel="next" href="bessel_derivatives.html" title="Derivatives of the Bessel Functions">
@@ -269,11 +269,11 @@ for small <span class="emphasis"><em>x</em></span>:
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/bivariate_statistics.html b/libs/math/doc/html/math_toolkit/bivariate_statistics.html
index bfb5a9ce03..a202d146f5 100644
--- a/libs/math/doc/html/math_toolkit/bivariate_statistics.html
+++ b/libs/math/doc/html/math_toolkit/bivariate_statistics.html
@@ -4,7 +4,7 @@
 <title>Bivariate Statistics</title>
 <link rel="stylesheet" href="../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../vector_functionals.html" title="Chapter&#160;6.&#160;Vector Functionals">
 <link rel="prev" href="univariate_statistics.html" title="Univariate Statistics">
 <link rel="next" href="signal_statistics.html" title="Signal Statistics">
@@ -115,11 +115,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/brent_minima.html b/libs/math/doc/html/math_toolkit/brent_minima.html
index c213a5ed11..630d944369 100644
--- a/libs/math/doc/html/math_toolkit/brent_minima.html
+++ b/libs/math/doc/html/math_toolkit/brent_minima.html
@@ -4,7 +4,7 @@
 <title>Locating Function Minima using Brent's algorithm</title>
 <link rel="stylesheet" href="../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../root_finding.html" title="Chapter&#160;9.&#160;Root Finding &amp; Minimization Algorithms">
 <link rel="prev" href="bad_roots.html" title="Examples Where Root Finding Goes Wrong">
 <link rel="next" href="root_comparison.html" title="Comparison of Root Finding Algorithms">
@@ -650,11 +650,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/building.html b/libs/math/doc/html/math_toolkit/building.html
index f856ffe9a1..c38bd2b69c 100644
--- a/libs/math/doc/html/math_toolkit/building.html
+++ b/libs/math/doc/html/math_toolkit/building.html
@@ -4,7 +4,7 @@
 <title>If and How to Build a Boost.Math Library, and its Examples and Tests</title>
 <link rel="stylesheet" href="../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../overview.html" title="Chapter&#160;1.&#160;Overview">
 <link rel="prev" href="perf_over1.html" title="Performance">
 <link rel="next" href="history1.html" title="History and What's New">
@@ -147,11 +147,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/c99.html b/libs/math/doc/html/math_toolkit/c99.html
index 5a2a411616..b12264dc7e 100644
--- a/libs/math/doc/html/math_toolkit/c99.html
+++ b/libs/math/doc/html/math_toolkit/c99.html
@@ -4,7 +4,7 @@
 <title>C99 C Functions</title>
 <link rel="stylesheet" href="../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../index.html" title="Math Toolkit 2.10.0">
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@@ -460,11 +460,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/cardinal_quadratic_b.html b/libs/math/doc/html/math_toolkit/cardinal_quadratic_b.html
new file mode 100644
index 0000000000..49eda64e23
--- /dev/null
+++ b/libs/math/doc/html/math_toolkit/cardinal_quadratic_b.html
@@ -0,0 +1,103 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
+<title>Cardinal Quadratic B-spline interpolation</title>
+<link rel="stylesheet" href="../math.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.10.0">
+<link rel="up" href="../interpolation.html" title="Chapter&#160;11.&#160;Interpolation">
+<link rel="prev" href="cubic_b.html" title="Cubic B-spline interpolation">
+<link rel="next" href="whittaker_shannon.html" title="Whittaker-Shannon interpolation">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
+<td align="center"><a href="../../../../../index.html">Home</a></td>
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+<td align="center"><a href="../../../../../more/index.htm">More</a></td>
+</tr></table>
+<hr>
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+<a accesskey="p" href="cubic_b.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../interpolation.html"><img src="../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="whittaker_shannon.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a>
+</div>
+<div class="section">
+<div class="titlepage"><div><div><h2 class="title" style="clear: both">
+<a name="math_toolkit.cardinal_quadratic_b"></a><a class="link" href="cardinal_quadratic_b.html" title="Cardinal Quadratic B-spline interpolation">Cardinal Quadratic B-spline
+    interpolation</a>
+</h2></div></div></div>
+<h4>
+<a name="math_toolkit.cardinal_quadratic_b.h0"></a>
+      <span class="phrase"><a name="math_toolkit.cardinal_quadratic_b.synopsis"></a></span><a class="link" href="cardinal_quadratic_b.html#math_toolkit.cardinal_quadratic_b.synopsis">Synopsis</a>
+    </h4>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">interpolators</span><span class="special">/</span><span class="identifier">cardinal_quadratic_b_spline</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+</pre>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">interpolators</span> <span class="special">{</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Real</span><span class="special">&gt;</span>
+<span class="keyword">class</span> <span class="identifier">cardinal_quadratic_b_spline</span>
+<span class="special">{</span>
+<span class="keyword">public</span><span class="special">:</span>
+    <span class="comment">// If you don't know the value of the derivative at the endpoints, leave them as nans and the routine will estimate them.</span>
+    <span class="comment">// y[0] = y(a), y[n - 1] = y(b), step_size = (b - a)/(n -1).</span>
+    <span class="identifier">cardinal_quadratic_b_spline</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">Real</span><span class="special">*</span> <span class="keyword">const</span> <span class="identifier">y</span><span class="special">,</span>
+                                <span class="identifier">size_t</span> <span class="identifier">n</span><span class="special">,</span>
+                                <span class="identifier">Real</span> <span class="identifier">t0</span> <span class="comment">/* initial time, left endpoint */</span><span class="special">,</span>
+                                <span class="identifier">Real</span> <span class="identifier">h</span>  <span class="comment">/*spacing, stepsize*/</span><span class="special">,</span>
+                                <span class="identifier">Real</span> <span class="identifier">left_endpoint_derivative</span> <span class="special">=</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">Real</span><span class="special">&gt;::</span><span class="identifier">quiet_NaN</span><span class="special">(),</span>
+                                <span class="identifier">Real</span> <span class="identifier">right_endpoint_derivative</span> <span class="special">=</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">Real</span><span class="special">&gt;::</span><span class="identifier">quiet_NaN</span><span class="special">())</span>
+
+    <span class="identifier">cardinal_quadratic_b_spline</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span><span class="special">&lt;</span><span class="identifier">Real</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">y</span><span class="special">,</span>
+                                <span class="identifier">Real</span> <span class="identifier">t0</span> <span class="comment">/* initial time, left endpoint */</span><span class="special">,</span>
+                                <span class="identifier">Real</span> <span class="identifier">h</span>  <span class="comment">/*spacing, stepsize*/</span><span class="special">,</span>
+                                <span class="identifier">Real</span> <span class="identifier">left_endpoint_derivative</span> <span class="special">=</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">Real</span><span class="special">&gt;::</span><span class="identifier">quiet_NaN</span><span class="special">(),</span>
+                                <span class="identifier">Real</span> <span class="identifier">right_endpoint_derivative</span> <span class="special">=</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">Real</span><span class="special">&gt;::</span><span class="identifier">quiet_NaN</span><span class="special">())</span>
+
+    <span class="identifier">Real</span> <span class="keyword">operator</span><span class="special">()(</span><span class="identifier">Real</span> <span class="identifier">t</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span>
+
+    <span class="identifier">Real</span> <span class="identifier">prime</span><span class="special">(</span><span class="identifier">Real</span> <span class="identifier">t</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span>
+<span class="special">};</span>
+<span class="special">}}}</span>
+</pre>
+<h4>
+<a name="math_toolkit.cardinal_quadratic_b.h1"></a>
+      <span class="phrase"><a name="math_toolkit.cardinal_quadratic_b.cardinal_quadratic_b_spline_inte"></a></span><a class="link" href="cardinal_quadratic_b.html#math_toolkit.cardinal_quadratic_b.cardinal_quadratic_b_spline_inte">Cardinal
+      Quadratic B-Spline Interpolation</a>
+    </h4>
+<p>
+      The cardinal quadratic B-spline interpolator is very nearly the same as the
+      cubic B-spline interpolator, with the modification that the basis functions
+      are constructed by convolving a box function with itself twice, rather than
+      three times as is done with the cubic B-spline.
+    </p>
+<p>
+      Since the basis functions are less smooth than the cubic B-spline, you will
+      nearly always wish to use the cubic B-spline interpolator rather than this.
+      However, this interpolator is occasionally useful for approximating functions
+      of reduced smoothness, as hence finds a uses internally in the Boost.Math library.
+    </p>
+<p>
+      It is reasonable to test this interpolator against the cubic b-spline interpolator
+      when you are approximating functions which are two or three times continuously
+      differentiable, but not three or four times differentiable.
+    </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
+      Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="cubic_b.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../interpolation.html"><img src="../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="whittaker_shannon.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>
diff --git a/libs/math/doc/html/math_toolkit/catmull_rom.html b/libs/math/doc/html/math_toolkit/catmull_rom.html
index 57f21fe67b..26cd21d83c 100644
--- a/libs/math/doc/html/math_toolkit/catmull_rom.html
+++ b/libs/math/doc/html/math_toolkit/catmull_rom.html
@@ -4,9 +4,9 @@
 <title>Catmull-Rom Splines</title>
 <link rel="stylesheet" href="../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../interpolation.html" title="Chapter&#160;11.&#160;Interpolation">
-<link rel="prev" href="barycentric.html" title="Barycentric Rational Interpolation">
+<link rel="prev" href="vector_barycentric.html" title="Vector-valued Barycentric Rational Interpolation">
 <link rel="next" href="../quadrature.html" title="Chapter&#160;12.&#160;Quadrature and Differentiation">
 </head>
 <body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
@@ -20,7 +20,7 @@
 </tr></table>
 <hr>
 <div class="spirit-nav">
-<a accesskey="p" href="barycentric.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../interpolation.html"><img src="../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="../quadrature.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a>
+<a accesskey="p" href="vector_barycentric.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../interpolation.html"><img src="../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="../quadrature.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a>
 </div>
 <div class="section">
 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
@@ -34,12 +34,12 @@
 
 <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
 
-    <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Point</span><span class="special">&gt;</span>
+    <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Point</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">RandomAccessContainer</span> <span class="special">=</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span><span class="special">&lt;</span><span class="identifier">Point</span><span class="special">&gt;</span> <span class="special">&gt;</span>
     <span class="keyword">class</span> <span class="identifier">catmull_rom</span>
     <span class="special">{</span>
     <span class="keyword">public</span><span class="special">:</span>
 
-        <span class="identifier">catmull_rom</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span><span class="special">&lt;</span><span class="identifier">Point</span><span class="special">&gt;&amp;&amp;</span> <span class="identifier">points</span><span class="special">,</span> <span class="keyword">bool</span> <span class="identifier">closed</span> <span class="special">=</span> <span class="keyword">false</span><span class="special">,</span> <span class="identifier">Real</span> <span class="identifier">alpha</span> <span class="special">=</span> <span class="special">(</span><span class="identifier">Real</span><span class="special">)</span> <span class="number">1</span><span class="special">/</span> <span class="special">(</span><span class="identifier">Real</span><span class="special">)</span> <span class="number">2</span><span class="special">)</span>
+        <span class="identifier">catmull_rom</span><span class="special">(</span><span class="identifier">RandomAccessContainer</span><span class="special">&amp;&amp;</span> <span class="identifier">points</span><span class="special">,</span> <span class="keyword">bool</span> <span class="identifier">closed</span> <span class="special">=</span> <span class="keyword">false</span><span class="special">,</span> <span class="identifier">Real</span> <span class="identifier">alpha</span> <span class="special">=</span> <span class="special">(</span><span class="identifier">Real</span><span class="special">)</span> <span class="number">1</span><span class="special">/</span> <span class="special">(</span><span class="identifier">Real</span><span class="special">)</span> <span class="number">2</span><span class="special">)</span>
 
         <span class="identifier">catmull_rom</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">initializer_list</span><span class="special">&lt;</span><span class="identifier">Point</span><span class="special">&gt;</span> <span class="identifier">l</span><span class="special">,</span> <span class="keyword">bool</span> <span class="identifier">closed</span> <span class="special">=</span> <span class="keyword">false</span><span class="special">,</span> <span class="keyword">typename</span> <span class="identifier">Point</span><span class="special">::</span><span class="identifier">value_type</span> <span class="identifier">alpha</span> <span class="special">=</span> <span class="special">(</span><span class="keyword">typename</span> <span class="identifier">Point</span><span class="special">::</span><span class="identifier">value_type</span><span class="special">)</span> <span class="number">1</span><span class="special">/</span> <span class="special">(</span><span class="keyword">typename</span> <span class="identifier">Point</span><span class="special">::</span><span class="identifier">value_type</span><span class="special">)</span> <span class="number">2</span><span class="special">);</span>
 
@@ -300,6 +300,34 @@
     </p>
 <h4>
 <a name="math_toolkit.catmull_rom.h6"></a>
+      <span class="phrase"><a name="math_toolkit.catmull_rom.generic_containers"></a></span><a class="link" href="catmull_rom.html#math_toolkit.catmull_rom.generic_containers">Generic
+      Containers</a>
+    </h4>
+<p>
+      The <code class="computeroutput"><span class="identifier">Point</span></code> type may be stored
+      in a different container than <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span></code>.
+      For example, here is how to store the points in a Boost.uBLAS vector:
+    </p>
+<pre class="programlisting"><span class="identifier">mypoint3d</span><span class="special">&lt;</span><span class="identifier">Real</span><span class="special">&gt;</span> <span class="identifier">p0</span><span class="special">(</span><span class="number">0.1</span><span class="special">,</span> <span class="number">0.2</span><span class="special">,</span> <span class="number">0.3</span><span class="special">);</span>
+<span class="identifier">mypoint3d</span><span class="special">&lt;</span><span class="identifier">Real</span><span class="special">&gt;</span> <span class="identifier">p1</span><span class="special">(</span><span class="number">0.2</span><span class="special">,</span> <span class="number">0.3</span><span class="special">,</span> <span class="number">0.4</span><span class="special">);</span>
+<span class="identifier">mypoint3d</span><span class="special">&lt;</span><span class="identifier">Real</span><span class="special">&gt;</span> <span class="identifier">p2</span><span class="special">(</span><span class="number">0.3</span><span class="special">,</span> <span class="number">0.4</span><span class="special">,</span> <span class="number">0.5</span><span class="special">);</span>
+<span class="identifier">mypoint3d</span><span class="special">&lt;</span><span class="identifier">Real</span><span class="special">&gt;</span> <span class="identifier">p3</span><span class="special">(</span><span class="number">0.4</span><span class="special">,</span> <span class="number">0.5</span><span class="special">,</span> <span class="number">0.6</span><span class="special">);</span>
+<span class="identifier">mypoint3d</span><span class="special">&lt;</span><span class="identifier">Real</span><span class="special">&gt;</span> <span class="identifier">p4</span><span class="special">(</span><span class="number">0.5</span><span class="special">,</span> <span class="number">0.6</span><span class="special">,</span> <span class="number">0.7</span><span class="special">);</span>
+<span class="identifier">mypoint3d</span><span class="special">&lt;</span><span class="identifier">Real</span><span class="special">&gt;</span> <span class="identifier">p5</span><span class="special">(</span><span class="number">0.6</span><span class="special">,</span> <span class="number">0.7</span><span class="special">,</span> <span class="number">0.8</span><span class="special">);</span>
+
+<span class="identifier">boost</span><span class="special">::</span><span class="identifier">numeric</span><span class="special">::</span><span class="identifier">ublas</span><span class="special">::</span><span class="identifier">vector</span><span class="special">&lt;</span><span class="identifier">mypoint3d</span><span class="special">&lt;</span><span class="identifier">Real</span><span class="special">&gt;&gt;</span> <span class="identifier">u</span><span class="special">(</span><span class="number">6</span><span class="special">);</span>
+<span class="identifier">u</span><span class="special">[</span><span class="number">0</span><span class="special">]</span> <span class="special">=</span> <span class="identifier">p0</span><span class="special">;</span>
+<span class="identifier">u</span><span class="special">[</span><span class="number">1</span><span class="special">]</span> <span class="special">=</span> <span class="identifier">p1</span><span class="special">;</span>
+<span class="identifier">u</span><span class="special">[</span><span class="number">2</span><span class="special">]</span> <span class="special">=</span> <span class="identifier">p2</span><span class="special">;</span>
+<span class="identifier">u</span><span class="special">[</span><span class="number">3</span><span class="special">]</span> <span class="special">=</span> <span class="identifier">p3</span><span class="special">;</span>
+<span class="identifier">u</span><span class="special">[</span><span class="number">4</span><span class="special">]</span> <span class="special">=</span> <span class="identifier">p4</span><span class="special">;</span>
+<span class="identifier">u</span><span class="special">[</span><span class="number">5</span><span class="special">]</span> <span class="special">=</span> <span class="identifier">p5</span><span class="special">;</span>
+
+<span class="comment">// Tests initializer_list:</span>
+<span class="identifier">catmull_rom</span><span class="special">&lt;</span><span class="identifier">mypoint3d</span><span class="special">&lt;</span><span class="identifier">Real</span><span class="special">&gt;,</span> <span class="keyword">decltype</span><span class="special">(</span><span class="identifier">u</span><span class="special">)&gt;</span> <span class="identifier">cat</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">move</span><span class="special">(</span><span class="identifier">u</span><span class="special">));</span>
+</pre>
+<h4>
+<a name="math_toolkit.catmull_rom.h7"></a>
       <span class="phrase"><a name="math_toolkit.catmull_rom.references"></a></span><a class="link" href="catmull_rom.html#math_toolkit.catmull_rom.references">References</a>
     </h4>
 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
@@ -317,11 +345,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
@@ -329,7 +357,7 @@
 </tr></table>
 <hr>
 <div class="spirit-nav">
-<a accesskey="p" href="barycentric.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../interpolation.html"><img src="../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="../quadrature.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a>
+<a accesskey="p" href="vector_barycentric.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../interpolation.html"><img src="../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="../quadrature.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a>
 </div>
 </body>
 </html>
diff --git a/libs/math/doc/html/math_toolkit/comp_compilers.html b/libs/math/doc/html/math_toolkit/comp_compilers.html
index fe7392da21..d844c1e461 100644
--- a/libs/math/doc/html/math_toolkit/comp_compilers.html
+++ b/libs/math/doc/html/math_toolkit/comp_compilers.html
@@ -4,7 +4,7 @@
 <title>Comparing Different Compilers</title>
 <link rel="stylesheet" href="../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../perf.html" title="Chapter&#160;20.&#160;Performance">
 <link rel="prev" href="tuning.html" title="Performance Tuning Macros">
 <link rel="next" href="comparisons.html" title="Comparisons to Other Open Source Libraries">
@@ -2395,11 +2395,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/comparisons.html b/libs/math/doc/html/math_toolkit/comparisons.html
index a05baf02d8..879cf6063f 100644
--- a/libs/math/doc/html/math_toolkit/comparisons.html
+++ b/libs/math/doc/html/math_toolkit/comparisons.html
@@ -4,7 +4,7 @@
 <title>Comparisons to Other Open Source Libraries</title>
 <link rel="stylesheet" href="../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../perf.html" title="Chapter&#160;20.&#160;Performance">
 <link rel="prev" href="comp_compilers.html" title="Comparing Different Compilers">
 <link rel="next" href="perf_test_app.html" title="The Performance Test Applications">
@@ -253,11 +253,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/compilers_overview.html b/libs/math/doc/html/math_toolkit/compilers_overview.html
index 3d9e51f1ff..cd03af3488 100644
--- a/libs/math/doc/html/math_toolkit/compilers_overview.html
+++ b/libs/math/doc/html/math_toolkit/compilers_overview.html
@@ -4,7 +4,7 @@
 <title>Compilers</title>
 <link rel="stylesheet" href="../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../overview.html" title="Chapter&#160;1.&#160;Overview">
 <link rel="prev" href="error_handling.html" title="Error Handling">
 <link rel="next" href="config_macros.html" title="Configuration Macros">
@@ -666,11 +666,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/complex_history.html b/libs/math/doc/html/math_toolkit/complex_history.html
index 2330bd87a2..d47c451648 100644
--- a/libs/math/doc/html/math_toolkit/complex_history.html
+++ b/libs/math/doc/html/math_toolkit/complex_history.html
@@ -4,7 +4,7 @@
 <title>History</title>
 <link rel="stylesheet" href="../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../inverse_complex.html" title="Chapter&#160;13.&#160;Complex Number Functions">
 <link rel="prev" href="atanh.html" title="atanh">
 <link rel="next" href="../quaternions.html" title="Chapter&#160;14.&#160;Quaternions">
@@ -37,11 +37,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/complex_implementation.html b/libs/math/doc/html/math_toolkit/complex_implementation.html
index 2ab40c74de..5373fdf79c 100644
--- a/libs/math/doc/html/math_toolkit/complex_implementation.html
+++ b/libs/math/doc/html/math_toolkit/complex_implementation.html
@@ -4,7 +4,7 @@
 <title>Implementation and Accuracy</title>
 <link rel="stylesheet" href="../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../inverse_complex.html" title="Chapter&#160;13.&#160;Complex Number Functions">
 <link rel="prev" href="../inverse_complex.html" title="Chapter&#160;13.&#160;Complex Number Functions">
 <link rel="next" href="asin.html" title="asin">
@@ -46,11 +46,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
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-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
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+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
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+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
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-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
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 <td align="left"></td>
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+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
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-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
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 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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-      <a class="indexterm" name="idm45603925695888"></a>
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 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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+<link rel="next" href="cardinal_quadratic_b.html" title="Cardinal Quadratic B-spline interpolation">
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@@ -303,11 +303,11 @@ Found in 3 iterations
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 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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@@ -315,7 +315,7 @@ Found in 3 iterations
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+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
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+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
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+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
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-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
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+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
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+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
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-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
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+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
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+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
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+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
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+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
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+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
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+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
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+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
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+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
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+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
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+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
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 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../dists.html" title="Distributions">
 <link rel="prev" href="bernoulli_dist.html" title="Bernoulli Distribution">
 <link rel="next" href="binomial_dist.html" title="Binomial Distribution">
@@ -605,11 +605,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/dist_ref/dists/binomial_dist.html b/libs/math/doc/html/math_toolkit/dist_ref/dists/binomial_dist.html
index ffbfe5b6c8..763023f6a4 100644
--- a/libs/math/doc/html/math_toolkit/dist_ref/dists/binomial_dist.html
+++ b/libs/math/doc/html/math_toolkit/dist_ref/dists/binomial_dist.html
@@ -4,7 +4,7 @@
 <title>Binomial Distribution</title>
 <link rel="stylesheet" href="../../../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../dists.html" title="Distributions">
 <link rel="prev" href="beta_dist.html" title="Beta Distribution">
 <link rel="next" href="cauchy_dist.html" title="Cauchy-Lorentz Distribution">
@@ -579,16 +579,13 @@
                 </td>
 <td>
                   <p>
-                    The <span class="bold"><strong>greatest</strong></span> number of successes
-                    that may be observed from n trials with success fraction p, at
-                    probability P. Note that the value returned is a real-number,
-                    and not an integer. Depending on the use case you may want to
-                    take either the floor or ceiling of the result. For example:
-                  </p>
-                  <p>
-                    <code class="computeroutput"><span class="identifier">quantile</span><span class="special">(</span><span class="identifier">binomial</span><span class="special">(</span><span class="identifier">n</span><span class="special">,</span>
-                    <span class="identifier">p</span><span class="special">),</span>
-                    <span class="identifier">P</span><span class="special">)</span></code>
+                    Given a binomial distribution with <span class="emphasis"><em>n</em></span> trials,
+                    success fraction <span class="emphasis"><em>p</em></span> and probability <span class="emphasis"><em>P</em></span>,
+                    finds the largest number of successes <span class="emphasis"><em>k</em></span>
+                    whose CDF is less than <span class="emphasis"><em>P</em></span>. It is strongly
+                    recommended that you read the tutorial <a class="link" href="../../pol_tutorial/understand_dis_quant.html" title="Understanding Quantiles of Discrete Distributions">Understanding
+                    Quantiles of Discrete Distributions</a> before using the quantile
+                    function.
                   </p>
                 </td>
 </tr>
@@ -601,16 +598,13 @@
                 </td>
 <td>
                   <p>
-                    The <span class="bold"><strong>smallest</strong></span> number of successes
-                    that may be observed from n trials with success fraction p, at
-                    probability P. Note that the value returned is a real-number,
-                    and not an integer. Depending on the use case you may want to
-                    take either the floor or ceiling of the result. For example:
-                  </p>
-                  <p>
-                    <code class="computeroutput"><span class="identifier">quantile</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">binomial</span><span class="special">(</span><span class="identifier">n</span><span class="special">,</span>
-                    <span class="identifier">p</span><span class="special">),</span>
-                    <span class="identifier">P</span><span class="special">))</span></code>
+                    Given a binomial distribution with <span class="emphasis"><em>n</em></span> trials,
+                    success fraction <span class="emphasis"><em>p</em></span> and probability <span class="emphasis"><em>Q</em></span>,
+                    finds the smallest number of successes <span class="emphasis"><em>k</em></span>
+                    whose CDF is greater than <span class="emphasis"><em>1-Q</em></span>. It is strongly
+                    recommended that you read the tutorial <a class="link" href="../../pol_tutorial/understand_dis_quant.html" title="Understanding Quantiles of Discrete Distributions">Understanding
+                    Quantiles of Discrete Distributions</a> before using the quantile
+                    function.
                   </p>
                 </td>
 </tr>
@@ -891,11 +885,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/dist_ref/dists/cauchy_dist.html b/libs/math/doc/html/math_toolkit/dist_ref/dists/cauchy_dist.html
index a84a5f0cc2..d21940f19a 100644
--- a/libs/math/doc/html/math_toolkit/dist_ref/dists/cauchy_dist.html
+++ b/libs/math/doc/html/math_toolkit/dist_ref/dists/cauchy_dist.html
@@ -4,7 +4,7 @@
 <title>Cauchy-Lorentz Distribution</title>
 <link rel="stylesheet" href="../../../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../dists.html" title="Distributions">
 <link rel="prev" href="binomial_dist.html" title="Binomial Distribution">
 <link rel="next" href="chi_squared_dist.html" title="Chi Squared Distribution">
@@ -288,11 +288,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/dist_ref/dists/chi_squared_dist.html b/libs/math/doc/html/math_toolkit/dist_ref/dists/chi_squared_dist.html
index 37936505e2..67037b37ad 100644
--- a/libs/math/doc/html/math_toolkit/dist_ref/dists/chi_squared_dist.html
+++ b/libs/math/doc/html/math_toolkit/dist_ref/dists/chi_squared_dist.html
@@ -4,7 +4,7 @@
 <title>Chi Squared Distribution</title>
 <link rel="stylesheet" href="../../../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../dists.html" title="Distributions">
 <link rel="prev" href="cauchy_dist.html" title="Cauchy-Lorentz Distribution">
 <link rel="next" href="exp_dist.html" title="Exponential Distribution">
@@ -394,11 +394,11 @@ independent, normally distributed random
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/dist_ref/dists/exp_dist.html b/libs/math/doc/html/math_toolkit/dist_ref/dists/exp_dist.html
index f1507721a2..16c47bba32 100644
--- a/libs/math/doc/html/math_toolkit/dist_ref/dists/exp_dist.html
+++ b/libs/math/doc/html/math_toolkit/dist_ref/dists/exp_dist.html
@@ -4,7 +4,7 @@
 <title>Exponential Distribution</title>
 <link rel="stylesheet" href="../../../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../dists.html" title="Distributions">
 <link rel="prev" href="chi_squared_dist.html" title="Chi Squared Distribution">
 <link rel="next" href="extreme_dist.html" title="Extreme Value Distribution">
@@ -311,11 +311,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/dist_ref/dists/extreme_dist.html b/libs/math/doc/html/math_toolkit/dist_ref/dists/extreme_dist.html
index f9f9a1b7e5..b1ccd4c3d9 100644
--- a/libs/math/doc/html/math_toolkit/dist_ref/dists/extreme_dist.html
+++ b/libs/math/doc/html/math_toolkit/dist_ref/dists/extreme_dist.html
@@ -4,7 +4,7 @@
 <title>Extreme Value Distribution</title>
 <link rel="stylesheet" href="../../../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../dists.html" title="Distributions">
 <link rel="prev" href="exp_dist.html" title="Exponential Distribution">
 <link rel="next" href="f_dist.html" title="F Distribution">
@@ -314,11 +314,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/dist_ref/dists/f_dist.html b/libs/math/doc/html/math_toolkit/dist_ref/dists/f_dist.html
index 610939cfaf..8a84ff19ca 100644
--- a/libs/math/doc/html/math_toolkit/dist_ref/dists/f_dist.html
+++ b/libs/math/doc/html/math_toolkit/dist_ref/dists/f_dist.html
@@ -4,7 +4,7 @@
 <title>F Distribution</title>
 <link rel="stylesheet" href="../../../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../dists.html" title="Distributions">
 <link rel="prev" href="extreme_dist.html" title="Extreme Value Distribution">
 <link rel="next" href="gamma_dist.html" title="Gamma (and Erlang) Distribution">
@@ -417,11 +417,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/dist_ref/dists/gamma_dist.html b/libs/math/doc/html/math_toolkit/dist_ref/dists/gamma_dist.html
index 226ca6f87e..253ba48e11 100644
--- a/libs/math/doc/html/math_toolkit/dist_ref/dists/gamma_dist.html
+++ b/libs/math/doc/html/math_toolkit/dist_ref/dists/gamma_dist.html
@@ -4,7 +4,7 @@
 <title>Gamma (and Erlang) Distribution</title>
 <link rel="stylesheet" href="../../../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../dists.html" title="Distributions">
 <link rel="prev" href="f_dist.html" title="F Distribution">
 <link rel="next" href="geometric_dist.html" title="Geometric Distribution">
@@ -347,11 +347,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/dist_ref/dists/geometric_dist.html b/libs/math/doc/html/math_toolkit/dist_ref/dists/geometric_dist.html
index 160e98569c..2269e025f0 100644
--- a/libs/math/doc/html/math_toolkit/dist_ref/dists/geometric_dist.html
+++ b/libs/math/doc/html/math_toolkit/dist_ref/dists/geometric_dist.html
@@ -4,7 +4,7 @@
 <title>Geometric Distribution</title>
 <link rel="stylesheet" href="../../../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../dists.html" title="Distributions">
 <link rel="prev" href="gamma_dist.html" title="Gamma (and Erlang) Distribution">
 <link rel="next" href="hyperexponential_dist.html" title="Hyperexponential Distribution">
@@ -824,11 +824,11 @@
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 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/dist_ref/dists/hyperexponential_dist.html b/libs/math/doc/html/math_toolkit/dist_ref/dists/hyperexponential_dist.html
index aaea724878..1bcf4b957c 100644
--- a/libs/math/doc/html/math_toolkit/dist_ref/dists/hyperexponential_dist.html
+++ b/libs/math/doc/html/math_toolkit/dist_ref/dists/hyperexponential_dist.html
@@ -4,7 +4,7 @@
 <title>Hyperexponential Distribution</title>
 <link rel="stylesheet" href="../../../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../dists.html" title="Distributions">
 <link rel="prev" href="geometric_dist.html" title="Geometric Distribution">
 <link rel="next" href="hypergeometric_dist.html" title="Hypergeometric Distribution">
@@ -1443,11 +1443,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/dist_ref/dists/hypergeometric_dist.html b/libs/math/doc/html/math_toolkit/dist_ref/dists/hypergeometric_dist.html
index eaf90f2bec..e45c9782e8 100644
--- a/libs/math/doc/html/math_toolkit/dist_ref/dists/hypergeometric_dist.html
+++ b/libs/math/doc/html/math_toolkit/dist_ref/dists/hypergeometric_dist.html
@@ -4,7 +4,7 @@
 <title>Hypergeometric Distribution</title>
 <link rel="stylesheet" href="../../../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../dists.html" title="Distributions">
 <link rel="prev" href="hyperexponential_dist.html" title="Hyperexponential Distribution">
 <link rel="next" href="inverse_chi_squared_dist.html" title="Inverse Chi Squared Distribution">
@@ -322,11 +322,11 @@
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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+++ b/libs/math/doc/html/math_toolkit/dist_ref/dists/nc_beta_dist.html
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 <title>Noncentral Beta Distribution</title>
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 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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@@ -4,7 +4,7 @@
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+<link rel="home" href="../../../index.html" title="Math Toolkit 2.10.0">
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 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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+++ b/libs/math/doc/html/math_toolkit/dist_ref/dists/nc_f_dist.html
@@ -4,7 +4,7 @@
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 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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@@ -4,7 +4,7 @@
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 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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diff --git a/libs/math/doc/html/math_toolkit/dist_ref/dists/negative_binomial_dist.html b/libs/math/doc/html/math_toolkit/dist_ref/dists/negative_binomial_dist.html
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@@ -4,7 +4,7 @@
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@@ -866,11 +866,11 @@
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 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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+<a accesskey="p" href="de_caveats.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../double_exponential.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="../fourier_integrals.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
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 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/ellint/ellint_1.html b/libs/math/doc/html/math_toolkit/ellint/ellint_1.html
index 77901bae10..8d552c6439 100644
--- a/libs/math/doc/html/math_toolkit/ellint/ellint_1.html
+++ b/libs/math/doc/html/math_toolkit/ellint/ellint_1.html
@@ -4,7 +4,7 @@
 <title>Elliptic Integrals of the First Kind - Legendre Form</title>
 <link rel="stylesheet" href="../../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../ellint.html" title="Elliptic Integrals">
 <link rel="prev" href="ellint_carlson.html" title="Elliptic Integrals - Carlson Form">
 <link rel="next" href="ellint_2.html" title="Elliptic Integrals of the Second Kind - Legendre Form">
@@ -80,7 +80,7 @@
         <span class="inlinemediaobject"><img src="../../../equations/ellint2.svg"></span>
       </p>
 <p>
-        Requires -1 &lt;= k &lt;= 1, otherwise returns the result of <a class="link" href="../error_handling.html#math_toolkit.error_handling.domain_error">domain_error</a>.
+        Requires k<sup>2</sup>sin<sup>2</sup>(phi) &lt; 1, otherwise returns the result of <a class="link" href="../error_handling.html#math_toolkit.error_handling.domain_error">domain_error</a>.
       </p>
 <p>
         The final <a class="link" href="../../policy.html" title="Chapter&#160;19.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a> argument is optional and can
@@ -101,7 +101,7 @@
         <span class="inlinemediaobject"><img src="../../../equations/ellint6.svg"></span>
       </p>
 <p>
-        Requires -1 &lt;= k &lt;= 1, otherwise returns the result of <a class="link" href="../error_handling.html#math_toolkit.error_handling.domain_error">domain_error</a>.
+        Requires |k| &lt; 1, otherwise returns the result of <a class="link" href="../error_handling.html#math_toolkit.error_handling.domain_error">domain_error</a>.
       </p>
 <p>
         The final <a class="link" href="../../policy.html" title="Chapter&#160;19.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a> argument is optional and can
@@ -263,11 +263,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/ellint/ellint_2.html b/libs/math/doc/html/math_toolkit/ellint/ellint_2.html
index 7cee5138a3..08bd270312 100644
--- a/libs/math/doc/html/math_toolkit/ellint/ellint_2.html
+++ b/libs/math/doc/html/math_toolkit/ellint/ellint_2.html
@@ -4,7 +4,7 @@
 <title>Elliptic Integrals of the Second Kind - Legendre Form</title>
 <link rel="stylesheet" href="../../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../ellint.html" title="Elliptic Integrals">
 <link rel="prev" href="ellint_1.html" title="Elliptic Integrals of the First Kind - Legendre Form">
 <link rel="next" href="ellint_3.html" title="Elliptic Integrals of the Third Kind - Legendre Form">
@@ -80,7 +80,7 @@
         <span class="inlinemediaobject"><img src="../../../equations/ellint3.svg"></span>
       </p>
 <p>
-        Requires -1 &lt;= k &lt;= 1, otherwise returns the result of <a class="link" href="../error_handling.html#math_toolkit.error_handling.domain_error">domain_error</a>.
+        Requires k<sup>2</sup>sin<sup>2</sup>(phi) &lt; 1, otherwise returns the result of <a class="link" href="../error_handling.html#math_toolkit.error_handling.domain_error">domain_error</a>.
       </p>
 <p>
         The final <a class="link" href="../../policy.html" title="Chapter&#160;19.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a> argument is optional and can
@@ -101,7 +101,7 @@
         <span class="inlinemediaobject"><img src="../../../equations/ellint7.svg"></span>
       </p>
 <p>
-        Requires -1 &lt;= k &lt;= 1, otherwise returns the result of <a class="link" href="../error_handling.html#math_toolkit.error_handling.domain_error">domain_error</a>.
+        Requires |k| &lt; 1, otherwise returns the result of <a class="link" href="../error_handling.html#math_toolkit.error_handling.domain_error">domain_error</a>.
       </p>
 <p>
         The final <a class="link" href="../../policy.html" title="Chapter&#160;19.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a> argument is optional and can
@@ -292,11 +292,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/ellint/ellint_3.html b/libs/math/doc/html/math_toolkit/ellint/ellint_3.html
index 872ebc3732..c28dd35a0e 100644
--- a/libs/math/doc/html/math_toolkit/ellint/ellint_3.html
+++ b/libs/math/doc/html/math_toolkit/ellint/ellint_3.html
@@ -4,7 +4,7 @@
 <title>Elliptic Integrals of the Third Kind - Legendre Form</title>
 <link rel="stylesheet" href="../../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../ellint.html" title="Elliptic Integrals">
 <link rel="prev" href="ellint_2.html" title="Elliptic Integrals of the Second Kind - Legendre Form">
 <link rel="next" href="ellint_d.html" title="Elliptic Integral D - Legendre Form">
@@ -81,7 +81,7 @@
         <span class="inlinemediaobject"><img src="../../../equations/ellint4.svg"></span>
       </p>
 <p>
-        Requires <span class="emphasis"><em>-1 &lt;= k &lt;= 1</em></span> and <span class="emphasis"><em>n &lt; 1/sin<sup>2</sup>(&#966;)</em></span>,
+        Requires <span class="emphasis"><em>k<sup>2</sup>sin<sup>2</sup>(phi) &lt; 1</em></span> and <span class="emphasis"><em>n &lt; 1/sin<sup>2</sup>(&#966;)</em></span>,
         otherwise returns the result of <a class="link" href="../error_handling.html#math_toolkit.error_handling.domain_error">domain_error</a>
         (outside this range the result would be complex).
       </p>
@@ -104,7 +104,7 @@
         <span class="inlinemediaobject"><img src="../../../equations/ellint8.svg"></span>
       </p>
 <p>
-        Requires <span class="emphasis"><em>-1 &lt;= k &lt;= 1</em></span> and <span class="emphasis"><em>n &lt; 1</em></span>,
+        Requires <span class="emphasis"><em>|k| &lt; 1</em></span> and <span class="emphasis"><em>n &lt; 1</em></span>,
         otherwise returns the result of <a class="link" href="../error_handling.html#math_toolkit.error_handling.domain_error">domain_error</a>
         (outside this range the result would be complex).
       </p>
@@ -335,11 +335,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/ellint/ellint_carlson.html b/libs/math/doc/html/math_toolkit/ellint/ellint_carlson.html
index b2542166f1..5ab6661138 100644
--- a/libs/math/doc/html/math_toolkit/ellint/ellint_carlson.html
+++ b/libs/math/doc/html/math_toolkit/ellint/ellint_carlson.html
@@ -4,7 +4,7 @@
 <title>Elliptic Integrals - Carlson Form</title>
 <link rel="stylesheet" href="../../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../ellint.html" title="Elliptic Integrals">
 <link rel="prev" href="ellint_intro.html" title="Elliptic Integral Overview">
 <link rel="next" href="ellint_1.html" title="Elliptic Integrals of the First Kind - Legendre Form">
@@ -971,11 +971,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/ellint/ellint_d.html b/libs/math/doc/html/math_toolkit/ellint/ellint_d.html
index 27772b3306..a82c773640 100644
--- a/libs/math/doc/html/math_toolkit/ellint/ellint_d.html
+++ b/libs/math/doc/html/math_toolkit/ellint/ellint_d.html
@@ -4,7 +4,7 @@
 <title>Elliptic Integral D - Legendre Form</title>
 <link rel="stylesheet" href="../../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../ellint.html" title="Elliptic Integrals">
 <link rel="prev" href="ellint_3.html" title="Elliptic Integrals of the Third Kind - Legendre Form">
 <link rel="next" href="jacobi_zeta.html" title="Jacobi Zeta Function">
@@ -58,9 +58,10 @@
         k)</em></span> and its complete counterpart <span class="emphasis"><em>D(k) = D(&#960;/2, k)</em></span>.
       </p>
 <p>
-        The return type of these functions is computed using the __arg_pomotion_rules
-        when the arguments are of different types: when they are the same type then
-        the result is the same type as the arguments.
+        The return type of these functions is computed using the <a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result
+        type calculation rules</em></span></a> when the arguments are of different
+        types: when they are the same type then the result is the same type as the
+        arguments.
       </p>
 <pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">&gt;</span>
 <a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ellint_d</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">k</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">phi</span><span class="special">);</span>
@@ -75,7 +76,7 @@
         <span class="inlinemediaobject"><img src="../../../equations/ellint_d.svg"></span>
       </p>
 <p>
-        Requires <span class="emphasis"><em>-1 &lt;= k &lt;= 1</em></span>, otherwise returns the result
+        Requires <span class="emphasis"><em>k<sup>2</sup>sin<sup>2</sup>(phi) &lt; 1</em></span>, otherwise returns the result
         of <a class="link" href="../error_handling.html#math_toolkit.error_handling.domain_error">domain_error</a>
         (outside this range the result would be complex).
       </p>
@@ -358,11 +359,11 @@ using
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/ellint/ellint_intro.html b/libs/math/doc/html/math_toolkit/ellint/ellint_intro.html
index 02f572ec92..f35257d266 100644
--- a/libs/math/doc/html/math_toolkit/ellint/ellint_intro.html
+++ b/libs/math/doc/html/math_toolkit/ellint/ellint_intro.html
@@ -4,7 +4,7 @@
 <title>Elliptic Integral Overview</title>
 <link rel="stylesheet" href="../../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../ellint.html" title="Elliptic Integrals">
 <link rel="prev" href="../ellint.html" title="Elliptic Integrals">
 <link rel="next" href="ellint_carlson.html" title="Elliptic Integrals - Carlson Form">
@@ -434,11 +434,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/ellint/heuman_lambda.html b/libs/math/doc/html/math_toolkit/ellint/heuman_lambda.html
index b1886c8a1f..8a67d180b0 100644
--- a/libs/math/doc/html/math_toolkit/ellint/heuman_lambda.html
+++ b/libs/math/doc/html/math_toolkit/ellint/heuman_lambda.html
@@ -4,7 +4,7 @@
 <title>Heuman Lambda Function</title>
 <link rel="stylesheet" href="../../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../ellint.html" title="Elliptic Integrals">
 <link rel="prev" href="jacobi_zeta.html" title="Jacobi Zeta Function">
 <link rel="next" href="../jacobi.html" title="Jacobi Elliptic Functions">
@@ -53,9 +53,10 @@
         <span class="inlinemediaobject"><img src="../../../equations/heuman_lambda.svg"></span>
       </p>
 <p>
-        The return type of this function is computed using the __arg_pomotion_rules
-        when the arguments are of different types: when they are the same type then
-        the result is the same type as the arguments.
+        The return type of this function is computed using the <a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result
+        type calculation rules</em></span></a> when the arguments are of different
+        types: when they are the same type then the result is the same type as the
+        arguments.
       </p>
 <p>
         Requires <span class="emphasis"><em>-1 &lt;= k &lt;= 1</em></span>, otherwise returns the result
@@ -204,11 +205,11 @@ using
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/ellint/jacobi_zeta.html b/libs/math/doc/html/math_toolkit/ellint/jacobi_zeta.html
index 89c87bc864..448ae5a049 100644
--- a/libs/math/doc/html/math_toolkit/ellint/jacobi_zeta.html
+++ b/libs/math/doc/html/math_toolkit/ellint/jacobi_zeta.html
@@ -4,7 +4,7 @@
 <title>Jacobi Zeta Function</title>
 <link rel="stylesheet" href="../../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../ellint.html" title="Elliptic Integrals">
 <link rel="prev" href="ellint_d.html" title="Elliptic Integral D - Legendre Form">
 <link rel="next" href="heuman_lambda.html" title="Heuman Lambda Function">
@@ -53,9 +53,20 @@
         <span class="inlinemediaobject"><img src="../../../equations/jacobi_zeta.svg"></span>
       </p>
 <p>
-        The return type of this function is computed using the __arg_pomotion_rules
-        when the arguments are of different types: when they are the same type then
-        the result is the same type as the arguments.
+        Please note the use of &#966;, and <span class="emphasis"><em>k</em></span> as the parameters, the
+        function is often defined as <span class="emphasis"><em>Z(&#966;, m)</em></span> with <span class="emphasis"><em>m
+        = k<sup>2</sup></em></span>, see for example <a href="http://mathworld.wolfram.com/JacobiZetaFunction.html" target="_top">Weisstein,
+        Eric W. "Jacobi Zeta Function." From MathWorld--A Wolfram Web Resource.</a>
+        Or else as <a href="https://dlmf.nist.gov/22.16#E32" target="_top"><span class="emphasis"><em>Z(x, k)</em></span></a>
+        with <span class="emphasis"><em>&#966; = am(x, k)</em></span>, where <span class="emphasis"><em>am</em></span> is the
+        <a href="https://dlmf.nist.gov/22.16#E1" target="_top">Jacobi amplitude function</a>
+        which is equivalent to <span class="emphasis"><em>asin(jacobi_elliptic(k, x))</em></span>.
+      </p>
+<p>
+        The return type of this function is computed using the <a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result
+        type calculation rules</em></span></a> when the arguments are of different
+        types: when they are the same type then the result is the same type as the
+        arguments.
       </p>
 <p>
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 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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--- a/libs/math/doc/html/math_toolkit/factorials.html
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 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../factorials.html" title="Factorials and Binomial Coefficients">
 <link rel="prev" href="sf_rising_factorial.html" title="Rising Factorial">
 <link rel="next" href="sf_binomial.html" title="Binomial Coefficients">
@@ -93,11 +93,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/factorials/sf_rising_factorial.html b/libs/math/doc/html/math_toolkit/factorials/sf_rising_factorial.html
index 12ea77a58b..f7a46fb7df 100644
--- a/libs/math/doc/html/math_toolkit/factorials/sf_rising_factorial.html
+++ b/libs/math/doc/html/math_toolkit/factorials/sf_rising_factorial.html
@@ -4,7 +4,7 @@
 <title>Rising Factorial</title>
 <link rel="stylesheet" href="../../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../factorials.html" title="Factorials and Binomial Coefficients">
 <link rel="prev" href="sf_double_factorial.html" title="Double Factorial">
 <link rel="next" href="sf_falling_factorial.html" title="Falling Factorial">
@@ -97,11 +97,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/fastest_typdefs.html b/libs/math/doc/html/math_toolkit/fastest_typdefs.html
index c6dafd126a..4b87b86775 100644
--- a/libs/math/doc/html/math_toolkit/fastest_typdefs.html
+++ b/libs/math/doc/html/math_toolkit/fastest_typdefs.html
@@ -4,7 +4,7 @@
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 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../cstdfloat.html" title="Chapter&#160;3.&#160;Specified-width floating-point typedefs">
 <link rel="prev" href="minimum_typdefs.html" title="Minimum-width floating-point typedefs">
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@@ -47,11 +47,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/float128.html b/libs/math/doc/html/math_toolkit/float128.html
index 4dfa215509..c2f2953a7a 100644
--- a/libs/math/doc/html/math_toolkit/float128.html
+++ b/libs/math/doc/html/math_toolkit/float128.html
@@ -4,7 +4,7 @@
 <title>Implementation of Float128 type</title>
 <link rel="stylesheet" href="../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../cstdfloat.html" title="Chapter&#160;3.&#160;Specified-width floating-point typedefs">
 <link rel="prev" href="float128_hints.html" title="Hints on using float128 (and __float128)">
 <link rel="next" href="float128/overloading.html" title="Overloading template functions with float128_t">
@@ -77,7 +77,7 @@
 <p>
       The <code class="computeroutput"><span class="identifier">__float128</span></code> type is provided
       by the <a href="http://gcc.gnu.org/onlinedocs/libquadmath/" target="_top">libquadmath
-      library</a> on GCC or by Intel's FORTRAN library with Intel C++. THey also
+      library</a> on GCC or by Intel's FORTRAN library with Intel C++. They also
       provide a full set of <code class="computeroutput"><span class="special">&lt;</span><span class="identifier">cmath</span><span class="special">&gt;</span></code> functions in <code class="computeroutput"><span class="keyword">namespace</span>
       <span class="identifier">std</span></code>.
     </p>
@@ -87,10 +87,7 @@
       C __float128 quadmath type</a>
     </h5>
 <p>
-      [quadmath_snprintf_1]
-    </p>
-<p>
-      The source code is at <a href="../../../example/quadmath_snprintf.c" target="_top">quadmath_snprintf.c</a>.
+      The source code is at <a href="https://gcc.gnu.org/onlinedocs/gcc-9.1.0/libquadmath/quadmath_005fsnprintf.html#quadmath_005fsnprintf" target="_top">quadmath_snprintf.c</a>.
     </p>
 <h5>
 <a name="math_toolkit.float128.h1"></a>
@@ -158,11 +155,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/float128/exp_function.html b/libs/math/doc/html/math_toolkit/float128/exp_function.html
index 73ebf1f61c..cb4250c7d5 100644
--- a/libs/math/doc/html/math_toolkit/float128/exp_function.html
+++ b/libs/math/doc/html/math_toolkit/float128/exp_function.html
@@ -4,7 +4,7 @@
 <title>Exponential function</title>
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 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../float128.html" title="Implementation of Float128 type">
 <link rel="prev" href="overloading.html" title="Overloading template functions with float128_t">
 <link rel="next" href="typeinfo.html" title="typeinfo">
@@ -54,11 +54,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/float128/overloading.html b/libs/math/doc/html/math_toolkit/float128/overloading.html
index 7dd9141e47..0e0de67e5c 100644
--- a/libs/math/doc/html/math_toolkit/float128/overloading.html
+++ b/libs/math/doc/html/math_toolkit/float128/overloading.html
@@ -4,7 +4,7 @@
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 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.10.0">
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 <link rel="prev" href="../float128.html" title="Implementation of Float128 type">
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@@ -80,11 +80,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/float128/typeinfo.html b/libs/math/doc/html/math_toolkit/float128/typeinfo.html
index ceecdadac5..190a5dcb66 100644
--- a/libs/math/doc/html/math_toolkit/float128/typeinfo.html
+++ b/libs/math/doc/html/math_toolkit/float128/typeinfo.html
@@ -4,7 +4,7 @@
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 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../float128.html" title="Implementation of Float128 type">
 <link rel="prev" href="exp_function.html" title="Exponential function">
 <link rel="next" href="../../constants.html" title="Chapter&#160;4.&#160;Mathematical Constants">
@@ -61,11 +61,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/float128_hints.html b/libs/math/doc/html/math_toolkit/float128_hints.html
index e62ef2fee8..16d968f0a0 100644
--- a/libs/math/doc/html/math_toolkit/float128_hints.html
+++ b/libs/math/doc/html/math_toolkit/float128_hints.html
@@ -4,7 +4,7 @@
 <title>Hints on using float128 (and __float128)</title>
 <link rel="stylesheet" href="../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../cstdfloat.html" title="Chapter&#160;3.&#160;Specified-width floating-point typedefs">
 <link rel="prev" href="examples.html" title="Examples">
 <link rel="next" href="float128.html" title="Implementation of Float128 type">
@@ -90,11 +90,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/float_comparison.html b/libs/math/doc/html/math_toolkit/float_comparison.html
index 1f6c53a248..d4e0f917cd 100644
--- a/libs/math/doc/html/math_toolkit/float_comparison.html
+++ b/libs/math/doc/html/math_toolkit/float_comparison.html
@@ -4,7 +4,7 @@
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 <link rel="stylesheet" href="../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../utils.html" title="Chapter&#160;2.&#160;Floating Point Utilities">
 <link rel="prev" href="next_float/ulp.html" title="Obtaining the Size of a Unit In the Last Place - ULP">
 <link rel="next" href="cond.html" title="Condition Numbers">
@@ -395,11 +395,11 @@ epsilon_difference = 0.000000000</pre>
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/fourier_integrals.html b/libs/math/doc/html/math_toolkit/fourier_integrals.html
new file mode 100644
index 0000000000..72cccce93c
--- /dev/null
+++ b/libs/math/doc/html/math_toolkit/fourier_integrals.html
@@ -0,0 +1,273 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
+<title>Fourier Integrals</title>
+<link rel="stylesheet" href="../math.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.10.0">
+<link rel="up" href="../quadrature.html" title="Chapter&#160;12.&#160;Quadrature and Differentiation">
+<link rel="prev" href="double_exponential/de_refes.html" title="References">
+<link rel="next" href="naive_monte_carlo.html" title="Naive Monte Carlo Integration">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
+<td align="center"><a href="../../../../../index.html">Home</a></td>
+<td align="center"><a href="../../../../../libs/libraries.htm">Libraries</a></td>
+<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td>
+<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td>
+<td align="center"><a href="../../../../../more/index.htm">More</a></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="double_exponential/de_refes.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../quadrature.html"><img src="../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="naive_monte_carlo.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a>
+</div>
+<div class="section">
+<div class="titlepage"><div><div><h2 class="title" style="clear: both">
+<a name="math_toolkit.fourier_integrals"></a><a class="link" href="fourier_integrals.html" title="Fourier Integrals">Fourier Integrals</a>
+</h2></div></div></div>
+<h4>
+<a name="math_toolkit.fourier_integrals.h0"></a>
+      <span class="phrase"><a name="math_toolkit.fourier_integrals.synopsis"></a></span><a class="link" href="fourier_integrals.html#math_toolkit.fourier_integrals.synopsis">Synopsis</a>
+    </h4>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">quadrature</span><span class="special">/</span><span class="identifier">ooura_fourier_integrals</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+
+<span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span> <span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">quadrature</span> <span class="special">{</span>
+
+<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Real</span><span class="special">&gt;</span>
+<span class="keyword">class</span> <span class="identifier">ooura_fourier_sin</span> <span class="special">{</span>
+<span class="keyword">public</span><span class="special">:</span>
+    <span class="identifier">ooura_fourier_sin</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">Real</span> <span class="identifier">relative_error_tolerance</span> <span class="special">=</span> <span class="identifier">tools</span><span class="special">::</span><span class="identifier">root_epsilon</span><span class="special">&lt;</span><span class="identifier">Real</span><span class="special">&gt;(),</span> <span class="identifier">size_t</span> <span class="identifier">levels</span> <span class="special">=</span> <span class="keyword">sizeof</span><span class="special">(</span><span class="identifier">Real</span><span class="special">));</span>
+
+    <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">F</span><span class="special">&gt;</span>
+    <span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special">&lt;</span><span class="identifier">Real</span><span class="special">,</span> <span class="identifier">Real</span><span class="special">&gt;</span> <span class="identifier">integrate</span><span class="special">(</span><span class="identifier">F</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">f</span><span class="special">,</span> <span class="identifier">Real</span> <span class="identifier">omega</span><span class="special">);</span>
+
+<span class="special">};</span>
+
+
+<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Real</span><span class="special">&gt;</span>
+<span class="keyword">class</span> <span class="identifier">ooura_fourier_cos</span> <span class="special">{</span>
+<span class="keyword">public</span><span class="special">:</span>
+    <span class="identifier">ooura_fourier_cos</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">Real</span> <span class="identifier">relative_error_tolerance</span> <span class="special">=</span> <span class="identifier">tools</span><span class="special">::</span><span class="identifier">root_epsilon</span><span class="special">&lt;</span><span class="identifier">Real</span><span class="special">&gt;(),</span> <span class="identifier">size_t</span> <span class="identifier">levels</span> <span class="special">=</span> <span class="keyword">sizeof</span><span class="special">(</span><span class="identifier">Real</span><span class="special">))</span>
+
+    <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">F</span><span class="special">&gt;</span>
+    <span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special">&lt;</span><span class="identifier">Real</span><span class="special">,</span> <span class="identifier">Real</span><span class="special">&gt;</span> <span class="identifier">integrate</span><span class="special">(</span><span class="identifier">F</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">f</span><span class="special">,</span> <span class="identifier">Real</span> <span class="identifier">omega</span><span class="special">);</span>
+<span class="special">};</span>
+
+<span class="special">}}}</span> <span class="comment">// namespaces</span>
+</pre>
+<p>
+      Ooura's method for Fourier integrals computes
+    </p>
+<p>
+      &#8198;  &#8198; &#8747;<sub>0</sub><sup>&#8734;</sup> f(t)sin(&#969; t) dt
+    </p>
+<p>
+      and
+    </p>
+<p>
+      &#8198;  &#8198; &#8747;<sub>0</sub><sup>&#8734;</sup> f(t)cos(&#969;  t) dt
+    </p>
+<p>
+      by a double exponentially decaying transformation. These integrals arise when
+      computing continuous Fourier transform of odd and even functions, respectively.
+      Oscillatory integrals are known to cause trouble for standard quadrature methods,
+      so these routines are provided to cope with the most common oscillatory use
+      case.
+    </p>
+<p>
+      The basic usage is shown below:
+    </p>
+<pre class="programlisting"><span class="identifier">ooura_fourier_sin</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span><span class="identifier">integrator</span> <span class="special">=</span> <span class="identifier">ooura_fourier_sin</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;();</span>
+<span class="comment">// Use the default tolerance root_epsilon and eight levels for type double.</span>
+
+<span class="keyword">auto</span> <span class="identifier">f</span> <span class="special">=</span> <span class="special">[](</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">)</span>
+<span class="special">{</span> <span class="comment">// Simple reciprocal function for sinc.</span>
+	<span class="keyword">return</span> <span class="number">1</span> <span class="special">/</span> <span class="identifier">x</span><span class="special">;</span>
+<span class="special">};</span>
+
+<span class="keyword">double</span> <span class="identifier">omega</span> <span class="special">=</span> <span class="number">1</span><span class="special">;</span>
+<span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">,</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="identifier">result</span> <span class="special">=</span> <span class="identifier">integrator</span><span class="special">.</span><span class="identifier">integrate</span><span class="special">(</span><span class="identifier">f</span><span class="special">,</span> <span class="identifier">omega</span><span class="special">);</span>
+<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Integral = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">result</span><span class="special">.</span><span class="identifier">first</span> <span class="special">&lt;&lt;</span> <span class="string">", relative error estimate "</span> <span class="special">&lt;&lt;</span> <span class="identifier">result</span><span class="special">.</span><span class="identifier">second</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+</pre>
+<p>
+      and compare with the expected value &#960;/2 of the integral.
+    </p>
+<pre class="programlisting"><span class="keyword">constexpr</span> <span class="keyword">double</span> <span class="identifier">expected</span> <span class="special">=</span> <span class="identifier">half_pi</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;();</span>
+<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"pi/2 =     "</span> <span class="special">&lt;&lt;</span> <span class="identifier">expected</span> <span class="special">&lt;&lt;</span> <span class="string">", difference "</span> <span class="special">&lt;&lt;</span> <span class="identifier">result</span><span class="special">.</span><span class="identifier">first</span> <span class="special">-</span> <span class="identifier">expected</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+</pre>
+<p>
+      The output is
+    </p>
+<pre class="programlisting"><span class="identifier">integral</span> <span class="special">=</span> <span class="number">1.5707963267948966</span><span class="special">,</span> <span class="identifier">relative</span> <span class="identifier">error</span> <span class="identifier">estimate</span> <span class="number">1.2655356398390254e-11</span>
+<span class="identifier">pi</span><span class="special">/</span><span class="number">2</span> <span class="special">=</span>     <span class="number">1.5707963267948966</span><span class="special">,</span> <span class="identifier">difference</span> <span class="number">0</span>
+</pre>
+<div class="note"><table border="0" summary="Note">
+<tr>
+<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../doc/src/images/note.png"></td>
+<th align="left">Note</th>
+</tr>
+<tr><td align="left" valign="top"><p>
+        This integrator is more insistent about examining the error estimate, than
+        (say) tanh-sinh, which just returns the value of the integral.
+      </p></td></tr>
+</table></div>
+<p>
+      With the macro BOOST_MATH_INSTRUMENT_OOURA defined, we can follow the progress:
+    </p>
+<pre class="programlisting"><span class="identifier">ooura_fourier_sin</span> <span class="identifier">with</span> <span class="identifier">relative</span> <span class="identifier">error</span> <span class="identifier">goal</span> <span class="number">1.4901161193847656e-08</span> <span class="special">&amp;</span> <span class="number">8</span> <span class="identifier">levels</span><span class="special">.</span>
+<span class="identifier">h</span> <span class="special">=</span> <span class="number">1.000000000000000</span><span class="special">,</span> <span class="identifier">I_h</span> <span class="special">=</span> <span class="number">1.571890732004545</span> <span class="special">=</span> <span class="number">0x1</span><span class="special">.</span><span class="number">92676e56d</span><span class="number">853500</span><span class="identifier">p</span><span class="special">+</span><span class="number">0</span><span class="special">,</span> <span class="identifier">absolute</span> <span class="identifier">error</span> <span class="identifier">estimate</span> <span class="special">=</span> <span class="identifier">nan</span>
+<span class="identifier">h</span> <span class="special">=</span> <span class="number">0.500000000000000</span><span class="special">,</span> <span class="identifier">I_h</span> <span class="special">=</span> <span class="number">1.570793292491940</span> <span class="special">=</span> <span class="number">0x1</span><span class="special">.</span><span class="number">921f</span><span class="number">825</span><span class="identifier">c076f600p</span><span class="special">+</span><span class="number">0</span><span class="special">,</span> <span class="identifier">absolute</span> <span class="identifier">error</span> <span class="identifier">estimate</span> <span class="special">=</span> <span class="number">1.097439512605325e-03</span>
+<span class="identifier">h</span> <span class="special">=</span> <span class="number">0.250000000000000</span><span class="special">,</span> <span class="identifier">I_h</span> <span class="special">=</span> <span class="number">1.570796326814776</span> <span class="special">=</span> <span class="number">0x1</span><span class="special">.</span><span class="number">921f</span><span class="identifier">b54458acf00p</span><span class="special">+</span><span class="number">0</span><span class="special">,</span> <span class="identifier">absolute</span> <span class="identifier">error</span> <span class="identifier">estimate</span> <span class="special">=</span> <span class="number">3.034322835882008e-06</span>
+<span class="identifier">h</span> <span class="special">=</span> <span class="number">0.125000000000000</span><span class="special">,</span> <span class="identifier">I_h</span> <span class="special">=</span> <span class="number">1.570796326794897</span> <span class="special">=</span> <span class="number">0x1</span><span class="special">.</span><span class="number">921f</span><span class="identifier">b54442d1800p</span><span class="special">+</span><span class="number">0</span><span class="special">,</span> <span class="identifier">absolute</span> <span class="identifier">error</span> <span class="identifier">estimate</span> <span class="special">=</span> <span class="number">1.987898734512328e-11</span>
+<span class="identifier">Integral</span> <span class="special">=</span> <span class="number">1.570796326794897e+00</span><span class="special">,</span> <span class="identifier">relative</span> <span class="identifier">error</span> <span class="identifier">estimate</span> <span class="number">1.265535639839025e-11</span>
+<span class="identifier">pi</span><span class="special">/</span><span class="number">2</span> <span class="special">=</span>     <span class="number">1.570796326794897e+00</span><span class="special">,</span> <span class="identifier">difference</span> <span class="number">0.000000000000000e+00</span>
+</pre>
+<p>
+      Working code of this example is at <a href="../../../example/ooura_fourier_integrals_example.cpp" target="_top">ooura_fourier_integrals_example.cpp</a>
+    </p>
+<p>
+      A classical cosine transform is presented below:
+    </p>
+<pre class="programlisting"><span class="keyword">auto</span> <span class="identifier">integrator</span> <span class="special">=</span> <span class="identifier">ooura_fourier_cos</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;();</span>
+<span class="comment">// Use the default tolerance root_epsilon and eight levels for type double.</span>
+
+<span class="keyword">auto</span> <span class="identifier">f</span> <span class="special">=</span> <span class="special">[](</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">)</span>
+<span class="special">{</span> <span class="comment">// More complex example function.</span>
+	<span class="keyword">return</span> <span class="number">1</span> <span class="special">/</span> <span class="special">(</span><span class="identifier">x</span> <span class="special">*</span> <span class="identifier">x</span> <span class="special">+</span> <span class="number">1</span><span class="special">);</span>
+<span class="special">};</span>
+
+<span class="keyword">double</span> <span class="identifier">omega</span> <span class="special">=</span> <span class="number">1</span><span class="special">;</span>
+
+<span class="keyword">auto</span> <span class="special">[</span><span class="identifier">result</span><span class="special">,</span> <span class="identifier">relative_error</span><span class="special">]</span> <span class="special">=</span> <span class="identifier">integrator</span><span class="special">.</span><span class="identifier">integrate</span><span class="special">(</span><span class="identifier">f</span><span class="special">,</span> <span class="identifier">omega</span><span class="special">);</span>
+<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Integral = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">result</span> <span class="special">&lt;&lt;</span> <span class="string">", relative error estimate "</span> <span class="special">&lt;&lt;</span> <span class="identifier">relative_error</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+</pre>
+<p>
+      The value of this integral should be &#960;/(2e) and can be shown :
+    </p>
+<pre class="programlisting"><span class="keyword">constexpr</span> <span class="keyword">double</span> <span class="identifier">expected</span> <span class="special">=</span> <span class="identifier">half_pi</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;()</span> <span class="special">/</span> <span class="identifier">e</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;();</span>
+<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"pi/(2e) =  "</span> <span class="special">&lt;&lt;</span> <span class="identifier">expected</span> <span class="special">&lt;&lt;</span> <span class="string">", difference "</span> <span class="special">&lt;&lt;</span> <span class="identifier">result</span> <span class="special">-</span> <span class="identifier">expected</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+</pre>
+<p>
+      or with the macro BOOST_MATH_INSTRUMENT_OOURA defined, we can follow the progress:
+    </p>
+<pre class="programlisting">
+ooura_fourier_cos with relative error goal 1.4901161193847656e-08 &amp; 8 levels.
+epsilon for type = 2.2204460492503131e-16
+h = 1.000000000000000, I_h = 0.588268622591776 = 0x1.2d318b7e96dbe00p-1, absolute error estimate = nan
+h = 0.500000000000000, I_h = 0.577871642184837 = 0x1.27decab8f07b200p-1, absolute error estimate = 1.039698040693926e-02
+h = 0.250000000000000, I_h = 0.577863671186883 = 0x1.27ddbf42969be00p-1, absolute error estimate = 7.970997954576120e-06
+h = 0.125000000000000, I_h = 0.577863674895461 = 0x1.27ddbf6271dc000p-1, absolute error estimate = 3.708578555361441e-09
+Integral = 5.778636748954611e-01, relative error estimate 6.417739540441515e-09
+pi/(2e)  = 5.778636748954609e-01, difference 2.220446049250313e-16
+
+</pre>
+<p>
+      Working code of this example is at <a href="../../../example/ooura_fourier_integrals_cosine_example.cpp" target="_top">ooura_fourier_integrals_consine_example.cpp</a>
+    </p>
+<h6>
+<a name="math_toolkit.fourier_integrals.h1"></a>
+      <span class="phrase"><a name="math_toolkit.fourier_integrals.performance"></a></span><a class="link" href="fourier_integrals.html#math_toolkit.fourier_integrals.performance">Performance</a>
+    </h6>
+<p>
+      The integrator precomputes nodes and weights, and hence can be reused for many
+      different frequencies with good efficiency. The integrator is pimpl'd and hence
+      can be shared between threads without a memcpy of the nodes and weights.
+    </p>
+<p>
+      Ooura and Mori's paper identifies criteria for rapid convergence based on the
+      position of the poles of the integrand in the complex plane. If these poles
+      are too close to the real axis the convergence is slow. It is not trivial to
+      predict the convergence rate a priori, so if you are interested in figuring
+      out if the convergence is rapid, compile with <code class="computeroutput"><span class="special">-</span><span class="identifier">DBOOST_MATH_INSTRUMENT_OOURA</span></code> and some amount
+      of printing will give you a good idea of how well this method is performing.
+    </p>
+<h6>
+<a name="math_toolkit.fourier_integrals.h2"></a>
+      <span class="phrase"><a name="math_toolkit.fourier_integrals.multi_precision"></a></span><a class="link" href="fourier_integrals.html#math_toolkit.fourier_integrals.multi_precision">Higher
+      precision</a>
+    </h6>
+<p>
+      It is simple to extend to higher precision using <a href="../../../../../libs/multiprecision/doc/html/index.html" target="_top">Boost.Multiprecision</a>.
+    </p>
+<pre class="programlisting"><span class="comment">// Use the default parameters for tolerance root_epsilon and eight levels for a type of 8 bytes.</span>
+<span class="comment">//auto integrator = ooura_fourier_cos&lt;Real&gt;();</span>
+<span class="comment">// Decide on a (tight) tolerance.</span>
+<span class="keyword">const</span> <span class="identifier">Real</span> <span class="identifier">tol</span> <span class="special">=</span> <span class="number">2</span> <span class="special">*</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">Real</span><span class="special">&gt;::</span><span class="identifier">epsilon</span><span class="special">();</span>
+<span class="keyword">auto</span> <span class="identifier">integrator</span> <span class="special">=</span> <span class="identifier">ooura_fourier_cos</span><span class="special">&lt;</span><span class="identifier">Real</span><span class="special">&gt;(</span><span class="identifier">tol</span><span class="special">,</span> <span class="number">8</span><span class="special">);</span> <span class="comment">// Loops or gets worse for more than 8.</span>
+
+<span class="keyword">auto</span> <span class="identifier">f</span> <span class="special">=</span> <span class="special">[](</span><span class="identifier">Real</span> <span class="identifier">x</span><span class="special">)</span>
+<span class="special">{</span> <span class="comment">// More complex example function.</span>
+	<span class="keyword">return</span> <span class="number">1</span> <span class="special">/</span> <span class="special">(</span><span class="identifier">x</span> <span class="special">*</span> <span class="identifier">x</span> <span class="special">+</span> <span class="number">1</span><span class="special">);</span>
+<span class="special">};</span>
+
+<span class="keyword">double</span> <span class="identifier">omega</span> <span class="special">=</span> <span class="number">1</span><span class="special">;</span>
+<span class="keyword">auto</span> <span class="special">[</span><span class="identifier">result</span><span class="special">,</span> <span class="identifier">relative_error</span><span class="special">]</span> <span class="special">=</span> <span class="identifier">integrator</span><span class="special">.</span><span class="identifier">integrate</span><span class="special">(</span><span class="identifier">f</span><span class="special">,</span> <span class="identifier">omega</span><span class="special">);</span>
+</pre>
+<pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Integral = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">result</span> <span class="special">&lt;&lt;</span> <span class="string">", relative error estimate "</span> <span class="special">&lt;&lt;</span> <span class="identifier">relative_error</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+
+<span class="keyword">const</span> <span class="identifier">Real</span> <span class="identifier">expected</span> <span class="special">=</span> <span class="identifier">half_pi</span><span class="special">&lt;</span><span class="identifier">Real</span><span class="special">&gt;()</span> <span class="special">/</span> <span class="identifier">e</span><span class="special">&lt;</span><span class="identifier">Real</span><span class="special">&gt;();</span> <span class="comment">// Expect integral = 1/(2e)</span>
+<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"pi/(2e)  = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">expected</span> <span class="special">&lt;&lt;</span> <span class="string">", difference "</span> <span class="special">&lt;&lt;</span> <span class="identifier">result</span> <span class="special">-</span> <span class="identifier">expected</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+</pre>
+<p>
+      with output:
+    </p>
+<pre class="programlisting">
+Integral = 0.5778636748954608589550465916563501587, relative error estimate 4.609814684522163895264277312610830278e-17
+pi/(2e) = 0.5778636748954608659545328919193707407, difference -6.999486300263020581921171645255733758e-18
+
+</pre>
+<p>
+      And with diagnostics on:
+    </p>
+<pre class="programlisting">
+ooura_fourier_cos with relative error goal 3.851859888774471706111955885169854637e-34 &amp; 15 levels.
+epsilon for type = 1.925929944387235853055977942584927319e-34
+h = 1.000000000000000000000000000000000, I_h = 0.588268622591776615359568690603776 = 0.5882686225917766153595686906037760, absolute error estimate = nan
+h = 0.500000000000000000000000000000000, I_h = 0.577871642184837461311756940493259 = 0.5778716421848374613117569404932595, absolute error estimate = 1.039698040693915404781175011051656e-02
+h = 0.250000000000000000000000000000000, I_h = 0.577863671186882539559996800783122 = 0.5778636711868825395599968007831220, absolute error estimate = 7.970997954921751760139710137450075e-06
+h = 0.125000000000000000000000000000000, I_h = 0.577863674895460885593491133506723 = 0.5778636748954608855934911335067232, absolute error estimate = 3.708578346033494332723601147051768e-09
+h = 0.062500000000000000000000000000000, I_h = 0.577863674895460858955046591656350 = 0.5778636748954608589550465916563502, absolute error estimate = 2.663844454185037302771663314961535e-17
+h = 0.031250000000000000000000000000000, I_h = 0.577863674895460858955046591656348 = 0.5778636748954608589550465916563484, absolute error estimate = 1.733336949948512267750380148326435e-33
+h = 0.015625000000000000000000000000000, I_h = 0.577863674895460858955046591656348 = 0.5778636748954608589550465916563479, absolute error estimate = 4.814824860968089632639944856462318e-34
+h = 0.007812500000000000000000000000000, I_h = 0.577863674895460858955046591656347 = 0.5778636748954608589550465916563473, absolute error estimate = 6.740754805355325485695922799047246e-34
+h = 0.003906250000000000000000000000000, I_h = 0.577863674895460858955046591656347 = 0.5778636748954608589550465916563475, absolute error estimate = 1.925929944387235853055977942584927e-34
+Integral = 5.778636748954608589550465916563475e-01, relative error estimate 3.332844800697411177051445985473052e-34
+pi/(2e)  = 5.778636748954608589550465916563481e-01, difference -6.740754805355325485695922799047246e-34
+
+</pre>
+<p>
+      Working code of this example is at <a href="../../../example/ooura_fourier_integrals_multiprecision_example.cpp" target="_top">ooura_fourier_integrals_multiprecision_example.cpp</a>
+    </p>
+<p>
+      For more examples of other functions and tests, see the full test suite at
+      <a href="../../../test/ooura_fourier_integral_test.cpp" target="_top">ooura_fourier_integral_test.cpp</a>.
+    </p>
+<h4>
+<a name="math_toolkit.fourier_integrals.h3"></a>
+      <span class="phrase"><a name="math_toolkit.fourier_integrals.references"></a></span><a class="link" href="fourier_integrals.html#math_toolkit.fourier_integrals.references">References</a>
+    </h4>
+<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem">
+          Ooura, Takuya, and Masatake Mori, <span class="emphasis"><em>A robust double exponential
+          formula for Fourier-type integrals.</em></span> Journal of computational
+          and applied mathematics 112.1-2 (1999): 229-241.
+        </li></ul></div>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
+      Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="double_exponential/de_refes.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../quadrature.html"><img src="../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="naive_monte_carlo.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a>
+</div>
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+</html>
diff --git a/libs/math/doc/html/math_toolkit/fp_facets.html b/libs/math/doc/html/math_toolkit/fp_facets.html
index 5f6578179a..940a0af7b8 100644
--- a/libs/math/doc/html/math_toolkit/fp_facets.html
+++ b/libs/math/doc/html/math_toolkit/fp_facets.html
@@ -4,7 +4,7 @@
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 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../utils.html" title="Chapter&#160;2.&#160;Floating Point Utilities">
 <link rel="prev" href="sign_functions.html" title="Sign Manipulation Functions">
 <link rel="next" href="fp_facets/facets_intro.html" title="Introduction">
@@ -75,11 +75,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/fp_facets/examples.html b/libs/math/doc/html/math_toolkit/fp_facets/examples.html
index 892e2d3979..48a70baa3d 100644
--- a/libs/math/doc/html/math_toolkit/fp_facets/examples.html
+++ b/libs/math/doc/html/math_toolkit/fp_facets/examples.html
@@ -4,7 +4,7 @@
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 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.10.0">
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 <link rel="next" href="portability.html" title="Portability">
@@ -241,11 +241,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/fp_facets/facets_intro.html b/libs/math/doc/html/math_toolkit/fp_facets/facets_intro.html
index a69a8edd69..54e69ab311 100644
--- a/libs/math/doc/html/math_toolkit/fp_facets/facets_intro.html
+++ b/libs/math/doc/html/math_toolkit/fp_facets/facets_intro.html
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-<link rel="home" href="../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.10.0">
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 <link rel="prev" href="../fp_facets.html" title="Facets for Floating-Point Infinities and NaNs">
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@@ -363,11 +363,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/fp_facets/portability.html b/libs/math/doc/html/math_toolkit/fp_facets/portability.html
index 79b811775b..c1537e46e6 100644
--- a/libs/math/doc/html/math_toolkit/fp_facets/portability.html
+++ b/libs/math/doc/html/math_toolkit/fp_facets/portability.html
@@ -4,7 +4,7 @@
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 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.10.0">
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@@ -34,11 +34,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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diff --git a/libs/math/doc/html/math_toolkit/fp_facets/rationale.html b/libs/math/doc/html/math_toolkit/fp_facets/rationale.html
index 8ef6f39b1a..1de20efa10 100644
--- a/libs/math/doc/html/math_toolkit/fp_facets/rationale.html
+++ b/libs/math/doc/html/math_toolkit/fp_facets/rationale.html
@@ -4,7 +4,7 @@
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-<link rel="home" href="../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.10.0">
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@@ -51,11 +51,11 @@
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 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/fp_facets/reference.html b/libs/math/doc/html/math_toolkit/fp_facets/reference.html
index ff1452e0b1..fc8a413cf8 100644
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+++ b/libs/math/doc/html/math_toolkit/fp_facets/reference.html
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 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.10.0">
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@@ -474,11 +474,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/fpclass.html b/libs/math/doc/html/math_toolkit/fpclass.html
index 03a81bd830..1f66a3a382 100644
--- a/libs/math/doc/html/math_toolkit/fpclass.html
+++ b/libs/math/doc/html/math_toolkit/fpclass.html
@@ -4,7 +4,7 @@
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 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
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+<link rel="home" href="../index.html" title="Math Toolkit 2.10.0">
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@@ -235,11 +235,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/future.html b/libs/math/doc/html/math_toolkit/future.html
index 3ef325c119..119c948804 100644
--- a/libs/math/doc/html/math_toolkit/future.html
+++ b/libs/math/doc/html/math_toolkit/future.html
@@ -4,7 +4,7 @@
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+<link rel="home" href="../index.html" title="Math Toolkit 2.10.0">
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@@ -131,11 +131,11 @@
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 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/gauss.html b/libs/math/doc/html/math_toolkit/gauss.html
index fe777ab976..475abe1a23 100644
--- a/libs/math/doc/html/math_toolkit/gauss.html
+++ b/libs/math/doc/html/math_toolkit/gauss.html
@@ -4,7 +4,7 @@
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-<link rel="home" href="../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../index.html" title="Math Toolkit 2.10.0">
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 <link rel="prev" href="trapezoidal.html" title="Trapezoidal Quadrature">
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@@ -198,11 +198,11 @@
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 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/gauss_kronrod.html b/libs/math/doc/html/math_toolkit/gauss_kronrod.html
index f5b00c2a00..8226d4d557 100644
--- a/libs/math/doc/html/math_toolkit/gauss_kronrod.html
+++ b/libs/math/doc/html/math_toolkit/gauss_kronrod.html
@@ -4,7 +4,7 @@
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 <link rel="stylesheet" href="../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../index.html" title="Math Toolkit 2.10.0">
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 <link rel="prev" href="gauss.html" title="Gauss-Legendre quadrature">
 <link rel="next" href="double_exponential.html" title="Double-exponential quadrature">
@@ -174,7 +174,8 @@
     </h4>
 <p>
       The Gauss-Kronrod quadrature support integrands defined on the real line and
-      returning complex values.
+      returning complex values. In this case, the template argument is the real type,
+      and the complex type is deduced via the return type of the function.
     </p>
 <h4>
 <a name="math_toolkit.gauss_kronrod.h4"></a>
@@ -269,11 +270,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/getting_best.html b/libs/math/doc/html/math_toolkit/getting_best.html
index 9a6341c050..25ca9ce176 100644
--- a/libs/math/doc/html/math_toolkit/getting_best.html
+++ b/libs/math/doc/html/math_toolkit/getting_best.html
@@ -4,7 +4,7 @@
 <title>Getting the Best Performance from this Library: Compiler and Compiler Options</title>
 <link rel="stylesheet" href="../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../perf.html" title="Chapter&#160;20.&#160;Performance">
 <link rel="prev" href="interp.html" title="Interpreting these Results">
 <link rel="next" href="tradoffs.html" title="Trading Accuracy for Performance">
@@ -160,11 +160,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/greatest_typdefs.html b/libs/math/doc/html/math_toolkit/greatest_typdefs.html
index 30ae1901f9..2882d229c3 100644
--- a/libs/math/doc/html/math_toolkit/greatest_typdefs.html
+++ b/libs/math/doc/html/math_toolkit/greatest_typdefs.html
@@ -4,7 +4,7 @@
 <title>Greatest-width floating-point typedef</title>
 <link rel="stylesheet" href="../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../cstdfloat.html" title="Chapter&#160;3.&#160;Specified-width floating-point typedefs">
 <link rel="prev" href="fastest_typdefs.html" title="Fastest floating-point typedefs">
 <link rel="next" href="macros.html" title="Floating-Point Constant Macros">
@@ -79,11 +79,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/hankel.html b/libs/math/doc/html/math_toolkit/hankel.html
index da6f92892d..0074bcf6bf 100644
--- a/libs/math/doc/html/math_toolkit/hankel.html
+++ b/libs/math/doc/html/math_toolkit/hankel.html
@@ -4,7 +4,7 @@
 <title>Hankel Functions</title>
 <link rel="stylesheet" href="../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../special.html" title="Chapter&#160;7.&#160;Special Functions">
 <link rel="prev" href="bessel/bessel_derivatives.html" title="Derivatives of the Bessel Functions">
 <link rel="next" href="hankel/cyl_hankel.html" title="Cyclic Hankel Functions">
@@ -33,11 +33,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/hankel/cyl_hankel.html b/libs/math/doc/html/math_toolkit/hankel/cyl_hankel.html
index 95323cbb6c..0e95c8a1ba 100644
--- a/libs/math/doc/html/math_toolkit/hankel/cyl_hankel.html
+++ b/libs/math/doc/html/math_toolkit/hankel/cyl_hankel.html
@@ -4,7 +4,7 @@
 <title>Cyclic Hankel Functions</title>
 <link rel="stylesheet" href="../../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../hankel.html" title="Hankel Functions">
 <link rel="prev" href="../hankel.html" title="Hankel Functions">
 <link rel="next" href="sph_hankel.html" title="Spherical Hankel Functions">
@@ -145,11 +145,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/hankel/sph_hankel.html b/libs/math/doc/html/math_toolkit/hankel/sph_hankel.html
index 347892318c..a674a4f25d 100644
--- a/libs/math/doc/html/math_toolkit/hankel/sph_hankel.html
+++ b/libs/math/doc/html/math_toolkit/hankel/sph_hankel.html
@@ -4,7 +4,7 @@
 <title>Spherical Hankel Functions</title>
 <link rel="stylesheet" href="../../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../hankel.html" title="Hankel Functions">
 <link rel="prev" href="cyl_hankel.html" title="Cyclic Hankel Functions">
 <link rel="next" href="../airy.html" title="Airy Functions">
@@ -107,11 +107,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/high_precision.html b/libs/math/doc/html/math_toolkit/high_precision.html
index e8acab8b26..8141956f59 100644
--- a/libs/math/doc/html/math_toolkit/high_precision.html
+++ b/libs/math/doc/html/math_toolkit/high_precision.html
@@ -4,7 +4,7 @@
 <title>Using Boost.Math with High-Precision Floating-Point Libraries</title>
 <link rel="stylesheet" href="../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../using_udt.html" title="Chapter&#160;18.&#160;Use with User-Defined Floating-Point Types - Boost.Multiprecision and others">
 <link rel="prev" href="../using_udt.html" title="Chapter&#160;18.&#160;Use with User-Defined Floating-Point Types - Boost.Multiprecision and others">
 <link rel="next" href="high_precision/why_high_precision.html" title="Why use a high-precision library rather than built-in floating-point types?">
@@ -62,7 +62,11 @@
           <a href="http://www.mpfr.org/" target="_top">GNU MPFR library</a>
         </li>
 <li class="listitem">
-          __float128
+          <a href="https://gcc.gnu.org/onlinedocs/gcc-9.1.0/libquadmath/index.html" target="_top">GCC
+          128-bit floating-point type</a>
+        </li>
+<li class="listitem">
+          Intel _Quad type
         </li>
 </ul></div>
 <p>
@@ -94,11 +98,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/high_precision/e_float.html b/libs/math/doc/html/math_toolkit/high_precision/e_float.html
index 95bbcbdfcc..79c2192e9a 100644
--- a/libs/math/doc/html/math_toolkit/high_precision/e_float.html
+++ b/libs/math/doc/html/math_toolkit/high_precision/e_float.html
@@ -4,7 +4,7 @@
 <title>Using e_float Library</title>
 <link rel="stylesheet" href="../../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../high_precision.html" title="Using Boost.Math with High-Precision Floating-Point Libraries">
 <link rel="prev" href="use_mpfr.html" title="Using With MPFR or GMP - High-Precision Floating-Point Library">
 <link rel="next" href="use_ntl.html" title="Using NTL Library">
@@ -51,11 +51,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/high_precision/float128.html b/libs/math/doc/html/math_toolkit/high_precision/float128.html
index 77f75a85b1..202154026e 100644
--- a/libs/math/doc/html/math_toolkit/high_precision/float128.html
+++ b/libs/math/doc/html/math_toolkit/high_precision/float128.html
@@ -4,7 +4,7 @@
 <title>Using with GCC's __float128 datatype</title>
 <link rel="stylesheet" href="../../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../high_precision.html" title="Using Boost.Math with High-Precision Floating-Point Libraries">
 <link rel="prev" href="use_multiprecision.html" title="Using Boost.Multiprecision">
 <link rel="next" href="use_mpfr.html" title="Using With MPFR or GMP - High-Precision Floating-Point Library">
@@ -35,10 +35,11 @@
       </p>
 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 <li class="listitem">
-            Provides std::numeric_limits&lt;__float128&gt; support.
+            Provides <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">__float128</span><span class="special">&gt;</span></code>
+            support.
           </li>
 <li class="listitem">
-            Provides overloads of the standard library math function for type <code class="computeroutput"><span class="identifier">__float128</span></code>and which forward to the
+            Provides overloads of the standard library math functions for type <code class="computeroutput"><span class="identifier">__float128</span></code> and which forward to the
             libquadmath equivalents.
           </li>
 </ul></div>
@@ -48,11 +49,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/high_precision/use_mpfr.html b/libs/math/doc/html/math_toolkit/high_precision/use_mpfr.html
index 2f215c115e..42e93be0a1 100644
--- a/libs/math/doc/html/math_toolkit/high_precision/use_mpfr.html
+++ b/libs/math/doc/html/math_toolkit/high_precision/use_mpfr.html
@@ -4,7 +4,7 @@
 <title>Using With MPFR or GMP - High-Precision Floating-Point Library</title>
 <link rel="stylesheet" href="../../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../high_precision.html" title="Using Boost.Math with High-Precision Floating-Point Libraries">
 <link rel="prev" href="float128.html" title="Using with GCC's __float128 datatype">
 <link rel="next" href="e_float.html" title="Using e_float Library">
@@ -100,11 +100,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/high_precision/use_multiprecision.html b/libs/math/doc/html/math_toolkit/high_precision/use_multiprecision.html
index e89f72d2f5..d8fda50372 100644
--- a/libs/math/doc/html/math_toolkit/high_precision/use_multiprecision.html
+++ b/libs/math/doc/html/math_toolkit/high_precision/use_multiprecision.html
@@ -4,7 +4,7 @@
 <title>Using Boost.Multiprecision</title>
 <link rel="stylesheet" href="../../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../high_precision.html" title="Using Boost.Math with High-Precision Floating-Point Libraries">
 <link rel="prev" href="why_high_precision.html" title="Why use a high-precision library rather than built-in floating-point types?">
 <link rel="next" href="float128.html" title="Using with GCC's __float128 datatype">
@@ -57,23 +57,21 @@
 <p>
         So now we can demonstrate with some trivial calculations:
       </p>
-<pre class="programlisting"><span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span>
-<span class="special">{</span>
-</pre>
 <p>
         Using <code class="computeroutput"><span class="keyword">typedef</span> <span class="identifier">cpp_dec_float_50</span></code>
-        hides the complexity of multiprecision to allow us to define variables with
+        hides the complexity of multiprecision, allows us to define variables with
         50 decimal digit precision just like built-in <code class="computeroutput"><span class="keyword">double</span></code>.
       </p>
 <pre class="programlisting"><span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">::</span><span class="identifier">cpp_dec_float_50</span><span class="special">;</span>
 
-<span class="identifier">cpp_dec_float_50</span> <span class="identifier">seventh</span> <span class="special">=</span> <span class="identifier">cpp_dec_float_50</span><span class="special">(</span><span class="number">1</span><span class="special">)</span> <span class="special">/</span> <span class="number">7</span><span class="special">;</span>
+<span class="identifier">cpp_dec_float_50</span> <span class="identifier">seventh</span> <span class="special">=</span> <span class="identifier">cpp_dec_float_50</span><span class="special">(</span><span class="number">1</span><span class="special">)</span> <span class="special">/</span> <span class="number">7</span><span class="special">;</span>  <span class="comment">// 1 / 7</span>
 </pre>
 <p>
         By default, output would only show the standard 6 decimal digits, so set
-        precision to show all 50 significant digits.
+        precision to show all 50 significant digits, including any trailing zeros.
       </p>
 <pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span><span class="special">.</span><span class="identifier">precision</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">cpp_dec_float_50</span><span class="special">&gt;::</span><span class="identifier">digits10</span><span class="special">);</span>
+<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">showpoint</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> <span class="comment">// Append any trailing zeros.</span>
 <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">seventh</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
 </pre>
 <p>
@@ -82,22 +80,28 @@
 <pre class="programlisting"><span class="number">0.14285714285714285714285714285714285714285714285714</span>
 </pre>
 <p>
-        We can also use constants, guaranteed to be initialized with the very last
-        bit of precision.
+        We can also use Boost.Math <a class="link" href="../constants.html" title="The Mathematical Constants">constants</a>
+        like &#960;, guaranteed to be initialized with the very last bit of precision for
+        the floating-point type.
       </p>
-<pre class="programlisting"><span class="identifier">cpp_dec_float_50</span> <span class="identifier">circumference</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">constants</span><span class="special">::</span><span class="identifier">pi</span><span class="special">&lt;</span><span class="identifier">cpp_dec_float_50</span><span class="special">&gt;()</span> <span class="special">*</span> <span class="number">2</span> <span class="special">*</span> <span class="identifier">seventh</span><span class="special">;</span>
-
-<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">circumference</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+<pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"pi = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">constants</span><span class="special">::</span><span class="identifier">pi</span><span class="special">&lt;</span><span class="identifier">cpp_dec_float_50</span><span class="special">&gt;()</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+<span class="identifier">cpp_dec_float_50</span> <span class="identifier">circumference</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">constants</span><span class="special">::</span><span class="identifier">pi</span><span class="special">&lt;</span><span class="identifier">cpp_dec_float_50</span><span class="special">&gt;()</span> <span class="special">*</span> <span class="number">2</span> <span class="special">*</span> <span class="identifier">seventh</span><span class="special">;</span>
+<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"c =  "</span><span class="special">&lt;&lt;</span> <span class="identifier">circumference</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
 </pre>
 <p>
         which outputs
       </p>
-<pre class="programlisting"><span class="number">0.89759790102565521098932668093700082405633411410717</span>
+<pre class="programlisting"><span class="identifier">pi</span> <span class="special">=</span> <span class="number">3.1415926535897932384626433832795028841971693993751</span>
+
+<span class="identifier">c</span> <span class="special">=</span>  <span class="number">0.89759790102565521098932668093700082405633411410717</span>
 </pre>
+<p>
+        The full source of this example is at <a href="../../../../example/big_seventh.cpp" target="_top">big_seventh.cpp</a>
+      </p>
 <h6>
 <a name="math_toolkit.high_precision.use_multiprecision.h1"></a>
         <span class="phrase"><a name="math_toolkit.high_precision.use_multiprecision.using_boost_multiprecision_to_ge"></a></span><a class="link" href="use_multiprecision.html#math_toolkit.high_precision.use_multiprecision.using_boost_multiprecision_to_ge">Using
-        Boost.Multiprecision to generate a high-precision array of sin coefficents
+        Boost.Multiprecision to generate a high-precision array of sine coefficents
         for use with FFT.</a>
       </h6>
 <p>
@@ -105,18 +109,37 @@
         exceeding that of standard built-in types such as <code class="computeroutput"><span class="keyword">float</span></code>,
         <code class="computeroutput"><span class="keyword">double</span></code> and <code class="computeroutput"><span class="keyword">long</span>
         <span class="keyword">double</span></code>. For extended-precision calculations,
-        Boost.Multiprecision supplies a template data type called <code class="computeroutput"><span class="identifier">cpp_dec_float</span></code>.
-        The number of decimal digits of precision is fixed at compile-time via template
-        parameter.
+        Boost.Multiprecision supplies a template data type called <code class="computeroutput"><span class="identifier">cpp_bin_float</span></code>.
+        The number of decimal digits of precision is fixed at compile-time via a
+        template parameter.
       </p>
 <p>
-        To use these floating-point types and constants, we need some includes:
+        One often needs to compute tables of numbers in mathematical software. To
+        avoid the <a href="https://en.wikipedia.org/wiki/Rounding#Table-maker's_dilemma" target="_top">Table-maker's
+        dilemma</a> it is necessary to use a higher precision type to compute
+        the table values so that they have the nearest representable bit-pattern
+        for the type, say <code class="computeroutput"><span class="keyword">double</span></code>, of
+        the table value.
+      </p>
+<p>
+        This example is a program <code class="computeroutput"><span class="identifier">fft_since_table</span><span class="special">.</span><span class="identifier">cpp</span></code> that
+        writes a header file <code class="computeroutput"><span class="identifier">sines</span><span class="special">.</span><span class="identifier">hpp</span></code> containing
+        an array of sine coefficients for use with a Fast Fourier Transform (FFT),
+        that can be included by the FFT program.
+      </p>
+<p>
+        To use Boost.Multiprecision's high-precision floating-point types and constants,
+        we need some includes:
       </p>
 <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">constants</span><span class="special">/</span><span class="identifier">constants</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
 <span class="comment">// using boost::math::constants::pi;</span>
 
-<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">cpp_dec_float</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
-<span class="comment">// using boost::multiprecision::cpp_dec_float</span>
+<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">cpp_bin_float</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span> <span class="comment">// for</span>
+<span class="comment">// using boost::multiprecision::cpp_bin_float and</span>
+<span class="comment">// using boost::multiprecision::cpp_bin_float_50;</span>
+<span class="comment">// using boost::multiprecision::cpp_bin_float_quad;</span>
+
+<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">array</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span> <span class="comment">// or &lt;array&gt; for std::array</span>
 
 <span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">iostream</span><span class="special">&gt;</span>
 <span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">limits</span><span class="special">&gt;</span>
@@ -127,43 +150,15 @@
 <span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">fstream</span><span class="special">&gt;</span>
 </pre>
 <p>
-        Define a text string which is a C++ comment with the program licence, copyright
-        etc. You could of course, tailor this to your needs, including your copyright
-        claim. There are versions of <code class="computeroutput"><span class="identifier">array</span></code>
-        provided by Boost.Array in <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">array</span></code>
-        or the C++11 std::array, but since not all platforms provide C++11 support,
-        this program provides the Boost version as fallback.
-      </p>
-<pre class="programlisting"><span class="keyword">static</span> <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">prolog</span> <span class="special">=</span>
-<span class="special">{</span>
-  <span class="string">"// Use, modification and distribution are subject to the\n"</span>
-  <span class="string">"// Boost Software License, Version 1.0.\n"</span>
-  <span class="string">"// (See accompanying file LICENSE_1_0.txt\n"</span>
-  <span class="string">"// or copy at "</span><span class="string">"http://www.boost.org/LICENSE_1_0.txt)\n\n"</span>
-
-  <span class="string">"// Copyright ???? 2013.\n\n"</span>
-
-  <span class="string">"// Use boost/array if std::array (C++11 feature) is not available.\n"</span>
-  <span class="string">"#ifdef  BOOST_NO_CXX11_HDR_ARRAY\n"</span>
-  <span class="string">"#include &lt;boost/array/array.hpp&gt;\n"</span>
-  <span class="string">"#else\n"</span>
-  <span class="string">"#include &lt;array&gt;\n"</span>
-  <span class="string">"#endif\n\n"</span>
-<span class="special">};</span>
-
-
-<span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">::</span><span class="identifier">cpp_dec_float_50</span><span class="special">;</span>
+        First, this example defines a prolog text string which is a C++ comment with
+        the program licence, copyright etc. (You would of course, tailor this to
+        your needs, including <span class="bold"><strong>your</strong></span> copyright claim).
+        This will appear at the top of the written header file <code class="computeroutput"><span class="identifier">sines</span><span class="special">.</span><span class="identifier">hpp</span></code>.
+      </p>
+<pre class="programlisting"><span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">::</span><span class="identifier">cpp_bin_float_50</span><span class="special">;</span>
 <span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">constants</span><span class="special">::</span><span class="identifier">pi</span><span class="special">;</span>
-<span class="comment">// VS 2010 (wrongly) requires these at file scope, not local scope in `main`.</span>
-<span class="comment">// This program also requires `-std=c++11` option to compile using Clang and GCC.</span>
-
-<span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span>
-<span class="special">{</span>
 </pre>
 <p>
-        One often needs to compute tables of numbers in mathematical software.
-      </p>
-<p>
         A fast Fourier transform (FFT), for example, may use a table of the values
         of sin((&#960;/2<sup>n</sup>) in its implementation details. In order to maximize the precision
         in the FFT implementation, the precision of the tabulated trigonometric values
@@ -174,29 +169,29 @@
         1 &lt;= n &lt;= 31.
       </p>
 <p>
-        This program makes use of, among other program elements, the data type <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">::</span><span class="identifier">cpp_dec_float_50</span></code> for a precision of 50
+        This program makes use of, among other program elements, the data type <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">::</span><span class="identifier">cpp_bin_float_50</span></code> for a precision of 50
         decimal digits from Boost.Multiprecision, the value of constant &#960; retrieved
         from Boost.Math, guaranteed to be initialized with the very last bit of precision
-        for the type, here <code class="computeroutput"><span class="identifier">cpp_dec_float_50</span></code>,
+        for the type, here <code class="computeroutput"><span class="identifier">cpp_bin_float_50</span></code>,
         and a C++11 lambda function combined with <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">for_each</span><span class="special">()</span></code>.
       </p>
 <p>
-        define the number of values in the array.
+        define the number of values (32) in the array of sines.
       </p>
 <pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> <span class="identifier">size</span> <span class="special">=</span> <span class="number">32U</span><span class="special">;</span>
-<span class="identifier">cpp_dec_float_50</span> <span class="identifier">p</span> <span class="special">=</span> <span class="identifier">pi</span><span class="special">&lt;</span><span class="identifier">cpp_dec_float_50</span><span class="special">&gt;();</span>
-<span class="identifier">cpp_dec_float_50</span> <span class="identifier">p2</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">constants</span><span class="special">::</span><span class="identifier">pi</span><span class="special">&lt;</span><span class="identifier">cpp_dec_float_50</span><span class="special">&gt;();</span>
+<span class="comment">//cpp_bin_float_50 p = pi&lt;cpp_bin_float_50&gt;();</span>
+<span class="identifier">cpp_bin_float_50</span> <span class="identifier">p</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">constants</span><span class="special">::</span><span class="identifier">pi</span><span class="special">&lt;</span><span class="identifier">cpp_bin_float_50</span><span class="special">&gt;();</span>
 
-<span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span> <span class="special">&lt;</span><span class="identifier">cpp_dec_float_50</span><span class="special">&gt;</span> <span class="identifier">sin_values</span> <span class="special">(</span><span class="identifier">size</span><span class="special">);</span>
+<span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span> <span class="special">&lt;</span><span class="identifier">cpp_bin_float_50</span><span class="special">&gt;</span> <span class="identifier">sin_values</span> <span class="special">(</span><span class="identifier">size</span><span class="special">);</span>
 <span class="keyword">unsigned</span> <span class="identifier">n</span> <span class="special">=</span> <span class="number">1U</span><span class="special">;</span>
 <span class="comment">// Generate the sine values.</span>
 <span class="identifier">std</span><span class="special">::</span><span class="identifier">for_each</span>
 <span class="special">(</span>
   <span class="identifier">sin_values</span><span class="special">.</span><span class="identifier">begin</span> <span class="special">(),</span>
   <span class="identifier">sin_values</span><span class="special">.</span><span class="identifier">end</span> <span class="special">(),</span>
-  <span class="special">[&amp;</span><span class="identifier">n</span><span class="special">](</span><span class="identifier">cpp_dec_float_50</span><span class="special">&amp;</span> <span class="identifier">y</span><span class="special">)</span>
+  <span class="special">[&amp;</span><span class="identifier">n</span><span class="special">](</span><span class="identifier">cpp_bin_float_50</span><span class="special">&amp;</span> <span class="identifier">y</span><span class="special">)</span>
   <span class="special">{</span>
-    <span class="identifier">y</span> <span class="special">=</span> <span class="identifier">sin</span><span class="special">(</span> <span class="identifier">pi</span><span class="special">&lt;</span><span class="identifier">cpp_dec_float_50</span><span class="special">&gt;()</span> <span class="special">/</span> <span class="identifier">pow</span><span class="special">(</span><span class="identifier">cpp_dec_float_50</span> <span class="special">(</span><span class="number">2</span><span class="special">),</span> <span class="identifier">n</span><span class="special">));</span>
+    <span class="identifier">y</span> <span class="special">=</span> <span class="identifier">sin</span><span class="special">(</span> <span class="identifier">pi</span><span class="special">&lt;</span><span class="identifier">cpp_bin_float_50</span><span class="special">&gt;()</span> <span class="special">/</span> <span class="identifier">pow</span><span class="special">(</span><span class="identifier">cpp_bin_float_50</span> <span class="special">(</span><span class="number">2</span><span class="special">),</span> <span class="identifier">n</span><span class="special">));</span>
     <span class="special">++</span><span class="identifier">n</span><span class="special">;</span>
   <span class="special">}</span>
 <span class="special">);</span>
@@ -204,7 +199,7 @@
 <p>
         Define the floating-point type for the generated file, either built-in <code class="computeroutput"><span class="keyword">double</span><span class="special">,</span> </code>float,
         or <code class="computeroutput"><span class="keyword">long</span> <span class="keyword">double</span></code>,
-        or a user defined type like <code class="computeroutput"><span class="identifier">cpp_dec_float_50</span></code>.
+        or a user defined type like <code class="computeroutput"><span class="identifier">cpp_bin_float_50</span></code>.
       </p>
 <pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">string</span> <span class="identifier">fp_type</span> <span class="special">=</span> <span class="string">"double"</span><span class="special">;</span>
 
@@ -214,24 +209,31 @@
 <p>
         By default, output would only show the standard 6 decimal digits, so set
         precision to show enough significant digits for the chosen floating-point
-        type. For <code class="computeroutput"><span class="identifier">cpp_dec_float_50</span></code>
+        type. For <code class="computeroutput"><span class="identifier">cpp_bin_float_50</span></code>
         is 50. (50 decimal digits should be ample for most applications).
       </p>
-<pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">streamsize</span> <span class="identifier">precision</span> <span class="special">=</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">cpp_dec_float_50</span><span class="special">&gt;::</span><span class="identifier">digits10</span><span class="special">;</span>
+<pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">streamsize</span> <span class="identifier">precision</span> <span class="special">=</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">cpp_bin_float_50</span><span class="special">&gt;::</span><span class="identifier">digits10</span><span class="special">;</span>
 
-<span class="comment">//  std::cout.precision(std::numeric_limits&lt;cpp_dec_float_50&gt;::digits10);</span>
-<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">precision</span> <span class="special">&lt;&lt;</span> <span class="string">" decimal digits precision. "</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Sines table precision is "</span> <span class="special">&lt;&lt;</span> <span class="identifier">precision</span> <span class="special">&lt;&lt;</span> <span class="string">" decimal digits. "</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
 </pre>
 <p>
-        Of course, one could also choose less, for example, 36 would be sufficient
-        for the most precise current <code class="computeroutput"><span class="keyword">long</span>
-        <span class="keyword">double</span></code> implementations using 128-bit.
-        In general, it should be a couple of decimal digits more (guard digits) than
-        <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">RealType</span><span class="special">&gt;::</span><span class="identifier">max_digits10</span></code> for the target system floating-point
-        type. If the implementation does not provide <code class="computeroutput"><span class="identifier">max_digits10</span></code>,
-        the the Kahan formula <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">RealType</span><span class="special">&gt;::</span><span class="identifier">digits</span>
-        <span class="special">*</span> <span class="number">3010</span><span class="special">/</span><span class="number">10000</span> <span class="special">+</span>
-        <span class="number">2</span></code> can be used instead.
+        Of course, one could also choose a lower precision for the table values,
+        for example,
+      </p>
+<p>
+        <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">streamsize</span> <span class="identifier">precision</span>
+        <span class="special">=</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">cpp_bin_float_quad</span><span class="special">&gt;::</span><span class="identifier">max_digits10</span><span class="special">;</span></code>
+      </p>
+<p>
+        128-bit 'quad' precision of 36 decimal digits would be sufficient for the
+        most precise current <code class="computeroutput"><span class="keyword">long</span> <span class="keyword">double</span></code>
+        implementations using 128-bit. In general, it should be a couple of decimal
+        digits more (guard digits) than <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">RealType</span><span class="special">&gt;::</span><span class="identifier">max_digits10</span></code>
+        for the target system floating-point type. (If the implementation does not
+        provide <code class="computeroutput"><span class="identifier">max_digits10</span></code>, the
+        the Kahan formula <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">RealType</span><span class="special">&gt;::</span><span class="identifier">digits</span> <span class="special">*</span> <span class="number">3010</span><span class="special">/</span><span class="number">10000</span>
+        <span class="special">+</span> <span class="number">2</span></code>
+        can be used instead).
       </p>
 <p>
         The compiler will read these values as decimal digits strings and use the
@@ -240,50 +242,48 @@
 <p>
         Now output all the sine table, to a file of your chosen name.
       </p>
-<pre class="programlisting">  <span class="keyword">const</span> <span class="keyword">char</span> <span class="identifier">sines_name</span><span class="special">[]</span> <span class="special">=</span> <span class="string">"sines.hpp"</span><span class="special">;</span>  <span class="comment">// In same directory as .exe</span>
+<pre class="programlisting"><span class="keyword">const</span> <span class="keyword">char</span> <span class="identifier">sines_name</span><span class="special">[]</span> <span class="special">=</span> <span class="string">"sines.hpp"</span><span class="special">;</span>  <span class="comment">// Assuming in same directory as .exe</span>
 
-  <span class="identifier">std</span><span class="special">::</span><span class="identifier">ofstream</span> <span class="identifier">fout</span><span class="special">(</span><span class="identifier">sines_name</span><span class="special">,</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">ios_base</span><span class="special">::</span><span class="identifier">out</span><span class="special">);</span>  <span class="comment">// Creates if no file exists,</span>
-  <span class="comment">// &amp; uses default overwrite/ ios::replace.</span>
-  <span class="keyword">if</span> <span class="special">(</span><span class="identifier">fout</span><span class="special">.</span><span class="identifier">is_open</span><span class="special">()</span> <span class="special">==</span> <span class="keyword">false</span><span class="special">)</span>
-  <span class="special">{</span>  <span class="comment">// failed to open OK!</span>
-    <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Open file "</span> <span class="special">&lt;&lt;</span> <span class="identifier">sines_name</span> <span class="special">&lt;&lt;</span> <span class="string">" failed!"</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
-    <span class="keyword">return</span> <span class="identifier">EXIT_FAILURE</span><span class="special">;</span>
-  <span class="special">}</span>
-  <span class="keyword">else</span>
-  <span class="special">{</span>
-    <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Open file "</span> <span class="special">&lt;&lt;</span> <span class="identifier">sines_name</span> <span class="special">&lt;&lt;</span> <span class="string">" for output OK."</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
-    <span class="identifier">fout</span> <span class="special">&lt;&lt;</span> <span class="identifier">prolog</span> <span class="special">&lt;&lt;</span> <span class="string">"// Table of "</span> <span class="special">&lt;&lt;</span> <span class="identifier">sin_values</span><span class="special">.</span><span class="identifier">size</span><span class="special">()</span> <span class="special">&lt;&lt;</span> <span class="string">" values with "</span>
-      <span class="special">&lt;&lt;</span> <span class="identifier">precision</span> <span class="special">&lt;&lt;</span> <span class="string">" decimal digits precision,\n"</span>
-      <span class="string">"// generated by program fft_sines_table.cpp.\n"</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+<span class="identifier">std</span><span class="special">::</span><span class="identifier">ofstream</span> <span class="identifier">fout</span><span class="special">(</span><span class="identifier">sines_name</span><span class="special">,</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">ios_base</span><span class="special">::</span><span class="identifier">out</span><span class="special">);</span>  <span class="comment">// Creates if no file exists,</span>
+<span class="comment">// &amp; uses default overwrite/ ios::replace.</span>
+<span class="keyword">if</span> <span class="special">(</span><span class="identifier">fout</span><span class="special">.</span><span class="identifier">is_open</span><span class="special">()</span> <span class="special">==</span> <span class="keyword">false</span><span class="special">)</span>
+<span class="special">{</span>  <span class="comment">// failed to open OK!</span>
+  <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Open file "</span> <span class="special">&lt;&lt;</span> <span class="identifier">sines_name</span> <span class="special">&lt;&lt;</span> <span class="string">" failed!"</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+  <span class="keyword">return</span> <span class="identifier">EXIT_FAILURE</span><span class="special">;</span>
+<span class="special">}</span>
+<span class="keyword">else</span>
+<span class="special">{</span> <span class="comment">// Write prolog etc as a C++ comment.</span>
+  <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Open file "</span> <span class="special">&lt;&lt;</span> <span class="identifier">sines_name</span> <span class="special">&lt;&lt;</span> <span class="string">" for output OK."</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+  <span class="identifier">fout</span> <span class="special">&lt;&lt;</span> <span class="identifier">prolog</span>
+  <span class="special">&lt;&lt;</span> <span class="string">"// Table of "</span> <span class="special">&lt;&lt;</span> <span class="identifier">sin_values</span><span class="special">.</span><span class="identifier">size</span><span class="special">()</span> <span class="special">&lt;&lt;</span> <span class="string">" values with "</span>
+    <span class="special">&lt;&lt;</span> <span class="identifier">precision</span> <span class="special">&lt;&lt;</span> <span class="string">" decimal digits precision,\n"</span>
+    <span class="string">"// generated by program fft_sines_table.cpp.\n"</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+
+<span class="identifier">fout</span> <span class="special">&lt;&lt;</span> <span class="string">"#include &lt;array&gt; // std::array"</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
 
-    <span class="identifier">fout</span> <span class="special">&lt;&lt;</span>
-<span class="string">"#ifdef BOOST_NO_CXX11_HDR_ARRAY"</span><span class="string">"\n"</span>
- <span class="string">"  static const boost::array&lt;double, "</span> <span class="special">&lt;&lt;</span> <span class="identifier">size</span> <span class="special">&lt;&lt;</span> <span class="string">"&gt; sines =\n"</span>
-<span class="string">"#else"</span><span class="string">"\n"</span>
-<span class="string">"  static const std::array&lt;double, "</span> <span class="special">&lt;&lt;</span> <span class="identifier">size</span> <span class="special">&lt;&lt;</span> <span class="string">"&gt; sines =\n"</span>
-<span class="string">"#endif"</span><span class="string">"\n"</span>
-    <span class="string">"{{\n"</span><span class="special">;</span> <span class="comment">// 2nd { needed for some GCC compiler versions.</span>
-    <span class="identifier">fout</span><span class="special">.</span><span class="identifier">precision</span><span class="special">(</span><span class="identifier">precision</span><span class="special">);</span>
+<span class="comment">// Write the table of sines as a C++ array.</span>
+  <span class="identifier">fout</span> <span class="special">&lt;&lt;</span>  <span class="string">"\nstatic const std::array&lt;double, "</span> <span class="special">&lt;&lt;</span> <span class="identifier">size</span> <span class="special">&lt;&lt;</span> <span class="string">"&gt; sines =\n"</span>
+  <span class="string">"{{\n"</span><span class="special">;</span> <span class="comment">// 2nd { needed for some old GCC compiler versions.</span>
+  <span class="identifier">fout</span><span class="special">.</span><span class="identifier">precision</span><span class="special">(</span><span class="identifier">precision</span><span class="special">);</span>
 
-    <span class="keyword">for</span> <span class="special">(</span><span class="keyword">unsigned</span> <span class="keyword">int</span> <span class="identifier">i</span> <span class="special">=</span> <span class="number">0U</span><span class="special">;</span> <span class="special">;)</span>
+  <span class="keyword">for</span> <span class="special">(</span><span class="keyword">unsigned</span> <span class="keyword">int</span> <span class="identifier">i</span> <span class="special">=</span> <span class="number">0U</span><span class="special">;</span> <span class="special">;)</span>
+  <span class="special">{</span>
+    <span class="identifier">fout</span> <span class="special">&lt;&lt;</span> <span class="string">"  "</span> <span class="special">&lt;&lt;</span> <span class="identifier">sin_values</span><span class="special">[</span><span class="identifier">i</span><span class="special">];</span>
+    <span class="keyword">if</span> <span class="special">(</span><span class="identifier">i</span> <span class="special">==</span> <span class="identifier">sin_values</span><span class="special">.</span><span class="identifier">size</span><span class="special">()-</span><span class="number">1</span><span class="special">)</span>
+    <span class="special">{</span> <span class="comment">// next is last value.</span>
+      <span class="identifier">fout</span> <span class="special">&lt;&lt;</span> <span class="string">"\n}};  // array sines\n"</span><span class="special">;</span> <span class="comment">// 2nd } needed for some old GCC compiler versions.</span>
+      <span class="keyword">break</span><span class="special">;</span>
+    <span class="special">}</span>
+    <span class="keyword">else</span>
     <span class="special">{</span>
-      <span class="identifier">fout</span> <span class="special">&lt;&lt;</span> <span class="string">"  "</span> <span class="special">&lt;&lt;</span> <span class="identifier">sin_values</span><span class="special">[</span><span class="identifier">i</span><span class="special">];</span>
-      <span class="keyword">if</span> <span class="special">(</span><span class="identifier">i</span> <span class="special">==</span> <span class="identifier">sin_values</span><span class="special">.</span><span class="identifier">size</span><span class="special">()-</span><span class="number">1</span><span class="special">)</span>
-      <span class="special">{</span> <span class="comment">// next is last value.</span>
-        <span class="identifier">fout</span> <span class="special">&lt;&lt;</span> <span class="string">"\n}};\n"</span><span class="special">;</span> <span class="comment">// 2nd } needed for some earlier GCC compiler versions.</span>
-        <span class="keyword">break</span><span class="special">;</span>
-      <span class="special">}</span>
-      <span class="keyword">else</span>
-      <span class="special">{</span>
-        <span class="identifier">fout</span> <span class="special">&lt;&lt;</span> <span class="string">",\n"</span><span class="special">;</span>
-        <span class="identifier">i</span><span class="special">++;</span>
-      <span class="special">}</span>
+      <span class="identifier">fout</span> <span class="special">&lt;&lt;</span> <span class="string">",\n"</span><span class="special">;</span>
+      <span class="identifier">i</span><span class="special">++;</span>
     <span class="special">}</span>
+  <span class="special">}</span> <span class="comment">// for</span>
 
-    <span class="identifier">fout</span><span class="special">.</span><span class="identifier">close</span><span class="special">();</span>
-    <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Close file "</span> <span class="special">&lt;&lt;</span> <span class="identifier">sines_name</span> <span class="special">&lt;&lt;</span> <span class="string">" for output OK."</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
-
-  <span class="special">}</span>
+  <span class="identifier">fout</span><span class="special">.</span><span class="identifier">close</span><span class="special">();</span>
+  <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Closed file "</span> <span class="special">&lt;&lt;</span> <span class="identifier">sines_name</span> <span class="special">&lt;&lt;</span> <span class="string">" for output."</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+<span class="special">}</span>
 </pre>
 <p>
         The output file generated can be seen at <a href="../../../../example/sines.hpp" target="_top">../../example/sines.hpp</a>
@@ -344,14 +344,17 @@
         knowledge engine can also be used to generate this table. The same command
         can be pasted into the compute box.
       </p>
+<p>
+        The full source of this example is at <a href="../../../../example/fft_sines_table.cpp" target="_top">fft_sines_table.cpp</a>
+      </p>
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/high_precision/use_ntl.html b/libs/math/doc/html/math_toolkit/high_precision/use_ntl.html
index c2401135b7..6cc4a07ccd 100644
--- a/libs/math/doc/html/math_toolkit/high_precision/use_ntl.html
+++ b/libs/math/doc/html/math_toolkit/high_precision/use_ntl.html
@@ -4,7 +4,7 @@
 <title>Using NTL Library</title>
 <link rel="stylesheet" href="../../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../high_precision.html" title="Using Boost.Math with High-Precision Floating-Point Libraries">
 <link rel="prev" href="e_float.html" title="Using e_float Library">
 <link rel="next" href="using_test.html" title="Using without expression templates for Boost.Test and others">
@@ -57,11 +57,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/high_precision/using_test.html b/libs/math/doc/html/math_toolkit/high_precision/using_test.html
index f42ead8a19..a154deab5b 100644
--- a/libs/math/doc/html/math_toolkit/high_precision/using_test.html
+++ b/libs/math/doc/html/math_toolkit/high_precision/using_test.html
@@ -4,7 +4,7 @@
 <title>Using without expression templates for Boost.Test and others</title>
 <link rel="stylesheet" href="../../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../high_precision.html" title="Using Boost.Math with High-Precision Floating-Point Libraries">
 <link rel="prev" href="use_ntl.html" title="Using NTL Library">
 <link rel="next" href="../real_concepts.html" title="Conceptual Requirements for Real Number Types">
@@ -127,11 +127,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/high_precision/why_high_precision.html b/libs/math/doc/html/math_toolkit/high_precision/why_high_precision.html
index fb0b16908f..80427e746a 100644
--- a/libs/math/doc/html/math_toolkit/high_precision/why_high_precision.html
+++ b/libs/math/doc/html/math_toolkit/high_precision/why_high_precision.html
@@ -4,7 +4,7 @@
 <title>Why use a high-precision library rather than built-in floating-point types?</title>
 <link rel="stylesheet" href="../../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../high_precision.html" title="Using Boost.Math with High-Precision Floating-Point Libraries">
 <link rel="prev" href="../high_precision.html" title="Using Boost.Math with High-Precision Floating-Point Libraries">
 <link rel="next" href="use_multiprecision.html" title="Using Boost.Multiprecision">
@@ -58,8 +58,8 @@
             is sometimes unpredictably inaccurate.
           </li>
 <li class="listitem">
-            Loss of precision or inaccuracy caused by extreme arguments or cancellation
-            error.
+            Loss of precision or inaccuracy caused by extreme arguments or <a href="http://en.wikipedia.org/wiki/Loss_of_significance" target="_top">cancellation
+            errors</a>.
           </li>
 <li class="listitem">
             An accuracy as good as possible for a chosen built-in floating-point
@@ -92,8 +92,9 @@
       </p>
 <p>
         If you require a value which is as accurate as can be represented in the
-        floating-point type, and is thus the closest representable value and has
-        an error less than 1/2 a <a href="http://en.wikipedia.org/wiki/Least_significant_bit" target="_top">least
+        floating-point type, and is thus the <a href="https://en.wikipedia.org/wiki/Floating-point_arithmetic#Representable_numbers%2c_conversion_and_rounding" target="_top">closest
+        representable value</a> correctly rounded to nearest, and has an error
+        less than 1/2 a <a href="http://en.wikipedia.org/wiki/Least_significant_bit" target="_top">least
         significant bit</a> or <a href="http://en.wikipedia.org/wiki/Unit_in_the_last_place" target="_top">ulp</a>
         it may be useful to use a higher-precision type, for example, <code class="computeroutput"><span class="identifier">cpp_dec_float_50</span></code>, to generate this value.
         Conversion of this value to a built-in floating-point type ('float', <code class="computeroutput"><span class="keyword">double</span></code> or <code class="computeroutput"><span class="keyword">long</span>
@@ -122,11 +123,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/hints.html b/libs/math/doc/html/math_toolkit/hints.html
index 511e6a8dad..5f3c7d03bc 100644
--- a/libs/math/doc/html/math_toolkit/hints.html
+++ b/libs/math/doc/html/math_toolkit/hints.html
@@ -4,7 +4,7 @@
 <title>Other Hints and tips</title>
 <link rel="stylesheet" href="../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../overview.html" title="Chapter&#160;1.&#160;Overview">
 <link rel="prev" href="conventions.html" title="Document Conventions">
 <link rel="next" href="directories.html" title="Directory and File Structure">
@@ -93,11 +93,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/history1.html b/libs/math/doc/html/math_toolkit/history1.html
index 42b7d5f61d..fb676497cc 100644
--- a/libs/math/doc/html/math_toolkit/history1.html
+++ b/libs/math/doc/html/math_toolkit/history1.html
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-<link rel="home" href="../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../overview.html" title="Chapter&#160;1.&#160;Overview">
 <link rel="prev" href="building.html" title="If and How to Build a Boost.Math Library, and its Examples and Tests">
 <link rel="next" href="overview_tr1.html" title="C99 and C++ TR1 C-style Functions">
@@ -35,6 +35,40 @@
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 <h5>
 <a name="math_toolkit.history1.h0"></a>
+      <span class="phrase"><a name="math_toolkit.history1.math_2_10_0_boost_1_71"></a></span><a class="link" href="history1.html#math_toolkit.history1.math_2_10_0_boost_1_71">Math-2.10.0
+      (Boost-1.71)</a>
+    </h5>
+<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
+<li class="listitem">
+          Catmull-Rom interpolator now works in C++11
+        </li>
+<li class="listitem">
+          Cardinal quadratic B-spline interpolation
+        </li>
+<li class="listitem">
+          Domain of elliptic integrals extended
+        </li>
+<li class="listitem">
+          sin_pi and cos_pi performance improvements
+        </li>
+<li class="listitem">
+          Forward-mode automatic differentiation
+        </li>
+<li class="listitem">
+          Vector valued barycentric rational interpolation
+        </li>
+<li class="listitem">
+          Ooura's method for evaluation of Fourier integrals
+        </li>
+<li class="listitem">
+          Multiple compatibility issues with Multiprecision fixed
+        </li>
+<li class="listitem">
+          Lambert-W fixed on a rare architecture
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+</ul></div>
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 <h5>
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+<a name="math_toolkit.history1.h33"></a>
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           Improved accuracy and testing of the inverse hypergeometric functions.
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 <h5>
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@@ -1083,7 +1117,7 @@ by switching to use the Students t distribution (or Normal distribution
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+<a name="math_toolkit.history1.h35"></a>
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 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/history2.html b/libs/math/doc/html/math_toolkit/history2.html
index 4d7c12a1f0..dacddb6f2e 100644
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+++ b/libs/math/doc/html/math_toolkit/history2.html
@@ -4,7 +4,7 @@
 <title>History and What's New</title>
 <link rel="stylesheet" href="../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../status.html" title="Chapter&#160;22.&#160;Library Status">
 <link rel="prev" href="../status.html" title="Chapter&#160;22.&#160;Library Status">
 <link rel="next" href="issues.html" title="Known Issues, and TODO List">
@@ -35,6 +35,40 @@
     </p>
 <h5>
 <a name="math_toolkit.history2.h0"></a>
+      <span class="phrase"><a name="math_toolkit.history2.math_2_10_0_boost_1_71"></a></span><a class="link" href="history2.html#math_toolkit.history2.math_2_10_0_boost_1_71">Math-2.10.0
+      (Boost-1.71)</a>
+    </h5>
+<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
+<li class="listitem">
+          Catmull-Rom interpolator now works in C++11
+        </li>
+<li class="listitem">
+          Cardinal quadratic B-spline interpolation
+        </li>
+<li class="listitem">
+          Domain of elliptic integrals extended
+        </li>
+<li class="listitem">
+          sin_pi and cos_pi performance improvements
+        </li>
+<li class="listitem">
+          Forward-mode automatic differentiation
+        </li>
+<li class="listitem">
+          Vector valued barycentric rational interpolation
+        </li>
+<li class="listitem">
+          Ooura's method for evaluation of Fourier integrals
+        </li>
+<li class="listitem">
+          Multiple compatibility issues with Multiprecision fixed
+        </li>
+<li class="listitem">
+          Lambert-W fixed on a rare architecture
+        </li>
+</ul></div>
+<h5>
+<a name="math_toolkit.history2.h1"></a>
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@@ -145,7 +179,7 @@
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           Polynomial arithmetic added to tools.
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@@ -641,7 +675,7 @@
           and Accurate Parallel Inversion of the Gamma Distribution, Thomas Luu</a>
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 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
@@ -777,14 +811,14 @@ by switching to use the Students t distribution (or Normal distribution
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 <p>
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 <h5>
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 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
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 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
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 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
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 <h5>
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@@ -941,7 +975,7 @@ by switching to use the Students t distribution (or Normal distribution
           <a href="https://svn.boost.org/trac/boost/ticket/5095" target="_top">#5113</a>.
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       <span class="phrase"><a name="math_toolkit.history2.boost_1_46_0"></a></span><a class="link" href="history2.html#math_toolkit.history2.boost_1_46_0">Boost-1.46.0</a>
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@@ -956,7 +990,7 @@ by switching to use the Students t distribution (or Normal distribution
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 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
@@ -973,7 +1007,7 @@ by switching to use the Students t distribution (or Normal distribution
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 <h5>
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       <span class="phrase"><a name="math_toolkit.history2.boost_1_44_0"></a></span><a class="link" href="history2.html#math_toolkit.history2.boost_1_44_0">Boost-1.44.0</a>
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 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
@@ -987,7 +1021,7 @@ by switching to use the Students t distribution (or Normal distribution
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 <h5>
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@@ -995,7 +1029,7 @@ by switching to use the Students t distribution (or Normal distribution
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 <h5>
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       <span class="phrase"><a name="math_toolkit.history2.boost_1_40_0"></a></span><a class="link" href="history2.html#math_toolkit.history2.boost_1_40_0">Boost-1.40.0</a>
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 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
@@ -1031,7 +1065,7 @@ by switching to use the Students t distribution (or Normal distribution
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 <h5>
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       <span class="phrase"><a name="math_toolkit.history2.boost_1_38_0"></a></span><a class="link" href="history2.html#math_toolkit.history2.boost_1_38_0">Boost-1.38.0</a>
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 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
@@ -1043,14 +1077,14 @@ by switching to use the Students t distribution (or Normal distribution
         </li>
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 <h5>
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+<a name="math_toolkit.history2.h33"></a>
       <span class="phrase"><a name="math_toolkit.history2.boost_1_37_0"></a></span><a class="link" href="history2.html#math_toolkit.history2.boost_1_37_0">Boost-1.37.0</a>
     </h5>
 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem">
           Improved accuracy and testing of the inverse hypergeometric functions.
         </li></ul></div>
 <h5>
-<a name="math_toolkit.history2.h33"></a>
+<a name="math_toolkit.history2.h34"></a>
       <span class="phrase"><a name="math_toolkit.history2.boost_1_36_0"></a></span><a class="link" href="history2.html#math_toolkit.history2.boost_1_36_0">Boost-1.36.0</a>
     </h5>
 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
@@ -1083,7 +1117,7 @@ by switching to use the Students t distribution (or Normal distribution
         </li>
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+<a name="math_toolkit.history2.h35"></a>
       <span class="phrase"><a name="math_toolkit.history2.boost_1_35_0_post_review_first_o"></a></span><a class="link" href="history2.html#math_toolkit.history2.boost_1_35_0_post_review_first_o">Boost-1.35.0:
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@@ -1115,7 +1149,7 @@ by switching to use the Students t distribution (or Normal distribution
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-<a name="math_toolkit.history2.h35"></a>
+<a name="math_toolkit.history2.h36"></a>
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+<a name="math_toolkit.history2.h37"></a>
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 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/internals.html b/libs/math/doc/html/math_toolkit/internals.html
index fb88b0b8a7..a3cc321cab 100644
--- a/libs/math/doc/html/math_toolkit/internals.html
+++ b/libs/math/doc/html/math_toolkit/internals.html
@@ -4,7 +4,7 @@
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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+<link rel="home" href="../index.html" title="Math Toolkit 2.10.0">
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@@ -44,11 +44,11 @@
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 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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+<link rel="home" href="../index.html" title="Math Toolkit 2.10.0">
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 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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+<link rel="home" href="../index.html" title="Math Toolkit 2.10.0">
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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+<link rel="home" href="../index.html" title="Math Toolkit 2.10.0">
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 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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@@ -99,11 +99,11 @@
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 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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@@ -69,11 +69,11 @@
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 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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+<link rel="home" href="../../index.html" title="Math Toolkit 2.10.0">
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@@ -65,11 +65,11 @@
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 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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@@ -69,11 +69,11 @@
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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index b7f52bf528..8e91c1572b 100644
--- a/libs/math/doc/html/math_toolkit/jacobi/jacobi_elliptic.html
+++ b/libs/math/doc/html/math_toolkit/jacobi/jacobi_elliptic.html
@@ -4,7 +4,7 @@
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-<link rel="home" href="../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.10.0">
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 <link rel="prev" href="jac_over.html" title="Overvew of the Jacobi Elliptic Functions">
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@@ -749,11 +749,11 @@
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 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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diff --git a/libs/math/doc/html/math_toolkit/jacobi/jacobi_nc.html b/libs/math/doc/html/math_toolkit/jacobi/jacobi_nc.html
index 59763aebdf..3a2af00895 100644
--- a/libs/math/doc/html/math_toolkit/jacobi/jacobi_nc.html
+++ b/libs/math/doc/html/math_toolkit/jacobi/jacobi_nc.html
@@ -4,7 +4,7 @@
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-<link rel="home" href="../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.10.0">
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@@ -69,11 +69,11 @@
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 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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diff --git a/libs/math/doc/html/math_toolkit/jacobi/jacobi_nd.html b/libs/math/doc/html/math_toolkit/jacobi/jacobi_nd.html
index 81e105c83e..8934321041 100644
--- a/libs/math/doc/html/math_toolkit/jacobi/jacobi_nd.html
+++ b/libs/math/doc/html/math_toolkit/jacobi/jacobi_nd.html
@@ -4,7 +4,7 @@
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-<link rel="home" href="../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.10.0">
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@@ -69,11 +69,11 @@
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 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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diff --git a/libs/math/doc/html/math_toolkit/jacobi/jacobi_ns.html b/libs/math/doc/html/math_toolkit/jacobi/jacobi_ns.html
index 3b1b73419b..67814b0e2f 100644
--- a/libs/math/doc/html/math_toolkit/jacobi/jacobi_ns.html
+++ b/libs/math/doc/html/math_toolkit/jacobi/jacobi_ns.html
@@ -4,7 +4,7 @@
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-<link rel="home" href="../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.10.0">
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@@ -69,11 +69,11 @@
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 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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diff --git a/libs/math/doc/html/math_toolkit/jacobi/jacobi_sc.html b/libs/math/doc/html/math_toolkit/jacobi/jacobi_sc.html
index aef7929c99..e39459d048 100644
--- a/libs/math/doc/html/math_toolkit/jacobi/jacobi_sc.html
+++ b/libs/math/doc/html/math_toolkit/jacobi/jacobi_sc.html
@@ -4,7 +4,7 @@
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-<link rel="home" href="../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.10.0">
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@@ -69,11 +69,11 @@
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 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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diff --git a/libs/math/doc/html/math_toolkit/jacobi/jacobi_sd.html b/libs/math/doc/html/math_toolkit/jacobi/jacobi_sd.html
index 344bfe1be6..2d3971ad6c 100644
--- a/libs/math/doc/html/math_toolkit/jacobi/jacobi_sd.html
+++ b/libs/math/doc/html/math_toolkit/jacobi/jacobi_sd.html
@@ -4,7 +4,7 @@
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-<link rel="home" href="../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.10.0">
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@@ -69,11 +69,11 @@
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 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/jacobi/jacobi_sn.html b/libs/math/doc/html/math_toolkit/jacobi/jacobi_sn.html
index d621f4d9d7..7a36f9c197 100644
--- a/libs/math/doc/html/math_toolkit/jacobi/jacobi_sn.html
+++ b/libs/math/doc/html/math_toolkit/jacobi/jacobi_sn.html
@@ -4,7 +4,7 @@
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+<link rel="home" href="../../index.html" title="Math Toolkit 2.10.0">
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 <link rel="next" href="../lambert_w.html" title="Lambert W function">
@@ -65,11 +65,11 @@
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 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/lambert_w.html b/libs/math/doc/html/math_toolkit/lambert_w.html
index 2eca85ea12..29a63cb174 100644
--- a/libs/math/doc/html/math_toolkit/lambert_w.html
+++ b/libs/math/doc/html/math_toolkit/lambert_w.html
@@ -4,7 +4,7 @@
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-<link rel="home" href="../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../special.html" title="Chapter&#160;7.&#160;Special Functions">
 <link rel="prev" href="jacobi/jacobi_sn.html" title="Jacobi Elliptic Function sn">
 <link rel="next" href="zetas.html" title="Zeta Functions">
@@ -797,9 +797,10 @@ with the functions <code class="computeroutput"><span class="identifier">lambert
       for the C++ type being used, it is usually necessary to use a higher precision
       type for intermediate computation, finally static-casting back to the smaller
       desired result type. This strategy is used by <a href="https://www.maplesoft.com" target="_top">Maple</a>
-      and WolframAlpha, for example, using arbitrary precision arithmetic, and some
-      of their high-precision values are used for testing this library. This method
-      is also used to provide some <a href="../../../../../libs/test/doc/html/index.html" target="_top">Boost.Test</a>
+      and <a href="http://www.wolframalpha.com/" target="_top">Wolfram Alpha</a>, for example,
+      using arbitrary precision arithmetic, and some of their high-precision values
+      are used for testing this library. This method is also used to provide some
+      <a href="https://www.boost.org/doc/libs/release/libs/test/doc/html/index.html" target="_top">Boost.Test</a>
       values using <a href="../../../../../libs/multiprecision/doc/html/index.html" target="_top">Boost.Multiprecision</a>,
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       <code class="computeroutput"><span class="keyword">static_cast</span></code> to a <code class="computeroutput"><span class="keyword">float</span></code>, <code class="computeroutput"><span class="keyword">double</span></code>
@@ -820,8 +821,9 @@ with the functions <code class="computeroutput"><span class="identifier">lambert
       is not justified and the algorithms here do not implement this. But because
       the Boost.Lambert_W algorithms has been tested using <a href="../../../../../libs/multiprecision/doc/html/index.html" target="_top">Boost.Multiprecision</a>,
       users who require this can always easily achieve the nearest representation
-      for __fundamental - if the application justifies the very large extra computation
-      cost.
+      for <a href="http://en.cppreference.com/w/cpp/language/types" target="_top">fundamental
+      (built-in) types</a> - if the application justifies the very large extra
+      computation cost.
     </p>
 <h6>
 <a name="math_toolkit.lambert_w.h16"></a>
@@ -1749,8 +1751,8 @@ if (f(w) / f'</span><span class="special">(</span><span class="identifier">w</sp
 <p>
       See source at: <a href="../../../example/lambert_w_simple_examples.cpp" target="_top">lambert_w_simple_examples.cpp</a>
       <a href="../../../test/test_lambert_w.cpp" target="_top">test_lambert_w.cpp</a> contains
-      routine tests using <a href="../../../../../libs/test/doc/html/index.html" target="_top">Boost.Test</a>.
-      <a href="../../sf/lambert_w_errors_graph.cpp" target="_top">lambert_w_errors_graph.cpp</a>
+      routine tests using <a href="https://www.boost.org/doc/libs/release/libs/test/doc/html/index.html" target="_top">Boost.Test</a>.
+      <a href="../../../tools/lambert_w_errors_graph.cpp" target="_top">lambert_w_errors_graph.cpp</a>
       generating error graphs.
     </p>
 <h6>
@@ -1890,11 +1892,11 @@ if (f(w) / f'</span><span class="special">(</span><span class="identifier">w</sp
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/lanczos.html b/libs/math/doc/html/math_toolkit/lanczos.html
index 003923e279..d0f0d60ecc 100644
--- a/libs/math/doc/html/math_toolkit/lanczos.html
+++ b/libs/math/doc/html/math_toolkit/lanczos.html
@@ -4,7 +4,7 @@
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 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../index.html" title="Math Toolkit 2.10.0">
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 <link rel="next" href="remez.html" title="The Remez Method">
@@ -560,11 +560,11 @@
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 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/logs_and_tables.html b/libs/math/doc/html/math_toolkit/logs_and_tables.html
index 12505af621..8585eabc0d 100644
--- a/libs/math/doc/html/math_toolkit/logs_and_tables.html
+++ b/libs/math/doc/html/math_toolkit/logs_and_tables.html
@@ -4,7 +4,7 @@
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-<link rel="home" href="../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../index.html" title="Math Toolkit 2.10.0">
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 <link rel="next" href="logs_and_tables/all_table.html" title="Tables of Error Rates for all Functions">
@@ -35,11 +35,11 @@
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 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/logs_and_tables/all_table.html b/libs/math/doc/html/math_toolkit/logs_and_tables/all_table.html
index 4885df2206..6bcf3166aa 100644
--- a/libs/math/doc/html/math_toolkit/logs_and_tables/all_table.html
+++ b/libs/math/doc/html/math_toolkit/logs_and_tables/all_table.html
@@ -4,7 +4,7 @@
 <title>Tables of Error Rates for all Functions</title>
 <link rel="stylesheet" href="../../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../logs_and_tables.html" title="Error logs and tables">
 <link rel="prev" href="../logs_and_tables.html" title="Error logs and tables">
 <link rel="next" href="logs.html" title="Error Logs For Error Rate Tables">
@@ -12048,11 +12048,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/logs_and_tables/logs.html b/libs/math/doc/html/math_toolkit/logs_and_tables/logs.html
index 34dfaa90d8..11567759ce 100644
--- a/libs/math/doc/html/math_toolkit/logs_and_tables/logs.html
+++ b/libs/math/doc/html/math_toolkit/logs_and_tables/logs.html
@@ -4,7 +4,7 @@
 <title>Error Logs For Error Rate Tables</title>
 <link rel="stylesheet" href="../../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../logs_and_tables.html" title="Error logs and tables">
 <link rel="prev" href="all_table.html" title="Tables of Error Rates for all Functions">
 <link rel="next" href="../../status.html" title="Chapter&#160;22.&#160;Library Status">
@@ -3141,11 +3141,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/macros.html b/libs/math/doc/html/math_toolkit/macros.html
index 302b225a17..8c9f8945a1 100644
--- a/libs/math/doc/html/math_toolkit/macros.html
+++ b/libs/math/doc/html/math_toolkit/macros.html
@@ -4,7 +4,7 @@
 <title>Floating-Point Constant Macros</title>
 <link rel="stylesheet" href="../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../cstdfloat.html" title="Chapter&#160;3.&#160;Specified-width floating-point typedefs">
 <link rel="prev" href="greatest_typdefs.html" title="Greatest-width floating-point typedef">
 <link rel="next" href="examples.html" title="Examples">
@@ -71,11 +71,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/main_faq.html b/libs/math/doc/html/math_toolkit/main_faq.html
index 717af4c989..10c6d4c279 100644
--- a/libs/math/doc/html/math_toolkit/main_faq.html
+++ b/libs/math/doc/html/math_toolkit/main_faq.html
@@ -1,10 +1,10 @@
 <html>
 <head>
 <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
-<title>Frequently Asked Questions FAQ</title>
+<title>Boost.Math Frequently Asked Questions (FAQs)</title>
 <link rel="stylesheet" href="../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../overview.html" title="Chapter&#160;1.&#160;Overview">
 <link rel="prev" href="overview_tr1.html" title="C99 and C++ TR1 C-style Functions">
 <link rel="next" href="contact.html" title="Contact Info and Support">
@@ -24,7 +24,8 @@
 </div>
 <div class="section">
 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
-<a name="math_toolkit.main_faq"></a><a class="link" href="main_faq.html" title="Frequently Asked Questions FAQ">Frequently Asked Questions FAQ</a>
+<a name="math_toolkit.main_faq"></a><a class="link" href="main_faq.html" title="Boost.Math Frequently Asked Questions (FAQs)">Boost.Math Frequently Asked Questions
+    (FAQs)</a>
 </h2></div></div></div>
 <div class="orderedlist"><ol class="orderedlist" type="1">
 <li class="listitem">
@@ -64,9 +65,10 @@
 <p class="simpara">
           Fear not - you are not alone! Many examples are available for functions
           and distributions. Some are referenced directly from the text. Others can
-          be found at \boost_latest_release\libs\math\example. If you are a Visual
-          Studio user, you should be able to create projects from each of these,
-          making sure that the Boost library is in the include directories list.
+          be found at <code class="computeroutput"><span class="special">\</span><span class="identifier">boost_latest_release</span><span class="special">\</span><span class="identifier">libs</span><span class="special">\</span><span class="identifier">math</span><span class="special">\</span><span class="identifier">example</span></code>,
+          for example If you are a Visual Studio user, you should be able to create
+          projects from each of these, making sure that the Boost library is in the
+          include directories list (there are usually NO libraries that must be built).
         </p>
 </li>
 <li class="listitem">
@@ -76,7 +78,7 @@
         </p>
 <p class="simpara">
           You can add an include path, for example, your Boost place /boost-latest_release,
-          for example <code class="computeroutput"><span class="identifier">X</span><span class="special">:/</span><span class="identifier">boost_1_45_0</span><span class="special">/</span></code>
+          for example <code class="computeroutput"><span class="identifier">X</span><span class="special">:/</span><span class="identifier">boost_1_70_0</span><span class="special">/</span></code>
           if you have a separate partition X for Boost releases. Or you can use an
           environment variable BOOST_ROOT set to your Boost place, and include that.
           Visual Studio before 2010 provided Tools, Options, VC++ Directories to
@@ -292,15 +294,44 @@
           multiprecision arithmetic</a> and <a href="http://svn.boost.org/svn/boost/trunk/libs/multiprecision/doc/html/boost_multiprecision/tut/conversions.html" target="_top">conversion</a>.
         </p>
 </li>
+<li class="listitem">
+<p class="simpara">
+          <span class="emphasis"><em>How do I choose between Boost.Multiprecision cpp_bin_50 and cpp_dec_50?</em></span>
+        </p>
+<p class="simpara">
+          Unless you have a specific reason to choose <code class="computeroutput"><span class="identifier">cpp_dec_</span></code>,
+          then the default choice should be <code class="computeroutput"><span class="identifier">cpp_bin_</span></code>,
+          for example using the convenience <code class="computeroutput"><span class="identifier">typedefs</span></code>
+          like <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">::</span><span class="identifier">cpp_bin_50</span></code> or <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">::</span><span class="identifier">cpp_bin_100</span></code>.
+        </p>
+<p class="simpara">
+          In general, both work well and give the same results and at roughly the
+          same speed with <code class="computeroutput"><span class="identifier">cpp_dec_50</span></code>
+          sometimes faster.
+        </p>
+<p class="simpara">
+          cpp_dec_ was developed first paving the way for cpp_bin_. cpp_dec_ has
+          several guard digits and is not rounded at all, using 'brute force' to
+          get the promised number of decimal digits correct, but making it difficult
+          to reason about precision and computational uncertainty, for example see
+          <span class="bold"><strong>https://svn.boost.org/trac10/ticket/12133</strong></span>.
+          It also has a fast but imprecise division operator giving surprising results
+          sometimes, see <span class="bold"><strong>https://svn.boost.org/trac10/ticket/11178</strong></span>.
+        </p>
+<p class="simpara">
+          cpp_bin_ is correctly/exactly rounded making it possible to reason about
+          both the precision and rounding of the results.
+        </p>
+</li>
 </ol></div>
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/main_intro.html b/libs/math/doc/html/math_toolkit/main_intro.html
index d50408ff87..591335872a 100644
--- a/libs/math/doc/html/math_toolkit/main_intro.html
+++ b/libs/math/doc/html/math_toolkit/main_intro.html
@@ -4,7 +4,7 @@
 <title>About the Math Toolkit</title>
 <link rel="stylesheet" href="../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../overview.html" title="Chapter&#160;1.&#160;Overview">
 <link rel="prev" href="../overview.html" title="Chapter&#160;1.&#160;Overview">
 <link rel="next" href="navigation.html" title="Navigation">
@@ -35,18 +35,18 @@
       Point Utilities</a>
     </h5>
 <p>
-      Utility functions for dealing with floating point arithmetic, includes functions
+      Utility functions for dealing with floating-point arithmetic, includes functions
       for floating point classification (fpclassify, isnan, isinf etc), sign manipulation,
       rounding, comparison, and computing the distance between floating point numbers.
     </p>
 <h5>
 <a name="math_toolkit.main_intro.h1"></a>
       <span class="phrase"><a name="math_toolkit.main_intro.specific_width_floating_point_ty"></a></span><a class="link" href="main_intro.html#math_toolkit.main_intro.specific_width_floating_point_ty">Specific
-      Width Floating Point Types</a>
+      Width Floating-Point Types</a>
     </h5>
 <p>
       A set of typedefs similar to those provided by <code class="computeroutput"><span class="special">&lt;</span><span class="identifier">cstdint</span><span class="special">&gt;</span></code>
-      but for floating point types.
+      but for floating-point types.
     </p>
 <h5>
 <a name="math_toolkit.main_intro.h2"></a>
@@ -142,7 +142,7 @@
       <span class="phrase"><a name="math_toolkit.main_intro.interpolation"></a></span><a class="link" href="main_intro.html#math_toolkit.main_intro.interpolation">Interpolation</a>
     </h5>
 <p>
-      Function interpolation via Barycentic or cubic B_spline approximations.
+      Function interpolation via Barycentric or cubic B_spline approximations.
     </p>
 <h5>
 <a name="math_toolkit.main_intro.h8"></a>
@@ -150,8 +150,8 @@
       Integration and Differentiation</a>
     </h5>
 <p>
-      A reasonably comprehensive set of routines for integration (trapezoidal, Gaus-Legendre,
-      Gaus-Kronrod and double-exponential) and differentiation.
+      A reasonably comprehensive set of routines for integration (trapezoidal, Gauss-Legendre,
+      Gauss-Kronrod and double-exponential) and differentiation.
     </p>
 <p>
       The integration routines are all usable for functions returning complex results
@@ -168,11 +168,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/main_tr1.html b/libs/math/doc/html/math_toolkit/main_tr1.html
index d668d328df..63d2d44e46 100644
--- a/libs/math/doc/html/math_toolkit/main_tr1.html
+++ b/libs/math/doc/html/math_toolkit/main_tr1.html
@@ -4,7 +4,7 @@
 <title>C99 and TR1 C Functions Overview</title>
 <link rel="stylesheet" href="../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../extern_c.html" title='Chapter&#160;8.&#160;TR1 and C99 external "C" Functions'>
 <link rel="prev" href="../extern_c.html" title='Chapter&#160;8.&#160;TR1 and C99 external "C" Functions'>
 <link rel="next" href="c99.html" title="C99 C Functions">
@@ -600,11 +600,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/mem_typedef.html b/libs/math/doc/html/math_toolkit/mem_typedef.html
index 3ba15e9631..6d40ff7653 100644
--- a/libs/math/doc/html/math_toolkit/mem_typedef.html
+++ b/libs/math/doc/html/math_toolkit/mem_typedef.html
@@ -4,7 +4,7 @@
 <title>Quaternion Member Typedefs</title>
 <link rel="stylesheet" href="../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../quaternions.html" title="Chapter&#160;14.&#160;Quaternions">
 <link rel="prev" href="spec.html" title="Quaternion Specializations">
 <link rel="next" href="quat_mem_fun.html" title="Quaternion Member Functions">
@@ -55,11 +55,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/minimum_typdefs.html b/libs/math/doc/html/math_toolkit/minimum_typdefs.html
index 9baff91995..a4b8b56f31 100644
--- a/libs/math/doc/html/math_toolkit/minimum_typdefs.html
+++ b/libs/math/doc/html/math_toolkit/minimum_typdefs.html
@@ -4,7 +4,7 @@
 <title>Minimum-width floating-point typedefs</title>
 <link rel="stylesheet" href="../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../cstdfloat.html" title="Chapter&#160;3.&#160;Specified-width floating-point typedefs">
 <link rel="prev" href="exact_typdefs.html" title="Exact-Width Floating-Point typedefs">
 <link rel="next" href="fastest_typdefs.html" title="Fastest floating-point typedefs">
@@ -45,11 +45,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/multiprecision.html b/libs/math/doc/html/math_toolkit/multiprecision.html
index 076a819a5c..6d8f9c26a6 100644
--- a/libs/math/doc/html/math_toolkit/multiprecision.html
+++ b/libs/math/doc/html/math_toolkit/multiprecision.html
@@ -4,7 +4,7 @@
 <title>Cost of High-Precision Non-built-in Floating-point</title>
 <link rel="stylesheet" href="../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../perf.html" title="Chapter&#160;20.&#160;Performance">
 <link rel="prev" href="tradoffs.html" title="Trading Accuracy for Performance">
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@@ -109,11 +109,11 @@
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+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
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+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
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+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
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+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
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+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
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+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
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+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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--- a/libs/math/doc/html/math_toolkit/number_series/tangent_numbers.html
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 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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@@ -94,11 +94,11 @@
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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--- a/libs/math/doc/html/math_toolkit/oct_overview.html
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@@ -4,7 +4,7 @@
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+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
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-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
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+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
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+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
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+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
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+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
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-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
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+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
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-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
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+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
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+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
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+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
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+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
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+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
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+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
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-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
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+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
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+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
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@@ -4,7 +4,7 @@
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 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/pol_ref/precision_pol.html b/libs/math/doc/html/math_toolkit/pol_ref/precision_pol.html
index 7b46e0777b..e307597d4b 100644
--- a/libs/math/doc/html/math_toolkit/pol_ref/precision_pol.html
+++ b/libs/math/doc/html/math_toolkit/pol_ref/precision_pol.html
@@ -4,7 +4,7 @@
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-<link rel="home" href="../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../pol_ref.html" title="Policy Reference">
 <link rel="prev" href="discrete_quant_ref.html" title="Discrete Quantile Policies">
 <link rel="next" href="iteration_pol.html" title="Iteration Limits Policies">
@@ -93,11 +93,11 @@
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 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/pol_tutorial.html b/libs/math/doc/html/math_toolkit/pol_tutorial.html
index fc9ca9534a..078397e0fa 100644
--- a/libs/math/doc/html/math_toolkit/pol_tutorial.html
+++ b/libs/math/doc/html/math_toolkit/pol_tutorial.html
@@ -4,7 +4,7 @@
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 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../policy.html" title="Chapter&#160;19.&#160;Policies: Controlling Precision, Error Handling etc">
 <link rel="prev" href="pol_overview.html" title="Policy Overview">
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@@ -49,11 +49,11 @@
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 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/pol_tutorial/ad_hoc_dist_policies.html b/libs/math/doc/html/math_toolkit/pol_tutorial/ad_hoc_dist_policies.html
index e474de43ea..a13fffe7eb 100644
--- a/libs/math/doc/html/math_toolkit/pol_tutorial/ad_hoc_dist_policies.html
+++ b/libs/math/doc/html/math_toolkit/pol_tutorial/ad_hoc_dist_policies.html
@@ -4,7 +4,7 @@
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 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../pol_tutorial.html" title="Policy Tutorial">
 <link rel="prev" href="changing_policy_defaults.html" title="Changing the Policy Defaults">
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@@ -88,11 +88,11 @@
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 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/pol_tutorial/ad_hoc_sf_policies.html b/libs/math/doc/html/math_toolkit/pol_tutorial/ad_hoc_sf_policies.html
index 3fb85b793c..1453a26295 100644
--- a/libs/math/doc/html/math_toolkit/pol_tutorial/ad_hoc_sf_policies.html
+++ b/libs/math/doc/html/math_toolkit/pol_tutorial/ad_hoc_sf_policies.html
@@ -4,7 +4,7 @@
 <title>Changing the Policy on an Ad Hoc Basis for the Special Functions</title>
 <link rel="stylesheet" href="../../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../pol_tutorial.html" title="Policy Tutorial">
 <link rel="prev" href="ad_hoc_dist_policies.html" title="Setting Policies for Distributions on an Ad Hoc Basis">
 <link rel="next" href="namespace_policies.html" title="Setting Policies at Namespace or Translation Unit Scope">
@@ -157,11 +157,11 @@ errno = 33
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/pol_tutorial/changing_policy_defaults.html b/libs/math/doc/html/math_toolkit/pol_tutorial/changing_policy_defaults.html
index 292028ad7b..47797b2043 100644
--- a/libs/math/doc/html/math_toolkit/pol_tutorial/changing_policy_defaults.html
+++ b/libs/math/doc/html/math_toolkit/pol_tutorial/changing_policy_defaults.html
@@ -4,7 +4,7 @@
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 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../pol_tutorial.html" title="Policy Tutorial">
 <link rel="prev" href="policy_usage.html" title="So How are Policies Used Anyway?">
 <link rel="next" href="ad_hoc_dist_policies.html" title="Setting Policies for Distributions on an Ad Hoc Basis">
@@ -241,11 +241,11 @@ errno is set to: 33
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/pol_tutorial/namespace_policies.html b/libs/math/doc/html/math_toolkit/pol_tutorial/namespace_policies.html
index d6ec0a5b74..b742c81967 100644
--- a/libs/math/doc/html/math_toolkit/pol_tutorial/namespace_policies.html
+++ b/libs/math/doc/html/math_toolkit/pol_tutorial/namespace_policies.html
@@ -4,7 +4,7 @@
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 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../pol_tutorial.html" title="Policy Tutorial">
 <link rel="prev" href="ad_hoc_sf_policies.html" title="Changing the Policy on an Ad Hoc Basis for the Special Functions">
 <link rel="next" href="user_def_err_pol.html" title="Calling User Defined Error Handlers">
@@ -349,11 +349,11 @@ Result of quantile(complement(binom, 0.05)) is: 8
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/pol_tutorial/policy_tut_defaults.html b/libs/math/doc/html/math_toolkit/pol_tutorial/policy_tut_defaults.html
index f7a43aa928..06a3a085c2 100644
--- a/libs/math/doc/html/math_toolkit/pol_tutorial/policy_tut_defaults.html
+++ b/libs/math/doc/html/math_toolkit/pol_tutorial/policy_tut_defaults.html
@@ -4,7 +4,7 @@
 <title>Policies Have Sensible Defaults</title>
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 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../pol_tutorial.html" title="Policy Tutorial">
 <link rel="prev" href="what_is_a_policy.html" title="So Just What is a Policy Anyway?">
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@@ -141,11 +141,11 @@
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 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/pol_tutorial/policy_usage.html b/libs/math/doc/html/math_toolkit/pol_tutorial/policy_usage.html
index 477627f143..c13401863b 100644
--- a/libs/math/doc/html/math_toolkit/pol_tutorial/policy_usage.html
+++ b/libs/math/doc/html/math_toolkit/pol_tutorial/policy_usage.html
@@ -4,7 +4,7 @@
 <title>So How are Policies Used Anyway?</title>
 <link rel="stylesheet" href="../../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../pol_tutorial.html" title="Policy Tutorial">
 <link rel="prev" href="policy_tut_defaults.html" title="Policies Have Sensible Defaults">
 <link rel="next" href="changing_policy_defaults.html" title="Changing the Policy Defaults">
@@ -56,11 +56,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/pol_tutorial/understand_dis_quant.html b/libs/math/doc/html/math_toolkit/pol_tutorial/understand_dis_quant.html
index 714649a362..a5a52db4ea 100644
--- a/libs/math/doc/html/math_toolkit/pol_tutorial/understand_dis_quant.html
+++ b/libs/math/doc/html/math_toolkit/pol_tutorial/understand_dis_quant.html
@@ -4,7 +4,7 @@
 <title>Understanding Quantiles of Discrete Distributions</title>
 <link rel="stylesheet" href="../../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../pol_tutorial.html" title="Policy Tutorial">
 <link rel="prev" href="user_def_err_pol.html" title="Calling User Defined Error Handlers">
 <link rel="next" href="../pol_ref.html" title="Policy Reference">
@@ -400,11 +400,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/pol_tutorial/user_def_err_pol.html b/libs/math/doc/html/math_toolkit/pol_tutorial/user_def_err_pol.html
index d2f56ebdf1..f6ed275fa1 100644
--- a/libs/math/doc/html/math_toolkit/pol_tutorial/user_def_err_pol.html
+++ b/libs/math/doc/html/math_toolkit/pol_tutorial/user_def_err_pol.html
@@ -4,7 +4,7 @@
 <title>Calling User Defined Error Handlers</title>
 <link rel="stylesheet" href="../../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../pol_tutorial.html" title="Policy Tutorial">
 <link rel="prev" href="namespace_policies.html" title="Setting Policies at Namespace or Translation Unit Scope">
 <link rel="next" href="understand_dis_quant.html" title="Understanding Quantiles of Discrete Distributions">
@@ -437,11 +437,11 @@ Result of tgamma(-190.5) is: 0
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/pol_tutorial/what_is_a_policy.html b/libs/math/doc/html/math_toolkit/pol_tutorial/what_is_a_policy.html
index 5cbf5c6b14..9583605654 100644
--- a/libs/math/doc/html/math_toolkit/pol_tutorial/what_is_a_policy.html
+++ b/libs/math/doc/html/math_toolkit/pol_tutorial/what_is_a_policy.html
@@ -4,7 +4,7 @@
 <title>So Just What is a Policy Anyway?</title>
 <link rel="stylesheet" href="../../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../pol_tutorial.html" title="Policy Tutorial">
 <link rel="prev" href="../pol_tutorial.html" title="Policy Tutorial">
 <link rel="next" href="policy_tut_defaults.html" title="Policies Have Sensible Defaults">
@@ -84,11 +84,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
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 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
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+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
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+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
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-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
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         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
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+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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@@ -44,11 +44,11 @@
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 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
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 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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diff --git a/libs/math/doc/html/math_toolkit/refs.html b/libs/math/doc/html/math_toolkit/refs.html
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@@ -198,11 +198,11 @@
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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diff --git a/libs/math/doc/html/math_toolkit/root_comparison/root_n_comparison.html b/libs/math/doc/html/math_toolkit/root_comparison/root_n_comparison.html
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--- a/libs/math/doc/html/math_toolkit/root_comparison/root_n_comparison.html
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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@@ -4,7 +4,7 @@
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@@ -149,11 +149,11 @@
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 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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@@ -4,7 +4,7 @@
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+<link rel="home" href="../../index.html" title="Math Toolkit 2.10.0">
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 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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@@ -4,7 +4,7 @@
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-<link rel="home" href="../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.10.0">
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@@ -255,11 +255,11 @@
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 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
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+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
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+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
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+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
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+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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index 0000000000..22ea51dfd6
--- /dev/null
+++ b/libs/math/doc/html/math_toolkit/sf_poly/de_refes.html
@@ -0,0 +1,64 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
+<title>References</title>
+<link rel="stylesheet" href="../../math.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.9.0">
+<link rel="up" href="../sf_poly.html" title="Polynomials">
+<link rel="prev" href="b_spline.html" title="Cardinal B-splines">
+<link rel="next" href="../bessel.html" title="Bessel Functions">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td>
+<td align="center"><a href="../../../../../../index.html">Home</a></td>
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+<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td>
+<td align="center"><a href="../../../../../../more/index.htm">More</a></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="b_spline.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../sf_poly.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="../bessel.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
+</div>
+<div class="section">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="math_toolkit.sf_poly.de_refes"></a><a class="link" href="de_refes.html" title="References">References</a>
+</h3></div></div></div>
+<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
+<li class="listitem">
+            I.J. Schoenberg, <span class="emphasis"><em>Cardinal Spline Interpolation</em></span>,
+            SIAM Volume 12, 1973
+          </li>
+<li class="listitem">
+            Rainer Kress, <span class="emphasis"><em>Numerical Analysis</em></span>, Springer, 1998
+          </li>
+<li class="listitem">
+            Peter Massopust, <span class="emphasis"><em>On Some Generalizations of B-splines</em></span>,
+            arxiv preprint, 2019
+          </li>
+<li class="listitem">
+            Michael Unser and Thierry Blu, <span class="emphasis"><em>Fractional Splines and Wavelets</em></span>,
+            SIAM Review, Volume 42, No. 1
+          </li>
+</ul></div>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+      Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="b_spline.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../sf_poly.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="../bessel.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>
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 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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@@ -4,7 +4,7 @@
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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+<link rel="home" href="../../index.html" title="Math Toolkit 2.10.0">
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 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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--- a/libs/math/doc/html/math_toolkit/stat_tut/overview/objects.html
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@@ -117,11 +117,11 @@
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 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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+<link rel="home" href="../../../index.html" title="Math Toolkit 2.10.0">
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@@ -58,11 +58,11 @@
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 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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@@ -4,7 +4,7 @@
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+<link rel="home" href="../../index.html" title="Math Toolkit 2.10.0">
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 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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diff --git a/libs/math/doc/html/math_toolkit/stat_tut/weg.html b/libs/math/doc/html/math_toolkit/stat_tut/weg.html
index a0af090174..1ecda3644d 100644
--- a/libs/math/doc/html/math_toolkit/stat_tut/weg.html
+++ b/libs/math/doc/html/math_toolkit/stat_tut/weg.html
@@ -4,7 +4,7 @@
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 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.10.0">
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@@ -112,11 +112,11 @@
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 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/stat_tut/weg/binom_eg.html b/libs/math/doc/html/math_toolkit/stat_tut/weg/binom_eg.html
index 57b1d5b78c..e8f15e69e0 100644
--- a/libs/math/doc/html/math_toolkit/stat_tut/weg/binom_eg.html
+++ b/libs/math/doc/html/math_toolkit/stat_tut/weg/binom_eg.html
@@ -4,7 +4,7 @@
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+<link rel="home" href="../../../index.html" title="Math Toolkit 2.10.0">
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@@ -44,11 +44,11 @@
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 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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diff --git a/libs/math/doc/html/math_toolkit/stat_tut/weg/binom_eg/binom_conf.html b/libs/math/doc/html/math_toolkit/stat_tut/weg/binom_eg/binom_conf.html
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+++ b/libs/math/doc/html/math_toolkit/stat_tut/weg/binom_eg/binom_conf.html
@@ -4,7 +4,7 @@
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+<link rel="home" href="../../../../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../binom_eg.html" title="Binomial Distribution Examples">
 <link rel="prev" href="binomial_quiz_example.html" title="Binomial Quiz Example">
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@@ -224,11 +224,11 @@ _______________________________________________________________________
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 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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diff --git a/libs/math/doc/html/math_toolkit/stat_tut/weg/binom_eg/binom_size_eg.html b/libs/math/doc/html/math_toolkit/stat_tut/weg/binom_eg/binom_size_eg.html
index 31f7dbe536..124d1864a0 100644
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+++ b/libs/math/doc/html/math_toolkit/stat_tut/weg/binom_eg/binom_size_eg.html
@@ -4,7 +4,7 @@
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+<link rel="home" href="../../../../index.html" title="Math Toolkit 2.10.0">
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@@ -143,11 +143,11 @@ ____________________________
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 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/stat_tut/weg/binom_eg/binomial_coinflip_example.html b/libs/math/doc/html/math_toolkit/stat_tut/weg/binom_eg/binomial_coinflip_example.html
index 304952714d..a6add120ab 100644
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+++ b/libs/math/doc/html/math_toolkit/stat_tut/weg/binom_eg/binomial_coinflip_example.html
@@ -4,7 +4,7 @@
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 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
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+<link rel="home" href="../../../../index.html" title="Math Toolkit 2.10.0">
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@@ -185,7 +185,18 @@
 <p>
             The last (0 to 10 heads) must, of course, be 100% probability.
           </p>
-<pre class="programlisting"><span class="special">}</span>
+<pre class="programlisting">      <span class="keyword">double</span> <span class="identifier">probability</span> <span class="special">=</span> <span class="number">0.3</span><span class="special">;</span>
+      <span class="keyword">double</span> <span class="identifier">q</span> <span class="special">=</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">flip</span><span class="special">,</span> <span class="identifier">probability</span><span class="special">);</span>
+      <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Quantile (flip, "</span> <span class="special">&lt;&lt;</span> <span class="identifier">probability</span> <span class="special">&lt;&lt;</span> <span class="string">") = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">q</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> <span class="comment">// Quantile (flip, 0.3) = 3</span>
+      <span class="identifier">probability</span> <span class="special">=</span> <span class="number">0.6</span><span class="special">;</span>
+      <span class="identifier">q</span> <span class="special">=</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">flip</span><span class="special">,</span> <span class="identifier">probability</span><span class="special">);</span>
+      <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Quantile (flip, "</span> <span class="special">&lt;&lt;</span> <span class="identifier">probability</span> <span class="special">&lt;&lt;</span> <span class="string">") = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">q</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> <span class="comment">// Quantile (flip, 0.6) = 5</span>
+
+
+
+
+
+<span class="special">}</span>
 <span class="keyword">catch</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">exception</span><span class="special">&amp;</span> <span class="identifier">e</span><span class="special">)</span>
 <span class="special">{</span>
   <span class="comment">//</span>
@@ -257,11 +268,11 @@ Probability of getting upto (&lt;=) heads
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/stat_tut/weg/binom_eg/binomial_quiz_example.html b/libs/math/doc/html/math_toolkit/stat_tut/weg/binom_eg/binomial_quiz_example.html
index 725a2bc016..2d1dff6dfa 100644
--- a/libs/math/doc/html/math_toolkit/stat_tut/weg/binom_eg/binomial_quiz_example.html
+++ b/libs/math/doc/html/math_toolkit/stat_tut/weg/binom_eg/binomial_quiz_example.html
@@ -4,7 +4,7 @@
 <title>Binomial Quiz Example</title>
 <link rel="stylesheet" href="../../../../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../../../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../../../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../binom_eg.html" title="Binomial Distribution Examples">
 <link rel="prev" href="binomial_coinflip_example.html" title="Binomial Coin-Flipping Example">
 <link rel="next" href="binom_conf.html" title="Calculating Confidence Limits on the Frequency of Occurrence for a Binomial Distribution">
@@ -441,11 +441,11 @@ If guessing then percentiles 1 to 99% will get 0 to 7.788 right.
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/stat_tut/weg/c_sharp.html b/libs/math/doc/html/math_toolkit/stat_tut/weg/c_sharp.html
index c109861561..9f7424fea0 100644
--- a/libs/math/doc/html/math_toolkit/stat_tut/weg/c_sharp.html
+++ b/libs/math/doc/html/math_toolkit/stat_tut/weg/c_sharp.html
@@ -4,7 +4,7 @@
 <title>Using the Distributions from Within C#</title>
 <link rel="stylesheet" href="../../../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../weg.html" title="Worked Examples">
 <link rel="prev" href="nag_library.html" title="Comparison with C, R, FORTRAN-style Free Functions">
 <link rel="next" href="../variates.html" title="Random Variates and Distribution Parameters">
@@ -41,11 +41,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/stat_tut/weg/cs_eg.html b/libs/math/doc/html/math_toolkit/stat_tut/weg/cs_eg.html
index 2b9486247b..88f50569a4 100644
--- a/libs/math/doc/html/math_toolkit/stat_tut/weg/cs_eg.html
+++ b/libs/math/doc/html/math_toolkit/stat_tut/weg/cs_eg.html
@@ -4,7 +4,7 @@
 <title>Chi Squared Distribution Examples</title>
 <link rel="stylesheet" href="../../../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../weg.html" title="Worked Examples">
 <link rel="prev" href="st_eg/paired_st.html" title="Comparing two paired samples with the Student's t distribution">
 <link rel="next" href="cs_eg/chi_sq_intervals.html" title="Confidence Intervals on the Standard Deviation">
@@ -38,11 +38,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/stat_tut/weg/cs_eg/chi_sq_intervals.html b/libs/math/doc/html/math_toolkit/stat_tut/weg/cs_eg/chi_sq_intervals.html
index 1fd713dd84..61131f74cb 100644
--- a/libs/math/doc/html/math_toolkit/stat_tut/weg/cs_eg/chi_sq_intervals.html
+++ b/libs/math/doc/html/math_toolkit/stat_tut/weg/cs_eg/chi_sq_intervals.html
@@ -4,7 +4,7 @@
 <title>Confidence Intervals on the Standard Deviation</title>
 <link rel="stylesheet" href="../../../../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../../../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../../../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../cs_eg.html" title="Chi Squared Distribution Examples">
 <link rel="prev" href="../cs_eg.html" title="Chi Squared Distribution Examples">
 <link rel="next" href="chi_sq_test.html" title="Chi-Square Test for the Standard Deviation">
@@ -219,11 +219,11 @@ ________________________________________
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/stat_tut/weg/cs_eg/chi_sq_size.html b/libs/math/doc/html/math_toolkit/stat_tut/weg/cs_eg/chi_sq_size.html
index b5590160c3..45837d2b72 100644
--- a/libs/math/doc/html/math_toolkit/stat_tut/weg/cs_eg/chi_sq_size.html
+++ b/libs/math/doc/html/math_toolkit/stat_tut/weg/cs_eg/chi_sq_size.html
@@ -4,7 +4,7 @@
 <title>Estimating the Required Sample Sizes for a Chi-Square Test for the Standard Deviation</title>
 <link rel="stylesheet" href="../../../../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../../../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../../../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../cs_eg.html" title="Chi Squared Distribution Examples">
 <link rel="prev" href="chi_sq_test.html" title="Chi-Square Test for the Standard Deviation">
 <link rel="next" href="../f_eg.html" title="F Distribution Examples">
@@ -165,11 +165,11 @@ _______________________________________________________________
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/stat_tut/weg/cs_eg/chi_sq_test.html b/libs/math/doc/html/math_toolkit/stat_tut/weg/cs_eg/chi_sq_test.html
index 7f4afeec6a..fe5a24965d 100644
--- a/libs/math/doc/html/math_toolkit/stat_tut/weg/cs_eg/chi_sq_test.html
+++ b/libs/math/doc/html/math_toolkit/stat_tut/weg/cs_eg/chi_sq_test.html
@@ -4,7 +4,7 @@
 <title>Chi-Square Test for the Standard Deviation</title>
 <link rel="stylesheet" href="../../../../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../../../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../../../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../cs_eg.html" title="Chi Squared Distribution Examples">
 <link rel="prev" href="chi_sq_intervals.html" title="Confidence Intervals on the Standard Deviation">
 <link rel="next" href="chi_sq_size.html" title="Estimating the Required Sample Sizes for a Chi-Square Test for the Standard Deviation">
@@ -280,11 +280,11 @@ Standard Deviation  &gt; 10.000            ACCEPTED
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/stat_tut/weg/dist_construct_eg.html b/libs/math/doc/html/math_toolkit/stat_tut/weg/dist_construct_eg.html
index e9033706da..10eac18c2d 100644
--- a/libs/math/doc/html/math_toolkit/stat_tut/weg/dist_construct_eg.html
+++ b/libs/math/doc/html/math_toolkit/stat_tut/weg/dist_construct_eg.html
@@ -4,7 +4,7 @@
 <title>Distribution Construction Examples</title>
 <link rel="stylesheet" href="../../../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../weg.html" title="Worked Examples">
 <link rel="prev" href="../weg.html" title="Worked Examples">
 <link rel="next" href="st_eg.html" title="Student's t Distribution Examples">
@@ -30,12 +30,12 @@
 <p>
           The structure of distributions is rather different from some other statistical
           libraries, for example, those written in less object-oriented language
-          like FORTRAN and C: these provide a few arguments to each free function.
+          like FORTRAN and C that provide a few arguments to each free function.
         </p>
 <p>
-          Boost.Math library provides each distribution as a template C++ class.
-          A distribution is constructed with a few arguments, and then member and
-          non-member functions are used to find values of the distribution, often
+          Boost.Math library instead provides each distribution as a template C++
+          class. A distribution is constructed with a few arguments, and then member
+          and non-member functions are used to find values of the distribution, often
           a function of a random variate.
         </p>
 <p>
@@ -44,8 +44,17 @@
         </p>
 <p>
           To demonstrate the use with a high precision User-defined floating-point
-          type <code class="computeroutput"><span class="identifier">cpp_dec_float</span></code> we also
-          need an include from Boost.Multiprecision.
+          type <code class="computeroutput"><span class="identifier">cpp_bin_float</span></code>, we
+          also need an include from Boost.Multiprecision. (We could equally well
+          have used a <code class="computeroutput"><span class="identifier">cpp_dec_float</span></code>
+          multiprecision type).
+        </p>
+<p>
+          We choose a typedef <code class="computeroutput"><span class="identifier">cpp_bin_float_50</span></code>
+          to provide a 50 decimal digit type, but we could equally have chosen at
+          128-bit type <code class="computeroutput"><span class="identifier">cpp_bin_float_quad</span></code>,
+          or on some platforms <code class="computeroutput"><span class="identifier">__float128</span></code>,
+          providing about 35 decimal digits.
         </p>
 <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">negative_binomial</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span> <span class="comment">// for negative_binomial_distribution</span>
   <span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">negative_binomial_distribution</span><span class="special">;</span> <span class="comment">// default type is double.</span>
@@ -55,7 +64,7 @@
 <span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">gamma</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span> <span class="comment">// for gamma_distribution.</span>
 <span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">normal</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span> <span class="comment">// for normal_distribution.</span>
 
-<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">cpp_dec_float</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span> <span class="comment">// for cpp_dec_float_100</span>
+<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">cpp_bin_float</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span> <span class="comment">// for cpp_bin_float_50</span>
 </pre>
 <p>
           Several examples of constructing distributions follow:
@@ -104,7 +113,7 @@
 </tr>
 <tr><td align="left" valign="top"><p>
             This convenience typedef is <span class="bold"><strong>not provided</strong></span>
-            if a clash would occur with the name of a function: currently only <code class="computeroutput"><span class="identifier">beta</span></code> and <code class="computeroutput"><span class="identifier">gamma</span></code>
+            if a clash would occur with the name of a function; currently only <code class="computeroutput"><span class="identifier">beta</span></code> and <code class="computeroutput"><span class="identifier">gamma</span></code>
             fall into this category.
           </p></td></tr>
 </table></div>
@@ -124,12 +133,14 @@
 <pre class="programlisting"><span class="identifier">negative_binomial</span> <span class="identifier">mydist10</span><span class="special">(</span><span class="number">5.</span><span class="special">,</span> <span class="number">0.4</span><span class="special">);</span> <span class="comment">// Both arguments double.</span>
 </pre>
 <p>
-          And automatic conversion takes place, so you can use integers and floats:
+          And automatic conversion of arguments takes place, so you can use integers
+          and floats:
         </p>
-<pre class="programlisting"><span class="identifier">negative_binomial</span> <span class="identifier">mydist11</span><span class="special">(</span><span class="number">5</span><span class="special">,</span> <span class="number">0.4</span><span class="special">);</span> <span class="comment">// Using provided typedef double, int and double arguments.</span>
+<pre class="programlisting"><span class="identifier">negative_binomial</span> <span class="identifier">mydist11</span><span class="special">(</span><span class="number">5</span><span class="special">,</span> <span class="number">0.4</span><span class="special">);</span> <span class="comment">// Using provided typedef of type double, and int and double arguments.</span>
 </pre>
 <p>
-          This is probably the most common usage.
+          This is probably the most common usage. Other combination are possible
+          too:
         </p>
 <pre class="programlisting"><span class="identifier">negative_binomial</span> <span class="identifier">mydist12</span><span class="special">(</span><span class="number">5.</span><span class="special">,</span> <span class="number">0.4F</span><span class="special">);</span> <span class="comment">// Double and float arguments.</span>
 <span class="identifier">negative_binomial</span> <span class="identifier">mydist13</span><span class="special">(</span><span class="number">5</span><span class="special">,</span> <span class="number">1</span><span class="special">);</span> <span class="comment">// Both arguments integer.</span>
@@ -143,7 +154,7 @@
 <p>
           For cases when the typdef distribution name would clash with a math special
           function (currently only beta and gamma) the typedef is deliberately not
-          provided, and the longer version of the name must be used. For example
+          provided, and the longer version of the name must be used, so for example,
           do not use:
         </p>
 <pre class="programlisting"><span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">beta</span><span class="special">;</span>
@@ -186,33 +197,37 @@ error C3861: 'mybetad0': identifier not found
 <span class="identifier">negative_binomial_distribution</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span>         <span class="identifier">mydist5</span><span class="special">(</span><span class="number">8</span><span class="special">,</span> <span class="number">1</span><span class="special">);</span>
 
 <span class="comment">// Explicit double precision:</span>
-<span class="identifier">negative_binomial_distribution</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span>        <span class="identifier">mydist6</span><span class="special">(</span><span class="number">8.</span><span class="special">,</span> <span class="number">0.25</span><span class="special">);</span>
+<span class="identifier">negative_binomial_distribution</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span>        <span class="identifier">mydist6</span><span class="special">(</span><span class="number">5.</span><span class="special">,</span> <span class="number">0.4</span><span class="special">);</span>
 
 <span class="comment">// Explicit long double precision:</span>
 <span class="identifier">negative_binomial_distribution</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span>   <span class="identifier">mydist7</span><span class="special">(</span><span class="number">8.</span><span class="special">,</span> <span class="number">0.25</span><span class="special">);</span>
 </pre>
 <p>
-          And you can use your own RealType, for example, <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">cpp_dec_float_50</span></code>
-          (an arbitrary 50 decimal digits precision type), then we can write:
+          And you can use your own template RealType, for example, <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">cpp_bin_float_50</span></code> (an arbitrary 50 decimal
+          digits precision type), then we can write:
         </p>
 <pre class="programlisting"> <span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">;</span>
+ <span class="identifier">negative_binomial_distribution</span><span class="special">&lt;</span><span class="identifier">cpp_bin_float_50</span><span class="special">&gt;</span>  <span class="identifier">mydist8</span><span class="special">(</span><span class="number">8</span><span class="special">,</span> <span class="number">0.25</span><span class="special">);</span>
 
- <span class="identifier">negative_binomial_distribution</span><span class="special">&lt;</span><span class="identifier">cpp_dec_float_50</span><span class="special">&gt;</span>  <span class="identifier">mydist8</span><span class="special">(</span><span class="number">8</span><span class="special">,</span> <span class="number">0.25</span><span class="special">);</span>
  <span class="comment">// `integer` arguments are promoted to your RealType exactly, but</span>
  <span class="comment">// `double` argument are converted to RealType,</span>
- <span class="comment">// possibly losing precision, so don't write:</span>
+ <span class="comment">// most likely losing precision!</span>
 
- <span class="identifier">negative_binomial_distribution</span><span class="special">&lt;</span><span class="identifier">cpp_dec_float_50</span><span class="special">&gt;</span>  <span class="identifier">mydist20</span><span class="special">(</span><span class="number">8</span><span class="special">,</span> <span class="number">0.23456789012345678901234567890</span><span class="special">);</span>
-<span class="comment">// to avoid truncation of second parameter to `0.2345678901234567`.</span>
+   <span class="comment">// So DON'T be tempted to write the 'obvious':</span>
+ <span class="identifier">negative_binomial_distribution</span><span class="special">&lt;</span><span class="identifier">cpp_bin_float_50</span><span class="special">&gt;</span>  <span class="identifier">mydist20</span><span class="special">(</span><span class="number">8</span><span class="special">,</span> <span class="number">0.23456789012345678901234567890</span><span class="special">);</span>
+<span class="comment">// to avoid truncation of second parameter to `0.2345678901234567` and loss of precision.</span>
 
- <span class="identifier">negative_binomial_distribution</span><span class="special">&lt;</span><span class="identifier">cpp_dec_float_50</span><span class="special">&gt;</span>  <span class="identifier">mydist21</span><span class="special">(</span><span class="number">8</span><span class="special">,</span> <span class="identifier">cpp_dec_float_50</span><span class="special">(</span><span class="string">"0.23456789012345678901234567890"</span><span class="special">)</span> <span class="special">);</span>
+<span class="comment">// Instead pass a quoted decimal digit string:</span>
+ <span class="identifier">negative_binomial_distribution</span><span class="special">&lt;</span><span class="identifier">cpp_bin_float_50</span><span class="special">&gt;</span>  <span class="identifier">mydist21</span><span class="special">(</span><span class="number">8</span><span class="special">,</span> <span class="identifier">cpp_bin_float_50</span><span class="special">(</span><span class="string">"0.23456789012345678901234567890"</span><span class="special">)</span> <span class="special">);</span>
 
  <span class="comment">// Ensure that all potentially significant digits are shown.</span>
- <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span><span class="special">.</span><span class="identifier">precision</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">cpp_dec_float_50</span><span class="special">&gt;::</span><span class="identifier">digits10</span><span class="special">);</span>
- <span class="identifier">cpp_dec_float_50</span> <span class="identifier">x</span><span class="special">(</span><span class="string">"1.23456789012345678901234567890"</span><span class="special">);</span>
+ <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span><span class="special">.</span><span class="identifier">precision</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">cpp_bin_float_50</span><span class="special">&gt;::</span><span class="identifier">digits10</span><span class="special">);</span>
+   <span class="comment">// </span>
+ <span class="identifier">cpp_bin_float_50</span> <span class="identifier">x</span><span class="special">(</span><span class="string">"1.23456789012345678901234567890"</span><span class="special">);</span>
  <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">pdf</span><span class="special">(</span><span class="identifier">mydist8</span><span class="special">,</span> <span class="identifier">x</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
 </pre>
 <pre class="programlisting"><span class="identifier">showing</span>  <span class="number">0.00012630010495970320103876754721976419438231705359935</span>
+            <span class="number">0.00012630010495970320103876754721976419438231528547467</span>
 </pre>
 <div class="warning"><table border="0" summary="Warning">
 <tr>
@@ -241,17 +256,17 @@ error C3861: 'mybetad0': identifier not found
           Then the now <code class="computeroutput"><span class="keyword">double</span> <span class="identifier">x</span></code>
           is passed to function <code class="computeroutput"><span class="identifier">pdf</span></code>,
           and this truncated <code class="computeroutput"><span class="keyword">double</span></code>
-          value is finally promoted to <code class="computeroutput"><span class="identifier">cpp_dec_float_50</span></code>.
+          value is finally promoted to <code class="computeroutput"><span class="identifier">cpp_bin_float_50</span></code>.
         </p>
 <p>
           Another way of quietly getting the wrong answer is to write:
         </p>
-<pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">pdf</span><span class="special">(</span><span class="identifier">mydist8</span><span class="special">,</span> <span class="identifier">cpp_dec_float_50</span><span class="special">(</span><span class="number">1.23456789012345678901234567890</span><span class="special">))</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+<pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">pdf</span><span class="special">(</span><span class="identifier">mydist8</span><span class="special">,</span> <span class="identifier">cpp_bin_float_50</span><span class="special">(</span><span class="number">1.23456789012345678901234567890</span><span class="special">))</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
 </pre>
 <p>
           A correct way from a multi-digit string value is
         </p>
-<pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">pdf</span><span class="special">(</span><span class="identifier">mydist8</span><span class="special">,</span> <span class="identifier">cpp_dec_float_50</span><span class="special">(</span><span class="string">"1.23456789012345678901234567890"</span><span class="special">))</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+<pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">pdf</span><span class="special">(</span><span class="identifier">mydist8</span><span class="special">,</span> <span class="identifier">cpp_bin_float_50</span><span class="special">(</span><span class="string">"1.23456789012345678901234567890"</span><span class="special">))</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
 </pre>
 <div class="tip"><table border="0" summary="Tip">
 <tr>
@@ -289,11 +304,11 @@ error C3861: 'mybetad0': identifier not found
 <pre class="programlisting"><span class="identifier">normal_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">mean</span> <span class="special">=</span> <span class="number">0</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">sd</span> <span class="special">=</span> <span class="number">1</span><span class="special">);</span>
 </pre>
 <p>
-          So in this case we can write:
+          So in this case we can more tersely write:
         </p>
 <pre class="programlisting">  <span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">normal</span><span class="special">;</span>
 
-  <span class="identifier">normal</span> <span class="identifier">norm1</span><span class="special">;</span>       <span class="comment">// Standard normal distribution.</span>
+  <span class="identifier">normal</span> <span class="identifier">norm1</span><span class="special">;</span>       <span class="comment">// Standard normal distribution N[0,1].</span>
   <span class="identifier">normal</span> <span class="identifier">norm2</span><span class="special">(</span><span class="number">2</span><span class="special">);</span>    <span class="comment">// Mean = 2, std deviation = 1.</span>
   <span class="identifier">normal</span> <span class="identifier">norm3</span><span class="special">(</span><span class="number">2</span><span class="special">,</span> <span class="number">3</span><span class="special">);</span> <span class="comment">// Mean = 2, std deviation = 3.</span>
 
@@ -316,11 +331,11 @@ error C3861: 'mybetad0': identifier not found
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/stat_tut/weg/error_eg.html b/libs/math/doc/html/math_toolkit/stat_tut/weg/error_eg.html
index 5c30e9228a..30917de46b 100644
--- a/libs/math/doc/html/math_toolkit/stat_tut/weg/error_eg.html
+++ b/libs/math/doc/html/math_toolkit/stat_tut/weg/error_eg.html
@@ -4,7 +4,7 @@
 <title>Error Handling Example</title>
 <link rel="stylesheet" href="../../../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../weg.html" title="Worked Examples">
 <link rel="prev" href="nccs_eg/nccs_power_eg.html" title="Tables of the power function of the chi2 test.">
 <link rel="next" href="find_eg.html" title="Find Location and Scale Examples">
@@ -189,11 +189,11 @@ errno is set to: 33
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/stat_tut/weg/f_eg.html b/libs/math/doc/html/math_toolkit/stat_tut/weg/f_eg.html
index d2bb7c81a6..523f43ec83 100644
--- a/libs/math/doc/html/math_toolkit/stat_tut/weg/f_eg.html
+++ b/libs/math/doc/html/math_toolkit/stat_tut/weg/f_eg.html
@@ -4,7 +4,7 @@
 <title>F Distribution Examples</title>
 <link rel="stylesheet" href="../../../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../weg.html" title="Worked Examples">
 <link rel="prev" href="cs_eg/chi_sq_size.html" title="Estimating the Required Sample Sizes for a Chi-Square Test for the Standard Deviation">
 <link rel="next" href="binom_eg.html" title="Binomial Distribution Examples">
@@ -312,11 +312,11 @@ Standard deviation 1 is greater than standard deviation 2 ACCEPTED
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/stat_tut/weg/find_eg.html b/libs/math/doc/html/math_toolkit/stat_tut/weg/find_eg.html
index ede3d63752..6dbf90e510 100644
--- a/libs/math/doc/html/math_toolkit/stat_tut/weg/find_eg.html
+++ b/libs/math/doc/html/math_toolkit/stat_tut/weg/find_eg.html
@@ -4,7 +4,7 @@
 <title>Find Location and Scale Examples</title>
 <link rel="stylesheet" href="../../../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../weg.html" title="Worked Examples">
 <link rel="prev" href="error_eg.html" title="Error Handling Example">
 <link rel="next" href="find_eg/find_location_eg.html" title="Find Location (Mean) Example">
@@ -38,11 +38,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/stat_tut/weg/find_eg/find_location_eg.html b/libs/math/doc/html/math_toolkit/stat_tut/weg/find_eg/find_location_eg.html
index e02e216d79..83eb9f257a 100644
--- a/libs/math/doc/html/math_toolkit/stat_tut/weg/find_eg/find_location_eg.html
+++ b/libs/math/doc/html/math_toolkit/stat_tut/weg/find_eg/find_location_eg.html
@@ -4,7 +4,7 @@
 <title>Find Location (Mean) Example</title>
 <link rel="stylesheet" href="../../../../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../../../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../../../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../find_eg.html" title="Find Location and Scale Examples">
 <link rel="prev" href="../find_eg.html" title="Find Location and Scale Examples">
 <link rel="next" href="find_scale_eg.html" title="Find Scale (Standard Deviation) Example">
@@ -173,11 +173,11 @@ Normal distribution with mean = 0.355146 has fraction &gt; 2 = 0.05
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/stat_tut/weg/find_eg/find_mean_and_sd_eg.html b/libs/math/doc/html/math_toolkit/stat_tut/weg/find_eg/find_mean_and_sd_eg.html
index 0fb94d2a04..8979e65cf0 100644
--- a/libs/math/doc/html/math_toolkit/stat_tut/weg/find_eg/find_mean_and_sd_eg.html
+++ b/libs/math/doc/html/math_toolkit/stat_tut/weg/find_eg/find_mean_and_sd_eg.html
@@ -4,7 +4,7 @@
 <title>Find mean and standard deviation example</title>
 <link rel="stylesheet" href="../../../../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../../../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../../../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../find_eg.html" title="Find Location and Scale Examples">
 <link rel="prev" href="find_scale_eg.html" title="Find Scale (Standard Deviation) Example">
 <link rel="next" href="../nag_library.html" title="Comparison with C, R, FORTRAN-style Free Functions">
@@ -438,11 +438,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/stat_tut/weg/find_eg/find_scale_eg.html b/libs/math/doc/html/math_toolkit/stat_tut/weg/find_eg/find_scale_eg.html
index e856e38f62..31e3d6de03 100644
--- a/libs/math/doc/html/math_toolkit/stat_tut/weg/find_eg/find_scale_eg.html
+++ b/libs/math/doc/html/math_toolkit/stat_tut/weg/find_eg/find_scale_eg.html
@@ -4,7 +4,7 @@
 <title>Find Scale (Standard Deviation) Example</title>
 <link rel="stylesheet" href="../../../../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
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@@ -192,11 +192,11 @@ Normal distribution with mean = 0.946339 has fraction &gt; -2 = 0.999
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 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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 <link rel="prev" href="inverse_chi_squared_eg.html" title="Inverse Chi-Squared Distribution Bayes Example">
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@@ -36,11 +36,11 @@
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 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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@@ -1270,11 +1270,11 @@ test at the 5% significance
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 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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-<link rel="home" href="../../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../../index.html" title="Math Toolkit 2.10.0">
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 <link rel="prev" href="geometric_eg.html" title="Geometric Distribution Examples">
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 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
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+<link rel="home" href="../../../../index.html" title="Math Toolkit 2.10.0">
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@@ -204,11 +204,11 @@ ___________________________________________
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 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../../../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../../../index.html" title="Math Toolkit 2.10.0">
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 <link rel="prev" href="neg_binom_conf.html" title="Calculating Confidence Limits on the Frequency of Occurrence for the Negative Binomial Distribution">
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@@ -190,11 +190,11 @@ ____________________________
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/stat_tut/weg/neg_binom_eg/negative_binomial_example1.html b/libs/math/doc/html/math_toolkit/stat_tut/weg/neg_binom_eg/negative_binomial_example1.html
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 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../../../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../../../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../neg_binom_eg.html" title="Negative Binomial Distribution Examples">
 <link rel="prev" href="neg_binom_size_eg.html" title="Estimating Sample Sizes for the Negative Binomial.">
 <link rel="next" href="negative_binomial_example2.html" title="Negative Binomial Table Printing Example.">
@@ -478,11 +478,11 @@ If confidence of meeting quota is 0.95, then finishing house is 21
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/stat_tut/weg/neg_binom_eg/negative_binomial_example2.html b/libs/math/doc/html/math_toolkit/stat_tut/weg/neg_binom_eg/negative_binomial_example2.html
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-<link rel="home" href="../../../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../../../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../neg_binom_eg.html" title="Negative Binomial Distribution Examples">
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 <link rel="next" href="../normal_example.html" title="Normal Distribution Examples">
@@ -119,11 +119,11 @@
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 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
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+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
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         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
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-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
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 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
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 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
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 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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+<link rel="home" href="../index.html" title="Math Toolkit 2.10.0">
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 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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@@ -4,7 +4,7 @@
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+<link rel="home" href="../index.html" title="Math Toolkit 2.10.0">
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 <link rel="prev" href="create.html" title="Quaternion Creation Functions">
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@@ -127,11 +127,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/trapezoidal.html b/libs/math/doc/html/math_toolkit/trapezoidal.html
index 54615094e0..e65e42dc47 100644
--- a/libs/math/doc/html/math_toolkit/trapezoidal.html
+++ b/libs/math/doc/html/math_toolkit/trapezoidal.html
@@ -4,7 +4,7 @@
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 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../quadrature.html" title="Chapter&#160;12.&#160;Quadrature and Differentiation">
 <link rel="prev" href="../quadrature.html" title="Chapter&#160;12.&#160;Quadrature and Differentiation">
 <link rel="next" href="gauss.html" title="Gauss-Legendre quadrature">
@@ -227,11 +227,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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diff --git a/libs/math/doc/html/math_toolkit/tuning.html b/libs/math/doc/html/math_toolkit/tuning.html
index f1b23782fe..f854f2685c 100644
--- a/libs/math/doc/html/math_toolkit/tuning.html
+++ b/libs/math/doc/html/math_toolkit/tuning.html
@@ -4,7 +4,7 @@
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 <link rel="stylesheet" href="../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../perf.html" title="Chapter&#160;20.&#160;Performance">
 <link rel="prev" href="multiprecision.html" title="Cost of High-Precision Non-built-in Floating-point">
 <link rel="next" href="comp_compilers.html" title="Comparing Different Compilers">
@@ -2158,11 +2158,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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diff --git a/libs/math/doc/html/math_toolkit/tutorial.html b/libs/math/doc/html/math_toolkit/tutorial.html
index 0f85798fba..9773fbc00f 100644
--- a/libs/math/doc/html/math_toolkit/tutorial.html
+++ b/libs/math/doc/html/math_toolkit/tutorial.html
@@ -4,7 +4,7 @@
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 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../constants.html" title="Chapter&#160;4.&#160;Mathematical Constants">
 <link rel="prev" href="constants_intro.html" title="Introduction">
 <link rel="next" href="tutorial/non_templ.html" title="Use in non-template code">
@@ -36,11 +36,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/tutorial/non_templ.html b/libs/math/doc/html/math_toolkit/tutorial/non_templ.html
index 689c0c21d9..501c79ed9a 100644
--- a/libs/math/doc/html/math_toolkit/tutorial/non_templ.html
+++ b/libs/math/doc/html/math_toolkit/tutorial/non_templ.html
@@ -4,7 +4,7 @@
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 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../tutorial.html" title="Tutorial">
 <link rel="prev" href="../tutorial.html" title="Tutorial">
 <link rel="next" href="templ.html" title="Use in template code">
@@ -69,11 +69,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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diff --git a/libs/math/doc/html/math_toolkit/tutorial/templ.html b/libs/math/doc/html/math_toolkit/tutorial/templ.html
index 657a964f4d..feaffc3fb6 100644
--- a/libs/math/doc/html/math_toolkit/tutorial/templ.html
+++ b/libs/math/doc/html/math_toolkit/tutorial/templ.html
@@ -4,7 +4,7 @@
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 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.10.0">
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@@ -140,11 +140,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/tutorial/user_def.html b/libs/math/doc/html/math_toolkit/tutorial/user_def.html
index a0444c7079..0dcb8b1d12 100644
--- a/libs/math/doc/html/math_toolkit/tutorial/user_def.html
+++ b/libs/math/doc/html/math_toolkit/tutorial/user_def.html
@@ -4,7 +4,7 @@
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 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.10.0">
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 <link rel="prev" href="templ.html" title="Use in template code">
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@@ -319,11 +319,11 @@ the constant will be constructed from a string on each call.
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/univariate_statistics.html b/libs/math/doc/html/math_toolkit/univariate_statistics.html
index 541e478dd8..d4b89966c1 100644
--- a/libs/math/doc/html/math_toolkit/univariate_statistics.html
+++ b/libs/math/doc/html/math_toolkit/univariate_statistics.html
@@ -4,7 +4,7 @@
 <title>Univariate Statistics</title>
 <link rel="stylesheet" href="../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../vector_functionals.html" title="Chapter&#160;6.&#160;Vector Functionals">
 <link rel="prev" href="../vector_functionals.html" title="Chapter&#160;6.&#160;Vector Functionals">
 <link rel="next" href="bivariate_statistics.html" title="Bivariate Statistics">
@@ -334,11 +334,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/value_op.html b/libs/math/doc/html/math_toolkit/value_op.html
index 4138740a7f..b8849ae291 100644
--- a/libs/math/doc/html/math_toolkit/value_op.html
+++ b/libs/math/doc/html/math_toolkit/value_op.html
@@ -4,7 +4,7 @@
 <title>Quaternion Value Operations</title>
 <link rel="stylesheet" href="../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../index.html" title="Math Toolkit 2.10.0">
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 <link rel="next" href="create.html" title="Quaternion Creation Functions">
@@ -92,11 +92,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/vector_barycentric.html b/libs/math/doc/html/math_toolkit/vector_barycentric.html
new file mode 100644
index 0000000000..df3414b347
--- /dev/null
+++ b/libs/math/doc/html/math_toolkit/vector_barycentric.html
@@ -0,0 +1,129 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
+<title>Vector-valued Barycentric Rational Interpolation</title>
+<link rel="stylesheet" href="../math.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.10.0">
+<link rel="up" href="../interpolation.html" title="Chapter&#160;11.&#160;Interpolation">
+<link rel="prev" href="barycentric.html" title="Barycentric Rational Interpolation">
+<link rel="next" href="catmull_rom.html" title="Catmull-Rom Splines">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
+<td align="center"><a href="../../../../../index.html">Home</a></td>
+<td align="center"><a href="../../../../../libs/libraries.htm">Libraries</a></td>
+<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td>
+<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td>
+<td align="center"><a href="../../../../../more/index.htm">More</a></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="barycentric.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../interpolation.html"><img src="../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="catmull_rom.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a>
+</div>
+<div class="section">
+<div class="titlepage"><div><div><h2 class="title" style="clear: both">
+<a name="math_toolkit.vector_barycentric"></a><a class="link" href="vector_barycentric.html" title="Vector-valued Barycentric Rational Interpolation">Vector-valued Barycentric
+    Rational Interpolation</a>
+</h2></div></div></div>
+<h4>
+<a name="math_toolkit.vector_barycentric.h0"></a>
+      <span class="phrase"><a name="math_toolkit.vector_barycentric.synopsis"></a></span><a class="link" href="vector_barycentric.html#math_toolkit.vector_barycentric.synopsis">Synopsis</a>
+    </h4>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">interpolators</span><span class="special">/</span><span class="identifier">vector_barycentric_rational</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+
+<span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
+
+<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">TimeContainer</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">SpaceContainer</span><span class="special">&gt;</span>
+<span class="keyword">class</span> <span class="identifier">vector_barycentric_rational</span>
+<span class="special">{</span>
+<span class="keyword">public</span><span class="special">:</span>
+    <span class="keyword">using</span> <span class="identifier">Real</span> <span class="special">=</span> <span class="keyword">typename</span> <span class="identifier">TimeContainer</span><span class="special">::</span><span class="identifier">value_type</span><span class="special">;</span>
+    <span class="keyword">using</span> <span class="identifier">Point</span> <span class="special">=</span> <span class="keyword">typename</span> <span class="identifier">SpaceContainer</span><span class="special">::</span><span class="identifier">value_type</span><span class="special">;</span>
+    <span class="identifier">vector_barycentric_rational</span><span class="special">(</span><span class="identifier">TimeContainer</span><span class="special">&amp;&amp;</span> <span class="identifier">times</span><span class="special">,</span> <span class="identifier">SpaceContainer</span><span class="special">&amp;&amp;</span> <span class="identifier">points</span><span class="special">,</span> <span class="identifier">size_t</span> <span class="identifier">approximation_order</span> <span class="special">=</span> <span class="number">3</span><span class="special">);</span>
+
+    <span class="keyword">void</span> <span class="keyword">operator</span><span class="special">()(</span><span class="identifier">Point</span><span class="special">&amp;</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">Real</span> <span class="identifier">t</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span>
+
+    <span class="identifier">Point</span> <span class="keyword">operator</span><span class="special">()(</span><span class="identifier">Real</span> <span class="identifier">t</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span>
+
+    <span class="keyword">void</span> <span class="identifier">prime</span><span class="special">(</span><span class="identifier">Point</span><span class="special">&amp;</span> <span class="identifier">dxdt</span><span class="special">,</span> <span class="identifier">Real</span> <span class="identifier">t</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span>
+
+    <span class="identifier">Point</span> <span class="identifier">prime</span><span class="special">(</span><span class="identifier">Real</span> <span class="identifier">t</span><span class="special">);</span>
+
+    <span class="keyword">void</span> <span class="identifier">eval_with_prime</span><span class="special">(</span><span class="identifier">Point</span><span class="special">&amp;</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">Point</span><span class="special">&amp;</span> <span class="identifier">dxdt</span><span class="special">,</span> <span class="identifier">Real</span> <span class="identifier">t</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span>
+
+    <span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special">&lt;</span><span class="identifier">Point</span><span class="special">,</span> <span class="identifier">Point</span><span class="special">&gt;</span> <span class="identifier">eval_with_prime</span><span class="special">(</span><span class="identifier">Real</span> <span class="identifier">t</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span>
+<span class="special">};</span>
+
+<span class="special">}}</span>
+</pre>
+<h4>
+<a name="math_toolkit.vector_barycentric.h1"></a>
+      <span class="phrase"><a name="math_toolkit.vector_barycentric.description"></a></span><a class="link" href="vector_barycentric.html#math_toolkit.vector_barycentric.description">Description</a>
+    </h4>
+<p>
+      The <span class="emphasis"><em>n</em></span> dimensional vector-valued barycentric rational interpolator
+      is exactly the same as <span class="emphasis"><em>n</em></span> scalar-valued barycentric rational
+      interpolators. This is provided primarily for convenience and a slight improvement
+      in efficiency over using <span class="emphasis"><em>n</em></span> different rational interpolators
+      and combining their results.
+    </p>
+<p>
+      Use of the class requires a <code class="computeroutput"><span class="identifier">Point</span></code>-type
+      which has size known at compile time. These requirements are satisfied by (for
+      example) <code class="computeroutput"><span class="identifier">Eigen</span><span class="special">::</span><span class="identifier">Vector2d</span></code>s and <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">array</span><span class="special">&lt;</span><span class="identifier">Real</span><span class="special">,</span> <span class="identifier">N</span><span class="special">&gt;</span></code> classes. The call to the constructor computes
+      the weights:
+    </p>
+<pre class="programlisting"><span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">vector_barycentric_rational</span><span class="special">;</span>
+<span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="identifier">t</span><span class="special">(</span><span class="number">100</span><span class="special">);</span>
+<span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span><span class="special">&lt;</span><span class="identifier">Eigen</span><span class="special">::</span><span class="identifier">Vector2d</span><span class="special">&gt;</span> <span class="identifier">y</span><span class="special">(</span><span class="number">100</span><span class="special">);</span>
+<span class="comment">// initialize t and y . . .</span>
+<span class="identifier">vector_barycentric_rational</span><span class="special">&lt;</span><span class="keyword">decltype</span><span class="special">(</span><span class="identifier">t</span><span class="special">),</span> <span class="keyword">decltype</span><span class="special">(</span><span class="identifier">y</span><span class="special">)&gt;</span> <span class="identifier">interpolant</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">move</span><span class="special">(</span><span class="identifier">t</span><span class="special">),</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">move</span><span class="special">(</span><span class="identifier">y</span><span class="special">));</span>
+</pre>
+<p>
+      To evaluate the interpolant, use
+    </p>
+<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">t</span> <span class="special">=</span> <span class="number">2.3</span><span class="special">;</span>
+<span class="identifier">Eigen</span><span class="special">::</span><span class="identifier">Vector2d</span> <span class="identifier">y</span> <span class="special">=</span> <span class="identifier">interpolant</span><span class="special">(</span><span class="identifier">t</span><span class="special">);</span>
+</pre>
+<p>
+      If you want to populate a vector passed into the interpolant, rather than get
+      it returned, that syntax is supported:
+    </p>
+<pre class="programlisting"><span class="identifier">Eigen</span><span class="special">::</span><span class="identifier">Vector2d</span> <span class="identifier">y</span><span class="special">;</span>
+<span class="identifier">interpolant</span><span class="special">(</span><span class="identifier">y</span><span class="special">,</span> <span class="identifier">t</span><span class="special">);</span>
+</pre>
+<p>
+      We tested this with <code class="computeroutput"><span class="identifier">Eigen</span><span class="special">::</span><span class="identifier">Vector</span></code>s and found no performance benefit,
+      but other <code class="computeroutput"><span class="identifier">Point</span></code>-types might
+      not be the same.
+    </p>
+<p>
+      To evaluate the derivative of the interpolant use
+    </p>
+<pre class="programlisting"><span class="keyword">auto</span> <span class="special">[</span><span class="identifier">y</span><span class="special">,</span> <span class="identifier">y_prime</span><span class="special">]</span> <span class="special">=</span> <span class="identifier">interpolant</span><span class="special">.</span><span class="identifier">eval_with_prime</span><span class="special">(</span><span class="identifier">x</span><span class="special">);</span>
+</pre>
+<p>
+      Computation of the derivative requires evaluation, so if you can try to use
+      both values at once.
+    </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
+      Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="barycentric.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../interpolation.html"><img src="../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="catmull_rom.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a>
+</div>
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+</html>
diff --git a/libs/math/doc/html/math_toolkit/whittaker_shannon.html b/libs/math/doc/html/math_toolkit/whittaker_shannon.html
new file mode 100644
index 0000000000..91b011c672
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@@ -0,0 +1,120 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
+<title>Whittaker-Shannon interpolation</title>
+<link rel="stylesheet" href="../math.css" type="text/css">
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+<a accesskey="p" href="cardinal_quadratic_b.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../interpolation.html"><img src="../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="barycentric.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a>
+</div>
+<div class="section">
+<div class="titlepage"><div><div><h2 class="title" style="clear: both">
+<a name="math_toolkit.whittaker_shannon"></a><a class="link" href="whittaker_shannon.html" title="Whittaker-Shannon interpolation">Whittaker-Shannon interpolation</a>
+</h2></div></div></div>
+<h4>
+<a name="math_toolkit.whittaker_shannon.h0"></a>
+      <span class="phrase"><a name="math_toolkit.whittaker_shannon.synopsis"></a></span><a class="link" href="whittaker_shannon.html#math_toolkit.whittaker_shannon.synopsis">Synopsis</a>
+    </h4>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">interpolators</span><span class="special">/</span><span class="identifier">whittaker_shannon</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+</pre>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span> <span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">interpolators</span> <span class="special">{</span>
+
+  <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RandomAccessContainer</span><span class="special">&gt;</span>
+  <span class="keyword">class</span> <span class="identifier">whittaker_shannon</span>
+  <span class="special">{</span>
+  <span class="keyword">public</span><span class="special">:</span>
+
+      <span class="keyword">using</span> <span class="identifier">Real</span> <span class="special">=</span> <span class="identifier">RandomAccessContainer</span><span class="special">::</span><span class="identifier">value_type</span><span class="special">;</span>
+
+      <span class="identifier">whittaker_shannon</span><span class="special">(</span><span class="identifier">RandomAccessContainer</span><span class="special">&amp;&amp;</span> <span class="identifier">v</span><span class="special">,</span> <span class="identifier">Real</span> <span class="identifier">left_endpoint</span><span class="special">,</span> <span class="identifier">Real</span> <span class="identifier">step_size</span><span class="special">);</span>
+
+      <span class="identifier">Real</span> <span class="keyword">operator</span><span class="special">()(</span><span class="identifier">Real</span> <span class="identifier">x</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span>
+
+      <span class="identifier">Real</span> <span class="identifier">prime</span><span class="special">(</span><span class="identifier">Real</span> <span class="identifier">x</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span>
+  <span class="special">};</span>
+
+<span class="special">}}}</span> <span class="comment">// namespaces</span>
+</pre>
+<h4>
+<a name="math_toolkit.whittaker_shannon.h1"></a>
+      <span class="phrase"><a name="math_toolkit.whittaker_shannon.whittaker_shannon_interpolation"></a></span><a class="link" href="whittaker_shannon.html#math_toolkit.whittaker_shannon.whittaker_shannon_interpolation">Whittaker-Shannon
+      Interpolation</a>
+    </h4>
+<p>
+      The Whittaker-Shannon interpolator takes equispaced data and interpolates between
+      them via a sum of sinc functions. This interpolation is stable and infinitely
+      smooth, but has linear complexity in the data, making it slow relative to compactly-supported
+      b-splines. In addition, we cannot pass an infinite amount of data into the
+      class, and must truncate the (perhaps) infinite sinc series to a finite number
+      of terms. Since the sinc function has slow 1/x decay, the truncation of the
+      series can incur large error. Hence this interpolator works best when operating
+      on samples of compactly supported functions. Here is an example of interpolating
+      a smooth "bump function":
+    </p>
+<pre class="programlisting"><span class="keyword">auto</span> <span class="identifier">bump</span> <span class="special">=</span> <span class="special">[](</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">)</span> <span class="special">{</span> <span class="keyword">if</span> <span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">abs</span><span class="special">(</span><span class="identifier">x</span><span class="special">)</span> <span class="special">&gt;=</span> <span class="number">1</span><span class="special">)</span> <span class="special">{</span> <span class="keyword">return</span> <span class="number">0.0</span><span class="special">;</span> <span class="special">}</span> <span class="keyword">return</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">exp</span><span class="special">(-</span><span class="number">1.0</span><span class="special">/(</span><span class="number">1.0</span><span class="special">-</span><span class="identifier">x</span><span class="special">*</span><span class="identifier">x</span><span class="special">));</span> <span class="special">};</span>
+
+<span class="keyword">double</span> <span class="identifier">t0</span> <span class="special">=</span> <span class="special">-</span><span class="number">1</span><span class="special">;</span>
+<span class="identifier">size_t</span> <span class="identifier">n</span> <span class="special">=</span> <span class="number">2049</span><span class="special">;</span>
+<span class="keyword">double</span> <span class="identifier">h</span> <span class="special">=</span> <span class="number">2.0</span><span class="special">/(</span><span class="identifier">n</span><span class="special">-</span><span class="number">1.0</span><span class="special">);</span>
+
+<span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="identifier">v</span><span class="special">(</span><span class="identifier">n</span><span class="special">);</span>
+<span class="keyword">for</span><span class="special">(</span><span class="identifier">size_t</span> <span class="identifier">i</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span> <span class="identifier">i</span> <span class="special">&lt;</span> <span class="identifier">n</span><span class="special">;</span> <span class="special">++</span><span class="identifier">i</span><span class="special">)</span> <span class="special">{</span>
+    <span class="keyword">double</span> <span class="identifier">t</span> <span class="special">=</span> <span class="identifier">t0</span> <span class="special">+</span> <span class="identifier">i</span><span class="special">*</span><span class="identifier">h</span><span class="special">;</span>
+    <span class="identifier">v</span><span class="special">[</span><span class="identifier">i</span><span class="special">]</span> <span class="special">=</span> <span class="identifier">bump</span><span class="special">(</span><span class="identifier">t</span><span class="special">);</span>
+<span class="special">}</span>
+
+
+<span class="keyword">auto</span> <span class="identifier">ws</span> <span class="special">=</span> <span class="identifier">whittaker_shannon</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">move</span><span class="special">(</span><span class="identifier">v</span><span class="special">),</span> <span class="identifier">t0</span><span class="special">,</span> <span class="identifier">h</span><span class="special">);</span>
+
+<span class="keyword">double</span> <span class="identifier">y</span> <span class="special">=</span> <span class="identifier">ws</span><span class="special">(</span><span class="number">0.3</span><span class="special">);</span>
+</pre>
+<p>
+      The derivative of the interpolant can also be evaluated, but the accuracy is
+      not as high:
+    </p>
+<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">yp</span> <span class="special">=</span> <span class="identifier">ws</span><span class="special">.</span><span class="identifier">prime</span><span class="special">(</span><span class="number">0.3</span><span class="special">);</span>
+</pre>
+<h4>
+<a name="math_toolkit.whittaker_shannon.h2"></a>
+      <span class="phrase"><a name="math_toolkit.whittaker_shannon.complexity_and_performance"></a></span><a class="link" href="whittaker_shannon.html#math_toolkit.whittaker_shannon.complexity_and_performance">Complexity
+      and Performance</a>
+    </h4>
+<p>
+      The call to the constructor requires &#119926;(1) operations, simply moving data into
+      the class. Each call the the interpolant is &#119926;(<span class="emphasis"><em>n</em></span>), where
+      <span class="emphasis"><em>n</em></span> is the number of points to interpolate.
+    </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
+      Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="cardinal_quadratic_b.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../interpolation.html"><img src="../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="barycentric.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>
diff --git a/libs/math/doc/html/math_toolkit/zetas.html b/libs/math/doc/html/math_toolkit/zetas.html
index 6a81aba7d1..c4d13bfa74 100644
--- a/libs/math/doc/html/math_toolkit/zetas.html
+++ b/libs/math/doc/html/math_toolkit/zetas.html
@@ -4,7 +4,7 @@
 <title>Zeta Functions</title>
 <link rel="stylesheet" href="../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../special.html" title="Chapter&#160;7.&#160;Special Functions">
 <link rel="prev" href="lambert_w.html" title="Lambert W function">
 <link rel="next" href="zetas/zeta.html" title="Riemann Zeta Function">
@@ -30,11 +30,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/math_toolkit/zetas/zeta.html b/libs/math/doc/html/math_toolkit/zetas/zeta.html
index d9c2719fd3..cda4bd15fc 100644
--- a/libs/math/doc/html/math_toolkit/zetas/zeta.html
+++ b/libs/math/doc/html/math_toolkit/zetas/zeta.html
@@ -4,7 +4,7 @@
 <title>Riemann Zeta Function</title>
 <link rel="stylesheet" href="../../math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.10.0">
 <link rel="up" href="../zetas.html" title="Zeta Functions">
 <link rel="prev" href="../zetas.html" title="Zeta Functions">
 <link rel="next" href="../expint.html" title="Exponential Integrals">
@@ -373,11 +373,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/octonions.html b/libs/math/doc/html/octonions.html
index bade3a38d0..0ad80854c4 100644
--- a/libs/math/doc/html/octonions.html
+++ b/libs/math/doc/html/octonions.html
@@ -4,8 +4,8 @@
 <title>Chapter&#160;15.&#160;Octonions</title>
 <link rel="stylesheet" href="math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="index.html" title="Math Toolkit 2.9.0">
-<link rel="up" href="index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="index.html" title="Math Toolkit 2.10.0">
+<link rel="up" href="index.html" title="Math Toolkit 2.10.0">
 <link rel="prev" href="math_toolkit/quat_todo.html" title="To Do">
 <link rel="next" href="math_toolkit/oct_overview.html" title="Overview">
 </head>
@@ -48,11 +48,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/overview.html b/libs/math/doc/html/overview.html
index 105c9dc3f6..c971517aa5 100644
--- a/libs/math/doc/html/overview.html
+++ b/libs/math/doc/html/overview.html
@@ -4,9 +4,9 @@
 <title>Chapter&#160;1.&#160;Overview</title>
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-<link rel="up" href="index.html" title="Math Toolkit 2.9.0">
-<link rel="prev" href="index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="index.html" title="Math Toolkit 2.10.0">
+<link rel="up" href="index.html" title="Math Toolkit 2.10.0">
+<link rel="prev" href="index.html" title="Math Toolkit 2.10.0">
 <link rel="next" href="math_toolkit/main_intro.html" title="About the Math Toolkit">
 </head>
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@@ -46,18 +46,19 @@
     Library, and its Examples and Tests</a></span></dt>
 <dt><span class="section"><a href="math_toolkit/history1.html">History and What's New</a></span></dt>
 <dt><span class="section"><a href="math_toolkit/overview_tr1.html">C99 and C++ TR1 C-style Functions</a></span></dt>
-<dt><span class="section"><a href="math_toolkit/main_faq.html">Frequently Asked Questions FAQ</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/main_faq.html">Boost.Math Frequently Asked Questions
+    (FAQs)</a></span></dt>
 <dt><span class="section"><a href="math_toolkit/contact.html">Contact Info and Support</a></span></dt>
 </dl>
 </div>
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/perf.html b/libs/math/doc/html/perf.html
index bd4ef13b3d..f7cf1558bf 100644
--- a/libs/math/doc/html/perf.html
+++ b/libs/math/doc/html/perf.html
@@ -4,8 +4,8 @@
 <title>Chapter&#160;20.&#160;Performance</title>
 <link rel="stylesheet" href="math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="index.html" title="Math Toolkit 2.9.0">
-<link rel="up" href="index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="index.html" title="Math Toolkit 2.10.0">
+<link rel="up" href="index.html" title="Math Toolkit 2.10.0">
 <link rel="prev" href="math_toolkit/pol_ref/pol_ref_ref.html" title="Policy Class Reference">
 <link rel="next" href="math_toolkit/perf_over2.html" title="Performance Overview">
 </head>
@@ -45,11 +45,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/policy.html b/libs/math/doc/html/policy.html
index 6f4cfb50c0..1e6f056866 100644
--- a/libs/math/doc/html/policy.html
+++ b/libs/math/doc/html/policy.html
@@ -4,8 +4,8 @@
 <title>Chapter&#160;19.&#160;Policies: Controlling Precision, Error Handling etc</title>
 <link rel="stylesheet" href="math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="index.html" title="Math Toolkit 2.9.0">
-<link rel="up" href="index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="index.html" title="Math Toolkit 2.10.0">
+<link rel="up" href="index.html" title="Math Toolkit 2.10.0">
 <link rel="prev" href="math_toolkit/archetypes.html" title="Conceptual Archetypes for Reals and Distributions">
 <link rel="next" href="math_toolkit/pol_overview.html" title="Policy Overview">
 </head>
@@ -74,11 +74,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/poly.html b/libs/math/doc/html/poly.html
index 9f47da0e5e..4059375c25 100644
--- a/libs/math/doc/html/poly.html
+++ b/libs/math/doc/html/poly.html
@@ -4,8 +4,8 @@
 <title>Chapter&#160;10.&#160;Polynomials and Rational Functions</title>
 <link rel="stylesheet" href="math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="index.html" title="Math Toolkit 2.9.0">
-<link rel="up" href="index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="index.html" title="Math Toolkit 2.10.0">
+<link rel="up" href="index.html" title="Math Toolkit 2.10.0">
 <link rel="prev" href="math_toolkit/root_comparison/elliptic_comparison.html" title="Comparison of Elliptic Integral Root Finding Algoritghms">
 <link rel="next" href="math_toolkit/polynomials.html" title="Polynomials">
 </head>
@@ -36,11 +36,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/quadrature.html b/libs/math/doc/html/quadrature.html
index 18a9483345..61051f5154 100644
--- a/libs/math/doc/html/quadrature.html
+++ b/libs/math/doc/html/quadrature.html
@@ -4,8 +4,8 @@
 <title>Chapter&#160;12.&#160;Quadrature and Differentiation</title>
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-<link rel="home" href="index.html" title="Math Toolkit 2.9.0">
-<link rel="up" href="index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="index.html" title="Math Toolkit 2.10.0">
+<link rel="up" href="index.html" title="Math Toolkit 2.10.0">
 <link rel="prev" href="math_toolkit/catmull_rom.html" title="Catmull-Rom Splines">
 <link rel="next" href="math_toolkit/trapezoidal.html" title="Trapezoidal Quadrature">
 </head>
@@ -47,19 +47,21 @@
 <dt><span class="section"><a href="math_toolkit/double_exponential/de_caveats.html">Caveats</a></span></dt>
 <dt><span class="section"><a href="math_toolkit/double_exponential/de_refes.html">References</a></span></dt>
 </dl></dd>
+<dt><span class="section"><a href="math_toolkit/fourier_integrals.html">Fourier Integrals</a></span></dt>
 <dt><span class="section"><a href="math_toolkit/naive_monte_carlo.html">Naive Monte Carlo Integration</a></span></dt>
 <dt><span class="section"><a href="math_toolkit/diff.html">Numerical Differentiation</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/autodiff.html">Automatic Differentiation</a></span></dt>
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 </div>
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/quaternions.html b/libs/math/doc/html/quaternions.html
index 218e030d23..a21a137d3c 100644
--- a/libs/math/doc/html/quaternions.html
+++ b/libs/math/doc/html/quaternions.html
@@ -4,8 +4,8 @@
 <title>Chapter&#160;14.&#160;Quaternions</title>
 <link rel="stylesheet" href="math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="index.html" title="Math Toolkit 2.9.0">
-<link rel="up" href="index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="index.html" title="Math Toolkit 2.10.0">
+<link rel="up" href="index.html" title="Math Toolkit 2.10.0">
 <link rel="prev" href="math_toolkit/complex_history.html" title="History">
 <link rel="next" href="math_toolkit/quat_overview.html" title="Overview">
 </head>
@@ -49,11 +49,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/root_finding.html b/libs/math/doc/html/root_finding.html
index 7ae38671b3..da3bded02e 100644
--- a/libs/math/doc/html/root_finding.html
+++ b/libs/math/doc/html/root_finding.html
@@ -4,8 +4,8 @@
 <title>Chapter&#160;9.&#160;Root Finding &amp; Minimization Algorithms</title>
 <link rel="stylesheet" href="math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="index.html" title="Math Toolkit 2.9.0">
-<link rel="up" href="index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="index.html" title="Math Toolkit 2.10.0">
+<link rel="up" href="index.html" title="Math Toolkit 2.10.0">
 <link rel="prev" href="math_toolkit/tr1_ref.html" title="TR1 C Functions Quick Reference">
 <link rel="next" href="math_toolkit/roots_noderiv.html" title="Root Finding Without Derivatives">
 </head>
@@ -116,11 +116,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/special.html b/libs/math/doc/html/special.html
index 51cdae5fca..caea96aa71 100644
--- a/libs/math/doc/html/special.html
+++ b/libs/math/doc/html/special.html
@@ -4,8 +4,8 @@
 <title>Chapter&#160;7.&#160;Special Functions</title>
 <link rel="stylesheet" href="math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="index.html" title="Math Toolkit 2.9.0">
-<link rel="up" href="index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="index.html" title="Math Toolkit 2.10.0">
+<link rel="up" href="index.html" title="Math Toolkit 2.10.0">
 <link rel="prev" href="math_toolkit/norms.html" title="Norms">
 <link rel="next" href="math_toolkit/number_series.html" title="Number Series">
 </head>
@@ -203,11 +203,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/standalone_HTML.manifest b/libs/math/doc/html/standalone_HTML.manifest
index 60f8356c76..be58fede5a 100644
--- a/libs/math/doc/html/standalone_HTML.manifest
+++ b/libs/math/doc/html/standalone_HTML.manifest
@@ -287,7 +287,10 @@ math_toolkit/polynomials.html
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 interpolation.html
 math_toolkit/cubic_b.html
+math_toolkit/cardinal_quadratic_b.html
+math_toolkit/whittaker_shannon.html
 math_toolkit/barycentric.html
+math_toolkit/vector_barycentric.html
 math_toolkit/catmull_rom.html
 quadrature.html
 math_toolkit/trapezoidal.html
@@ -304,8 +307,10 @@ math_toolkit/double_exponential/de_levels.html
 math_toolkit/double_exponential/de_thread.html
 math_toolkit/double_exponential/de_caveats.html
 math_toolkit/double_exponential/de_refes.html
+math_toolkit/fourier_integrals.html
 math_toolkit/naive_monte_carlo.html
 math_toolkit/diff.html
+math_toolkit/autodiff.html
 math_toolkit/diff0.html
 inverse_complex.html
 math_toolkit/complex_implementation.html
diff --git a/libs/math/doc/html/status.html b/libs/math/doc/html/status.html
index d3a86fce76..4b5f6200b1 100644
--- a/libs/math/doc/html/status.html
+++ b/libs/math/doc/html/status.html
@@ -4,8 +4,8 @@
 <title>Chapter&#160;22.&#160;Library Status</title>
 <link rel="stylesheet" href="math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="index.html" title="Math Toolkit 2.9.0">
-<link rel="up" href="index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="index.html" title="Math Toolkit 2.10.0">
+<link rel="up" href="index.html" title="Math Toolkit 2.10.0">
 <link rel="prev" href="math_toolkit/logs_and_tables/logs.html" title="Error Logs For Error Rate Tables">
 <link rel="next" href="math_toolkit/history2.html" title="History and What's New">
 </head>
@@ -36,11 +36,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/using_udt.html b/libs/math/doc/html/using_udt.html
index 1d7767899b..96e6323770 100644
--- a/libs/math/doc/html/using_udt.html
+++ b/libs/math/doc/html/using_udt.html
@@ -4,8 +4,8 @@
 <title>Chapter&#160;18.&#160;Use with User-Defined Floating-Point Types - Boost.Multiprecision and others</title>
 <link rel="stylesheet" href="math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="index.html" title="Math Toolkit 2.9.0">
-<link rel="up" href="index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="index.html" title="Math Toolkit 2.10.0">
+<link rel="up" href="index.html" title="Math Toolkit 2.10.0">
 <link rel="prev" href="math_toolkit/internals/test_data.html" title="Graphing, Profiling, and Generating Test Data for Special Functions">
 <link rel="next" href="math_toolkit/high_precision.html" title="Using Boost.Math with High-Precision Floating-Point Libraries">
 </head>
@@ -56,11 +56,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/utils.html b/libs/math/doc/html/utils.html
index 5fd2b9623c..fea98d257a 100644
--- a/libs/math/doc/html/utils.html
+++ b/libs/math/doc/html/utils.html
@@ -4,8 +4,8 @@
 <title>Chapter&#160;2.&#160;Floating Point Utilities</title>
 <link rel="stylesheet" href="math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="index.html" title="Math Toolkit 2.9.0">
-<link rel="up" href="index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="index.html" title="Math Toolkit 2.10.0">
+<link rel="up" href="index.html" title="Math Toolkit 2.10.0">
 <link rel="prev" href="math_toolkit/contact.html" title="Contact Info and Support">
 <link rel="next" href="math_toolkit/rounding.html" title="Rounding Truncation and Integer Conversion">
 </head>
@@ -71,11 +71,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html/vector_functionals.html b/libs/math/doc/html/vector_functionals.html
index da9da8d71e..cf6763468f 100644
--- a/libs/math/doc/html/vector_functionals.html
+++ b/libs/math/doc/html/vector_functionals.html
@@ -4,8 +4,8 @@
 <title>Chapter&#160;6.&#160;Vector Functionals</title>
 <link rel="stylesheet" href="math.css" type="text/css">
 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="index.html" title="Math Toolkit 2.9.0">
-<link rel="up" href="index.html" title="Math Toolkit 2.9.0">
+<link rel="home" href="index.html" title="Math Toolkit 2.10.0">
+<link rel="up" href="index.html" title="Math Toolkit 2.10.0">
 <link rel="prev" href="math_toolkit/future.html" title="Extras/Future Directions">
 <link rel="next" href="math_toolkit/univariate_statistics.html" title="Univariate Statistics">
 </head>
@@ -37,11 +37,11 @@
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
-      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
-      Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
-      and Xiaogang Zhang<p>
+      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
+      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
+      Daryle Walker and Xiaogang Zhang<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
diff --git a/libs/math/doc/html4_symbols.qbk b/libs/math/doc/html4_symbols.qbk
index 3c0ae907bb..c6f5eb8a28 100644
--- a/libs/math/doc/html4_symbols.qbk
+++ b/libs/math/doc/html4_symbols.qbk
@@ -14,7 +14,7 @@
 [/ Also some miscellaneous math characters added to this list - see the end.]
 [/ For others see also math_toolkit.symbols.qbk]
 
-[/ To use, enclose the template name in square brackets, for example: [pi]]
+[/ To use, enclose the template name in square brackets, for example: [pi] ]
 
 [template fnof[]'''&#x192;'''] [/ � Latin small f with hook = function = florin]
 [/ Capital Greek start with capital letter, lower case all small.]
diff --git a/libs/math/doc/index.idx b/libs/math/doc/index.idx
index d5585ae760..d77e8ee318 100644
--- a/libs/math/doc/index.idx
+++ b/libs/math/doc/index.idx
@@ -1,6 +1,11 @@
 # Boost.Math Indexing terms file.
 # Copyright John Maddock 2009 - 2012
-# Copyright Paul A. Bristow 2009 - 2012
+# Copyright Paul A. Bristow 2009 - 2019
+
+FAQ \<FAQ\w*\>
+
+cpp_bin_float \<cpp_bin_\w*\> 
+cpp_dec_float \<cpp_dec_\w*\>
 
 "Lanczos approximation" lanczos
 
@@ -10,6 +15,8 @@ expression \<express\w*\>
 
 constants  \<constant\w*\>
 
+multiprecision  \<\w*\multiprecision\w*\>
+
 !scan-path boost/math .*\.hpp true
 
 !exclude policy precision apply evaluation polynomial name helper 
@@ -41,7 +48,6 @@ Cephes
 
 DCDFLIB
 
-
 !rewrite-name "(?i)(?:A|The)\s+(.*)" "\1"
 !rewrite-name "Additional Implementation Notes" "Implementation Notes"
 !rewrite-name "(?i)Calculating(?:\s+the)?\s+(.*)" "\1"
diff --git a/libs/math/doc/interpolators/cardinal_quadratic_b_spline.qbk b/libs/math/doc/interpolators/cardinal_quadratic_b_spline.qbk
new file mode 100644
index 0000000000..219e6d208a
--- /dev/null
+++ b/libs/math/doc/interpolators/cardinal_quadratic_b_spline.qbk
@@ -0,0 +1,56 @@
+[/
+Copyright (c) 2019 Nick Thompson
+Use, modification and distribution are subject to the
+Boost Software License, Version 1.0. (See accompanying file
+LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+]
+
+[section:cardinal_quadratic_b Cardinal Quadratic B-spline interpolation]
+
+[heading Synopsis]
+``
+  #include <boost/math/interpolators/cardinal_quadratic_b_spline.hpp>
+``
+
+    namespace boost{ namespace math{ namespace interpolators {
+
+    template <class Real>
+    class cardinal_quadratic_b_spline
+    {
+    public:
+        // If you don't know the value of the derivative at the endpoints, leave them as nans and the routine will estimate them.
+        // y[0] = y(a), y[n - 1] = y(b), step_size = (b - a)/(n -1).
+        cardinal_quadratic_b_spline(const Real* const y,
+                                    size_t n,
+                                    Real t0 /* initial time, left endpoint */,
+                                    Real h  /*spacing, stepsize*/,
+                                    Real left_endpoint_derivative = std::numeric_limits<Real>::quiet_NaN(),
+                                    Real right_endpoint_derivative = std::numeric_limits<Real>::quiet_NaN())
+
+        cardinal_quadratic_b_spline(std::vector<Real> const & y,
+                                    Real t0 /* initial time, left endpoint */,
+                                    Real h  /*spacing, stepsize*/,
+                                    Real left_endpoint_derivative = std::numeric_limits<Real>::quiet_NaN(),
+                                    Real right_endpoint_derivative = std::numeric_limits<Real>::quiet_NaN())
+
+        Real operator()(Real t) const;
+
+        Real prime(Real t) const;
+    };
+    }}}
+
+[heading Cardinal Quadratic B-Spline Interpolation]
+
+The cardinal quadratic B-spline interpolator is very nearly the same as the cubic B-spline interpolator,
+with the modification that the basis functions are constructed by convolving a box function with itself twice,
+rather than three times as is done with the cubic B-spline.
+
+Since the basis functions are less smooth than the cubic B-spline,
+you will nearly always wish to use the cubic B-spline interpolator rather than this.
+However, this interpolator is occasionally useful for approximating functions of reduced smoothness,
+as hence finds a uses internally in the Boost.Math library.
+
+It is reasonable to test this interpolator against the cubic b-spline interpolator when you are approximating functions which are two or three times continuously differentiable, but not three or four times differentiable.
+
+[endsect]
+[/section:cardinal_quadratic_b]
diff --git a/libs/math/doc/interpolators/catmull_rom.qbk b/libs/math/doc/interpolators/catmull_rom.qbk
index 6d4f4e35ae..90f377af92 100644
--- a/libs/math/doc/interpolators/catmull_rom.qbk
+++ b/libs/math/doc/interpolators/catmull_rom.qbk
@@ -15,12 +15,12 @@
 
 namespace boost{ namespace math{
 
-    template<class Point>
+    template<class Point, class RandomAccessContainer = std::vector<Point> >
     class catmull_rom
     {
     public:
 
-        catmull_rom(std::vector<Point>&& points, bool closed = false, Real alpha = (Real) 1/ (Real) 2)
+        catmull_rom(RandomAccessContainer&& points, bool closed = false, Real alpha = (Real) 1/ (Real) 2)
 
         catmull_rom(std::initializer_list<Point> l, bool closed = false, typename Point::value_type alpha = (typename Point::value_type) 1/ (typename Point::value_type) 2);
 
@@ -217,6 +217,30 @@ This causes the class to call a `resize()` on the input vector.
 If `v.capacity() >= v.size() + 3`, then no problems arise; there are no reallocs, and in practice this condition is almost always satisfied.
 However, if `v.capacity() < v.size() + 3`, the realloc causes a performance penalty of roughly 20%.
 
+[heading Generic Containers]
+
+The `Point` type may be stored in a different container than `std::vector`.
+For example, here is how to store the points in a Boost.uBLAS vector:
+
+    mypoint3d<Real> p0(0.1, 0.2, 0.3);
+    mypoint3d<Real> p1(0.2, 0.3, 0.4);
+    mypoint3d<Real> p2(0.3, 0.4, 0.5);
+    mypoint3d<Real> p3(0.4, 0.5, 0.6);
+    mypoint3d<Real> p4(0.5, 0.6, 0.7);
+    mypoint3d<Real> p5(0.6, 0.7, 0.8);
+
+    boost::numeric::ublas::vector<mypoint3d<Real>> u(6);
+    u[0] = p0;
+    u[1] = p1;
+    u[2] = p2;
+    u[3] = p3;
+    u[4] = p4;
+    u[5] = p5;
+
+    // Tests initializer_list:
+    catmull_rom<mypoint3d<Real>, decltype(u)> cat(std::move(u));
+
+
 [heading References]
 
 * Cem Yuksel, Scott Schaefer, and John Keyser, ['Parameterization and applications of Catmull–Rom curves], Computer-Aided Design 43 (2011) 747–755.
diff --git a/libs/math/doc/interpolators/vector_barycentric_rational.qbk b/libs/math/doc/interpolators/vector_barycentric_rational.qbk
new file mode 100644
index 0000000000..335ecf3723
--- /dev/null
+++ b/libs/math/doc/interpolators/vector_barycentric_rational.qbk
@@ -0,0 +1,76 @@
+[/
+  Copyright 2019 Nick Thompson
+
+  Distributed under the Boost Software License, Version 1.0.
+  (See accompanying file LICENSE_1_0.txt or copy at
+  http://www.boost.org/LICENSE_1_0.txt).
+]
+
+[section:vector_barycentric Vector-valued Barycentric Rational Interpolation]
+
+[heading Synopsis]
+
+``
+#include <boost/math/interpolators/vector_barycentric_rational.hpp>
+
+namespace boost{ namespace math{
+
+template<class TimeContainer, class SpaceContainer>
+class vector_barycentric_rational
+{
+public:
+    using Real = typename TimeContainer::value_type;
+    using Point = typename SpaceContainer::value_type;
+    vector_barycentric_rational(TimeContainer&& times, SpaceContainer&& points, size_t approximation_order = 3);
+
+    void operator()(Point& x, Real t) const;
+
+    Point operator()(Real t) const;
+
+    void prime(Point& dxdt, Real t) const;
+
+    Point prime(Real t);
+
+    void eval_with_prime(Point& x, Point& dxdt, Real t) const;
+
+    std::pair<Point, Point> eval_with_prime(Real t) const;
+};
+
+}}
+``
+
+[heading Description]
+
+The /n/ dimensional vector-valued barycentric rational interpolator is exactly the same as /n/ scalar-valued barycentric rational interpolators.
+This is provided primarily for convenience and a slight improvement in efficiency over using /n/ different rational interpolators and combining their results.
+
+Use of the class requires a `Point`-type which has size known at compile time.
+These requirements are satisfied by (for example) `Eigen::Vector2d`s and `std::array<Real, N>` classes.
+The call to the constructor computes the weights:
+
+    using boost::math::vector_barycentric_rational;
+    std::vector<double> t(100);
+    std::vector<Eigen::Vector2d> y(100);
+    // initialize t and y . . .
+    vector_barycentric_rational<decltype(t), decltype(y)> interpolant(std::move(t), std::move(y));
+
+To evaluate the interpolant, use
+
+    double t = 2.3;
+    Eigen::Vector2d y = interpolant(t);
+
+If you want to populate a vector passed into the interpolant, rather than get it returned, that syntax is supported:
+
+    Eigen::Vector2d y;
+    interpolant(y, t);
+
+We tested this with `Eigen::Vector`s and found no performance benefit, but other `Point`-types might not be the same.
+
+To evaluate the derivative of the interpolant use
+
+    auto [y, y_prime] = interpolant.eval_with_prime(x);
+
+Computation of the derivative requires evaluation, so if you can try to use both values at once.
+
+
+[endsect] [/section:vector_barycentric Vector Barycentric Rational Interpolation]
diff --git a/libs/math/doc/interpolators/whittaker_shannon.qbk b/libs/math/doc/interpolators/whittaker_shannon.qbk
new file mode 100644
index 0000000000..701651f536
--- /dev/null
+++ b/libs/math/doc/interpolators/whittaker_shannon.qbk
@@ -0,0 +1,69 @@
+[/
+Copyright (c) 2019 Nick Thompson
+Use, modification and distribution are subject to the
+Boost Software License, Version 1.0. (See accompanying file
+LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+]
+
+[section:whittaker_shannon Whittaker-Shannon interpolation]
+
+[heading Synopsis]
+``
+  #include <boost/math/interpolators/whittaker_shannon.hpp>
+``
+
+  namespace boost { namespace math { namespace interpolators {
+
+    template <class RandomAccessContainer>
+    class whittaker_shannon
+    {
+    public:
+
+        using Real = RandomAccessContainer::value_type;
+
+        whittaker_shannon(RandomAccessContainer&& v, Real left_endpoint, Real step_size);
+
+        Real operator()(Real x) const;
+
+        Real prime(Real x) const;
+    };
+
+  }}} // namespaces
+
+
+[heading Whittaker-Shannon Interpolation]
+
+The Whittaker-Shannon interpolator takes equispaced data and interpolates between them via a sum of sinc functions.
+This interpolation is stable and infinitely smooth, but has linear complexity in the data, making it slow relative to compactly-supported b-splines.
+In addition, we cannot pass an infinite amount of data into the class, and must truncate the (perhaps) infinite sinc series to a finite number of terms.
+Since the sinc function has slow 1/x decay, the truncation of the series can incur large error.
+Hence this interpolator works best when operating on samples of compactly supported functions.
+Here is an example of interpolating a smooth "bump function":
+
+    auto bump = [](double x) { if (std::abs(x) >= 1) { return 0.0; } return std::exp(-1.0/(1.0-x*x)); };
+
+    double t0 = -1;
+    size_t n = 2049;
+    double h = 2.0/(n-1.0);
+
+    std::vector<double> v(n);
+    for(size_t i = 0; i < n; ++i) {
+        double t = t0 + i*h;
+        v[i] = bump(t);
+    }
+
+
+    auto ws = whittaker_shannon(std::move(v), t0, h);
+
+    double y = ws(0.3);
+
+The derivative of the interpolant can also be evaluated, but the accuracy is not as high:
+
+    double yp = ws.prime(0.3);
+
+[heading Complexity and Performance]
+
+The call to the constructor requires [bigo](1) operations, simply moving data into the class.
+Each call the the interpolant is [bigo](/n/), where /n/ is the number of points to interpolate.
+
+[endsect] [/section:whittaker_shannon]
diff --git a/libs/math/doc/math.qbk b/libs/math/doc/math.qbk
index c10ab1b997..3b2723dfd8 100644
--- a/libs/math/doc/math.qbk
+++ b/libs/math/doc/math.qbk
@@ -1,15 +1,15 @@
 [book Math Toolkit
     [quickbook 1.7]
-    [copyright 2006, 2007, 2008, 2009, 2010, 2012, 2013, 2014, 2017 Nikhar Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan Råde, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker and Xiaogang Zhang]
+    [copyright 2006-2019 Nikhar Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan Råde, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker and Xiaogang Zhang]
     [/purpose ISBN 0-9504833-2-X  978-0-9504833-2-0, Classification 519.2-dc22]
     [license
         Distributed under the Boost Software License, Version 1.0.
         (See accompanying file LICENSE_1_0.txt or copy at
         [@http://www.boost.org/LICENSE_1_0.txt])
     ]
-    [authors [Agrawal, Nikhar], [Bikineev, Anton], [Bristow, Paul A.], [Holin, Hubert], [Guazzone, Marco], [Kormanyos, Christopher], [Lalande, Bruno], [Maddock, John], [Murphy, Jeremy W.], [Råde, Johan], [Sobotta, Benjamin], [Sewani, Gautam], [Thompson, Nicholas], [van den Berg, Thijs], [Walker, Daryle], [Zhang, Xiaogang]]
+    [authors [Agrawal, Nikhar], [Bikineev, Anton], [Bristow, Paul A.], [Holin, Hubert], [Guazzone, Marco], [Kormanyos, Christopher], [Lalande, Bruno], [Maddock, John], [Murphy, Jeremy W.], [Pulver, Matthew], [Råde, Johan], [Sobotta, Benjamin], [Sewani, Gautam], [Thompson, Nicholas], [van den Berg, Thijs], [Walker, Daryle], [Zhang, Xiaogang]]
     [/last-revision $Date$]
-    [version 2.9.0]
+    [version 2.10.0]
 ]
 
 [template mathpart[id title]
@@ -402,9 +402,13 @@ and use the function's name as the link text.]
 [def __MPFR [@http://www.mpfr.org/ GNU MPFR library]]
 [def __GMP [@http://gmplib.org/ GNU Multiple Precision Arithmetic Library]]
 [def __multiprecision [@boost:/libs/multiprecision/doc/html/index.html Boost.Multiprecision]]
+
+[def __gcc_quad_type [@https://gcc.gnu.org/onlinedocs/gcc-9.1.0/libquadmath/index.html GCC 128-bit floating-point type]]
+
 [def __cpp_dec_float [@boost:/libs/multiprecision/doc/html/boost_multiprecision/tut/floats/cpp_dec_float.html cpp_dec_float]]
 [def __cpp_bin_float [@boost:/libs/multiprecision/doc/html/boost_multiprecision/tut/floats/cpp_bin_float.html cpp_bin_float]]
-[def __boost_test [@boost:/libs/test/doc/html/index.html Boost.Test]]
+[/ @boost:/libs/test/doc/index.html  doesn't work for Boost.Test non-quickbook, so use instead]
+[def __boost_test [@https://www.boost.org/doc/libs/release/libs/test/doc/html/index.html  Boost.Test]]
 [def __boost_timer [@boost:/libs/timer/doc/index.html Boost.Timer]]
 [def __boost_test_fp [@boost:/libs/test/doc/html/boost_test/users_guide/testing_tools/testing_floating_points.html Boost.Test floating-point comparison]]
 [def __boost_math_fp [link math_toolkit.float_comparison Boost.Math floating-point utilities]]
@@ -418,7 +422,6 @@ and use the function's name as the link text.]
 [def __Mathworld [@http://mathworld.wolfram.com Wolfram MathWorld]]
 [def __Mathematica [@http://www.wolfram.com/products/mathematica/index.html Wolfram Mathematica]]
 [def __Maple [@https://www.maplesoft.com Maple]]
-
 [def __WolframAlpha [@http://www.wolframalpha.com/ Wolfram Alpha]]
 [def __TOMS748 [@http://portal.acm.org/citation.cfm?id=210111 TOMS Algorithm 748: enclosing zeros of continuous functions]]
 [def __TOMS910 [@http://portal.acm.org/citation.cfm?id=1916469 TOMS Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations]]
@@ -658,7 +661,10 @@ and as a CD ISBN 0-9504833-2-X  978-0-9504833-2-0, Classification 519.2-dc22.
 
 [mathpart interpolation Interpolation]
 [include interpolators/cubic_b_spline.qbk]
+[include interpolators/cardinal_quadratic_b_spline.qbk]
+[include interpolators/whittaker_shannon.qbk]
 [include interpolators/barycentric_rational_interpolation.qbk]
+[include interpolators/vector_barycentric_rational.qbk]
 [include interpolators/catmull_rom.qbk]
 [endmathpart]
 
@@ -667,8 +673,10 @@ and as a CD ISBN 0-9504833-2-X  978-0-9504833-2-0, Classification 519.2-dc22.
 [include quadrature/gauss.qbk]
 [include quadrature/gauss_kronrod.qbk]
 [include quadrature/double_exponential.qbk]
+[include quadrature/ooura_fourier_integrals.qbk]
 [include quadrature/naive_monte_carlo.qbk]
 [include differentiation/numerical_differentiation.qbk]
+[include differentiation/autodiff.qbk]
 [include differentiation/lanczos_smoothing.qbk]
 [endmathpart]
 
diff --git a/libs/math/doc/overview/faq.qbk b/libs/math/doc/overview/faq.qbk
index 98159b5dcc..dd879491ff 100644
--- a/libs/math/doc/overview/faq.qbk
+++ b/libs/math/doc/overview/faq.qbk
@@ -1,4 +1,4 @@
-[section:main_faq Frequently Asked Questions FAQ]
+[section:main_faq Boost.Math Frequently Asked Questions (FAQs)]
 
 # ['I'm a FORTRAN/NAG/SPSS/SAS/Cephes/MathCad/R user
 and I don't see where the functions like dnorm(mean, sd) are in Boost.Math?]
@@ -22,14 +22,15 @@ see [@http://sourceforge.net/projects/distexplorer/ Statistical Distribution Exp
 # ['I'm allegic to reading manuals and prefer to learn from examples.]
 
   Fear not - you are not alone! Many examples are available for functions and distributions.
-Some are referenced directly from the text.  Others can be found at \boost_latest_release\libs\math\example.
+Some are referenced directly from the text.  Others can be found at `\boost_latest_release\libs\math\example`,
+for example 
 If you are a Visual Studio user, you should be able to create projects from each of these,
-making sure that the Boost library is in the include directories list.
+making sure that the Boost library is in the include directories list (there are usually NO libraries that must be built).
 
 # ['How do I make sure that the Boost library is in the Visual Studio include directories list?]
 
   You can add an include path, for example,  your Boost place /boost-latest_release,
-for example `X:/boost_1_45_0/` if you have a separate partition X for Boost releases.
+for example `X:/boost_1_70_0/` if you have a separate partition X for Boost releases.
 Or you can use an environment variable BOOST_ROOT set to your Boost place, and include that.
 Visual Studio before 2010 provided Tools, Options, VC++ Directories to control directories:
 Visual Studio 2010 instead provides property sheets to assist.
@@ -133,6 +134,22 @@ __cpp_dec_float is a useful user-defined type to provide a fixed number of decim
 See [@http://svn.boost.org/svn/boost/trunk/libs/multiprecision/doc/html/boost_multiprecision/intro.html mixed multiprecision arithmetic]
 and [@http://svn.boost.org/svn/boost/trunk/libs/multiprecision/doc/html/boost_multiprecision/tut/conversions.html conversion].
 
+# ['How do I choose between Boost.Multiprecision cpp_bin_50 and cpp_dec_50?]
+
+  Unless you have a specific reason to choose `cpp_dec_`, then the default choice should be `cpp_bin_`, for example using the convenience `typedefs` like
+`boost::multiprecision::cpp_bin_50` or `boost::multiprecision::cpp_bin_100`.
+
+  In general, both work well and give the same results and at roughly the same speed with `cpp_dec_50` sometimes faster.
+
+  cpp_dec_ was developed first paving the way for cpp_bin_. cpp_dec_ has several guard digits and is not rounded at all, using 'brute force' to get the promised number of decimal digits correct,
+but making it difficult to reason about precision and computational uncertainty, for example see [*https://svn.boost.org/trac10/ticket/12133].
+It also has a fast but imprecise division operator giving surprising results sometimes, see [*https://svn.boost.org/trac10/ticket/11178].
+
+  cpp_bin_ is correctly/exactly rounded making it possible to reason about both the precision and rounding of the results.
+
+
+
+
 
 [endsect] [/section:faq Frequently Asked Questions]
 
diff --git a/libs/math/doc/overview/overview.qbk b/libs/math/doc/overview/overview.qbk
index 3f2cfa7f91..6c4c8b5b91 100644
--- a/libs/math/doc/overview/overview.qbk
+++ b/libs/math/doc/overview/overview.qbk
@@ -4,13 +4,13 @@ This library is divided into several interconnected parts:
 
 [h4 Floating Point Utilities]
 
-Utility functions for dealing with floating point arithmetic, includes functions
+Utility functions for dealing with floating-point arithmetic, includes functions
 for floating point classification (fpclassify, isnan, isinf etc), sign manipulation,
 rounding, comparison, and computing the distance between floating point numbers.
 
-[h4 Specific Width Floating Point Types]
+[h4 Specific Width Floating-Point Types]
 
-A set of typedefs similar to those provided by `<cstdint>` but for floating point types.
+A set of typedefs similar to those provided by `<cstdint>` but for floating-point types.
 
 [h4 Mathematical Constants]
 
@@ -77,11 +77,11 @@ Tools for manipulating polynomials and for efficient evaluation of rationals or
 
 [h4 Interpolation]
 
-Function interpolation via Barycentic or cubic B_spline approximations.
+Function interpolation via Barycentric or cubic B_spline approximations.
 
 [h4 Numerical Integration and Differentiation]
 
-A reasonably comprehensive set of routines for integration (trapezoidal, Gaus-Legendre, Gaus-Kronrod and double-exponential) and differentiation.
+A reasonably comprehensive set of routines for integration (trapezoidal, Gauss-Legendre, Gauss-Kronrod and double-exponential) and differentiation.
 
 The integration routines are all usable for functions returning complex results - and as a result for contour integrals as well.
 
diff --git a/libs/math/doc/overview/roadmap.qbk b/libs/math/doc/overview/roadmap.qbk
index 2816182fbd..4667fcc94f 100644
--- a/libs/math/doc/overview/roadmap.qbk
+++ b/libs/math/doc/overview/roadmap.qbk
@@ -7,6 +7,18 @@ All bug reports including closed ones can be viewed
 [@https://svn.boost.org/trac/boost/query?status=assigned&status=closed&status=new&status=reopened&component=math&col=id&col=summary&col=status&col=type&col=milestone&col=component&order=priority here]
 and [@https://github.com/boostorg/math/issues?utf8=%E2%9C%93&q=is%3Aissue here].
 
+[h4 Math-2.10.0 (Boost-1.71)]
+
+* Catmull-Rom interpolator now works in C++11
+* Cardinal quadratic B-spline interpolation
+* Domain of elliptic integrals extended
+* sin_pi and cos_pi performance improvements
+* Forward-mode automatic differentiation
+* Vector valued barycentric rational interpolation
+* Ooura's method for evaluation of Fourier integrals
+* Multiple compatibility issues with Multiprecision fixed
+* Lambert-W fixed on a rare architecture
+
 [h4 Math-2.9.0 (Boost-1.70)]
 
 * Add Lanczos smoothing derivatives
diff --git a/libs/math/doc/quadrature/gauss_kronrod.qbk b/libs/math/doc/quadrature/gauss_kronrod.qbk
index 1518784705..9ce4c36c6d 100644
--- a/libs/math/doc/quadrature/gauss_kronrod.qbk
+++ b/libs/math/doc/quadrature/gauss_kronrod.qbk
@@ -93,6 +93,7 @@ and numbers of points.
 [heading Complex Quadrature]
 
 The Gauss-Kronrod quadrature support integrands defined on the real line and returning complex values.
+In this case, the template argument is the real type, and the complex type is deduced via the return type of the function.
 
 [heading Examples]
 
diff --git a/libs/math/doc/quadrature/ooura_fourier_integrals.qbk b/libs/math/doc/quadrature/ooura_fourier_integrals.qbk
new file mode 100644
index 0000000000..e084bb7384
--- /dev/null
+++ b/libs/math/doc/quadrature/ooura_fourier_integrals.qbk
@@ -0,0 +1,126 @@
+[/
+Copyright (c) 2019 Nick Thompson
+Copyright (c) 2019 Paul A. Bristow
+Use, modification and distribution are subject to the
+Boost Software License, Version 1.0. (See accompanying file
+LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+]
+
+[section:fourier_integrals Fourier Integrals]
+
+[import ../../example/ooura_fourier_integrals_example.cpp]
+[import ../../example/ooura_fourier_integrals_cosine_example.cpp]
+[import ../../example/ooura_fourier_integrals_multiprecision_example.cpp]
+
+[heading Synopsis]
+
+``
+    #include <boost/math/quadrature/ooura_fourier_integrals.hpp>
+    
+    namespace boost { namespace math { namespace quadrature {
+
+    template<class Real>
+    class ooura_fourier_sin {
+    public:
+        ooura_fourier_sin(const Real relative_error_tolerance = tools::root_epsilon<Real>(), size_t levels = sizeof(Real));
+
+        template<class F>
+        std::pair<Real, Real> integrate(F const & f, Real omega);
+
+    };
+
+
+    template<class Real>
+    class ooura_fourier_cos {
+    public:
+        ooura_fourier_cos(const Real relative_error_tolerance = tools::root_epsilon<Real>(), size_t levels = sizeof(Real))
+
+        template<class F>
+        std::pair<Real, Real> integrate(F const & f, Real omega);
+    };
+
+    }}} // namespaces
+``
+
+Ooura's method for Fourier integrals computes
+
+[sixemspace] [sixemspace] [int][sub 0][super [infin]] f(t)sin([omega] t) dt
+
+and
+
+[sixemspace] [sixemspace] [int][sub 0][super [infin]] f(t)cos([omega]  t) dt
+
+by a double exponentially decaying transformation.
+These integrals arise when computing continuous Fourier transform of odd and even functions, respectively.
+Oscillatory integrals are known to cause trouble for standard quadrature methods, so these routines are provided to cope with the most common oscillatory use case.
+
+The basic usage is shown below:
+
+[ooura_fourier_integrals_example_1]
+
+and compare with the expected value [pi]/2 of the integral.
+
+[ooura_fourier_integrals_example_2]
+
+The output is
+
+[ooura_fourier_integrals_example_output_1]
+
+[note This integrator is more insistent about examining the error estimate, than (say) tanh-sinh, which just returns the value of the integral.]
+
+With the macro BOOST_MATH_INSTRUMENT_OOURA defined, we can follow the progress:
+
+[ooura_fourier_integrals_example_diagnostic_output_1]
+
+Working code of this example is at [@../../example/ooura_fourier_integrals_example.cpp ooura_fourier_integrals_example.cpp]
+ 
+A classical cosine transform is presented below:
+
+[ooura_fourier_integrals_cosine_example_1]
+
+The value of this integral should be [pi]/(2e) and can be shown :
+
+[ooura_fourier_integrals_cosine_example_2]
+
+or with the macro BOOST_MATH_INSTRUMENT_OOURA defined, we can follow the progress:
+
+[ooura_fourier_integrals_example_cosine_diagnostic_output_1]
+
+Working code of this example is at [@../../example/ooura_fourier_integrals_cosine_example.cpp ooura_fourier_integrals_consine_example.cpp]
+
+[h5:performance Performance]
+The integrator precomputes nodes and weights, and hence can be reused for many different frequencies with good efficiency.
+The integrator is pimpl'd and hence can be shared between threads without a memcpy of the nodes and weights.
+
+Ooura and Mori's paper identifies criteria for rapid convergence based on the position of the poles of the integrand in the complex plane.
+If these poles are too close to the real axis the convergence is slow.
+It is not trivial to predict the convergence rate a priori, so if you are interested in figuring out if the convergence is rapid, compile with `-DBOOST_MATH_INSTRUMENT_OOURA`
+and some amount of printing will give you a good idea of how well this method is performing.
+
+[h5:multi_precision Higher precision]
+
+It is simple to extend to higher precision using __multiprecision.
+
+[ooura_fourier_integrals_multiprecision_example_1]
+
+[ooura_fourier_integrals_multiprecision_example_2]
+
+with output:
+[ooura_fourier_integrals_example_multiprecision_output_1]
+
+And with diagnostics on:
+
+[ooura_fourier_integrals_example_multiprecision_diagnostic_output_1]
+
+Working code of this example is at [@../../example/ooura_fourier_integrals_multiprecision_example.cpp ooura_fourier_integrals_multiprecision_example.cpp]
+
+For more examples of other functions and tests, see the full test suite at
+[@../../test/ooura_fourier_integral_test.cpp ooura_fourier_integral_test.cpp]. 
+
+[heading References]
+
+* Ooura, Takuya, and Masatake Mori, ['A robust double exponential formula for Fourier-type integrals.] Journal of computational and applied mathematics 112.1-2 (1999): 229-241.
+
+
+[endsect] [/section:fourier_integrals Fourier Integrals]
+
diff --git a/libs/math/doc/sf/ellint_legendre.qbk b/libs/math/doc/sf/ellint_legendre.qbk
index 38ff3bcb35..59c435ab72 100644
--- a/libs/math/doc/sf/ellint_legendre.qbk
+++ b/libs/math/doc/sf/ellint_legendre.qbk
@@ -51,7 +51,7 @@ Returns the incomplete elliptic integral of the first kind ['F([phi], k)]:
 
 [equation ellint2]
 
-Requires -1 <= k <= 1, otherwise returns the result of __domain_error.
+Requires k[super 2]sin[super 2](phi) < 1, otherwise returns the result of __domain_error.
 
 [optional_policy]
 
@@ -65,7 +65,7 @@ Returns the complete elliptic integral of the first kind ['K(k)]:
 
 [equation ellint6]
 
-Requires -1 <= k <= 1, otherwise returns the result of __domain_error.
+Requires |k| < 1, otherwise returns the result of __domain_error.
 
 [optional_policy]
 
@@ -154,7 +154,7 @@ Returns the incomplete elliptic integral of the second kind ['E([phi], k)]:
 
 [equation ellint3]
 
-Requires -1 <= k <= 1, otherwise returns the result of __domain_error.
+Requires k[super 2]sin[super 2](phi) < 1, otherwise returns the result of __domain_error.
 
 [optional_policy]
 
@@ -168,7 +168,7 @@ Returns the complete elliptic integral of the second kind ['E(k)]:
 
 [equation ellint7]
 
-Requires -1 <= k <= 1, otherwise returns the result of __domain_error.
+Requires |k| < 1, otherwise returns the result of __domain_error.
 
 [optional_policy]
 
@@ -257,7 +257,7 @@ Returns the incomplete elliptic integral of the third kind ['[Pi](n, [phi], k)]:
 
 [equation ellint4]
 
-Requires ['-1 <= k <= 1] and ['n < 1/sin[super 2]([phi])], otherwise 
+Requires ['k[super 2]sin[super 2](phi) < 1] and ['n < 1/sin[super 2]([phi])], otherwise 
 returns the result of __domain_error (outside this range the result 
 would be complex).
 
@@ -273,7 +273,7 @@ Returns the complete elliptic integral of the first kind ['[Pi](n, k)]:
 
 [equation ellint8]
 
-Requires ['-1 <= k <= 1] and ['n < 1], otherwise returns the 
+Requires ['|k| < 1] and ['n < 1], otherwise returns the 
 result of __domain_error (outside this range the result would be complex).
 
 [optional_policy]
@@ -367,7 +367,7 @@ and
 These two functions evaluate the incomplete elliptic integral 
 ['D([phi], k)] and its complete counterpart ['D(k) = D([pi]/2, k)].
 
-The return type of these functions is computed using the __arg_pomotion_rules
+The return type of these functions is computed using the __arg_promotion_rules
 when the arguments are of different types: when they are the same type then the result
 is the same type as the arguments.
 
@@ -381,7 +381,7 @@ Returns the incomplete elliptic integral:
 
 [equation ellint_d]
 
-Requires ['-1 <= k <= 1], otherwise 
+Requires ['k[super 2]sin[super 2](phi) < 1], otherwise 
 returns the result of __domain_error (outside this range the result 
 would be complex).
 
@@ -471,7 +471,12 @@ This function evaluates the Jacobi Zeta Function ['Z([phi], k)]
 
 [equation jacobi_zeta]
 
-The return type of this function is computed using the __arg_pomotion_rules
+Please note the use of [phi], and /k/ as the parameters, the function is often defined as ['Z([phi], m)]
+with ['m = k[super 2]], see for example  [@http://mathworld.wolfram.com/JacobiZetaFunction.html Weisstein, Eric W. "Jacobi Zeta Function." From MathWorld--A Wolfram Web Resource.]
+Or else as [@https://dlmf.nist.gov/22.16#E32 ['Z(x, k)]] with ['[phi] = am(x, k)], where ['am] is the [@https://dlmf.nist.gov/22.16#E1 Jacobi amplitude function] which is equivalent to
+['asin(jacobi_elliptic(k, x))].
+
+The return type of this function is computed using the __arg_promotion_rules
 when the arguments are of different types: when they are the same type then the result
 is the same type as the arguments.
 
@@ -541,7 +546,7 @@ This function evaluates the Heuman Lambda Function ['[Lambda][sub 0]([phi], k)]
 
 [equation heuman_lambda]
 
-The return type of this function is computed using the __arg_pomotion_rules
+The return type of this function is computed using the __arg_promotion_rules
 when the arguments are of different types: when they are the same type then the result
 is the same type as the arguments.
 
diff --git a/libs/math/doc/sf/lambert_w.qbk b/libs/math/doc/sf/lambert_w.qbk
index 4edb9482e2..6da963d836 100644
--- a/libs/math/doc/sf/lambert_w.qbk
+++ b/libs/math/doc/sf/lambert_w.qbk
@@ -352,7 +352,7 @@ for example, using __halley or __schroder methods.
 For C++, the most precise results possible, closest to the nearest __representable for the C++ type being used,
 it is usually necessary to use a higher precision type for intermediate computation,
 finally static-casting back to the smaller desired result type.
-This strategy is used by __Maple and WolframAlpha, for example, using arbitrary precision arithmetic,
+This strategy is used by __Maple and __WolframAlpha, for example, using arbitrary precision arithmetic,
 and some of their high-precision values are used for testing this library.
 This method is also used to provide some __boost_test values using __multiprecision,
 typically, a 50 decimal digit type like `cpp_bin_float_50`
@@ -367,7 +367,7 @@ In practical applications, the increased computation required
 (often towards a thousand-fold slower and requiring much additional code for __multiprecision)
 is not justified and the algorithms here do not implement this.
 But because the Boost.Lambert_W algorithms has been tested using __multiprecision,
-users who require this can always easily achieve the nearest representation for __fundamental
+users who require this can always easily achieve the nearest representation for __fundamental_types
 - if the application justifies the very large extra computation cost.
 
 [h5 Evolution of this implementation]
@@ -724,7 +724,7 @@ precision can be much lower, as might be expected.
 See source at:
 [@../../example/lambert_w_simple_examples.cpp lambert_w_simple_examples.cpp]
 [@../../test/test_lambert_w.cpp test_lambert_w.cpp] contains routine tests using __boost_test.
-[@../sf/lambert_w_errors_graph.cpp lambert_w_errors_graph.cpp] generating error graphs.
+[@../../tools/lambert_w_errors_graph.cpp lambert_w_errors_graph.cpp] generating error graphs.
 
 [h5:quadrature_testing  Testing with quadrature]
 
diff --git a/libs/math/example/Jamfile.v2 b/libs/math/example/Jamfile.v2
index 3cc8d56e2d..a33e113e76 100644
--- a/libs/math/example/Jamfile.v2
+++ b/libs/math/example/Jamfile.v2
@@ -61,6 +61,9 @@ test-suite examples :
    [ run error_policies_example.cpp  ]
    [ run error_policy_example.cpp : : : <exception-handling>off:<build>no  ]
    [ run f_test.cpp  ]
+   # [ run fft_sines_table.cpp  : : : [ requires cxx11_numeric_limits ] ]
+   # No need to re-run this routinely as it only creates a table of sines for a documentation example.
+
    [ run find_location_example.cpp : : : <exception-handling>off:<build>no  ]
    [ run find_mean_and_sd_normal.cpp : : : <exception-handling>off:<build>no  ]
    [ run find_root_example.cpp : : : <exception-handling>off:<build>no  ]
@@ -76,7 +79,6 @@ test-suite examples :
    [ run lambert_w_simple_examples.cpp  : : : [ requires cxx11_numeric_limits ] ]
    [ run lambert_w_precision_example.cpp  : : : [ check-target-builds ../config//has_float128 "GCC libquadmath and __float128 support" : <linkflags>-lquadmath ] [ requires cxx11_numeric_limits cxx11_explicit_conversion_operators ] ]
 
-
    [ run inverse_gamma_example.cpp  ]
    [ run inverse_gamma_distribution_example.cpp : : : <exception-handling>off:<build>no  ]
    [ run laplace_example.cpp : : : <exception-handling>off:<build>no  ]
@@ -132,17 +134,26 @@ test-suite examples :
    [ run series.cpp  ]
    [ run continued_fractions.cpp  ]
 
-   [ run root_elliptic_finding.cpp /boost/timer : : : release <link>static  [ requires cxx11_unified_initialization_syntax cxx11_defaulted_functions ] <target-os>freebsd:<linkflags>"-lrt" <target-os>linux:<linkflags>"-lrt -lpthread" ]
-   [ run root_finding_algorithms.cpp /boost/timer : : : release <link>static  [ requires cxx11_hdr_tuple cxx11_unified_initialization_syntax ] <target-os>freebsd:<linkflags>"-lrt" <target-os>linux:<linkflags>"-lrt -lpthread" ]
-   [ run root_n_finding_algorithms.cpp /boost/timer : : : release <link>static  [ requires cxx11_unified_initialization_syntax cxx11_defaulted_functions ] <target-os>freebsd:<linkflags>"-lrt" <target-os>linux:<linkflags>"-lrt -lpthread" ]
-
-   [ explicit root_elliptic_finding  ]
-   [ explicit root_finding_algorithms  ]
-   [ explicit root_n_finding_algorithms  ]
-
    [ run barycentric_interpolation_example.cpp : : : [ requires cxx11_smart_ptr cxx11_function_template_default_args cxx11_unified_initialization_syntax cxx11_defaulted_functions cxx11_allocator cxx11_auto_declarations cxx11_lambdas ]  ]
    [ run barycentric_interpolation_example_2.cpp : : : [ requires cxx11_smart_ptr cxx11_function_template_default_args cxx11_unified_initialization_syntax cxx11_defaulted_functions cxx11_allocator cxx11_auto_declarations cxx11_lambdas ]  ]
    [ run cubic_b_spline_example.cpp : : : [ requires cxx11_smart_ptr cxx11_hdr_random cxx11_defaulted_functions ]  ]
    [ compile naive_monte_carlo_example.cpp : [ requires cxx11_auto_declarations cxx11_lambdas cxx11_unified_initialization_syntax cxx11_hdr_thread cxx11_hdr_atomic cxx11_decltype cxx11_hdr_future cxx11_hdr_chrono cxx11_hdr_random cxx11_allocator ] ]  # requires user input, can't run it, take a long time too!
    [ run catmull_rom_example.cpp : : : [ requires cxx17_if_constexpr cxx11_auto_declarations cxx17_std_apply ] ] # Actually the C++17 features used is std::size, not if constexpr; looks like there isn't yet a test for it.
+   [ run autodiff_black_scholes_brief.cpp : : : [ requires cxx11_inline_namespaces ] ]
+   [ run autodiff_black_scholes.cpp : : : [ requires cxx11_inline_namespaces ] ]
+   [ run autodiff_fourth_power.cpp : : : [ requires cxx11_inline_namespaces ] ]
+   [ run autodiff_mixed_partials.cpp : : : [ requires cxx11_inline_namespaces ] ]
+   [ run autodiff_multiprecision.cpp : : : [ requires cxx11_inline_namespaces ] ]
+   [ run ooura_fourier_integrals_example.cpp : : : [ requires cxx11_lambdas cxx11_inline_namespaces cxx11_auto_declarations ] ]
+   [ run ooura_fourier_integrals_cosine_example.cpp : : : [ requires cxx11_inline_namespaces cxx11_auto_declarations cxx17_std_apply ] ]
+   [ run ooura_fourier_integrals_multiprecision_example.cpp : : : [ check-target-builds ../config//has_float128 "GCC libquadmath and __float128 support" : <linkflags>-lquadmath ] [ requires cxx11_inline_namespaces cxx11_auto_declarations cxx17_std_apply ] ]
+
 ;
+
+run root_elliptic_finding.cpp /boost/timer : : : release <link>static  [ requires cxx11_unified_initialization_syntax cxx11_defaulted_functions ] <target-os>freebsd:<linkflags>"-lrt" <target-os>linux:<linkflags>"-lrt -lpthread" ;
+run root_finding_algorithms.cpp /boost/timer : : : release <link>static  [ requires cxx11_hdr_tuple cxx11_unified_initialization_syntax ] <target-os>freebsd:<linkflags>"-lrt" <target-os>linux:<linkflags>"-lrt -lpthread" ;
+run root_n_finding_algorithms.cpp /boost/timer : : : release <link>static  [ requires cxx11_unified_initialization_syntax cxx11_defaulted_functions ] <target-os>freebsd:<linkflags>"-lrt" <target-os>linux:<linkflags>"-lrt -lpthread" ;
+
+explicit root_elliptic_finding  ;
+explicit root_finding_algorithms  ;
+explicit root_n_finding_algorithms  ;
diff --git a/libs/math/example/autodiff_black_scholes.cpp b/libs/math/example/autodiff_black_scholes.cpp
new file mode 100644
index 0000000000..b7fcd9c0aa
--- /dev/null
+++ b/libs/math/example/autodiff_black_scholes.cpp
@@ -0,0 +1,195 @@
+//           Copyright Matthew Pulver 2018 - 2019.
+// Distributed under the Boost Software License, Version 1.0.
+//      (See accompanying file LICENSE_1_0.txt or copy at
+//           https://www.boost.org/LICENSE_1_0.txt)
+
+#include <boost/math/differentiation/autodiff.hpp>
+#include <iostream>
+#include <stdexcept>
+
+using namespace boost::math::constants;
+using namespace boost::math::differentiation;
+
+// Equations and function/variable names are from
+// https://en.wikipedia.org/wiki/Greeks_(finance)#Formulas_for_European_option_Greeks
+
+// Standard normal probability density function
+template <typename X>
+X phi(X const& x) {
+  return one_div_root_two_pi<X>() * exp(-0.5 * x * x);
+}
+
+// Standard normal cumulative distribution function
+template <typename X>
+X Phi(X const& x) {
+  return 0.5 * erfc(-one_div_root_two<X>() * x);
+}
+
+enum class CP { call, put };
+
+// Assume zero annual dividend yield (q=0).
+template <typename Price, typename Sigma, typename Tau, typename Rate>
+promote<Price, Sigma, Tau, Rate> black_scholes_option_price(CP cp,
+                                                            double K,
+                                                            Price const& S,
+                                                            Sigma const& sigma,
+                                                            Tau const& tau,
+                                                            Rate const& r) {
+  using namespace std;
+  auto const d1 = (log(S / K) + (r + sigma * sigma / 2) * tau) / (sigma * sqrt(tau));
+  auto const d2 = (log(S / K) + (r - sigma * sigma / 2) * tau) / (sigma * sqrt(tau));
+  switch (cp) {
+    case CP::call:
+      return S * Phi(d1) - exp(-r * tau) * K * Phi(d2);
+    case CP::put:
+      return exp(-r * tau) * K * Phi(-d2) - S * Phi(-d1);
+    default:
+      throw std::runtime_error("Invalid CP value.");
+  }
+}
+
+int main() {
+  double const K = 100.0;  // Strike price.
+  auto const variables = make_ftuple<double, 3, 3, 1, 1>(105, 5, 30.0 / 365, 1.25 / 100);
+  auto const& S = std::get<0>(variables);      // Stock price.
+  auto const& sigma = std::get<1>(variables);  // Volatility.
+  auto const& tau = std::get<2>(variables);    // Time to expiration in years. (30 days).
+  auto const& r = std::get<3>(variables);      // Interest rate.
+  auto const call_price = black_scholes_option_price(CP::call, K, S, sigma, tau, r);
+  auto const put_price = black_scholes_option_price(CP::put, K, S, sigma, tau, r);
+
+  double const d1 = static_cast<double>((log(S / K) + (r + sigma * sigma / 2) * tau) / (sigma * sqrt(tau)));
+  double const d2 = static_cast<double>((log(S / K) + (r - sigma * sigma / 2) * tau) / (sigma * sqrt(tau)));
+  double const formula_call_delta = +Phi(+d1);
+  double const formula_put_delta = -Phi(-d1);
+  double const formula_vega = static_cast<double>(S * phi(d1) * sqrt(tau));
+  double const formula_call_theta =
+      static_cast<double>(-S * phi(d1) * sigma / (2 * sqrt(tau)) - r * K * exp(-r * tau) * Phi(+d2));
+  double const formula_put_theta =
+      static_cast<double>(-S * phi(d1) * sigma / (2 * sqrt(tau)) + r * K * exp(-r * tau) * Phi(-d2));
+  double const formula_call_rho = static_cast<double>(+K * tau * exp(-r * tau) * Phi(+d2));
+  double const formula_put_rho = static_cast<double>(-K * tau * exp(-r * tau) * Phi(-d2));
+  double const formula_gamma = static_cast<double>(phi(d1) / (S * sigma * sqrt(tau)));
+  double const formula_vanna = static_cast<double>(-phi(d1) * d2 / sigma);
+  double const formula_charm =
+      static_cast<double>(phi(d1) * (d2 * sigma * sqrt(tau) - 2 * r * tau) / (2 * tau * sigma * sqrt(tau)));
+  double const formula_vomma = static_cast<double>(S * phi(d1) * sqrt(tau) * d1 * d2 / sigma);
+  double const formula_veta = static_cast<double>(-S * phi(d1) * sqrt(tau) *
+                                                  (r * d1 / (sigma * sqrt(tau)) - (1 + d1 * d2) / (2 * tau)));
+  double const formula_speed =
+      static_cast<double>(-phi(d1) * (d1 / (sigma * sqrt(tau)) + 1) / (S * S * sigma * sqrt(tau)));
+  double const formula_zomma = static_cast<double>(phi(d1) * (d1 * d2 - 1) / (S * sigma * sigma * sqrt(tau)));
+  double const formula_color =
+      static_cast<double>(-phi(d1) / (2 * S * tau * sigma * sqrt(tau)) *
+                          (1 + (2 * r * tau - d2 * sigma * sqrt(tau)) * d1 / (sigma * sqrt(tau))));
+  double const formula_ultima =
+      -formula_vega * static_cast<double>((d1 * d2 * (1 - d1 * d2) + d1 * d1 + d2 * d2) / (sigma * sigma));
+
+  std::cout << std::setprecision(std::numeric_limits<double>::digits10)
+            << "autodiff black-scholes call price = " << call_price.derivative(0, 0, 0, 0) << '\n'
+            << "autodiff black-scholes put  price = " << put_price.derivative(0, 0, 0, 0) << '\n'
+            << "\n## First-order Greeks\n"
+            << "autodiff call delta = " << call_price.derivative(1, 0, 0, 0) << '\n'
+            << " formula call delta = " << formula_call_delta << '\n'
+            << "autodiff call vega  = " << call_price.derivative(0, 1, 0, 0) << '\n'
+            << " formula call vega  = " << formula_vega << '\n'
+            << "autodiff call theta = " << -call_price.derivative(0, 0, 1, 0)
+            << '\n'  // minus sign due to tau = T-time
+            << " formula call theta = " << formula_call_theta << '\n'
+            << "autodiff call rho   = " << call_price.derivative(0, 0, 0, 1) << '\n'
+            << " formula call rho   = " << formula_call_rho << '\n'
+            << '\n'
+            << "autodiff put delta = " << put_price.derivative(1, 0, 0, 0) << '\n'
+            << " formula put delta = " << formula_put_delta << '\n'
+            << "autodiff put vega  = " << put_price.derivative(0, 1, 0, 0) << '\n'
+            << " formula put vega  = " << formula_vega << '\n'
+            << "autodiff put theta = " << -put_price.derivative(0, 0, 1, 0) << '\n'
+            << " formula put theta = " << formula_put_theta << '\n'
+            << "autodiff put rho   = " << put_price.derivative(0, 0, 0, 1) << '\n'
+            << " formula put rho   = " << formula_put_rho << '\n'
+            << "\n## Second-order Greeks\n"
+            << "autodiff call gamma = " << call_price.derivative(2, 0, 0, 0) << '\n'
+            << "autodiff put  gamma = " << put_price.derivative(2, 0, 0, 0) << '\n'
+            << "      formula gamma = " << formula_gamma << '\n'
+            << "autodiff call vanna = " << call_price.derivative(1, 1, 0, 0) << '\n'
+            << "autodiff put  vanna = " << put_price.derivative(1, 1, 0, 0) << '\n'
+            << "      formula vanna = " << formula_vanna << '\n'
+            << "autodiff call charm = " << -call_price.derivative(1, 0, 1, 0) << '\n'
+            << "autodiff put  charm = " << -put_price.derivative(1, 0, 1, 0) << '\n'
+            << "      formula charm = " << formula_charm << '\n'
+            << "autodiff call vomma = " << call_price.derivative(0, 2, 0, 0) << '\n'
+            << "autodiff put  vomma = " << put_price.derivative(0, 2, 0, 0) << '\n'
+            << "      formula vomma = " << formula_vomma << '\n'
+            << "autodiff call veta = " << call_price.derivative(0, 1, 1, 0) << '\n'
+            << "autodiff put  veta = " << put_price.derivative(0, 1, 1, 0) << '\n'
+            << "      formula veta = " << formula_veta << '\n'
+            << "\n## Third-order Greeks\n"
+            << "autodiff call speed = " << call_price.derivative(3, 0, 0, 0) << '\n'
+            << "autodiff put  speed = " << put_price.derivative(3, 0, 0, 0) << '\n'
+            << "      formula speed = " << formula_speed << '\n'
+            << "autodiff call zomma = " << call_price.derivative(2, 1, 0, 0) << '\n'
+            << "autodiff put  zomma = " << put_price.derivative(2, 1, 0, 0) << '\n'
+            << "      formula zomma = " << formula_zomma << '\n'
+            << "autodiff call color = " << call_price.derivative(2, 0, 1, 0) << '\n'
+            << "autodiff put  color = " << put_price.derivative(2, 0, 1, 0) << '\n'
+            << "      formula color = " << formula_color << '\n'
+            << "autodiff call ultima = " << call_price.derivative(0, 3, 0, 0) << '\n'
+            << "autodiff put  ultima = " << put_price.derivative(0, 3, 0, 0) << '\n'
+            << "      formula ultima = " << formula_ultima << '\n';
+  return 0;
+}
+/*
+Output:
+autodiff black-scholes call price = 56.5136030677739
+autodiff black-scholes put  price = 51.4109161009333
+
+## First-order Greeks
+autodiff call delta = 0.773818444921273
+ formula call delta = 0.773818444921274
+autodiff call vega  = 9.05493427705736
+ formula call vega  = 9.05493427705736
+autodiff call theta = -275.73013426444
+ formula call theta = -275.73013426444
+autodiff call rho   = 2.03320550539396
+ formula call rho   = 2.03320550539396
+
+autodiff put delta = -0.226181555078726
+ formula put delta = -0.226181555078726
+autodiff put vega  = 9.05493427705736
+ formula put vega  = 9.05493427705736
+autodiff put theta = -274.481417851526
+ formula put theta = -274.481417851526
+autodiff put rho   = -6.17753255212599
+ formula put rho   = -6.17753255212599
+
+## Second-order Greeks
+autodiff call gamma = 0.00199851912993254
+autodiff put  gamma = 0.00199851912993254
+      formula gamma = 0.00199851912993254
+autodiff call vanna = 0.0410279463126531
+autodiff put  vanna = 0.0410279463126531
+      formula vanna = 0.0410279463126531
+autodiff call charm = -1.2505564233679
+autodiff put  charm = -1.2505564233679
+      formula charm = -1.2505564233679
+autodiff call vomma = -0.928114149313108
+autodiff put  vomma = -0.928114149313108
+      formula vomma = -0.928114149313107
+autodiff call veta = 26.7947073115641
+autodiff put  veta = 26.7947073115641
+      formula veta = 26.7947073115641
+
+## Third-order Greeks
+autodiff call speed = -2.90117322380992e-05
+autodiff put  speed = -2.90117322380992e-05
+      formula speed = -2.90117322380992e-05
+autodiff call zomma = -0.000604548369901419
+autodiff put  zomma = -0.000604548369901419
+      formula zomma = -0.000604548369901419
+autodiff call color = -0.0184014426606065
+autodiff put  color = -0.0184014426606065
+      formula color = -0.0184014426606065
+autodiff call ultima = -0.0922426864775683
+autodiff put  ultima = -0.0922426864775683
+      formula ultima = -0.0922426864775685
+**/
diff --git a/libs/math/example/autodiff_black_scholes_brief.cpp b/libs/math/example/autodiff_black_scholes_brief.cpp
new file mode 100644
index 0000000000..7078217b60
--- /dev/null
+++ b/libs/math/example/autodiff_black_scholes_brief.cpp
@@ -0,0 +1,70 @@
+//           Copyright Matthew Pulver 2018 - 2019.
+// Distributed under the Boost Software License, Version 1.0.
+//      (See accompanying file LICENSE_1_0.txt or copy at
+//           https://www.boost.org/LICENSE_1_0.txt)
+
+#include <boost/math/differentiation/autodiff.hpp>
+#include <iostream>
+#include <stdexcept>
+
+using namespace boost::math::constants;
+using namespace boost::math::differentiation;
+
+// Equations and function/variable names are from
+// https://en.wikipedia.org/wiki/Greeks_(finance)#Formulas_for_European_option_Greeks
+
+// Standard normal cumulative distribution function
+template <typename X>
+X Phi(X const& x) {
+  return 0.5 * erfc(-one_div_root_two<X>() * x);
+}
+
+enum class CP { call, put };
+
+// Assume zero annual dividend yield (q=0).
+template <typename Price, typename Sigma, typename Tau, typename Rate>
+promote<Price, Sigma, Tau, Rate> black_scholes_option_price(CP cp,
+                                                            double K,
+                                                            Price const& S,
+                                                            Sigma const& sigma,
+                                                            Tau const& tau,
+                                                            Rate const& r) {
+  using namespace std;
+  auto const d1 = (log(S / K) + (r + sigma * sigma / 2) * tau) / (sigma * sqrt(tau));
+  auto const d2 = (log(S / K) + (r - sigma * sigma / 2) * tau) / (sigma * sqrt(tau));
+  switch (cp) {
+    case CP::call:
+      return S * Phi(d1) - exp(-r * tau) * K * Phi(d2);
+    case CP::put:
+      return exp(-r * tau) * K * Phi(-d2) - S * Phi(-d1);
+    default:
+      throw std::runtime_error("Invalid CP value.");
+  }
+}
+
+int main() {
+  double const K = 100.0;                    // Strike price.
+  auto const S = make_fvar<double, 2>(105);  // Stock price.
+  double const sigma = 5;                    // Volatility.
+  double const tau = 30.0 / 365;             // Time to expiration in years. (30 days).
+  double const r = 1.25 / 100;               // Interest rate.
+  auto const call_price = black_scholes_option_price(CP::call, K, S, sigma, tau, r);
+  auto const put_price = black_scholes_option_price(CP::put, K, S, sigma, tau, r);
+
+  std::cout << "black-scholes call price = " << call_price.derivative(0) << '\n'
+            << "black-scholes put  price = " << put_price.derivative(0) << '\n'
+            << "call delta = " << call_price.derivative(1) << '\n'
+            << "put  delta = " << put_price.derivative(1) << '\n'
+            << "call gamma = " << call_price.derivative(2) << '\n'
+            << "put  gamma = " << put_price.derivative(2) << '\n';
+  return 0;
+}
+/*
+Output:
+black-scholes call price = 56.5136
+black-scholes put  price = 51.4109
+call delta = 0.773818
+put  delta = -0.226182
+call gamma = 0.00199852
+put  gamma = 0.00199852
+**/
diff --git a/libs/math/example/autodiff_fourth_power.cpp b/libs/math/example/autodiff_fourth_power.cpp
new file mode 100644
index 0000000000..50f280b6bb
--- /dev/null
+++ b/libs/math/example/autodiff_fourth_power.cpp
@@ -0,0 +1,34 @@
+//           Copyright Matthew Pulver 2018 - 2019.
+// Distributed under the Boost Software License, Version 1.0.
+//      (See accompanying file LICENSE_1_0.txt or copy at
+//           https://www.boost.org/LICENSE_1_0.txt)
+
+#include <boost/math/differentiation/autodiff.hpp>
+#include <iostream>
+
+template <typename T>
+T fourth_power(T const& x) {
+  T x4 = x * x;  // retval in operator*() uses x4's memory via NRVO.
+  x4 *= x4;      // No copies of x4 are made within operator*=() even when squaring.
+  return x4;     // x4 uses y's memory in main() via NRVO.
+}
+
+int main() {
+  using namespace boost::math::differentiation;
+
+  constexpr unsigned Order = 5;                  // Highest order derivative to be calculated.
+  auto const x = make_fvar<double, Order>(2.0);  // Find derivatives at x=2.
+  auto const y = fourth_power(x);
+  for (unsigned i = 0; i <= Order; ++i)
+    std::cout << "y.derivative(" << i << ") = " << y.derivative(i) << std::endl;
+  return 0;
+}
+/*
+Output:
+y.derivative(0) = 16
+y.derivative(1) = 32
+y.derivative(2) = 48
+y.derivative(3) = 48
+y.derivative(4) = 24
+y.derivative(5) = 0
+**/
diff --git a/libs/math/example/autodiff_mixed_partials.cpp b/libs/math/example/autodiff_mixed_partials.cpp
new file mode 100644
index 0000000000..551429e011
--- /dev/null
+++ b/libs/math/example/autodiff_mixed_partials.cpp
@@ -0,0 +1,293 @@
+//           Copyright Matthew Pulver 2018 - 2019.
+// Distributed under the Boost Software License, Version 1.0.
+//      (See accompanying file LICENSE_1_0.txt or copy at
+//           https://www.boost.org/LICENSE_1_0.txt)
+
+#include <boost/lexical_cast.hpp>
+#include <boost/math/differentiation/autodiff.hpp>
+#include <boost/mp11/tuple.hpp>
+#include <boost/mp11/utility.hpp>
+#include <boost/multiprecision/cpp_bin_float.hpp>
+#include <iostream>
+
+using namespace boost::math::differentiation;
+
+struct f {
+  template <typename W, typename X, typename Y, typename Z>
+  promote<W, X, Y, Z> operator()(W const& w, X const& x, Y const& y, Z const& z) const {
+    return exp(w * sin(x * log(y) / z) + sqrt(w * z / (x * y))) + w * w / tan(z);
+  }
+};
+
+// Derivatives calculated from symbolic differentiation by Mathematica for comparison. Script:
+// mixed_partials.nb
+static constexpr std::array<char const*, 240> answers{
+    {"19878.40628980434922342465374997798674242532797789489",
+     "20731.74838274939517275508122761443159515217855975002",
+     "14667.60767623939014840117674691707821648144188283774",
+     "1840.559936449813118734351750381849294157477519107602",
+     "-9219.318005237072129605008516120710807803827373819700",
+     "-7272.300634012811783845589472196110804386170683300081",
+     "-2135.296370062283924160196772166043360841114107521292",
+     "3095.081027251846799545897828297310835169325417217168",
+     "4249.026762908615627428402369471953790564918480025345",
+     "2063.989061062734416582172072883742097425754355167541",
+     "-885.5284114876496084068555333811894392182458751895290",
+     "-1962.133420441743158021558423645064067562765178375508",
+     "-1846.899830787084518564013512948598850243350915531775",
+     "-160.9590127603295755195950112199107484483554942817846",
+     "1091.039412341633994110997652976585409621806446647794",
+     "452.4395574345229946707651998323417632800605985181691",
+     "666.4013922727704990031159406121675703174518834914461",
+     "-415.6464114333629107803309520898363153301435468382605",
+     "-625.1464179039986361267627631122900331946746137220517",
+     "369.9491669772617110087494756677334192842413470837587",
+     "-24330.89613849389343130420303653062335840497802221681",
+     "-18810.41605175626752065686192937776868736029049989926",
+     "-4890.406122702359099863022925593448420259414896197252",
+     "8833.005054768976417065486877649473665597894570245307",
+     "8484.350739681613747819854384228795938450532463850094",
+     "3097.204151240398893507362023543393154680147349049848",
+     "-3255.045136783440612110181337652522080890693968833148",
+     "-4342.778553332193097878812792875447018366988006584840",
+     "-2407.987237906523486012534085031032446996713414362131",
+     "861.1173916470300084261504495377425043024739914571554",
+     "2436.743725763308619092960749816106318692933687303014",
+     "-19.24649610733827783846392798978023489104363382129689",
+     "187.7855148870511714395275130898958731897480766620821",
+     "-1259.466063335212195169531010871023748854744563232277",
+     "-709.6860523972158261343923419671629587637051060458295",
+     "1423.000558608604536932163648918899935569543711292466",
+     "484.9208133389233959103861107714757012185008046446372",
+     "763.9746885074453180462508029718247316712990115789154",
+     "-327.4162918228055568224139277603073169658358026440432",
+     "-1122.337707248494521123614369562896901904418640152220",
+     "23973.06007192346989337502250398494874845408708506720",
+     "8840.543151778796869949670401421984604862699128880003",
+     "-9082.571033221549378277312292526023838132689941236879",
+     "-12270.27378289258717737657881957466807305650429436397",
+     "-4320.434071420599854743576892819691675331049612545664",
+     "3281.351967707280898543984556670710235259118405463698",
+     "5880.336263083418767219493592767818708317492833223933",
+     "-1288.482785219706549809211085113790275109642879331959",
+     "-803.9713537626580526627976840414468844364935388365037",
+     "-2986.387245331698390346145949708414455858834967096376",
+     "-586.7316859822658306283656047992829723003491823675739",
+     "3929.073189280739356198769778905960586080418779863615",
+     "1453.728280983826630077825553258703050898056317382483",
+     "1037.878071685953829685046234106860743366780050925514",
+     "-1482.745805277401336553926171580259185140208053329753",
+     "-1877.134792933828810602377451370316364621357891989679",
+     "-931.7138710369298207131581126980851620513905805624544",
+     "254.6565590420322632851077818917210811815919344882311",
+     "1391.248064745611663849820246430123214796614030838600",
+     "-431.4820563154137955051720207563800896297257103310465",
+     "16975.34005365179555009050533000516107937041784876054",
+     "19662.60356303341709846238790020024593550984564081068",
+     "15765.85130704020004301064240357947656083104783442825",
+     "3972.155036195937013764185795634749937308876197976202",
+     "-8681.748539789720512499473840242996096730194203989543",
+     "-7703.183042460387656743498394861780784700076575106134",
+     "-3049.708696569518774040135942468704911634779352213044",
+     "2971.469685992270876159892302788930292108129670398058",
+     "4370.196499857550025657084783894747734031876677385611",
+     "2524.632473357435670756946837415389227139966527203701",
+     "-656.6080000236679071742450437463693211275208125750923",
+     "-2423.452917325258132591368397957959217829861665178601",
+     "-2074.987664204263204162199830716851483704870169031179",
+     "-381.2253794988132984501358802316138392247470857452486",
+     "1219.507245791997351017860252538035146744682380716428",
+     "805.3802239840836877339667281819652171888443003165988",
+     "838.4004190058912380470543219448821914235443115661655",
+     "-390.6125197108983831575656956558201636111305409512701",
+     "-828.2085489298235758253219930356006757081473789845849",
+     "293.8999854454994790079171865082094494146506490533363",
+     "-22965.85985843951977785883587223006628792405076928067",
+     "-20026.69101529929621743747554537576887048069629325374",
+     "-7316.092745063355996548975300169565482331369744607021",
+     "8632.466133972614659252310985982644793465043032940318",
+     "8987.046882870452266200748127338744248816756004290490",
+     "4199.925399536137541108783465785304128965582292174062",
+     "-2958.429850896062893179851696175634522187021390095560",
+     "-5665.563891218624062243686482808197054863235184904433",
+     "-2945.404552250341615883104643651287431663294281737652",
+     "555.6566272478262524735403145861484390537770707372992",
+     "2936.796403550079139218970638242013974322758744804216",
+     "651.5191650747110008135060635556227666232180743487328",
+     "444.7629427486155148584918602702161457622049333694568",
+     "-1390.989671799095801316658971275073184600067187023729",
+     "-1142.861468946763860859271224968631944511098747155437",
+     "1541.978723117340843491920690654997335632919116206279",
+     "455.7146063293814470171599782651235242129856311098151",
+     "998.7943503940357037260061331795191352937661538946216",
+     "-204.8485581981121295383497187536442450324011940647949",
+     "-1560.354115460478786113711476250386112014306509906244",
+     "25278.29450605247223516529112562423587288781657290275",
+     "11873.22337179046469888005044109378787446671408425048",
+     "-8242.187303368878103323785658604027555126374435611949",
+     "-15939.98056417465751946455567789306872745912255628512",
+     "-5648.833539698031486810309720694416837861242341227280",
+     "2751.513926122717118525029734574022921057261239749143",
+     "7349.432002479077129245930487320138527887196396579062",
+     "194.9972545980371127390142753318206783334452047502143",
+     "-402.8156857682688265622049800462325595907987257153782",
+     "-3518.871908683063371167722463713374376552181380727802",
+     "-1494.304793474682619087166400375396721307777439607909",
+     "4640.927509426080087451995953783429589632369803588940",
+     "1585.757705203227141964561144798400703219894640413562",
+     "1565.169992404407137888592924342582799362959736185298",
+     "-1513.259809733540018859089666188672238777297615451800",
+     "-2974.437872674680092826212901753475972242208819679978",
+     "-1203.236292653823441598437153564865951527142648802876",
+     "72.52425949879153384040698301599842998884036742649047",
+     "1871.625274253419949517250818647194858608124560073483",
+     "-2.489984337379681666361341362948045621969765070197429",
+     "14462.74423518633102580192225823524237502860825596609",
+     "18367.74740916432711689913219912502810575714860430297",
+     "16565.76324499673961400925630526921000337443450249297",
+     "6054.315252651102952034254100792777051580892954459740",
+     "-8084.981271982030146065497115893934803061545998433631",
+     "-7988.314359128201297240919364015959817416101519999194",
+     "-3989.319346941492698525859335371231602272119870228687",
+     "2616.721186534649016680934493970036169897788778926434",
+     "4420.859270970486562095630193355634655337290952862363",
+     "2973.033519764547909146474824627687039969488363657908",
+     "-324.1453016982713707989332262410969595194473127209825",
+     "-2843.242039958969221918101261762794653424879358390111",
+     "-2281.461806143289517702658392470195144560150025832652",
+     "-642.9353229582055924928927665183236308235598082837497",
+     "1299.287274176955358490409470855361289523321919337117",
+     "1238.597083372069762230817383681570828675426312803376",
+     "1021.334042770848165110529668635291528449691525937968",
+     "-329.0529345069271079573348500899329811170455711610811",
+     "-1046.254301544052075124857362060924818517694048905299",
+     "134.7343039554480655186788228552325941588620079791654",
+     "-21431.41643507661192392650726158493697457993678274754",
+     "-20856.88281479015784660571401663659059349708627445067",
+     "-9829.261970591930907585958999196966814861251125275804",
+     "7806.858647077811827981774785577363365546600234846335",
+     "9319.700085649568180114405924685286453652118439999060",
+     "5319.898768025758256383579171601100187435481641933401",
+     "-2387.954826466841736373447020403170264502066930376059",
+     "-6958.298525165359760665355886221309296550746152109847",
+     "-3468.539106391972560670887295398968213297736424267559",
+     "130.4167253342709401698825285623058661085645012029873",
+     "3371.139930235175987370940343096776588915600470241960",
+     "1569.232678004908105313880673484968847566948896728142",
+     "750.0912101179065245750415609380442359608197763310413",
+     "-1462.257209626597452197736652121394535208578921869658",
+     "-1661.577809630240615684355192771059515041884351493459",
+     "1509.628528603869133250456671040505284128185908768108",
+     "383.8950902580816259502239917715884779698864996879279",
+     "1248.051096343638013308778159911906703363730187986273",
+     "17.18569564265260274901760034571610990094333217519021",
+     "-2038.024598002604853054532645991188063394308018947374",
+     "26118.98132017823514803387529120810044029492871875474",
+     "14943.61943482227903328457116850255971625430735856355",
+     "-6650.686262276131072415580833374348889422387492668440",
+     "-19519.81529547404067945704333355155941895199228108631",
+     "-6983.190236500848647457042860591724089812405118922223",
+     "1899.297502873688983038424995203515277346497811783168",
+     "8715.003652642963488202943622358986745434720576722170",
+     "2368.150690681864301926962120618658083737878227231428",
+     "136.8920793093482831910443246272238406481527839521448",
+     "-3954.732706163417141961077488373290331419627965482785",
+     "-2673.556440231186786375595871506657802723673830409989",
+     "5078.483935249043594670125721926702845818403229980691",
+     "1643.459143721204817182772630730123271413273760820347",
+     "2182.216979506380293664703833586468523416961563720645",
+     "-1345.838830963620501537777318021157952722412472356094",
+     "-4309.285350629108413525304135326225818270616857298235",
+     "-1488.050869922417817689426519211523527088509094291312",
+     "-228.0584943070343720919835603886532454450555855354340",
+     "2373.398940425709177876367020236623713151456855728138",
+     "773.8481328103928058186643458500631723389600248582833",
+     "12294.40387737855548614823173849184004455244840062464",
+     "16977.34966571858301862913845572077593071467784570724",
+     "17057.17475622503175013658695220988017704387344177727",
+     "8121.189758511830935868344768490586007624092305459885",
+     "-7458.443541406284389918808653948439156033975014107187",
+     "-8134.131160882738058651976911725365291142418949378248",
+     "-4912.881158613784419581465435995807691111897279859302",
+     "2030.653136098933717888434825960516061206391833398177",
+     "4407.490527709412730881592594976776779312299897714205",
+     "3392.434568825892752350943548729559313328141534290860",
+     "104.0372355841506198680609232049783930050635078746762",
+     "-3180.817620484463214391157460812371170723810181051096",
+     "-2460.523987075069437321629265332968914260047631079537",
+     "-938.2209314069133432825590545267820890922150850657831",
+     "1315.246905571876456706320919211807375254975062430487",
+     "1735.862392405992188189147617586418269768276241147998",
+     "1209.759657223166954850207025399731503326968841680649",
+     "-227.3320054566642297128407910803774238020746116287390",
+     "-1266.126209991929259396966729664100401813091860201682",
+     "-123.0794572338149156803989321165094334755661021559442",
+     "-19806.90794333834685506732819834090525250045748665845",
+     "-21314.81635440575229337844631555492486744407550254908",
+     "-12317.58384430130805020250005527399703840208659666608",
+     "6349.418659888281474363154227419204673663621492760982",
+     "9489.819687696527735093973063679592839666155440941289",
+     "6409.538948456309994399374417972222747225748405617373",
+     "-1550.281799013125267606263057621300789555474258987989",
+     "-8109.711199785217512061886243157800006692908759687186",
+     "-3957.840330296874877742767473517819198882831790006004",
+     "-404.0796555836667858753163727999380679499192203780272",
+     "3693.614351301181980145006883746936633676934626580499",
+     "2716.146658322790064799415509615557123789406209068981",
+     "1094.591086641398900496318896947912437274250932576747",
+     "-1456.269645549946420883827817869876763706452982413420",
+     "-2244.380608735636962338392373719455877272151458411079",
+     "1268.593891556261871090883000459505759446497182073132",
+     "265.2206730327749346649809229271069944357537135668622",
+     "1496.091578778639488439197917198148587432113387871024",
+     "354.6137351047722781932932090799444060236757625488818",
+     "-2508.477110048684129181005769771219369377836598443263",
+     "26517.86140875157324686379805134248778305979287686214",
+     "17922.98387741915144079932445041215068937644694653527",
+     "-4328.259142127668040873054918170572859673703425721293",
+     "-22704.70245940080949074466622805971940616027152354999",
+     "-8268.613747173738971390434576274225941735552759965376",
+     "740.4056074392611464740778308961471299437619012164253",
+     "9848.900182836035080973766381422758538530595451048714",
+     "5213.598341476210337710365441072904970861063876340963",
+     "801.2462923723508233330997243930793458484750729415321",
+     "-4241.870133920767845856621968904769727964770527614244",
+     "-4092.241355868550570635569815488217469506874233892269",
+     "5074.435909206083943809967780457349942315503368249477",
+     "1607.765329254820915989772546102530187884674235100928",
+     "2861.155651116567526208762405651011317435252198548496",
+     "-918.9310546317296090214320737728927500362088478158839",
+     "-5803.211323646092019259074499814222806376618363553826",
+     "-1767.541897994477314401145980308432268207111761980100",
+     "-663.0646207520075726320417301262932382663072876188661",
+     "2837.903194613938414496183429129769829434890424213252",
+     "1976.319600747797717779881875290418720908121189218755"}};
+
+int main() {
+  using float50 = boost::multiprecision::cpp_bin_float_50;
+  constexpr std::size_t Nw = 3;  // Max order of derivative to calculate for w
+  constexpr std::size_t Nx = 2;  // Max order of derivative to calculate for x
+  constexpr std::size_t Ny = 4;  // Max order of derivative to calculate for y
+  constexpr std::size_t Nz = 3;  // Max order of derivative to calculate for z
+  auto const variables = make_ftuple<float50, Nw, Nx, Ny, Nz>(11, 12, 13, 14);
+  auto const v = boost::mp11::tuple_apply(f{}, variables);
+  std::size_t ia = 0;
+  double max_relative_error = 0;
+  for (std::size_t iw = 0; iw <= Nw; ++iw)
+    for (std::size_t ix = 0; ix <= Nx; ++ix)
+      for (std::size_t iy = 0; iy <= Ny; ++iy)
+        for (std::size_t iz = 0; iz <= Nz; ++iz) {
+          float50 const value = v.derivative(iw, ix, iy, iz);
+          float50 const answer = boost::lexical_cast<float50>(answers[ia++]);
+          double const error = static_cast<double>(fabs(value / answer - 1));
+          max_relative_error = (std::max)(error, max_relative_error);
+        }
+  std::cout << "max_relative_error = " << std::setprecision(3) << max_relative_error << " out of " << ia
+            << " calculated values." << std::endl;
+  return 0;
+}
+/*
+Output:
+max_relative_error = 6.82e-13 out of 240 calculated values. (for double)
+max_relative_error = 3.36e-47 out of 240 calculated values. (for cpp_bin_float_50)
+**/
diff --git a/libs/math/example/autodiff_multiprecision.cpp b/libs/math/example/autodiff_multiprecision.cpp
new file mode 100644
index 0000000000..81c7c27c5a
--- /dev/null
+++ b/libs/math/example/autodiff_multiprecision.cpp
@@ -0,0 +1,46 @@
+//           Copyright Matthew Pulver 2018 - 2019.
+// Distributed under the Boost Software License, Version 1.0.
+//      (See accompanying file LICENSE_1_0.txt or copy at
+//           https://www.boost.org/LICENSE_1_0.txt)
+
+#include <boost/math/differentiation/autodiff.hpp>
+#include <boost/multiprecision/cpp_bin_float.hpp>
+#include <iostream>
+
+using namespace boost::math::differentiation;
+
+template <typename W, typename X, typename Y, typename Z>
+promote<W, X, Y, Z> f(const W& w, const X& x, const Y& y, const Z& z) {
+  using namespace std;
+  return exp(w * sin(x * log(y) / z) + sqrt(w * z / (x * y))) + w * w / tan(z);
+}
+
+int main() {
+  using float50 = boost::multiprecision::cpp_bin_float_50;
+
+  constexpr unsigned Nw = 3;  // Max order of derivative to calculate for w
+  constexpr unsigned Nx = 2;  // Max order of derivative to calculate for x
+  constexpr unsigned Ny = 4;  // Max order of derivative to calculate for y
+  constexpr unsigned Nz = 3;  // Max order of derivative to calculate for z
+  // Declare 4 independent variables together into a std::tuple.
+  auto const variables = make_ftuple<float50, Nw, Nx, Ny, Nz>(11, 12, 13, 14);
+  auto const& w = std::get<0>(variables);  // Up to Nw derivatives at w=11
+  auto const& x = std::get<1>(variables);  // Up to Nx derivatives at x=12
+  auto const& y = std::get<2>(variables);  // Up to Ny derivatives at y=13
+  auto const& z = std::get<3>(variables);  // Up to Nz derivatives at z=14
+  auto const v = f(w, x, y, z);
+  // Calculated from Mathematica symbolic differentiation.
+  float50 const answer("1976.319600747797717779881875290418720908121189218755");
+  std::cout << std::setprecision(std::numeric_limits<float50>::digits10)
+            << "mathematica   : " << answer << '\n'
+            << "autodiff      : " << v.derivative(Nw, Nx, Ny, Nz) << '\n'
+            << std::setprecision(3)
+            << "relative error: " << (v.derivative(Nw, Nx, Ny, Nz) / answer - 1) << '\n';
+  return 0;
+}
+/*
+Output:
+mathematica   : 1976.3196007477977177798818752904187209081211892188
+autodiff      : 1976.3196007477977177798818752904187209081211892188
+relative error: 2.67e-50
+**/
diff --git a/libs/math/example/big_seventh.cpp b/libs/math/example/big_seventh.cpp
index 62585ec0cd..c661e2944e 100644
--- a/libs/math/example/big_seventh.cpp
+++ b/libs/math/example/big_seventh.cpp
@@ -40,38 +40,47 @@ To use these floating-point types and constants, we need some includes:
 #include <iostream>
 #include <limits>
 
-//` So now we can demonstrate with some trivial calculations:
+/*` So now we can demonstrate with some trivial calculations:
+*/
+
+//] //[big_seventh_example_1]
 
 int main()
 {
-/*`Using `typedef cpp_dec_float_50` hides the complexity of multiprecision to allow us
-  to define variables with 50 decimal digit precision just like built-in `double`.
+
+//[big_seventh_example_2
+/*`Using `typedef cpp_dec_float_50` hides the complexity of multiprecision,
+allows us  to define variables with 50 decimal digit precision just like built-in `double`.
 */
-  using boost::multiprecision::cpp_dec_float_50;
+	using boost::multiprecision::cpp_dec_float_50;
 
-  cpp_dec_float_50 seventh = cpp_dec_float_50(1) / 7;
+	cpp_dec_float_50 seventh = cpp_dec_float_50(1) / 7;  // 1 / 7
 
-  /*`By default, output would only show the standard 6 decimal digits,
-     so set precision to show all 50 significant digits.
-  */
-  std::cout.precision(std::numeric_limits<cpp_dec_float_50>::digits10);
-  std::cout << seventh << std::endl;
+/*`By default, output would only show the standard 6 decimal digits,
+ so set precision to show all 50 significant digits, including any trailing zeros.
+*/
+	std::cout.precision(std::numeric_limits<cpp_dec_float_50>::digits10);
+	std::cout << std::showpoint << std::endl; // Append any trailing zeros.
+	std::cout << seventh << std::endl;
 /*`which outputs:
 
   0.14285714285714285714285714285714285714285714285714
 
-We can also use constants, guaranteed to be initialized with the very last bit of precision.
+We can also use Boost.Math __constants like [pi],
+guaranteed to be initialized with the very last bit of precision for the floating-point type.
 */
 
-  cpp_dec_float_50 circumference = boost::math::constants::pi<cpp_dec_float_50>() * 2 * seventh;
-
-  std::cout << circumference << std::endl;
+   std::cout << "pi = " << boost::math::constants::pi<cpp_dec_float_50>() << std::endl;
+   cpp_dec_float_50 circumference = boost::math::constants::pi<cpp_dec_float_50>() * 2 * seventh;
+   std::cout << "c =  "<< circumference << std::endl;
 
 /*`which outputs
 
-    0.89759790102565521098932668093700082405633411410717
+  pi = 3.1415926535897932384626433832795028841971693993751
+
+  c =  0.89759790102565521098932668093700082405633411410717
 */
-//]  [/big_seventh_example_1]
+//]  [/big_seventh_example_2]
 
     return 0;
 } // int main()
@@ -80,10 +89,11 @@ We can also use constants, guaranteed to be initialized with the very last bit o
 /*
 //[big_seventh_example_output
 
-  0.14285714285714285714285714285714285714285714285714
-  0.89759790102565521098932668093700082405633411410717
+0.14285714285714285714285714285714285714285714285714
+pi = 3.1415926535897932384626433832795028841971693993751
+c =  0.89759790102565521098932668093700082405633411410717
 
-//]
+//] //[big_seventh_example_output]
 
 */
 
diff --git a/libs/math/example/binomial_coinflip_example.cpp b/libs/math/example/binomial_coinflip_example.cpp
index 26410f42e0..393e5ef878 100644
--- a/libs/math/example/binomial_coinflip_example.cpp
+++ b/libs/math/example/binomial_coinflip_example.cpp
@@ -160,6 +160,17 @@ Finally, print two tables of probability for the /exactly/ and /at least/ a numb
 /*`
 The last (0 to 10 heads) must, of course, be 100% probability.
 */
+		double probability = 0.3;
+		double q = quantile(flip, probability);
+		std::cout << "Quantile (flip, " << probability << ") = " << q << std::endl; // Quantile (flip, 0.3) = 3
+		probability = 0.6;
+		q = quantile(flip, probability);
+		std::cout << "Quantile (flip, " << probability << ") = " << q << std::endl; // Quantile (flip, 0.6) = 5
+
+
+
+
+
   }
   catch(const std::exception& e)
   {
diff --git a/libs/math/example/distribution_construction.cpp b/libs/math/example/distribution_construction.cpp
index 3fe10dc353..451fd5d156 100644
--- a/libs/math/example/distribution_construction.cpp
+++ b/libs/math/example/distribution_construction.cpp
@@ -21,10 +21,10 @@
 
 /*`
 The structure of distributions is rather different from some other statistical libraries,
-for example, those written in less object-oriented language like FORTRAN and C:
-these provide a few arguments to each free function.
+for example, those written in less object-oriented language like FORTRAN and C that
+provide a few arguments to each free function.
 
-Boost.Math library provides each distribution as a template C++ class.
+Boost.Math library instead provides each distribution as a template C++ class.
 A distribution is constructed with a few arguments, and then
 member and non-member functions are used to find values of the
 distribution, often a function of a random variate.
@@ -33,7 +33,12 @@ For this demonstration, first we need some includes to access the
 negative binomial distribution (and the binomial, beta and gamma distributions too).
 
 To demonstrate the use with a high precision User-defined floating-point type
-`cpp_dec_float` we also need an include from Boost.Multiprecision.
+`cpp_bin_float`, we also need an include from Boost.Multiprecision.
+(We could equally well have used a `cpp_dec_float` multiprecision type).
+
+We choose a typedef `cpp_bin_float_50` to provide a 50 decimal digit type,
+but we could equally have chosen at 128-bit type `cpp_bin_float_quad`, 
+or on some platforms `__float128`, providing about 35 decimal digits.
 */
 
 #include <boost/math/distributions/negative_binomial.hpp> // for negative_binomial_distribution
@@ -44,7 +49,7 @@ To demonstrate the use with a high precision User-defined floating-point type
 #include <boost/math/distributions/gamma.hpp> // for gamma_distribution.
 #include <boost/math/distributions/normal.hpp> // for normal_distribution.
 
-#include <boost/multiprecision/cpp_dec_float.hpp> // for cpp_dec_float_100
+#include <boost/multiprecision/cpp_bin_float.hpp> // for cpp_bin_float_50
 /*`
 Several examples of constructing distributions follow:
 */
@@ -87,7 +92,7 @@ and a success fraction 0.25, 25% or 1 in 4, is constructed like this:
 
   [caution
   This convenience typedef is [*not provided] if a clash would occur
-  with the name of a function: currently only `beta` and `gamma`
+  with the name of a function; currently only `beta` and `gamma`
   fall into this category.
   ]
 
@@ -106,11 +111,12 @@ and a success fraction 0.25, 25% or 1 in 4, is constructed like this:
   */
   negative_binomial mydist10(5., 0.4); // Both arguments double.
   /*`
-  And automatic conversion takes place, so you can use integers and floats:
+  And automatic conversion of arguments takes place, so you can use integers and floats:
   */
-  negative_binomial mydist11(5, 0.4); // Using provided typedef double, int and double arguments.
+  negative_binomial mydist11(5, 0.4); // Using provided typedef of type double, and int and double arguments.
   /*`
   This is probably the most common usage.
+	Other combination are possible too:
   */
   negative_binomial mydist12(5., 0.4F); // Double and float arguments.
   negative_binomial mydist13(5, 1); // Both arguments integer.
@@ -125,7 +131,7 @@ and a success fraction 0.25, 25% or 1 in 4, is constructed like this:
   For cases when the typdef distribution name would clash with a math special function
   (currently only beta and gamma)
   the typedef is deliberately not provided, and the longer version of the name
-  must be used.  For example do not use:
+  must be used, so for example, do not use:
 
      using boost::math::beta;
      beta mybetad0(1, 0.5); // Error beta is a math FUNCTION!
@@ -167,33 +173,37 @@ and a success fraction 0.25, 25% or 1 in 4, is constructed like this:
   negative_binomial_distribution<float>         mydist5(8, 1);
 
   // Explicit double precision:
-  negative_binomial_distribution<double>        mydist6(8., 0.25);
+  negative_binomial_distribution<double>        mydist6(5., 0.4);
 
   // Explicit long double precision:
   negative_binomial_distribution<long double>   mydist7(8., 0.25);
-
+		 
   /*`
-  And you can use your own RealType,
-  for example, `boost::math::cpp_dec_float_50` (an arbitrary 50 decimal digits precision type),
+  And you can use your own template RealType,
+  for example, `boost::math::cpp_bin_float_50` (an arbitrary 50 decimal digits precision type),
   then we can write:
   */
   using namespace boost::multiprecision;
+  negative_binomial_distribution<cpp_bin_float_50>  mydist8(8, 0.25);
 
-  negative_binomial_distribution<cpp_dec_float_50>  mydist8(8, 0.25);
   // `integer` arguments are promoted to your RealType exactly, but
   // `double` argument are converted to RealType,
-  // possibly losing precision, so don't write:
-
-  negative_binomial_distribution<cpp_dec_float_50>  mydist20(8, 0.23456789012345678901234567890);
- // to avoid truncation of second parameter to `0.2345678901234567`.
+  // most likely losing precision!
+	
+	// So DON'T be tempted to write the 'obvious':
+  negative_binomial_distribution<cpp_bin_float_50>  mydist20(8, 0.23456789012345678901234567890);
+ // to avoid truncation of second parameter to `0.2345678901234567` and loss of precision.
 
-  negative_binomial_distribution<cpp_dec_float_50>  mydist21(8, cpp_dec_float_50("0.23456789012345678901234567890") );
+ // Instead pass a quoted decimal digit string:
+  negative_binomial_distribution<cpp_bin_float_50>  mydist21(8, cpp_bin_float_50("0.23456789012345678901234567890") );
 
   // Ensure that all potentially significant digits are shown.
-  std::cout.precision(std::numeric_limits<cpp_dec_float_50>::digits10);
-  cpp_dec_float_50 x("1.23456789012345678901234567890");
+  std::cout.precision(std::numeric_limits<cpp_bin_float_50>::digits10);
+	// 
+  cpp_bin_float_50 x("1.23456789012345678901234567890");
   std::cout << pdf(mydist8, x) << std::endl;
 /*` showing  0.00012630010495970320103876754721976419438231705359935
+             0.00012630010495970320103876754721976419438231528547467
 
 [warning When using multiprecision, it is all too easy to get accidental truncation!]
 
@@ -208,15 +218,15 @@ This is because the value provided is truncated to a `double`, effectively
   `double x = 1.23456789012345678901234567890;`
 
 Then the now `double x` is passed to function `pdf`,
-and this truncated `double` value is finally promoted to `cpp_dec_float_50`.
+and this truncated `double` value is finally promoted to `cpp_bin_float_50`.
 
 Another way of quietly getting the wrong answer is to write:
 */
-  std::cout << pdf(mydist8, cpp_dec_float_50(1.23456789012345678901234567890)) << std::endl;
+  std::cout << pdf(mydist8, cpp_bin_float_50(1.23456789012345678901234567890)) << std::endl;
 /*`
 A correct way from a multi-digit string value is
 */
-  std::cout << pdf(mydist8, cpp_dec_float_50("1.23456789012345678901234567890")) << std::endl;
+  std::cout << pdf(mydist8, cpp_bin_float_50("1.23456789012345678901234567890")) << std::endl;
 /*`
 
 [tip Getting about 17 decimal digits followed by many zeros is often a sign of accidental truncation.]
@@ -241,11 +251,11 @@ defaults for the mean (zero) and standard deviation (unity) thus:
 
     normal_distribution(RealType mean = 0, RealType sd = 1);
 
-So in this case we can write:
+So in this case we can more tersely write:
 */
   using boost::math::normal;
 
-  normal norm1;       // Standard normal distribution.
+  normal norm1;       // Standard normal distribution N[0,1].
   normal norm2(2);    // Mean = 2, std deviation = 1.
   normal norm3(2, 3); // Mean = 2, std deviation = 3.
 
@@ -272,6 +282,13 @@ So in this case we can write:
 
 //] [/distribution_construction_output]
 
+
+  0.00012630010495970320103876754721976419438231528547467
+  0.0001263001049597031846506456931096717957680547488046
+  0.0001263001049597031846506456931096717957680547488046
+  0.00012630010495970320103876754721976419438231528547467
+
+
 */
 
 
diff --git a/libs/math/example/fft_sines_table.cpp b/libs/math/example/fft_sines_table.cpp
index 71cab534ae..cd04642ac4 100644
--- a/libs/math/example/fft_sines_table.cpp
+++ b/libs/math/example/fft_sines_table.cpp
@@ -19,21 +19,35 @@
 
 //[fft_sines_table_example_1
 
-/*`[h5 Using Boost.Multiprecision to generate a high-precision array of sin coefficents for use with FFT.]
+/*`[h5 Using Boost.Multiprecision to generate a high-precision array of sine coefficents for use with FFT.]
 
 The Boost.Multiprecision library can be used for computations requiring precision
 exceeding that of standard built-in types such as `float`, `double`
 and `long double`. For extended-precision calculations, Boost.Multiprecision
-supplies a template data type called `cpp_dec_float`. The number of decimal
-digits of precision is fixed at compile-time via template parameter.
+supplies a template data type called `cpp_bin_float`. The number of decimal
+digits of precision is fixed at compile-time via a template parameter.
 
-To use these floating-point types and constants, we need some includes:
+One often needs to compute tables of numbers in mathematical software.
+To avoid the
+[@https://en.wikipedia.org/wiki/Rounding#Table-maker's_dilemma Table-maker's dilemma]
+it is necessary to use a higher precision type to compute the table values so that they have
+the nearest representable bit-pattern for the type, say `double`, of the table value.
+
+This example is a program `fft_since_table.cpp` that writes a header file `sines.hpp`
+containing an array of sine coefficients for use with a Fast Fourier Transform (FFT),
+that can be included by the FFT program.
+
+To use Boost.Multiprecision's high-precision floating-point types and constants, we need some includes:
 */
 #include <boost/math/constants/constants.hpp>
 // using boost::math::constants::pi;
 
-#include <boost/multiprecision/cpp_dec_float.hpp>
-// using boost::multiprecision::cpp_dec_float
+#include <boost/multiprecision/cpp_bin_float.hpp> // for
+// using boost::multiprecision::cpp_bin_float and
+// using boost::multiprecision::cpp_bin_float_50;
+// using boost::multiprecision::cpp_bin_float_quad;
+
+#include <boost/array.hpp> // or <array> for std::array
 
 #include <iostream>
 #include <limits>
@@ -43,12 +57,13 @@ To use these floating-point types and constants, we need some includes:
 #include <iterator>
 #include <fstream>
 
-/*`Define a text string which is a C++ comment with the program licence, copyright etc.
-You could of course, tailor this to your needs, including your copyright claim.
-There are versions of `array` provided by Boost.Array in `boost::array` or
-the C++11 std::array, but since not all platforms provide C++11 support,
-this program provides the Boost version as fallback.
+/*`First, this example defines a prolog text string which is a C++ comment with the program licence, copyright etc.
+(You would of course, tailor this to your needs, including *your* copyright claim).
+This will appear at the top of the written header file `sines.hpp`.
 */
+
+//] [fft_sines_table_example_1]
+
 static const char* prolog =
 {
   "// Use, modification and distribution are subject to the\n"
@@ -56,27 +71,23 @@ static const char* prolog =
   "// (See accompanying file LICENSE_1_0.txt\n"
   "// or copy at ""http://www.boost.org/LICENSE_1_0.txt)\n\n"
 
-  "// Copyright ???? 2013.\n\n"
-
-  "// Use boost/array if std::array (C++11 feature) is not available.\n"
-  "#ifdef  BOOST_NO_CXX11_HDR_ARRAY\n"
-  "#include <boost/array/array.hpp>\n"
-  "#else\n"
-  "#include <array>\n"
-  "#endif\n\n"
+  "// Copyright A N Other, 2019.\n\n"
 };
 
+//[fft_sines_table_example_2
 
-using boost::multiprecision::cpp_dec_float_50;
+using boost::multiprecision::cpp_bin_float_50;
 using boost::math::constants::pi;
+
+//] [fft_sines_table_example_2]
+
 // VS 2010 (wrongly) requires these at file scope, not local scope in `main`.
 // This program also requires `-std=c++11` option to compile using Clang and GCC.
 
 int main()
 {
-/*`One often needs to compute tables of numbers in mathematical software.
-
-A fast Fourier transform (FFT), for example, may use a table of the values of
+//[fft_sines_table_example_3
+/*`A fast Fourier transform (FFT), for example, may use a table of the values of
 sin(([pi]/2[super n]) in its implementation details. In order to maximize the precision in
 the FFT implementation, the precision of the tabulated trigonometric values
 should exceed that of the built-in floating-point type used in the FFT.
@@ -85,37 +96,37 @@ The sample below computes a table of the values of sin([pi]/2[super n])
 in the range 1  <= n <= 31.
 
 This program makes use of, among other program elements, the data type
-`boost::multiprecision::cpp_dec_float_50`
+`boost::multiprecision::cpp_bin_float_50`
 for a precision of 50 decimal digits from Boost.Multiprecision,
 the value of constant [pi] retrieved from Boost.Math,
 guaranteed to be initialized with the very last bit of precision for the type,
-here `cpp_dec_float_50`,
+here `cpp_bin_float_50`,
 and a C++11 lambda function combined with `std::for_each()`.
 */
 
-/*`define the number of values in the array.
+/*`define the number of values (32) in the array of sines.
 */
 
   std::size_t size = 32U;
-  cpp_dec_float_50 p = pi<cpp_dec_float_50>();
-  cpp_dec_float_50 p2 = boost::math::constants::pi<cpp_dec_float_50>();
+  //cpp_bin_float_50 p = pi<cpp_bin_float_50>();
+  cpp_bin_float_50 p = boost::math::constants::pi<cpp_bin_float_50>();
 
-  std::vector <cpp_dec_float_50> sin_values (size);
+  std::vector <cpp_bin_float_50> sin_values (size);
   unsigned n = 1U;
   // Generate the sine values.
   std::for_each
   (
     sin_values.begin (),
     sin_values.end (),
-    [&n](cpp_dec_float_50& y)
+    [&n](cpp_bin_float_50& y)
     {
-      y = sin( pi<cpp_dec_float_50>() / pow(cpp_dec_float_50 (2), n));
+      y = sin( pi<cpp_bin_float_50>() / pow(cpp_bin_float_50 (2), n));
       ++n;
     }
   );
 
 /*`Define the floating-point type for the generated file, either built-in
-`double, `float, or `long double`, or a user defined type like `cpp_dec_float_50`.
+`double, `float, or `long double`, or a user defined type like `cpp_bin_float_50`.
 */
 
 std::string fp_type = "double";
@@ -125,26 +136,30 @@ std::cout << "Generating an `std::array` or `boost::array` for floating-point ty
 
 /*`By default, output would only show the standard 6 decimal digits,
 so set precision to show enough significant digits for the chosen floating-point type.
-For `cpp_dec_float_50` is 50. (50 decimal digits should be ample for most applications).
+For `cpp_bin_float_50` is 50. (50 decimal digits should be ample for most applications).
+
 */
-  std::streamsize precision = std::numeric_limits<cpp_dec_float_50>::digits10;
+  std::streamsize precision = std::numeric_limits<cpp_bin_float_50>::digits10;
+
+  std::cout << "Sines table precision is " << precision << " decimal digits. " << std::endl;
+
+/*`Of course, one could also choose a lower precision for the table values, for example,
 
-  //  std::cout.precision(std::numeric_limits<cpp_dec_float_50>::digits10);
-  std::cout << precision << " decimal digits precision. " << std::endl;
+`std::streamsize precision = std::numeric_limits<cpp_bin_float_quad>::max_digits10;`
 
-/*`Of course, one could also choose less, for example, 36 would be sufficient
+128-bit 'quad' precision of 36 decimal digits would be sufficient
 for the most precise current `long double` implementations using 128-bit.
 In general, it should be a couple of decimal digits more (guard digits) than
 `std::numeric_limits<RealType>::max_digits10` for the target system floating-point type.
-If the implementation does not provide `max_digits10`, the the Kahan formula
-`std::numeric_limits<RealType>::digits * 3010/10000 + 2` can be used instead.
+(If the implementation does not provide `max_digits10`, the the Kahan formula
+`std::numeric_limits<RealType>::digits * 3010/10000 + 2` can be used instead).
 
 The compiler will read these values as decimal digits strings and
 use the nearest representation for the floating-point type.
 
 Now output all the sine table, to a file of your chosen name.
 */
-  const char sines_name[] = "sines.hpp";  // In same directory as .exe
+  const char sines_name[] = "sines.hpp";  // Assuming in same directory as .exe
 
   std::ofstream fout(sines_name, std::ios_base::out);  // Creates if no file exists,
   // & uses default overwrite/ ios::replace.
@@ -154,19 +169,18 @@ Now output all the sine table, to a file of your chosen name.
     return EXIT_FAILURE;
   }
   else
-  {
+  { // Write prolog etc as a C++ comment.
     std::cout << "Open file " << sines_name << " for output OK." << std::endl;
-    fout << prolog << "// Table of " << sin_values.size() << " values with "
+    fout << prolog
+    << "// Table of " << sin_values.size() << " values with "
       << precision << " decimal digits precision,\n"
       "// generated by program fft_sines_table.cpp.\n" << std::endl;
 
-    fout <<
-"#ifdef BOOST_NO_CXX11_HDR_ARRAY""\n"
- "  static const boost::array<double, " << size << "> sines =\n"
-"#else""\n"
-"  static const std::array<double, " << size << "> sines =\n"
-"#endif""\n"
-    "{{\n"; // 2nd { needed for some GCC compiler versions.
+  fout << "#include <array> // std::array" << std::endl;
+
+  // Write the table of sines as a C++ array.
+    fout <<  "\nstatic const std::array<double, " << size << "> sines =\n"
+    "{{\n"; // 2nd { needed for some old GCC compiler versions.
     fout.precision(precision);
 
     for (unsigned int i = 0U; ;)
@@ -174,7 +188,7 @@ Now output all the sine table, to a file of your chosen name.
       fout << "  " << sin_values[i];
       if (i == sin_values.size()-1)
       { // next is last value.
-        fout << "\n}};\n"; // 2nd } needed for some earlier GCC compiler versions.
+        fout << "\n}};  // array sines\n"; // 2nd } needed for some old GCC compiler versions.
         break;
       }
       else
@@ -182,14 +196,14 @@ Now output all the sine table, to a file of your chosen name.
         fout << ",\n";
         i++;
       }
-    }
+    } // for
 
     fout.close();
-    std::cout << "Close file " << sines_name << " for output OK." << std::endl;
-
+    std::cout << "Closed file " << sines_name << " for output." << std::endl;
   }
 //`The output file generated can be seen at [@../../example/sines.hpp]
-//] [/fft_sines_table_example_1]
+
+//] [/fft_sines_table_example_3]
 
   return EXIT_SUCCESS;
 
diff --git a/libs/math/example/ooura_fourier_integrals_cosine_example.cpp b/libs/math/example/ooura_fourier_integrals_cosine_example.cpp
new file mode 100644
index 0000000000..218e94e1ce
--- /dev/null
+++ b/libs/math/example/ooura_fourier_integrals_cosine_example.cpp
@@ -0,0 +1,83 @@
+// Copyright Paul A. Bristow, 2019
+// Copyright Nick Thompson, 2019
+
+// Use, modification and distribution are subject to the
+// Boost Software License, Version 1.0.
+// (See accompanying file LICENSE_1_0.txt
+// or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+//#define BOOST_MATH_INSTRUMENT_OOURA // or -DBOOST_MATH_INSTRUMENT_OOURA etc for diagnostic output.
+
+#include <boost/math/quadrature/ooura_fourier_integrals.hpp> // For ooura_fourier_cos
+#include <boost/math/constants/constants.hpp>  // For pi (including for multiprecision types, if used.)
+
+#include <cmath>
+#include <iostream>
+#include <limits>
+#include <iostream>
+
+int main()
+{
+	try
+	{
+	std::cout.precision(std::numeric_limits<double>::max_digits10); // Show all potentially significant digits.
+
+	using boost::math::quadrature::ooura_fourier_cos;
+	using boost::math::constants::half_pi;
+	using boost::math::constants::e;
+
+ //[ooura_fourier_integrals_cosine_example_1
+	auto integrator = ooura_fourier_cos<double>();
+	// Use the default tolerance root_epsilon and eight levels for type double.
+
+	auto f = [](double x)
+	{ // More complex example function.
+		return 1 / (x * x + 1);
+	};
+
+	double omega = 1;
+
+	auto [result, relative_error] = integrator.integrate(f, omega);
+	std::cout << "Integral = " << result << ", relative error estimate " << relative_error << std::endl;
+
+	//] [/ooura_fourier_integrals_cosine_example_1]
+
+	//[ooura_fourier_integrals_cosine_example_2
+
+	constexpr double expected = half_pi<double>() / e<double>();
+	std::cout << "pi/(2e) =  " << expected << ", difference " << result - expected << std::endl;
+	//] [/ooura_fourier_integrals_cosine_example_2]
+	}
+	catch (std::exception const & ex)
+	{
+		// Lacking try&catch blocks, the program will abort after any throw, whereas the
+		// message below from the thrown exception will give some helpful clues as to the cause of the problem.
+		std::cout << "\n""Message from thrown exception was:\n   " << ex.what() << std::endl;
+	}
+
+} // int main()
+
+/*
+
+//[ooura_fourier_integrals_example_cosine_output_1
+``
+Integral = 0.57786367489546109, relative error estimate 6.4177395404415149e-09
+pi/(2e) =  0.57786367489546087, difference 2.2204460492503131e-16
+``
+//] [/ooura_fourier_integrals_example_cosine_output_1]
+
+
+//[ooura_fourier_integrals_example_cosine_diagnostic_output_1
+``
+ooura_fourier_cos with relative error goal 1.4901161193847656e-08 & 8 levels.
+epsilon for type = 2.2204460492503131e-16
+h = 1.000000000000000, I_h = 0.588268622591776 = 0x1.2d318b7e96dbe00p-1, absolute error estimate = nan
+h = 0.500000000000000, I_h = 0.577871642184837 = 0x1.27decab8f07b200p-1, absolute error estimate = 1.039698040693926e-02
+h = 0.250000000000000, I_h = 0.577863671186883 = 0x1.27ddbf42969be00p-1, absolute error estimate = 7.970997954576120e-06
+h = 0.125000000000000, I_h = 0.577863674895461 = 0x1.27ddbf6271dc000p-1, absolute error estimate = 3.708578555361441e-09
+Integral = 5.778636748954611e-01, relative error estimate 6.417739540441515e-09
+pi/(2e)  = 5.778636748954609e-01, difference 2.220446049250313e-16
+``
+//] [/ooura_fourier_integrals_example_cosine_diagnostic_output_1]
+
+*/
diff --git a/libs/math/example/ooura_fourier_integrals_example.cpp b/libs/math/example/ooura_fourier_integrals_example.cpp
new file mode 100644
index 0000000000..45f01df90a
--- /dev/null
+++ b/libs/math/example/ooura_fourier_integrals_example.cpp
@@ -0,0 +1,83 @@
+// Copyright Paul A. Bristow, 2019
+// Copyright Nick Thompson, 2019
+
+// Use, modification and distribution are subject to the
+// Boost Software License, Version 1.0.
+// (See accompanying file LICENSE_1_0.txt
+// or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+#ifdef BOOST_NO_CXX11_LAMBDAS
+#  error "This example requires a C++11 compiler that supports lambdas.  Try C++11 or later."
+#endif
+
+//#define BOOST_MATH_INSTRUMENT_OOURA // or -DBOOST_MATH_INSTRUMENT_OOURA etc for diagnostics.
+
+#include <boost/math/quadrature/ooura_fourier_integrals.hpp>
+#include <boost/math/constants/constants.hpp>  // For pi (including for multiprecision types, if used.)
+
+#include <cmath>
+#include <iostream>
+#include <limits>
+#include <iostream>
+
+int main()
+{
+	try
+	{
+	std::cout.precision(std::numeric_limits<double>::max_digits10); // Show all potentially significant digits.
+
+	using boost::math::quadrature::ooura_fourier_sin;
+  using boost::math::constants::half_pi;
+
+//[ooura_fourier_integrals_example_1
+	ooura_fourier_sin<double>integrator = ooura_fourier_sin<double>();
+	// Use the default tolerance root_epsilon and eight levels for type double.
+
+	auto f = [](double x)
+	{ // Simple reciprocal function for sinc.
+		return 1 / x;
+	};
+
+	double omega = 1;
+	std::pair<double, double> result = integrator.integrate(f, omega);
+	std::cout << "Integral = " << result.first << ", relative error estimate " << result.second << std::endl;
+
+//] [/ooura_fourier_integrals_example_1]
+
+//[ooura_fourier_integrals_example_2
+
+	constexpr double expected = half_pi<double>();
+	std::cout << "pi/2 =     " << expected << ", difference " << result.first - expected << std::endl;
+//] [/ooura_fourier_integrals_example_2]
+	}
+	catch (std::exception const & ex)
+	{
+		// Lacking try&catch blocks, the program will abort after any throw, whereas the
+		// message below from the thrown exception will give some helpful clues as to the cause of the problem.
+		std::cout << "\n""Message from thrown exception was:\n   " << ex.what() << std::endl;
+	}
+} // int main()
+
+/*
+
+//[ooura_fourier_integrals_example_output_1
+
+integral = 1.5707963267948966, relative error estimate 1.2655356398390254e-11
+pi/2 =     1.5707963267948966, difference 0
+
+//] [/ooura_fourier_integrals_example_output_1]
+
+
+//[ooura_fourier_integrals_example_diagnostic_output_1
+
+ooura_fourier_sin with relative error goal 1.4901161193847656e-08 & 8 levels.
+h = 1.000000000000000, I_h = 1.571890732004545 = 0x1.92676e56d853500p+0, absolute error estimate = nan
+h = 0.500000000000000, I_h = 1.570793292491940 = 0x1.921f825c076f600p+0, absolute error estimate = 1.097439512605325e-03
+h = 0.250000000000000, I_h = 1.570796326814776 = 0x1.921fb54458acf00p+0, absolute error estimate = 3.034322835882008e-06
+h = 0.125000000000000, I_h = 1.570796326794897 = 0x1.921fb54442d1800p+0, absolute error estimate = 1.987898734512328e-11
+Integral = 1.570796326794897e+00, relative error estimate 1.265535639839025e-11
+pi/2 =     1.570796326794897e+00, difference 0.000000000000000e+00
+
+//] [/ooura_fourier_integrals_example_diagnostic_output_1]
+
+*/
diff --git a/libs/math/example/ooura_fourier_integrals_multiprecision_example.cpp b/libs/math/example/ooura_fourier_integrals_multiprecision_example.cpp
new file mode 100644
index 0000000000..6c84e3b20c
--- /dev/null
+++ b/libs/math/example/ooura_fourier_integrals_multiprecision_example.cpp
@@ -0,0 +1,122 @@
+// Copyright Paul A. Bristow, 2019
+// Copyright Nick Thompson, 2019
+
+// Use, modification and distribution are subject to the
+// Boost Software License, Version 1.0.
+// (See accompanying file LICENSE_1_0.txt
+// or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+// This example requires C++17.
+
+#define BOOST_MATH_INSTRUMENT_OOURA // or -DBOOST_MATH_INSTRUMENT_OOURA etc for diagnostic output.
+
+#include <boost/math/quadrature/ooura_fourier_integrals.hpp>
+#include <boost/multiprecision/cpp_bin_float.hpp> // for cpp_bin_float_quad, cpp_bin_float_50...
+#include <boost/math/constants/constants.hpp>  // For pi (including for multiprecision types, if used.)
+
+#include <cmath>
+#include <iostream>
+#include <limits>
+#include <iostream>
+#include <exception>
+
+int main()
+{
+	try
+	{
+		typedef boost::multiprecision::cpp_bin_float_quad Real;
+
+		std::cout.precision(std::numeric_limits<Real>::max_digits10); // Show all potentially significant digits.
+
+		using boost::math::quadrature::ooura_fourier_cos;
+		using boost::math::constants::half_pi;
+		using boost::math::constants::e;
+
+	 //[ooura_fourier_integrals_multiprecision_example_1
+
+		// Use the default parameters for tolerance root_epsilon and eight levels for a type of 8 bytes.
+		//auto integrator = ooura_fourier_cos<Real>();
+		// Decide on a (tight) tolerance.
+		const Real tol = 2 * std::numeric_limits<Real>::epsilon();
+		auto integrator = ooura_fourier_cos<Real>(tol, 8); // Loops or gets worse for more than 8.
+
+		auto f = [](Real x)
+		{ // More complex example function.
+			return 1 / (x * x + 1);
+		};
+
+		double omega = 1;
+		auto [result, relative_error] = integrator.integrate(f, omega);
+
+		//] [/ooura_fourier_integrals_multiprecision_example_1]
+
+		//[ooura_fourier_integrals_multiprecision_example_2
+		std::cout << "Integral = " << result << ", relative error estimate " << relative_error << std::endl;
+
+		const Real expected = half_pi<Real>() / e<Real>(); // Expect integral = 1/(2e)
+		std::cout << "pi/(2e)  = " << expected << ", difference " << result - expected << std::endl;
+		//] [/ooura_fourier_integrals_multiprecision_example_2]
+	}
+	catch (std::exception const & ex)
+	{
+		// Lacking try&catch blocks, the program will abort after any throw, whereas the
+		// message below from the thrown exception will give some helpful clues as to the cause of the problem.
+		std::cout << "\n""Message from thrown exception was:\n   " << ex.what() << std::endl;
+	}
+} // int main()
+
+/*
+
+//[ooura_fourier_integrals_example_multiprecision_output_1
+``
+Integral = 0.5778636748954608589550465916563501587, relative error estimate 4.609814684522163895264277312610830278e-17
+pi/(2e) = 0.5778636748954608659545328919193707407, difference -6.999486300263020581921171645255733758e-18
+``
+//] [/ooura_fourier_integrals_example_multiprecision_output_1]
+
+
+//[ooura_fourier_integrals_example_multiprecision_diagnostic_output_1
+``
+ooura_fourier_cos with relative error goal 3.851859888774471706111955885169854637e-34 & 15 levels.
+epsilon for type = 1.925929944387235853055977942584927319e-34
+h = 1.000000000000000000000000000000000, I_h = 0.588268622591776615359568690603776 = 0.5882686225917766153595686906037760, absolute error estimate = nan
+h = 0.500000000000000000000000000000000, I_h = 0.577871642184837461311756940493259 = 0.5778716421848374613117569404932595, absolute error estimate = 1.039698040693915404781175011051656e-02
+h = 0.250000000000000000000000000000000, I_h = 0.577863671186882539559996800783122 = 0.5778636711868825395599968007831220, absolute error estimate = 7.970997954921751760139710137450075e-06
+h = 0.125000000000000000000000000000000, I_h = 0.577863674895460885593491133506723 = 0.5778636748954608855934911335067232, absolute error estimate = 3.708578346033494332723601147051768e-09
+h = 0.062500000000000000000000000000000, I_h = 0.577863674895460858955046591656350 = 0.5778636748954608589550465916563502, absolute error estimate = 2.663844454185037302771663314961535e-17
+h = 0.031250000000000000000000000000000, I_h = 0.577863674895460858955046591656348 = 0.5778636748954608589550465916563484, absolute error estimate = 1.733336949948512267750380148326435e-33
+h = 0.015625000000000000000000000000000, I_h = 0.577863674895460858955046591656348 = 0.5778636748954608589550465916563479, absolute error estimate = 4.814824860968089632639944856462318e-34
+h = 0.007812500000000000000000000000000, I_h = 0.577863674895460858955046591656347 = 0.5778636748954608589550465916563473, absolute error estimate = 6.740754805355325485695922799047246e-34
+h = 0.003906250000000000000000000000000, I_h = 0.577863674895460858955046591656347 = 0.5778636748954608589550465916563475, absolute error estimate = 1.925929944387235853055977942584927e-34
+Integral = 5.778636748954608589550465916563475e-01, relative error estimate 3.332844800697411177051445985473052e-34
+pi/(2e)  = 5.778636748954608589550465916563481e-01, difference -6.740754805355325485695922799047246e-34
+``
+//] [/ooura_fourier_integrals_example_multiprecision_diagnostic_output_1]
+
+
+Example of it going wrong below
+
+>ooura_fourier_cos with relative error goal 1.925929944387235853055977942584927319e-34 & 15 levels.
+1>epsilon for type = 1.925929944387235853055977942584927319e-34
+1>h = 1.000000000000000000000000000000000, I_h = 0.588268622591776615359568690603776 = 0.5882686225917766153595686906037760, absolute error estimate = nan
+1>h = 0.500000000000000000000000000000000, I_h = 0.577871642184837461311756940493259 = 0.5778716421848374613117569404932595, absolute error estimate = 1.039698040693915404781175011051656e-02
+1>h = 0.250000000000000000000000000000000, I_h = 0.577863671186882539559996800783122 = 0.5778636711868825395599968007831220, absolute error estimate = 7.970997954921751760139710137450075e-06
+1>h = 0.125000000000000000000000000000000, I_h = 0.577863674895460885593491133506723 = 0.5778636748954608855934911335067232, absolute error estimate = 3.708578346033494332723601147051768e-09
+1>h = 0.062500000000000000000000000000000, I_h = 0.577863674895460858955046591656350 = 0.5778636748954608589550465916563502, absolute error estimate = 2.663844454185037302771663314961535e-17
+1>h = 0.031250000000000000000000000000000, I_h = 0.577863674895460858955046591656348 = 0.5778636748954608589550465916563484, absolute error estimate = 1.733336949948512267750380148326435e-33
+1>h = 0.015625000000000000000000000000000, I_h = 0.577863674895460858955046591656348 = 0.5778636748954608589550465916563479, absolute error estimate = 4.814824860968089632639944856462318e-34
+1>h = 0.007812500000000000000000000000000, I_h = 0.577863674895460858955046591656347 = 0.5778636748954608589550465916563473, absolute error estimate = 6.740754805355325485695922799047246e-34
+1>h = 0.003906250000000000000000000000000, I_h = 0.577863674895460858955046591656347 = 0.5778636748954608589550465916563475, absolute error estimate = 1.925929944387235853055977942584927e-34
+1>h = 0.001953125000000000000000000000000, I_h = 0.577863674895460858955046591656346 = 0.5778636748954608589550465916563463, absolute error estimate = 1.155557966632341511833586765550956e-33
+1>h = 0.000976562500000000000000000000000, I_h = 0.577863674895460858955046591656350 = 0.5778636748954608589550465916563504, absolute error estimate = 4.140749380432557084070352576557594e-33
+1>h = 0.000488281250000000000000000000000, I_h = 0.577863674895460858955046591656348 = 0.5778636748954608589550465916563478, absolute error estimate = 2.600005424922768401625570222489652e-33
+1>h = 0.000244140625000000000000000000000, I_h = 0.577863674895460858955046591656342 = 0.5778636748954608589550465916563418, absolute error estimate = 6.066679324819792937126330519142521e-33
+1>h = 0.000122070312500000000000000000000, I_h = 0.577863674895460858955046591656347 = 0.5778636748954608589550465916563467, absolute error estimate = 4.911121358187451425292743753591565e-33
+1>h = 0.000061035156250000000000000000000, I_h = 0.577863674895460858955046591656342 = 0.5778636748954608589550465916563424, absolute error estimate = 4.333342374871280669375950370816086e-33
+1>h = 0.000030517578125000000000000000000, I_h = 0.577863674895460858955046591656328 = 0.5778636748954608589550465916563282, absolute error estimate = 1.415558509124618351996143787799922e-32
+
+
+
+
+
+*/
diff --git a/libs/math/example/sines.hpp b/libs/math/example/sines.hpp
index 0047999c6b..d4cbbbbf3d 100644
--- a/libs/math/example/sines.hpp
+++ b/libs/math/example/sines.hpp
@@ -3,23 +3,14 @@
 // (See accompanying file LICENSE_1_0.txt
 // or copy at http://www.boost.org/LICENSE_1_0.txt)
 
-// Copyright ???? 2013.
-
-// Use boost/array if std::array (C++11 feature) is not available.
-#ifdef  BOOST_NO_CXX11_HDR_ARRAY
-#include <boost/array/array.hpp>
-#else
-#include <array>
-#endif
+// Copyright A N Other, 2019.
 
 // Table of 32 values with 50 decimal digits precision,
 // generated by program fft_sines_table.cpp.
 
-#ifdef BOOST_NO_CXX11_HDR_ARRAY
-  static const boost::array<double, 32> sines =
-#else
-  static const std::array<double, 32> sines =
-#endif
+#include <array> // std::array
+
+static const std::array<double, 32> sines =
 {{
   1,
   0.70710678118654752440084436210484903928483593768847,
@@ -27,7 +18,7 @@
   0.19509032201612826784828486847702224092769161775195,
   0.098017140329560601994195563888641845861136673167501,
   0.049067674327418014254954976942682658314745363025753,
-  0.024541228522912288031734529459282925065466119239451,
+  0.024541228522912288031734529459282925065466119239452,
   0.012271538285719926079408261951003212140372319591769,
   0.0061358846491544753596402345903725809170578863173913,
   0.003067956762965976270145365490919842518944610213452,
@@ -44,13 +35,13 @@
   1.4980281131690112288542788461553611206917585861527e-06,
   7.4901405658471572113049856673065563715595930217207e-07,
   3.7450702829238412390316917908463317739740476297248e-07,
-  1.8725351414619534486882457659356361712045272098287e-07,
+  1.8725351414619534486882457659356361712045272098286e-07,
   9.3626757073098082799067286680885620193236507169473e-08,
   4.681337853654909269511551813854009695950362701667e-08,
   2.3406689268274552759505493419034844037886207223779e-08,
   1.1703344634137277181246213503238103798093456639976e-08,
-  5.8516723170686386908097901008341396943900085051757e-09,
+  5.8516723170686386908097901008341396943900085051756e-09,
   2.9258361585343193579282304690689559020175857150074e-09,
   1.4629180792671596805295321618659637103742615227834e-09,
   7.3145903963357984046044319684941757518633453150407e-10
-}};
+}};  // array sines
diff --git a/libs/math/test/Jamfile.v2 b/libs/math/test/Jamfile.v2
index 80e17a37ee..53c7a9e643 100644
--- a/libs/math/test/Jamfile.v2
+++ b/libs/math/test/Jamfile.v2
@@ -899,9 +899,17 @@ test-suite distribution_tests :
 test-suite misc :
    [ run test_print_info_on_type.cpp  ]
    [ run test_barycentric_rational.cpp ../../test/build//boost_unit_test_framework : : :  [ requires cxx11_smart_ptr cxx11_defaulted_functions cxx11_auto_declarations cxx11_unified_initialization_syntax ] [ check-target-builds ../config//has_float128 "GCC libquadmath and __float128 support" : <linkflags>-lquadmath ]  ]
+   [ run test_vector_barycentric_rational.cpp ../../test/build//boost_unit_test_framework : : :  [ requires cxx11_smart_ptr cxx11_defaulted_functions cxx11_auto_declarations cxx11_unified_initialization_syntax ]  [ check-target-builds ../../multiprecision/config//has_eigen : : <build>no ] ]
    [ run test_constant_generate.cpp : : : release <define>USE_CPP_FLOAT=1 <exception-handling>off:<build>no  ]
    [ run test_cubic_b_spline.cpp ../../test/build//boost_unit_test_framework : : :  [ requires cxx11_smart_ptr cxx11_defaulted_functions ] <debug-symbols>off <toolset>msvc:<cxxflags>/bigobj release ]
-   [ run catmull_rom_test.cpp ../../test/build//boost_unit_test_framework : : :  [ requires cxx17_if_constexpr cxx17_std_apply ] ] # does not in fact require C++17 constexpr; requires C++17 std::size.
+   [ run whittaker_shannon_test.cpp : : :  [ requires cxx11_auto_declarations cxx11_constexpr cxx11_smart_ptr cxx11_defaulted_functions ] ]
+   [ run cardinal_quadratic_b_spline_test.cpp : : :  [ requires cxx11_auto_declarations cxx11_constexpr cxx11_smart_ptr cxx11_defaulted_functions ] ]
+   [ run catmull_rom_test.cpp ../../test/build//boost_unit_test_framework : : : <define>TEST=1 [ requires cxx11_hdr_array cxx11_hdr_initializer_list ] : catmull_rom_test_1 ]
+   [ run catmull_rom_test.cpp ../../test/build//boost_unit_test_framework : : : <define>TEST=2 [ requires cxx11_hdr_array cxx11_hdr_initializer_list ] : catmull_rom_test_2 ]
+   [ run catmull_rom_test.cpp ../../test/build//boost_unit_test_framework : : : <define>TEST=3 [ requires cxx11_hdr_array cxx11_hdr_initializer_list ] : catmull_rom_test_3 ]
+   [ run compile_test/catmull_rom_incl_test.cpp compile_test_main  : : : [ requires cxx11_hdr_array cxx11_hdr_initializer_list ] ]
+   [ run compile_test/catmull_rom_concept_test.cpp compile_test_main   : : : [ requires cxx11_hdr_array cxx11_hdr_initializer_list ] ]
+   [ run ooura_fourier_integral_test.cpp ../../test/build//boost_unit_test_framework : : :  [ requires cxx17_if_constexpr cxx17_std_apply ] ]
    [ run univariate_statistics_test.cpp ../../test/build//boost_unit_test_framework : : :  [ requires cxx17_if_constexpr cxx17_std_apply ] ]
    [ run norms_test.cpp ../../test/build//boost_unit_test_framework : : :  [ requires cxx17_if_constexpr cxx17_std_apply ] ]
    [ run signal_statistics_test.cpp : : : [ requires cxx17_if_constexpr cxx17_std_apply ] ]
@@ -983,6 +991,7 @@ test-suite misc :
    [ run  compile_test/cstdfloat_concept_check_2.cpp  ]
    [ run  compile_test/cstdfloat_concept_check_3.cpp  ]
    [ run  compile_test/cstdfloat_concept_check_4.cpp  ]
+   [ run  test_cstdfloat.cpp ../../test/build//boost_unit_test_framework  : : : [ check-target-builds ../config//has_float128 "GCC libquadmath and __float128 support" : <linkflags>-lquadmath ] ]
    [ run  compile_test/sf_airy_incl_test.cpp compile_test_main  ]
    [ run  compile_test/sf_hankel_incl_test.cpp compile_test_main  ]
    [ run  compile_test/sf_jacobi_incl_test.cpp compile_test_main  ]
@@ -1241,6 +1250,14 @@ test-suite quadrature :
    [ run test_numerical_differentiation.cpp ../../test/build//boost_unit_test_framework  : : : <toolset>msvc:<cxxflags>/bigobj [ requires cxx11_auto_declarations cxx11_constexpr ] ]
    [ run  compile_test/numerical_differentiation_incl_test.cpp compile_test_main  : : : [ requires cxx11_auto_declarations cxx11_constexpr ] ]
    [ compile  compile_test/numerical_differentiation_concept_test.cpp  : [ requires cxx11_auto_declarations cxx11_constexpr ] ]
+   [ run test_autodiff_1.cpp ../../test/build//boost_unit_test_framework : : : <toolset>gcc-mingw:<cxxflags>-Wa,-mbig-obj <debug-symbols>off <toolset>msvc:<cxxflags>/bigobj release [ check-target-builds ../config//has_float128 "GCC libquadmath and __float128 support" : <linkflags>-lquadmath ] [ requires cxx11_inline_namespaces ] ]
+   [ run test_autodiff_2.cpp ../../test/build//boost_unit_test_framework : : : <toolset>gcc-mingw:<cxxflags>-Wa,-mbig-obj <debug-symbols>off <toolset>msvc:<cxxflags>/bigobj release [ check-target-builds ../config//has_float128 "GCC libquadmath and __float128 support" : <linkflags>-lquadmath ] [ requires cxx11_inline_namespaces ] ]
+   [ run test_autodiff_3.cpp ../../test/build//boost_unit_test_framework : : : <toolset>gcc-mingw:<cxxflags>-Wa,-mbig-obj <debug-symbols>off <toolset>msvc:<cxxflags>/bigobj release [ check-target-builds ../config//has_float128 "GCC libquadmath and __float128 support" : <linkflags>-lquadmath ] [ requires cxx11_inline_namespaces ] ]
+   [ run test_autodiff_4.cpp ../../test/build//boost_unit_test_framework : : : <toolset>gcc-mingw:<cxxflags>-Wa,-mbig-obj <debug-symbols>off <toolset>msvc:<cxxflags>/bigobj release [ check-target-builds ../config//has_float128 "GCC libquadmath and __float128 support" : <linkflags>-lquadmath ] [ requires cxx11_inline_namespaces ] ]
+   [ run test_autodiff_5.cpp ../../test/build//boost_unit_test_framework : : : <toolset>gcc-mingw:<cxxflags>-Wa,-mbig-obj <debug-symbols>off <toolset>msvc:<cxxflags>/bigobj release [ check-target-builds ../config//has_float128 "GCC libquadmath and __float128 support" : <linkflags>-lquadmath ] [ requires cxx11_inline_namespaces ] ]
+   [ run test_autodiff_6.cpp ../../test/build//boost_unit_test_framework : : : <toolset>gcc-mingw:<cxxflags>-Wa,-mbig-obj <debug-symbols>off <toolset>msvc:<cxxflags>/bigobj release [ check-target-builds ../config//has_float128 "GCC libquadmath and __float128 support" : <linkflags>-lquadmath ] [ requires cxx11_inline_namespaces ] ]
+   [ run test_autodiff_7.cpp ../../test/build//boost_unit_test_framework : : : <toolset>gcc-mingw:<cxxflags>-Wa,-mbig-obj <debug-symbols>off <toolset>msvc:<cxxflags>/bigobj release [ check-target-builds ../config//has_float128 "GCC libquadmath and __float128 support" : <linkflags>-lquadmath ] [ requires cxx11_inline_namespaces ] ]
+   [ run test_autodiff_8.cpp ../../test/build//boost_unit_test_framework : : : <toolset>gcc-mingw:<cxxflags>-Wa,-mbig-obj <debug-symbols>off <toolset>msvc:<cxxflags>/bigobj release [ check-target-builds ../config//has_float128 "GCC libquadmath and __float128 support" : <linkflags>-lquadmath ] [ requires cxx11_inline_namespaces ] ]
 ;
 
 build-project ../example ;
diff --git a/libs/math/test/cardinal_quadratic_b_spline_test.cpp b/libs/math/test/cardinal_quadratic_b_spline_test.cpp
new file mode 100644
index 0000000000..33ad0efe03
--- /dev/null
+++ b/libs/math/test/cardinal_quadratic_b_spline_test.cpp
@@ -0,0 +1,130 @@
+/*
+ * Copyright Nick Thompson, 2019
+ * Use, modification and distribution are subject to the
+ * Boost Software License, Version 1.0. (See accompanying file
+ * LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#include "math_unit_test.hpp"
+#include <numeric>
+#include <utility>
+#include <boost/math/interpolators/cardinal_quadratic_b_spline.hpp>
+using boost::math::interpolators::cardinal_quadratic_b_spline;
+
+template<class Real>
+void test_constant()
+{
+    Real c = 7.2;
+    Real t0 = 0;
+    Real h = Real(1)/Real(16);
+    size_t n = 512;
+    std::vector<Real> v(n, c);
+    auto qbs = cardinal_quadratic_b_spline<Real>(v.data(), v.size(), t0, h);
+
+    size_t i = 0;
+    while (i < n) {
+      Real t = t0 + i*h;
+      CHECK_ULP_CLOSE(c, qbs(t), 2);
+      CHECK_MOLLIFIED_CLOSE(0, qbs.prime(t), 100*std::numeric_limits<Real>::epsilon());
+      ++i;
+    }
+
+    i = 0;
+    while (i < n) {
+      Real t = t0 + i*h + h/2;
+      CHECK_ULP_CLOSE(c, qbs(t), 2);
+      CHECK_MOLLIFIED_CLOSE(0, qbs.prime(t), 300*std::numeric_limits<Real>::epsilon());
+      t = t0 + i*h + h/4;
+      CHECK_ULP_CLOSE(c, qbs(t), 2);
+      CHECK_MOLLIFIED_CLOSE(0, qbs.prime(t), 150*std::numeric_limits<Real>::epsilon());
+      ++i;
+    }
+}
+
+template<class Real>
+void test_linear()
+{
+    Real m = 8.3;
+    Real b = 7.2;
+    Real t0 = 0;
+    Real h = Real(1)/Real(16);
+    size_t n = 512;
+    std::vector<Real> y(n);
+    for (size_t i = 0; i < n; ++i) {
+      Real t = i*h;
+      y[i] = m*t + b;
+    }
+    auto qbs = cardinal_quadratic_b_spline<Real>(y.data(), y.size(), t0, h);
+
+    size_t i = 0;
+    while (i < n) {
+      Real t = t0 + i*h;
+      CHECK_ULP_CLOSE(m*t+b, qbs(t), 2);
+      CHECK_ULP_CLOSE(m, qbs.prime(t), 820);
+      ++i;
+    }
+
+    i = 0;
+    while (i < n) {
+      Real t = t0 + i*h + h/2;
+      CHECK_ULP_CLOSE(m*t+b, qbs(t), 2);
+      CHECK_MOLLIFIED_CLOSE(m, qbs.prime(t), 1500*std::numeric_limits<Real>::epsilon());
+      t = t0 + i*h + h/4;
+      CHECK_ULP_CLOSE(m*t+b, qbs(t), 3);
+      CHECK_MOLLIFIED_CLOSE(m, qbs.prime(t), 1500*std::numeric_limits<Real>::epsilon());
+      ++i;
+    }
+}
+
+template<class Real>
+void test_quadratic()
+{
+    Real a = 8.2;
+    Real b = 7.2;
+    Real c = -9.2;
+    Real t0 = 0;
+    Real h = Real(1)/Real(16);
+    size_t n = 513;
+    std::vector<Real> y(n);
+    for (size_t i = 0; i < n; ++i) {
+      Real t = i*h;
+      y[i] = a*t*t + b*t + c;
+    }
+    Real t_max = t0 + (n-1)*h;
+    auto qbs = cardinal_quadratic_b_spline<Real>(y, t0, h, b, 2*a*t_max + b);
+
+    size_t i = 0;
+    while (i < n) {
+      Real t = t0 + i*h;
+      CHECK_ULP_CLOSE(a*t*t + b*t + c, qbs(t), 2);
+      ++i;
+    }
+
+    i = 0;
+    while (i < n) {
+      Real t = t0 + i*h + h/2;
+      CHECK_ULP_CLOSE(a*t*t + b*t + c, qbs(t), 47);
+
+      t = t0 + i*h + h/4;
+      if (!CHECK_ULP_CLOSE(a*t*t + b*t + c, qbs(t), 104)) {
+          std::cerr << "  Problem abscissa t = " << t << "\n";
+      }
+      ++i;
+    }
+}
+
+int main()
+{
+    test_constant<float>();
+    test_constant<double>();
+    test_constant<long double>();
+
+    test_linear<float>();
+    test_linear<double>();
+    test_linear<long double>();
+
+    test_quadratic<double>();
+    test_quadratic<long double>();
+
+    return boost::math::test::report_errors();
+}
diff --git a/libs/math/test/catmull_rom_test.cpp b/libs/math/test/catmull_rom_test.cpp
index 08199b52b3..d24cf772ce 100644
--- a/libs/math/test/catmull_rom_test.cpp
+++ b/libs/math/test/catmull_rom_test.cpp
@@ -16,6 +16,7 @@
 #include <boost/math/interpolators/catmull_rom.hpp>
 #include <boost/multiprecision/cpp_bin_float.hpp>
 #include <boost/multiprecision/cpp_dec_float.hpp>
+#include <boost/numeric/ublas/vector.hpp>
 
 using std::abs;
 using boost::multiprecision::cpp_bin_float_50;
@@ -117,6 +118,9 @@ template<class Real>
 void test_circle()
 {
     using boost::math::constants::pi;
+    using std::cos;
+    using std::sin;
+
     std::cout << "Testing that the Catmull-Rom spline interpolates circles correctly on type "
               << boost::typeindex::type_id<Real>().pretty_name() << "\n";
 
@@ -331,7 +335,7 @@ private:
 
 // Must define the free function "size()":
 template<class Real>
-constexpr size_t size(const mypoint3d<Real>& c)
+BOOST_CONSTEXPR std::size_t size(const mypoint3d<Real>& c)
 {
     return 3;
 }
@@ -346,6 +350,8 @@ void test_data_representations()
     mypoint3d<Real> p3(0.4, 0.5, 0.6);
     mypoint3d<Real> p4(0.5, 0.6, 0.7);
     mypoint3d<Real> p5(0.6, 0.7, 0.8);
+
+
     // Tests initializer_list:
     catmull_rom<mypoint3d<Real>> cat({p0, p1, p2, p3, p4, p5});
 
@@ -360,8 +366,42 @@ void test_data_representations()
     BOOST_CHECK_CLOSE_FRACTION(p[2], p1[2], tol);
 }
 
+template<class Real>
+void test_random_access_container()
+{
+    std::cout << "Testing that the Catmull-Rom spline works with multiple data representations.\n";
+    mypoint3d<Real> p0(0.1, 0.2, 0.3);
+    mypoint3d<Real> p1(0.2, 0.3, 0.4);
+    mypoint3d<Real> p2(0.3, 0.4, 0.5);
+    mypoint3d<Real> p3(0.4, 0.5, 0.6);
+    mypoint3d<Real> p4(0.5, 0.6, 0.7);
+    mypoint3d<Real> p5(0.6, 0.7, 0.8);
+
+    boost::numeric::ublas::vector<mypoint3d<Real>> u(6);
+    u[0] = p0;
+    u[1] = p1;
+    u[2] = p2;
+    u[3] = p3;
+    u[4] = p4;
+    u[5] = p5;
+
+    // Tests initializer_list:
+    catmull_rom<mypoint3d<Real>, decltype(u)> cat(std::move(u));
+
+    Real tol = 0.001;
+    auto p = cat(cat.parameter_at_point(0));
+    BOOST_CHECK_CLOSE_FRACTION(p[0], p0[0], tol);
+    BOOST_CHECK_CLOSE_FRACTION(p[1], p0[1], tol);
+    BOOST_CHECK_CLOSE_FRACTION(p[2], p0[2], tol);
+    p = cat(cat.parameter_at_point(1));
+    BOOST_CHECK_CLOSE_FRACTION(p[0], p1[0], tol);
+    BOOST_CHECK_CLOSE_FRACTION(p[1], p1[1], tol);
+    BOOST_CHECK_CLOSE_FRACTION(p[2], p1[2], tol);
+}
+
 BOOST_AUTO_TEST_CASE(catmull_rom_test)
 {
+#if !defined(TEST) || (TEST == 1)
     test_data_representations<float>();
     test_alpha_distance<double>();
 
@@ -370,12 +410,18 @@ BOOST_AUTO_TEST_CASE(catmull_rom_test)
 
     test_circle<float>();
     test_circle<double>();
-
+#endif
+#if !defined(TEST) || (TEST == 2)
     test_helix<double>();
 
     test_affine_invariance<double, 1>();
     test_affine_invariance<double, 2>();
     test_affine_invariance<double, 3>();
     test_affine_invariance<double, 4>();
+
+    test_random_access_container<double>();
+#endif
+#if !defined(TEST) || (TEST == 3)
     test_affine_invariance<cpp_bin_float_50, 4>();
+#endif
 }
diff --git a/libs/math/test/compile_test/catmull_rom_concept_test.cpp b/libs/math/test/compile_test/catmull_rom_concept_test.cpp
index a9bd284051..9f7b2b498e 100644
--- a/libs/math/test/compile_test/catmull_rom_concept_test.cpp
+++ b/libs/math/test/compile_test/catmull_rom_concept_test.cpp
@@ -15,7 +15,7 @@ void compile_and_link_test()
     std::vector<boost::math::concepts::std_real_concept> p4{0.5, 0.6, 0.7};
     std::vector<boost::math::concepts::std_real_concept> p5{0.6, 0.7, 0.8};
     std::vector<std::vector<boost::math::concepts::std_real_concept>> v{p0, p1, p2, p3, p4, p5};
-    boost::math::catmull_rom<std::vector<boost::math::concepts::std_real_concept>> cat(v.data(), v.size());
+    boost::math::catmull_rom<std::vector<boost::math::concepts::std_real_concept>> cat(std::move(v));
     cat(0.0);
     cat.prime(0.0);
 }
diff --git a/libs/math/test/compile_test/catmull_rom_incl_test.cpp b/libs/math/test/compile_test/catmull_rom_incl_test.cpp
index d419ae9889..9cdaa09af0 100644
--- a/libs/math/test/compile_test/catmull_rom_incl_test.cpp
+++ b/libs/math/test/compile_test/catmull_rom_incl_test.cpp
@@ -22,7 +22,7 @@ void compile_and_link_test()
     std::vector<double> p4{0.5, 0.6, 0.7};
     std::vector<double> p5{0.6, 0.7, 0.8};
     std::vector<std::vector<double>> v{p0, p1, p2, p3, p4, p5};
-    boost::math::catmull_rom<std::vector<double>> cat(v.data(), v.size());
-    check_result<double>(cat(0.0));
-    check_result<double>(cat.prime(0.0));
+    boost::math::catmull_rom<std::vector<double>> cat(std::move(v));
+    check_result<std::vector<double>>(cat(0.0));
+    check_result<std::vector<double>>(cat.prime(0.0));
 }
diff --git a/libs/math/test/compile_test/sf_prime_incl_test.cpp b/libs/math/test/compile_test/sf_prime_incl_test.cpp
index 464ae48af2..6ab7584790 100644
--- a/libs/math/test/compile_test/sf_prime_incl_test.cpp
+++ b/libs/math/test/compile_test/sf_prime_incl_test.cpp
@@ -20,7 +20,8 @@ void compile_and_link_test()
    // Add constexpr tests here:
    //
 #ifdef BOOST_MATH_HAVE_CONSTEXPR_TABLES
-   constexpr boost::uint32_t ce_f = boost::math::prime(2);
+   constexpr boost::uint32_t ce_f = boost::math::prime(boost::math::max_prime);
+   static_assert(ce_f == 104729, "max_prime had incorrect value");
    check_result<boost::uint32_t>(ce_f);
 #endif
 }
diff --git a/libs/math/test/math_unit_test.hpp b/libs/math/test/math_unit_test.hpp
new file mode 100644
index 0000000000..79f3dab341
--- /dev/null
+++ b/libs/math/test/math_unit_test.hpp
@@ -0,0 +1,147 @@
+// Copyright Nick Thompson, 2019
+// Use, modification and distribution are subject to the
+// Boost Software License, Version 1.0.
+// (See accompanying file LICENSE_1_0.txt
+// or copy at http://www.boost.org/LICENSE_1_0.txt)
+#ifndef BOOST_MATH_TEST_TEST_HPP
+#define BOOST_MATH_TEST_TEST_HPP
+#include <atomic>
+#include <iostream>
+#include <iomanip>
+#include <cmath> // for std::isnan
+#include <boost/assert.hpp>
+#include <boost/math/special_functions/next.hpp>
+#include <boost/core/demangle.hpp>
+
+
+namespace boost { namespace math { namespace  test {
+
+namespace detail {
+    static std::atomic<int64_t> global_error_count{0};
+    static std::atomic<int64_t> total_ulp_distance{0};
+}
+
+template<class Real>
+bool check_mollified_close(Real expected, Real computed, Real tol, std::string const & filename, std::string const & function, int line)
+{
+    using std::isnan;
+    BOOST_ASSERT_MSG(!isnan(tol), "Tolerance cannot be a nan.");
+    BOOST_ASSERT_MSG(!isnan(expected), "Expected value cannot be a nan.");
+    BOOST_ASSERT_MSG(tol >= 0, "Tolerance must be non-negative.");
+    if (isnan(computed)) {
+        std::ios_base::fmtflags f( std::cerr.flags() );
+        std::cerr << std::setprecision(3);
+        std::cerr << "\033[0;31mError at " << filename << ":" << function << ":" << line << ":\n"
+                  << " \033[0m Computed value is a nan\n";
+        std::cerr.flags(f);
+        ++detail::global_error_count;
+        return false;
+    }
+    using std::max;
+    using std::abs;
+    Real denom = max(abs(expected), Real(1));
+    Real mollified_relative_error = abs(expected - computed)/denom;
+    if (mollified_relative_error > tol)
+    {
+        Real dist = abs(boost::math::float_distance(expected, computed));
+        detail::total_ulp_distance += static_cast<int64_t>(dist);
+        std::ios_base::fmtflags f( std::cerr.flags() );
+        std::cerr << std::setprecision(3);
+        std::cerr << "\033[0;31mError at " << filename << ":" << function << ":" << line << ":\n"
+                  << " \033[0m Mollified relative error in " << boost::core::demangle(typeid(Real).name())<< " precision is " << mollified_relative_error
+                  << ", which exceeds " << tol << ", error/tol  = " << mollified_relative_error/tol << ".\n"
+                  << std::setprecision(std::numeric_limits<Real>::digits10) << std::showpos
+                  << "  Expected: " << std::defaultfloat << std::fixed << expected << std::hexfloat << " = " << expected << "\n"
+                  << "  Computed: " << std::defaultfloat << std::fixed << computed << std::hexfloat << " = " << computed << "\n"
+                  << std::defaultfloat
+                  << "  ULP distance: " << dist << "\n";
+        std::cerr.flags(f);
+        ++detail::global_error_count;
+
+        return false;
+    }
+    return true;
+}
+
+template<class PreciseReal, class Real>
+bool check_ulp_close(PreciseReal expected1, Real computed, size_t ulps, std::string const & filename, std::string const & function, int line)
+{
+    using std::max;
+    using std::abs;
+    using std::isnan;
+    BOOST_ASSERT_MSG(sizeof(PreciseReal) >= sizeof(Real),
+                     "The expected number must be computed in higher (or equal) precision than the number being tested.");
+
+    BOOST_ASSERT_MSG(!isnan(expected1), "Expected value cannot be a nan.");
+    if (isnan(computed))
+    {
+        std::ios_base::fmtflags f( std::cerr.flags() );
+        std::cerr << std::setprecision(3);
+        std::cerr << "\033[0;31mError at " << filename << ":" << function << ":" << line << ":\n"
+                  << " \033[0m Computed value is a nan\n";
+        std::cerr.flags(f);
+        ++detail::global_error_count;
+        return false;
+    }
+
+    Real expected = Real(expected1);
+    Real dist = abs(boost::math::float_distance(expected, computed));
+    if (dist > ulps)
+    {
+        detail::total_ulp_distance += static_cast<int64_t>(dist);
+        Real denom = max(abs(expected), Real(1));
+        Real mollified_relative_error = abs(expected - computed)/denom;
+        std::ios_base::fmtflags f( std::cerr.flags() );
+        std::cerr << std::setprecision(3);
+        std::cerr << "\033[0;31mError at " << filename << ":" << function << ":" << line << ":\n"
+                  << " \033[0m ULP distance in " << boost::core::demangle(typeid(Real).name())<< " precision is " << dist
+                  << ", which exceeds " << ulps;
+                  if (ulps > 0)
+                  {
+                      std::cerr << ", error/ulps  = " << dist/static_cast<Real>(ulps) << ".\n";
+                  }
+                  else
+                  {
+                      std::cerr << ".\n";
+                  }
+        std::cerr << std::setprecision(std::numeric_limits<Real>::digits10) << std::showpos
+                  << "  Expected: " << std::defaultfloat << std::fixed << expected << std::hexfloat << " = " << expected << "\n"
+                  << "  Computed: " << std::defaultfloat << std::fixed << computed << std::hexfloat << " = " << computed << "\n"
+                  << std::defaultfloat
+                  << "  Mollified relative error: " << mollified_relative_error << "\n";
+        std::cerr.flags(f);
+        ++detail::global_error_count;
+        return false;
+    }
+    return true;
+}
+
+
+int report_errors()
+{
+    if (detail::global_error_count > 0)
+    {
+        std::cerr << "\033[0;31mError count: " << detail::global_error_count;
+        if (detail::total_ulp_distance > 0) {
+            std::cerr << ", total ulp distance = " << detail::total_ulp_distance << "\n";
+        }
+        else {
+            // else we overflowed the ULPs counter and all we could print is a bizarre negative number.
+            std::cerr << "\n";
+        }
+
+        detail::global_error_count = 0;
+        detail::total_ulp_distance = 0;
+        return 1;
+    }
+    std::cout << "\x1B[32mNo errors detected.\n";
+    return 0;
+}
+
+}}}
+
+#define CHECK_MOLLIFIED_CLOSE(X, Y, Z) boost::math::test::check_mollified_close< typename std::remove_reference<decltype((Y))>::type>((X), (Y), (Z), __FILE__, __func__, __LINE__)
+
+#define CHECK_ULP_CLOSE(X, Y, Z) boost::math::test::check_ulp_close((X), (Y), (Z), __FILE__, __func__, __LINE__)
+
+#endif
diff --git a/libs/math/test/ooura_fourier_integral_test.cpp b/libs/math/test/ooura_fourier_integral_test.cpp
new file mode 100644
index 0000000000..84c7afd886
--- /dev/null
+++ b/libs/math/test/ooura_fourier_integral_test.cpp
@@ -0,0 +1,377 @@
+// Copyright Nick Thompson, 2019
+// Use, modification and distribution are subject to the
+// Boost Software License, Version 1.0.
+// (See accompanying file LICENSE_1_0.txt
+// or copy at http://www.boost.org/LICENSE_1_0.txt)
+#define BOOST_TEST_MODULE test_ooura_fourier_transform
+
+#include <cmath>
+#include <iostream>
+#include <boost/type_index.hpp>
+#include <boost/test/included/unit_test.hpp>
+#include <boost/test/tools/floating_point_comparison.hpp>
+#include <boost/math/quadrature/ooura_fourier_integrals.hpp>
+#include <boost/multiprecision/cpp_bin_float.hpp>
+
+using boost::math::quadrature::ooura_fourier_sin;
+using boost::math::quadrature::ooura_fourier_cos;
+using boost::math::constants::pi;
+
+
+float float_tol = 10*std::numeric_limits<float>::epsilon();
+ooura_fourier_sin<float> float_sin_integrator(float_tol);
+
+double double_tol = 10*std::numeric_limits<double>::epsilon();
+ooura_fourier_sin<double> double_sin_integrator(double_tol);
+
+long double long_double_tol = 10*std::numeric_limits<long double>::epsilon();
+ooura_fourier_sin<long double> long_double_sin_integrator(long_double_tol);
+
+template<class Real>
+auto get_sin_integrator() {
+    if constexpr (std::is_same_v<Real, float>) {
+        return float_sin_integrator;
+    }
+    if constexpr (std::is_same_v<Real, double>) {
+        return double_sin_integrator;
+    }
+    if constexpr (std::is_same_v<Real, long double>) {
+        return long_double_sin_integrator;
+    }
+}
+
+ooura_fourier_cos<float> float_cos_integrator(float_tol);
+ooura_fourier_cos<double> double_cos_integrator(double_tol);
+ooura_fourier_cos<long double> long_double_cos_integrator(long_double_tol);
+
+template<class Real>
+auto get_cos_integrator() {
+    if constexpr (std::is_same_v<Real, float>) {
+        return float_cos_integrator;
+    }
+    if constexpr (std::is_same_v<Real, double>) {
+        return double_cos_integrator;
+    }
+    if constexpr (std::is_same_v<Real, long double>) {
+        return long_double_cos_integrator;
+    }
+}
+
+
+template<class Real>
+void test_ooura_eta()
+{
+    using boost::math::quadrature::detail::ooura_eta;
+    std::cout << "Testing eta function on type " << boost::typeindex::type_id<Real>().pretty_name()  << "\n";
+    {
+        Real x = 0;
+        Real alpha = 7;
+        auto [eta, eta_prime] = ooura_eta(x, alpha);
+        BOOST_CHECK_SMALL(eta, (std::numeric_limits<Real>::min)());
+        BOOST_CHECK_CLOSE_FRACTION(eta_prime, 2 + alpha + Real(1)/Real(4), 10*std::numeric_limits<Real>::epsilon());
+    }
+
+    {
+        Real alpha = 4;
+        for (Real z = 0.125; z < 500; z += 0.125) {
+            Real x = std::log(z);
+            auto [eta, eta_prime] = ooura_eta(x, alpha);
+            BOOST_CHECK_CLOSE_FRACTION(eta, 2*x + alpha*(1-1/z) + (z-1)/4, 10*std::numeric_limits<Real>::epsilon());
+            BOOST_CHECK_CLOSE_FRACTION(eta_prime, 2 + alpha/z + z/4, 10*std::numeric_limits<Real>::epsilon());
+        }
+    }
+}
+
+template<class Real>
+void test_ooura_sin_nodes_and_weights()
+{
+    using boost::math::quadrature::detail::ooura_sin_node_and_weight;
+    using boost::math::quadrature::detail::ooura_eta;
+    std::cout << "Testing nodes and weights on type " << boost::typeindex::type_id<Real>().pretty_name()  << "\n";
+    {
+        long n = 1;
+        Real alpha = 1;
+        Real h = 1;
+        auto [node, weight] = ooura_sin_node_and_weight(n, h, alpha);
+        Real expected_node = pi<Real>()/(1-exp(-ooura_eta(n*h, alpha).first));
+        BOOST_CHECK_CLOSE_FRACTION(node,  expected_node,10*std::numeric_limits<Real>::epsilon());
+    }
+}
+
+template<class Real>
+void test_ooura_alpha() {
+    std::cout << "Testing Ooura alpha on type " << boost::typeindex::type_id<Real>().pretty_name()  << "\n";
+    using std::sqrt;
+    using std::log1p;
+    using boost::math::quadrature::detail::calculate_ooura_alpha;
+    Real alpha = calculate_ooura_alpha(Real(1));
+    Real expected = 1/sqrt(16 + 4*log1p(pi<Real>()));
+    BOOST_CHECK_CLOSE_FRACTION(alpha, expected, 10*std::numeric_limits<Real>::epsilon());
+}
+
+void test_node_weight_precision_agreement()
+{
+    using std::abs;
+    using boost::math::quadrature::detail::ooura_sin_node_and_weight;
+    using boost::math::quadrature::detail::ooura_eta;
+    using boost::multiprecision::cpp_bin_float_quad;
+    std::cout << "Testing agreement in two different precisions of nodes and weights\n";
+    cpp_bin_float_quad alpha_quad = 1;
+    long int_max = 128;
+    cpp_bin_float_quad h_quad = 1/cpp_bin_float_quad(int_max);
+    double alpha_dbl = 1;
+    double h_dbl = static_cast<double>(h_quad);
+    std::cout << std::fixed;
+    for (long n = -1; n > -6*int_max; --n) {
+        auto [node_dbl, weight_dbl] = ooura_sin_node_and_weight(n, h_dbl, alpha_dbl);
+        auto p = ooura_sin_node_and_weight(n, h_quad, alpha_quad);
+        double node_quad = static_cast<double>(p.first);
+        double weight_quad = static_cast<double>(p.second);
+        auto node_dist = abs(boost::math::float_distance(node_quad, node_dbl));
+        if ( (weight_quad < 0 && weight_dbl > 0) || (weight_dbl < 0 && weight_quad > 0) ){
+            std::cout << "Weights at different precisions have different signs!\n";
+        } else {
+            auto weight_dist = abs(boost::math::float_distance(weight_quad, weight_dbl));
+            if (weight_dist > 100) {
+                std::cout << std::fixed;
+                std::cout <<"n =" << n << ", x = " << n*h_dbl << ", node distance = " << node_dist << ", weight distance = " << weight_dist << "\n";
+                std::cout << std::scientific;
+                std::cout << "computed weight = " << weight_dbl << ", actual weight = " << weight_quad << "\n";
+            }
+        }
+    }
+
+}
+
+template<class Real>
+void test_sinc()
+{
+    std::cout << "Testing sinc integral on type " << boost::typeindex::type_id<Real>().pretty_name()  << "\n";
+    using std::numeric_limits;
+    Real tol = 50*numeric_limits<Real>::epsilon();
+    auto integrator = get_sin_integrator<Real>();
+    auto f = [](Real x)->Real { return 1/x; };
+    Real omega = 1;
+    while (omega < 10)
+    {
+        auto [Is, err] = integrator.integrate(f, omega);
+        BOOST_CHECK_CLOSE_FRACTION(Is, pi<Real>()/2, tol);
+
+        auto [Isn, errn] = integrator.integrate(f, -omega);
+        BOOST_CHECK_CLOSE_FRACTION(Isn, -pi<Real>()/2, tol);
+        omega += 1;
+    }
+}
+
+
+template<class Real>
+void test_exp()
+{
+    std::cout << "Testing exponential integral on type " << boost::typeindex::type_id<Real>().pretty_name()  << "\n";
+    using std::exp;
+    using std::numeric_limits;
+    Real tol = 50*numeric_limits<Real>::epsilon();
+    auto integrator = get_sin_integrator<Real>();
+    auto f = [](Real x)->Real {return exp(-x);};
+    Real omega = 1;
+    while (omega < 5)
+    {
+        auto [Is, err] = integrator.integrate(f, omega);
+        Real exact = omega/(1+omega*omega);
+        BOOST_CHECK_CLOSE_FRACTION(Is, exact, tol);
+        omega += 1;
+    }
+}
+
+
+template<class Real>
+void test_root()
+{
+    std::cout << "Testing integral of sin(kx)/sqrt(x) on type " << boost::typeindex::type_id<Real>().pretty_name()  << "\n";
+    using std::sqrt;
+    using std::numeric_limits;
+    Real tol = 10*numeric_limits<Real>::epsilon();
+    auto integrator = get_sin_integrator<Real>();
+    auto f = [](Real x)->Real { return 1/sqrt(x);};
+    Real omega = 1;
+    while (omega < 5) {
+        auto [Is, err] = integrator.integrate(f, omega);
+        Real exact = sqrt(pi<Real>()/(2*omega));
+        BOOST_CHECK_CLOSE_FRACTION(Is, exact, 10*tol);
+        omega += 1;
+    }
+}
+
+// See: https://scicomp.stackexchange.com/questions/32790/numerical-evaluation-of-highly-oscillatory-integral/32799#32799
+template<class Real>
+Real asymptotic(Real lambda) {
+    using std::sin;
+    using std::cos;
+    using boost::math::constants::pi;
+    Real I1 = cos(lambda - pi<Real>()/4)*sqrt(2*pi<Real>()/lambda);
+    Real I2 = sin(lambda - pi<Real>()/4)*sqrt(2*pi<Real>()/(lambda*lambda*lambda))/8;
+    return I1 + I2;
+}
+
+template<class Real>
+void test_double_osc()
+{
+    std::cout << "Testing double oscillation on type " << boost::typeindex::type_id<Real>().pretty_name()  << "\n";
+    using std::sqrt;
+    using std::numeric_limits;
+    auto integrator = get_sin_integrator<Real>();
+    Real lambda = 7;
+    auto f = [&lambda](Real x)->Real { return cos(lambda*cos(x))/x; };
+    Real omega = 1;
+    auto [Is, err] = integrator.integrate(f, omega);
+    Real exact = asymptotic(lambda);
+    BOOST_CHECK_CLOSE_FRACTION(2*Is, exact, 0.05);
+}
+
+template<class Real>
+void test_zero_integrand()
+{
+    // Make sure relative error tolerance doesn't break on zero integrand:
+    std::cout << "Testing zero integrand on type " << boost::typeindex::type_id<Real>().pretty_name()  << "\n";
+    using std::sqrt;
+    using std::numeric_limits;
+    auto integrator = get_sin_integrator<Real>();
+    auto f = [](Real /* x */)->Real { return Real(0); };
+    Real omega = 1;
+    auto [Is, err] = integrator.integrate(f, omega);
+    Real exact = 0;
+    BOOST_CHECK_EQUAL(Is, exact);
+}
+
+
+// This works, but doesn't recover the precision you want in a unit test:
+// template<class Real>
+// void test_log()
+// {
+//     std::cout << "Testing integral of log(x)sin(x) on type " << boost::typeindex::type_id<Real>().pretty_name()  << "\n";
+//     using std::log;
+//     using std::exp;
+//     using std::numeric_limits;
+//     using boost::math::constants::euler;
+//     Real tol = 1000*numeric_limits<Real>::epsilon();
+//     auto f = [](Real x)->Real { return exp(-100*numeric_limits<Real>::epsilon()*x)*log(x);};
+//     Real omega = 1;
+//     Real Is = ooura_fourier_sin<decltype(f), Real>(f, omega, sqrt(numeric_limits<Real>::epsilon())/100);
+//     BOOST_CHECK_CLOSE_FRACTION(Is, -euler<Real>(), tol);
+// }
+
+
+template<class Real>
+void test_cos_integral1()
+{
+    std::cout << "Testing integral of cos(x)/(x*x+1) on type " << boost::typeindex::type_id<Real>().pretty_name()  << "\n";
+    using std::exp;
+    using boost::math::constants::half_pi;
+    using boost::math::constants::e;
+    using std::numeric_limits;
+    Real tol = 10*numeric_limits<Real>::epsilon();
+
+    auto integrator = get_cos_integrator<Real>();
+    auto f = [](Real x)->Real { return 1/(x*x+1);};
+    Real omega = 1;
+    auto [Is, err] = integrator.integrate(f, omega);
+    Real exact = half_pi<Real>()/e<Real>();
+    BOOST_CHECK_CLOSE_FRACTION(Is, exact, tol);
+}
+
+template<class Real>
+void test_cos_integral2()
+{
+    std::cout << "Testing integral of cos(x)/(x*x+1) on type " << boost::typeindex::type_id<Real>().pretty_name()  << "\n";
+    using std::exp;
+    using boost::math::constants::half_pi;
+    using boost::math::constants::e;
+    using std::numeric_limits;
+    Real tol = 10*numeric_limits<Real>::epsilon();
+
+    auto integrator = get_cos_integrator<Real>();
+    for (Real a = 1; a < 5; ++a) {
+        auto f = [&a](Real x)->Real { return exp(-a*x);};
+        for(Real omega = 1; omega < 5; ++omega) {
+            auto [Is, err] = integrator.integrate(f, omega);
+            Real exact = a/(a*a+omega*omega);
+            BOOST_CHECK_CLOSE_FRACTION(Is, exact, 10*tol);
+        }
+    }
+}
+
+template<class Real>
+void test_nodes()
+{
+    std::cout << "Testing nodes and weights on type " << boost::typeindex::type_id<Real>().pretty_name()  << "\n";
+    auto sin_integrator = get_sin_integrator<Real>();
+
+    auto const & big_nodes = sin_integrator.big_nodes();
+    for (auto & node_row : big_nodes) {
+        Real t0 = node_row[0];
+        for (size_t i = 1; i < node_row.size(); ++i) {
+            Real t1 = node_row[i];
+            BOOST_CHECK(t1 > t0);
+            t0 = t1;
+        }
+    }
+
+    auto const & little_nodes = sin_integrator.little_nodes();
+    for (auto & node_row : little_nodes) {
+        Real t0 = node_row[0];
+        for (size_t i = 1; i < node_row.size(); ++i) {
+            Real t1 = node_row[i];
+            BOOST_CHECK(t1 < t0);
+            t0 = t1;
+        }
+    }
+}
+
+
+BOOST_AUTO_TEST_CASE(ooura_fourier_transform_test)
+{
+    test_cos_integral1<float>();
+    test_cos_integral1<double>();
+    test_cos_integral1<long double>();
+
+    test_cos_integral2<float>();
+    test_cos_integral2<double>();
+    test_cos_integral2<long double>();
+
+    //test_node_weight_precision_agreement();
+    test_zero_integrand<float>();
+    test_zero_integrand<double>();
+
+    test_ooura_eta<float>();
+    test_ooura_eta<double>();
+    test_ooura_eta<long double>();
+
+    test_ooura_sin_nodes_and_weights<float>();
+    test_ooura_sin_nodes_and_weights<double>();
+    test_ooura_sin_nodes_and_weights<long double>();
+
+    test_ooura_alpha<float>();
+    test_ooura_alpha<double>();
+    test_ooura_alpha<long double>();
+
+    test_sinc<float>();
+    test_sinc<double>();
+    test_sinc<long double>();
+
+    test_exp<float>();
+    test_exp<double>();
+    test_exp<long double>();
+
+    test_root<float>();
+    test_root<double>();
+
+    test_double_osc<float>();
+    test_double_osc<double>();
+    // Takes too long!
+    //test_double_osc<long double>();
+
+    // This test should be last:
+    test_nodes<float>();
+    test_nodes<double>();
+    test_nodes<long double>();
+}
diff --git a/libs/math/test/test_autodiff.hpp b/libs/math/test/test_autodiff.hpp
new file mode 100644
index 0000000000..9a312af97c
--- /dev/null
+++ b/libs/math/test/test_autodiff.hpp
@@ -0,0 +1,225 @@
+//           Copyright Matthew Pulver 2018 - 2019.
+// Distributed under the Boost Software License, Version 1.0.
+//      (See accompanying file LICENSE_1_0.txt or copy at
+//           https://www.boost.org/LICENSE_1_0.txt)
+
+#ifndef BOOST_MATH_TEST_AUTODIFF_HPP
+#define BOOST_MATH_TEST_AUTODIFF_HPP
+
+#ifndef BOOST_TEST_MODULE
+#define BOOST_TEST_MODULE test_autodiff
+#endif
+
+#ifndef BOOST_ALLOW_DEPRECATED_HEADERS
+#define BOOST_ALLOW_DEPRECATED_HEADERS // artifact of sp_typeinfo.hpp inclusion from unit_test.hpp
+#endif
+
+#include <boost/math/tools/config.hpp>
+
+#include <boost/math/differentiation/autodiff.hpp>
+#include <boost/multiprecision/cpp_bin_float.hpp>
+#include <boost/multiprecision/cpp_dec_float.hpp>
+#include <boost/mp11/function.hpp>
+#include <boost/mp11/integral.hpp>
+#include <boost/mp11/list.hpp>
+#include <boost/mp11/utility.hpp>
+#include <boost/range/irange.hpp>
+#include <boost/test/included/unit_test.hpp>
+
+#include <algorithm>
+#include <cfenv>
+#include <cstdlib>
+#include <random>
+
+namespace mp11 = boost::mp11;
+namespace bmp = boost::multiprecision;
+
+#if defined(BOOST_USE_VALGRIND) || defined(BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS)
+using bin_float_types = mp11::mp_list<float>;
+#else
+using bin_float_types = mp11::mp_list<float, double, long double>;
+#endif
+
+// cpp_dec_float_50 cannot be used with close_at_tolerance
+/*using multiprecision_float_types =
+    mp_list<bmp::cpp_dec_float_50, bmp::cpp_bin_float_50>;*/
+
+#if !defined(BOOST_VERSION) || BOOST_VERSION < 107000 || defined(BOOST_USE_VALGRIND) || defined(BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS) || defined(BOOST_NO_STRESS_TEST)
+using multiprecision_float_types = mp11::mp_list<>;
+#else
+#define BOOST_AUTODIFF_TESTING_INCLUDE_MULTIPRECISION
+using multiprecision_float_types = mp11::mp_list<bmp::cpp_bin_float_50>;
+#endif
+
+using all_float_types = mp11::mp_append<bin_float_types, multiprecision_float_types>;
+
+using namespace boost::math::differentiation;
+
+namespace test_detail {
+template <typename T>
+using is_multiprecision_t =
+    mp11::mp_or<bmp::is_number<T>, bmp::is_number_expression<T>>;
+
+template<bool IfValue, typename ThenType, typename ElseType>
+using if_c = mp11::mp_eval_if_c<IfValue, ThenType, mp11::mp_identity_t, ElseType>;
+
+template<typename IfType, typename ThenType, typename ElseType>
+using if_t = if_c<IfType::value, ThenType, ElseType>;
+
+/**
+ * Simple struct to hold constants that are used in each test
+ * since BOOST_AUTO_TEST_CASE_TEMPLATE doesn't support fixtures.
+ */
+template <typename T, std::size_t OrderValue>
+struct test_constants_t {
+  static constexpr auto n_samples = if_t<mp11::mp_or<bmp::is_number<T>, bmp::is_number_expression<T>>, mp11::mp_int<10>, mp11::mp_int<25>>::value;      
+  static constexpr auto order = OrderValue;
+  static constexpr T pct_epsilon() BOOST_NOEXCEPT {
+	return (is_multiprecision_t<T>::value ? 2 : 1) * std::numeric_limits<T>::epsilon() * 100;
+  }
+};
+
+/**
+ * struct to emit pseudo-random values from a given interval.
+ * Endpoints are closed or open depending on whether or not they're infinite).
+ */
+
+template <typename T>
+struct RandomSample {
+  using numeric_limits_t = std::numeric_limits<T>;
+  using is_integer_t = mp11::mp_bool<std::numeric_limits<T>::is_integer>;
+
+  using distribution_param_t = if_t<
+      is_multiprecision_t<T>,
+      if_t<is_integer_t,
+                  if_c<numeric_limits_t::is_signed, int64_t, uint64_t>,
+                  long double>,
+      T>;
+  static_assert((std::numeric_limits<T>::is_integer &&
+                 std::numeric_limits<distribution_param_t>::is_integer) ||
+                    (!std::numeric_limits<T>::is_integer &&
+                     !std::numeric_limits<distribution_param_t>::is_integer),
+                "T and distribution_param_t must either both be integral or "
+                "both be not integral");
+
+  using dist_t = if_t<is_integer_t,
+	std::uniform_int_distribution<distribution_param_t>,
+	std::uniform_real_distribution<distribution_param_t>>;
+
+  struct get_integral_endpoint {
+    template <typename V>
+    constexpr distribution_param_t operator()(V finish) const noexcept {
+      return static_cast<distribution_param_t>(finish);
+    }
+  };
+
+  struct get_real_endpoint {
+    template <typename V>
+    constexpr distribution_param_t operator()(V finish) const noexcept {
+      return std::nextafter(static_cast<distribution_param_t>(finish),
+                            (std::numeric_limits<distribution_param_t>::max)());
+    }
+  };
+
+  using get_endpoint_t = if_t<is_integer_t, get_integral_endpoint, get_real_endpoint>;
+
+  template <typename U, typename V>
+  RandomSample(U start, V finish)
+      : rng_(std::random_device{}()),
+        dist_(static_cast<distribution_param_t>(start),
+              get_endpoint_t{}(finish)) {}
+
+  T next() noexcept { return static_cast<T>(dist_(rng_)); }
+  T normalize(const T& x) noexcept {
+    return x / ((dist_.max)() - (dist_.min)());
+  }
+
+  std::mt19937 rng_;
+  dist_t dist_;
+};
+static_assert(std::is_same<RandomSample<float>::dist_t,
+                           std::uniform_real_distribution<float>>::value,
+              "");
+static_assert(std::is_same<RandomSample<int64_t>::dist_t,
+                           std::uniform_int_distribution<int64_t>>::value,
+              "");
+static_assert(std::is_same<RandomSample<bmp::uint512_t>::dist_t,
+                           std::uniform_int_distribution<uint64_t>>::value,
+              "");
+static_assert(std::is_same<RandomSample<bmp::cpp_bin_float_50>::dist_t,
+                           std::uniform_real_distribution<long double>>::value,
+              "");
+
+}  // namespace test_detail
+
+template<typename T>
+auto isNearZero(const T& t) noexcept -> typename std::enable_if<!detail::is_fvar<T>::value, bool>::type
+{
+  using std::sqrt;
+  using bmp::sqrt;
+  using detail::sqrt;
+  using std::fabs;
+  using bmp::fabs;
+  using detail::fabs;
+  using boost::math::fpclassify;
+  using std::sqrt;
+  return fpclassify(fabs(t)) == FP_ZERO || fpclassify(fabs(t)) == FP_SUBNORMAL || boost::math::fpc::is_small(fabs(t), sqrt(std::numeric_limits<T>::epsilon()));
+}
+
+template<typename T>
+auto isNearZero(const T& t) noexcept -> typename std::enable_if<detail::is_fvar<T>::value, bool>::type
+{
+  using root_type = typename T::root_type;
+  return isNearZero(static_cast<root_type>(t));
+}
+
+template <typename T, std::size_t Order = 5>
+using test_constants_t = test_detail::test_constants_t<T, Order>;
+
+template <typename W, typename X, typename Y, typename Z>
+promote<W, X, Y, Z> mixed_partials_f(const W& w, const X& x, const Y& y,
+                                     const Z& z) {
+
+  return exp(w * sin(x * log(y) / z) + sqrt(w * z / (x * y))) + w * w / tan(z);
+}
+
+// Equations and function/variable names are from
+// https://en.wikipedia.org/wiki/Greeks_(finance)#Formulas_for_European_option_Greeks
+//
+// Standard normal probability density function
+template <typename T>
+T phi(const T& x) {
+  return boost::math::constants::one_div_root_two_pi<T>() * exp(-0.5 * x * x);
+}
+
+// Standard normal cumulative distribution function
+template <typename T>
+T Phi(const T& x) {
+  return 0.5 * erfc(-boost::math::constants::one_div_root_two<T>() * x);
+}
+
+enum class CP { call, put };
+
+// Assume zero annual dividend yield (q=0).
+template <typename Price, typename Sigma, typename Tau, typename Rate>
+promote<Price, Sigma, Tau, Rate> black_scholes_option_price(CP cp, double K,
+                                                            const Price& S,
+                                                            const Sigma& sigma,
+                                                            const Tau& tau,
+                                                            const Rate& r) {
+  const auto d1 =
+      (log(S / K) + (r + sigma * sigma / 2) * tau) / (sigma * sqrt(tau));
+  const auto d2 =
+      (log(S / K) + (r - sigma * sigma / 2) * tau) / (sigma * sqrt(tau));
+  if (cp == CP::call) {
+    return S * Phi(d1) - exp(-r * tau) * K * Phi(d2);
+  }
+  return exp(-r * tau) * K * Phi(-d2) - S * Phi(-d1);
+}
+
+template <typename T>
+T uncast_return(const T& x) {
+  return x == 0 ? 0 : 1;
+}
+
+#endif  // BOOST_MATH_TEST_AUTODIFF_HPP
diff --git a/libs/math/test/test_autodiff_1.cpp b/libs/math/test/test_autodiff_1.cpp
new file mode 100644
index 0000000000..9417d78bff
--- /dev/null
+++ b/libs/math/test/test_autodiff_1.cpp
@@ -0,0 +1,695 @@
+//           Copyright Matthew Pulver 2018 - 2019.
+// Distributed under the Boost Software License, Version 1.0.
+//      (See accompanying file LICENSE_1_0.txt or copy at
+//           https://www.boost.org/LICENSE_1_0.txt)
+
+#include "test_autodiff.hpp"
+
+BOOST_AUTO_TEST_SUITE(test_autodiff_1)
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(constructors, T, all_float_types) {
+  constexpr std::size_t m = 3;
+  constexpr std::size_t n = 4;
+  // Verify value-initialized instance has all 0 entries.
+  const autodiff_fvar<T, m> empty1 = autodiff_fvar<T, m>();
+  for (auto i : boost::irange(m + 1)) {
+    BOOST_CHECK_EQUAL(empty1.derivative(i), 0);
+  }
+  const auto empty2 = autodiff_fvar<T, m, n>();
+  for (auto i : boost::irange(m + 1)) {
+    for (auto j : boost::irange(n + 1)) {
+      BOOST_CHECK_EQUAL(empty2.derivative(i, j), 0);
+    }
+  }
+  // Single variable
+  const T cx = 10.0;
+  const auto x = make_fvar<T, m>(cx);
+  for (auto i : boost::irange(m + 1)) {
+    if (i == 0u) {
+      BOOST_CHECK_EQUAL(x.derivative(i), cx);
+    } else if (i == 1) {
+      BOOST_CHECK_EQUAL(x.derivative(i), 1);
+    } else {
+      BOOST_CHECK_EQUAL(x.derivative(i), 0);
+    }
+  }
+  const autodiff_fvar<T, n> xn = x;
+  for (auto i : boost::irange(n + 1)) {
+    if (i == 0) {
+      BOOST_CHECK_EQUAL(xn.derivative(i), cx);
+    } else if (i == 1) {
+      BOOST_CHECK_EQUAL(xn.derivative(i), 1);
+    } else {
+      BOOST_CHECK_EQUAL(xn.derivative(i), 0);
+    }
+  }
+  // Second independent variable
+  const T cy = 100.0;
+  const auto y = make_fvar<T, m, n>(cy);
+  for (auto i : boost::irange(m + 1)) {
+    for (auto j : boost::irange(n + 1)) {
+      if (i == 0 && j == 0) {
+        BOOST_CHECK_EQUAL(y.derivative(i, j), cy);
+      } else if (i == 0 && j == 1) {
+        BOOST_CHECK_EQUAL(y.derivative(i, j), 1.0);
+      } else {
+        BOOST_CHECK_EQUAL(y.derivative(i, j), 0.0);
+      }
+    }
+  }
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(implicit_constructors, T, all_float_types) {
+  constexpr std::size_t m = 3;
+  const autodiff_fvar<T, m> x = 3;
+  const autodiff_fvar<T, m> one = uncast_return(x);
+  const autodiff_fvar<T, m> two_and_a_half = 2.5;
+  BOOST_CHECK_EQUAL(static_cast<T>(x), 3.0);
+  BOOST_CHECK_EQUAL(static_cast<T>(one), 1.0);
+  BOOST_CHECK_EQUAL(static_cast<T>(two_and_a_half), 2.5);
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(assignment, T, all_float_types) {
+  constexpr std::size_t m = 3;
+  constexpr std::size_t n = 4;
+  const T cx = 10.0;
+  const T cy = 10.0;
+  autodiff_fvar<T, m, n>
+      empty; // Uninitialized variable<> may have non-zero values.
+  // Single variable
+  auto x = make_fvar<T, m>(cx);
+  empty = static_cast<decltype(empty)>(
+      x); // Test static_cast of single-variable to double-variable type.
+  for (auto i : boost::irange(m + 1)) {
+    for (auto j : boost::irange(n + 1)) {
+      if (i == 0 && j == 0) {
+        BOOST_CHECK_EQUAL(empty.derivative(i, j), cx);
+      } else if (i == 1 && j == 0) {
+        BOOST_CHECK_EQUAL(empty.derivative(i, j), 1.0);
+      } else {
+        BOOST_CHECK_EQUAL(empty.derivative(i, j), 0.0);
+      }
+    }
+  }
+  auto y = make_fvar<T, m, n>(cy);
+  empty = y; // default assignment operator
+  for (auto i : boost::irange(m + 1)) {
+    for (auto j : boost::irange(n + 1)) {
+      if (i == 0 && j == 0) {
+        BOOST_CHECK_EQUAL(empty.derivative(i, j), cy);
+      } else if (i == 0 && j == 1) {
+        BOOST_CHECK_EQUAL(empty.derivative(i, j), 1.0);
+      } else {
+        BOOST_CHECK_EQUAL(empty.derivative(i, j), 0.0);
+      }
+    }
+  }
+  empty = cx; // set a constant
+  for (auto i : boost::irange(m + 1)) {
+    for (auto j : boost::irange(n + 1)) {
+      if (i == 0 && j == 0) {
+        BOOST_CHECK_EQUAL(empty.derivative(i, j), cx);
+      } else {
+        BOOST_CHECK_EQUAL(empty.derivative(i, j), 0.0);
+      }
+    }
+  }
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(ostream, T, all_float_types) {
+  constexpr std::size_t m = 3;
+  const T cx = 10;
+  const auto x = make_fvar<T, m>(cx);
+  std::ostringstream ss;
+  ss << "x = " << x;
+  BOOST_CHECK_EQUAL(ss.str(), "x = depth(1)(10,1,0,0)");
+  ss.str(std::string());
+  const auto scalar = make_fvar<T,0>(cx);
+  ss << "scalar = " << scalar;
+  BOOST_CHECK_EQUAL(ss.str(), "scalar = depth(1)(10)");
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(addition_assignment, T, all_float_types) {
+  constexpr std::size_t m = 3;
+  constexpr std::size_t n = 4;
+  const T cx = 10.0;
+  auto sum = autodiff_fvar<T, m, n>(); // zero-initialized
+  // Single variable
+  const auto x = make_fvar<T, m>(cx);
+  sum += x;
+  for (auto i : boost::irange(m + 1)) {
+    for (auto j : boost::irange(n + 1)) {
+      if (i == 0 && j == 0) {
+        BOOST_CHECK_EQUAL(sum.derivative(i, j), cx);
+      } else if (i == 1 && j == 0) {
+        BOOST_CHECK_EQUAL(sum.derivative(i, j), 1.0);
+      } else {
+        BOOST_CHECK_EQUAL(sum.derivative(i, j), 0.0);
+      }
+    }
+  }
+  // Arithmetic constant
+  const T cy = 11.0;
+  sum = 0;
+  sum += cy;
+  for (auto i : boost::irange(m + 1)) {
+    for (auto j : boost::irange(n + 1)) {
+      if (i == 0 && j == 0) {
+        BOOST_CHECK_EQUAL(sum.derivative(i, j), cy);
+      } else {
+        BOOST_CHECK_EQUAL(sum.derivative(i, j), 0.0);
+      }
+    }
+  }
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(subtraction_assignment, T, all_float_types) {
+  constexpr std::size_t m = 3;
+  constexpr std::size_t n = 4;
+  const T cx = 10.0;
+  auto sum = autodiff_fvar<T, m, n>(); // zero-initialized
+  // Single variable
+  const auto x = make_fvar<T, m>(cx);
+  sum -= x;
+  for (auto i : boost::irange(m + 1)) {
+    for (auto j : boost::irange(n + 1)) {
+      if (i == 0 && j == 0) {
+        BOOST_CHECK_EQUAL(sum.derivative(i, j), -cx);
+      } else if (i == 1 && j == 0) {
+        BOOST_CHECK_EQUAL(sum.derivative(i, j), -1.0);
+      } else {
+        BOOST_CHECK_EQUAL(sum.derivative(i, j), 0.0);
+      }
+    }
+  }
+  // Arithmetic constant
+  const T cy = 11.0;
+  sum = 0;
+  sum -= cy;
+  for (auto i : boost::irange(m + 1)) {
+    for (auto j : boost::irange(n + 1)) {
+      if (i == 0 && j == 0) {
+        BOOST_CHECK_EQUAL(sum.derivative(i, j), -cy);
+      } else {
+        BOOST_CHECK_EQUAL(sum.derivative(i, j), 0.0);
+      }
+    }
+  }
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(multiplication_assignment, T, all_float_types) {
+  // Try explicit bracing based on feedback. Doesn't add very much except 26
+  // extra lines.
+  constexpr std::size_t m = 3;
+  constexpr std::size_t n = 4;
+  const T cx = 10.0;
+  auto product = autodiff_fvar<T, m, n>(1); // unit constant
+  // Single variable
+  auto x = make_fvar<T, m>(cx);
+  product *= x;
+  for (auto i : boost::irange(m + 1)) {
+    for (auto j : boost::irange(n + 1)) {
+      if (i == 0 && j == 0) {
+        BOOST_CHECK_EQUAL(product.derivative(i, j), cx);
+      } else if (i == 1 && j == 0) {
+        BOOST_CHECK_EQUAL(product.derivative(i, j), 1.0);
+      } else {
+        BOOST_CHECK_EQUAL(product.derivative(i, j), 0.0);
+      }
+    }
+  }
+  // Arithmetic constant
+  const T cy = 11.0;
+  product = 1;
+  product *= cy;
+  for (auto i : boost::irange(m + 1)) {
+    for (auto j : boost::irange(n + 1)) {
+      if (i == 0 && j == 0) {
+        BOOST_CHECK_EQUAL(product.derivative(i, j), cy);
+      } else {
+        BOOST_CHECK_EQUAL(product.derivative(i, j), 0.0);
+      }
+    }
+  }
+  // 0 * inf = nan
+  x = make_fvar<T, m>(0.0);
+  x *= std::numeric_limits<T>::infinity();
+  // std::cout << "x = " << x << std::endl;
+  for (auto i : boost::irange(m + 1)) {
+    if (i == 0) {
+      BOOST_CHECK(boost::math::isnan(static_cast<T>(x))); // Correct
+      // BOOST_CHECK_EQUAL(x.derivative(i) == 0.0); // Wrong. See
+      // multiply_assign_by_root_type().
+    } else if (i == 1) {
+      BOOST_CHECK(boost::math::isinf(x.derivative(i)));
+    } else {
+      BOOST_CHECK_EQUAL(x.derivative(i), 0.0);
+    }
+  }
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(division_assignment, T, all_float_types) {
+  constexpr std::size_t m = 3;
+  constexpr std::size_t n = 4;
+  const T cx = 16.0;
+  auto quotient = autodiff_fvar<T, m, n>(1); // unit constant
+  // Single variable
+  const auto x = make_fvar<T, m>(cx);
+  quotient /= x;
+  BOOST_CHECK_EQUAL(quotient.derivative(0, 0), 1 / cx);
+  BOOST_CHECK_EQUAL(quotient.derivative(1, 0), -1 / pow(cx, 2));
+  BOOST_CHECK_EQUAL(quotient.derivative(2, 0), 2 / pow(cx, 3));
+  BOOST_CHECK_EQUAL(quotient.derivative(3, 0), -6 / pow(cx, 4));
+  for (auto i : boost::irange(m + 1)) {
+    for (auto j : boost::irange(std::size_t(1), n + 1)) {
+      BOOST_CHECK_EQUAL(quotient.derivative(i, j), 0.0);
+    }
+  }
+  // Arithmetic constant
+  const T cy = 32.0;
+  quotient = 1;
+  quotient /= cy;
+  for (auto i : boost::irange(m + 1)) {
+    for (auto j : boost::irange(n + 1)) {
+      if (i == 0 && j == 0) {
+        BOOST_CHECK_EQUAL(quotient.derivative(i, j), 1 / cy);
+      } else {
+        BOOST_CHECK_EQUAL(quotient.derivative(i, j), 0.0);
+      }
+    }
+  }
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(unary_signs, T, all_float_types) {
+  constexpr std::size_t m = 3;
+  constexpr std::size_t n = 4;
+  const T cx = 16.0;
+  autodiff_fvar<T, m, n> lhs;
+  // Single variable
+  const auto x = make_fvar<T, m>(cx);
+  lhs = static_cast<decltype(lhs)>(-x);
+  for (auto i : boost::irange(m + 1)) {
+    for (auto j : boost::irange(n + 1)) {
+      if (i == 0 && j == 0) {
+        BOOST_CHECK_EQUAL(lhs.derivative(i, j), -cx);
+      } else if (i == 1 && j == 0) {
+        BOOST_CHECK_EQUAL(lhs.derivative(i, j), -1.0);
+      } else {
+        BOOST_CHECK_EQUAL(lhs.derivative(i, j), 0.0);
+      }
+    }
+  }
+  lhs = static_cast<decltype(lhs)>(+x);
+  for (auto i : boost::irange(m + 1)) {
+    for (auto j : boost::irange(n + 1)) {
+      if (i == 0 && j == 0) {
+        BOOST_CHECK_EQUAL(lhs.derivative(i, j), cx);
+      } else if (i == 1 && j == 0) {
+        BOOST_CHECK_EQUAL(lhs.derivative(i, j), 1.0);
+      } else {
+        BOOST_CHECK_EQUAL(lhs.derivative(i, j), 0.0);
+      }
+    }
+  }
+}
+
+// TODO 3 tests for 3 operator+() definitions.
+BOOST_AUTO_TEST_CASE_TEMPLATE(cast_double, T, all_float_types) {
+  const T ca(13);
+  const T i(12);
+  constexpr std::size_t m = 3;
+  const auto x = make_fvar<T, m>(ca);
+  BOOST_CHECK_LT(i, x);
+  BOOST_CHECK_EQUAL(i * x, i * ca);
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(int_double_casting, T, all_float_types) {
+  const T ca = 3.0;
+  const auto x0 = make_fvar<T, 0>(ca);
+  BOOST_CHECK_EQUAL(static_cast<T>(x0), ca);
+  const auto x1 = make_fvar<T, 1>(ca);
+  BOOST_CHECK_EQUAL(static_cast<T>(x1), ca);
+  const auto x2 = make_fvar<T, 2>(ca);
+  BOOST_CHECK_EQUAL(static_cast<T>(x2), ca);
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(scalar_addition, T, all_float_types) {
+  const T ca = 3.0;
+  const T cb = 4.0;
+  const auto sum0 = autodiff_fvar<T, 0>(ca) + autodiff_fvar<T, 0>(cb);
+  BOOST_CHECK_EQUAL(ca + cb, static_cast<T>(sum0));
+  const auto sum1 = autodiff_fvar<T, 0>(ca) + cb;
+  BOOST_CHECK_EQUAL(ca + cb, static_cast<T>(sum1));
+  const auto sum2 = ca + autodiff_fvar<T, 0>(cb);
+  BOOST_CHECK_EQUAL(ca + cb, static_cast<T>(sum2));
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(power8, T, all_float_types) {
+  constexpr std::size_t n = 8u;
+  const T ca = 3.0;
+  auto x = make_fvar<T, n>(ca);
+  // Test operator*=()
+  x *= x;
+  x *= x;
+  x *= x;
+  const T power_factorial = boost::math::factorial<T>(n);
+  for (auto i : boost::irange(n + 1)) {
+    BOOST_CHECK_CLOSE(
+        static_cast<T>(x.derivative(i)),
+        static_cast<T>(power_factorial /
+                       boost::math::factorial<T>(static_cast<unsigned>(n - i)) *
+                       pow(ca, n - i)),
+        std::numeric_limits<T>::epsilon());
+  }
+  x = make_fvar<T, n>(ca);
+  // Test operator*()
+  x = x * x * x * x * x * x * x * x;
+  for (auto i : boost::irange(n + 1)) {
+    BOOST_CHECK_CLOSE(
+        x.derivative(i),
+        power_factorial /
+            boost::math::factorial<T>(static_cast<unsigned>(n - i)) *
+            pow(ca, n - i),
+        std::numeric_limits<T>::epsilon());
+  }
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(dim1_multiplication, T, all_float_types) {
+  constexpr std::size_t m = 2;
+  constexpr std::size_t n = 3;
+  const T cy = 4.0;
+  auto y0 = make_fvar<T, m>(cy);
+  auto y = make_fvar<T, n>(cy);
+  y *= y0;
+  BOOST_CHECK_EQUAL(y.derivative(0), cy * cy);
+  BOOST_CHECK_EQUAL(y.derivative(1), 2 * cy);
+  BOOST_CHECK_EQUAL(y.derivative(2), 2.0);
+  BOOST_CHECK_EQUAL(y.derivative(3), 0.0);
+  y = y * cy;
+  BOOST_CHECK_EQUAL(y.derivative(0), cy * cy * cy);
+  BOOST_CHECK_EQUAL(y.derivative(1), 2 * cy * cy);
+  BOOST_CHECK_EQUAL(y.derivative(2), 2.0 * cy);
+  BOOST_CHECK_EQUAL(y.derivative(3), 0.0);
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(dim1and2_multiplication, T, all_float_types) {
+  constexpr std::size_t m = 2;
+  constexpr std::size_t n = 3;
+  const T cx = 3.0;
+  const T cy = 4.0;
+  auto x = make_fvar<T, m>(cx);
+  auto y = make_fvar<T, m, n>(cy);
+  y *= x;
+  BOOST_CHECK_EQUAL(y.derivative(0, 0), cx * cy);
+  BOOST_CHECK_EQUAL(y.derivative(0, 1), cx);
+  BOOST_CHECK_EQUAL(y.derivative(1, 0), cy);
+  BOOST_CHECK_EQUAL(y.derivative(1, 1), 1.0);
+  for (auto i : boost::irange(std::size_t(1), m)) {
+    for (auto j : boost::irange(std::size_t(1), n)) {
+      if (i == 1 && j == 1) {
+        BOOST_CHECK_EQUAL(y.derivative(i, j), 1.0);
+      } else {
+        BOOST_CHECK_EQUAL(y.derivative(i, j), 0.0);
+      }
+    }
+  }
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(dim2_addition, T, all_float_types) {
+  constexpr std::size_t m = 2;
+  constexpr std::size_t n = 3;
+  const T cx = 3.0;
+  const auto x = make_fvar<T, m>(cx);
+  BOOST_CHECK_EQUAL(x.derivative(0), cx);
+  BOOST_CHECK_EQUAL(x.derivative(1), 1.0);
+  BOOST_CHECK_EQUAL(x.derivative(2), 0.0);
+  const T cy = 4.0;
+  const auto y = make_fvar<T, m, n>(cy);
+  BOOST_CHECK_EQUAL(static_cast<T>(y.derivative(0)), cy);
+  BOOST_CHECK_EQUAL(static_cast<T>(y.derivative(1)),
+                    0.0); // partial of y w.r.t. x.
+
+  BOOST_CHECK_EQUAL(y.derivative(0, 0), cy);
+  BOOST_CHECK_EQUAL(y.derivative(0, 1), 1.0);
+  BOOST_CHECK_EQUAL(y.derivative(1, 0), 0.0);
+  BOOST_CHECK_EQUAL(y.derivative(1, 1), 0.0);
+  const auto z = x + y;
+  BOOST_CHECK_EQUAL(z.derivative(0, 0), cx + cy);
+  BOOST_CHECK_EQUAL(z.derivative(0, 1), 1.0);
+  BOOST_CHECK_EQUAL(z.derivative(1, 0), 1.0);
+  BOOST_CHECK_EQUAL(z.derivative(1, 1), 0.0);
+  // The following 4 are unnecessarily more expensive than the previous 4.
+  BOOST_CHECK_EQUAL(z.derivative(0).derivative(0), cx + cy);
+  BOOST_CHECK_EQUAL(z.derivative(0).derivative(1), 1.0);
+  BOOST_CHECK_EQUAL(z.derivative(1).derivative(0), 1.0);
+  BOOST_CHECK_EQUAL(z.derivative(1).derivative(1), 0.0);
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(dim2_multiplication, T, all_float_types) {
+  constexpr std::size_t m = 3;
+  constexpr std::size_t n = 4;
+  const T cx = 6.0;
+  const auto x = make_fvar<T, m>(cx);
+  const T cy = 5.0;
+  const auto y = make_fvar<T, 0, n>(cy);
+  const auto z = x * x * y * y * y;
+  BOOST_CHECK_EQUAL(z.derivative(0, 0), cx * cx * cy * cy * cy); // x^2 * y^3
+  BOOST_CHECK_EQUAL(z.derivative(0, 1), cx * cx * 3 * cy * cy);  // x^2 * 3y^2
+  BOOST_CHECK_EQUAL(z.derivative(0, 2), cx * cx * 6 * cy);       // x^2 * 6y
+  BOOST_CHECK_EQUAL(z.derivative(0, 3), cx * cx * 6);            // x^2 * 6
+  BOOST_CHECK_EQUAL(z.derivative(0, 4), 0.0);                    // x^2 * 0
+  BOOST_CHECK_EQUAL(z.derivative(1, 0), 2 * cx * cy * cy * cy);  // 2x * y^3
+  BOOST_CHECK_EQUAL(z.derivative(1, 1), 2 * cx * 3 * cy * cy);   // 2x * 3y^2
+  BOOST_CHECK_EQUAL(z.derivative(1, 2), 2 * cx * 6 * cy);        // 2x * 6y
+  BOOST_CHECK_EQUAL(z.derivative(1, 3), 2 * cx * 6);             // 2x * 6
+  BOOST_CHECK_EQUAL(z.derivative(1, 4), 0.0);                    // 2x * 0
+  BOOST_CHECK_EQUAL(z.derivative(2, 0), 2 * cy * cy * cy);       // 2 * y^3
+  BOOST_CHECK_EQUAL(z.derivative(2, 1), 2 * 3 * cy * cy);        // 2 * 3y^2
+  BOOST_CHECK_EQUAL(z.derivative(2, 2), 2 * 6 * cy);             // 2 * 6y
+  BOOST_CHECK_EQUAL(z.derivative(2, 3), 2 * 6);                  // 2 * 6
+  BOOST_CHECK_EQUAL(z.derivative(2, 4), 0.0);                    // 2 * 0
+  BOOST_CHECK_EQUAL(z.derivative(3, 0), 0.0);                    // 0 * y^3
+  BOOST_CHECK_EQUAL(z.derivative(3, 1), 0.0);                    // 0 * 3y^2
+  BOOST_CHECK_EQUAL(z.derivative(3, 2), 0.0);                    // 0 * 6y
+  BOOST_CHECK_EQUAL(z.derivative(3, 3), 0.0);                    // 0 * 6
+  BOOST_CHECK_EQUAL(z.derivative(3, 4), 0.0);                    // 0 * 0
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(dim2_multiplication_and_subtraction, T,
+                              all_float_types) {
+  constexpr std::size_t m = 3;
+  constexpr std::size_t n = 4;
+  const T cx = 6.0;
+  const auto x = make_fvar<T, m>(cx);
+  const T cy = 5.0;
+  const auto y = make_fvar<T, 0, n>(cy);
+  const auto z = x * x - y * y;
+  BOOST_CHECK_EQUAL(z.derivative(0, 0), cx * cx - cy * cy);
+  BOOST_CHECK_EQUAL(z.derivative(0, 1), -2 * cy);
+  BOOST_CHECK_EQUAL(z.derivative(0, 2), -2.0);
+  BOOST_CHECK_EQUAL(z.derivative(0, 3), 0.0);
+  BOOST_CHECK_EQUAL(z.derivative(0, 4), 0.0);
+  BOOST_CHECK_EQUAL(z.derivative(1, 0), 2 * cx);
+  BOOST_CHECK_EQUAL(z.derivative(2, 0), 2.0);
+  for (auto i : boost::irange(std::size_t(1), m + 1)) {
+    for (auto j : boost::irange(std::size_t(1), n + 1)) {
+      BOOST_CHECK_EQUAL(z.derivative(i, j), 0.0);
+    }
+  }
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(inverse, T, all_float_types) {
+  constexpr std::size_t m = 3;
+  const T cx = 4.0;
+  const auto x = make_fvar<T, m>(cx);
+  const auto xinv = x.inverse();
+  BOOST_CHECK_EQUAL(xinv.derivative(0), 1 / cx);
+  BOOST_CHECK_EQUAL(xinv.derivative(1), -1 / pow(cx, 2));
+  BOOST_CHECK_EQUAL(xinv.derivative(2), 2 / pow(cx, 3));
+  BOOST_CHECK_EQUAL(xinv.derivative(3), -6 / pow(cx, 4));
+  const auto zero = make_fvar<T, m>(0);
+  const auto inf = zero.inverse();
+  for (auto i : boost::irange(m + 1)) {
+    BOOST_CHECK_EQUAL(inf.derivative(i),
+                      (i % 2 == 1 ? -1 : 1) *
+                          std::numeric_limits<T>::infinity());
+  }
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(division, T, all_float_types) {
+  constexpr std::size_t m = 3;
+  constexpr std::size_t n = 4;
+  const T cx = 16.0;
+  auto x = make_fvar<T, m>(cx);
+  const T cy = 4.0;
+  auto y = make_fvar<T, 1, n>(cy);
+  auto z = x * x / (y * y);
+  BOOST_CHECK_EQUAL(z.derivative(0, 0), cx * cx / (cy * cy)); // x^2 * y^-2
+  BOOST_CHECK_EQUAL(z.derivative(0, 1), cx * cx * (-2) * pow(cy, -3));
+  BOOST_CHECK_EQUAL(z.derivative(0, 2), cx * cx * (6) * pow(cy, -4));
+  BOOST_CHECK_EQUAL(z.derivative(0, 3), cx * cx * (-24) * pow(cy, -5));
+  BOOST_CHECK_EQUAL(z.derivative(0, 4), cx * cx * (120) * pow(cy, -6));
+  BOOST_CHECK_EQUAL(z.derivative(1, 0), 2 * cx / (cy * cy));
+  BOOST_CHECK_EQUAL(z.derivative(1, 1), 2 * cx * (-2) * pow(cy, -3));
+  BOOST_CHECK_EQUAL(z.derivative(1, 2), 2 * cx * (6) * pow(cy, -4));
+  BOOST_CHECK_EQUAL(z.derivative(1, 3), 2 * cx * (-24) * pow(cy, -5));
+  BOOST_CHECK_EQUAL(z.derivative(1, 4), 2 * cx * (120) * pow(cy, -6));
+  BOOST_CHECK_EQUAL(z.derivative(2, 0), 2 / (cy * cy));
+  BOOST_CHECK_EQUAL(z.derivative(2, 1), 2 * (-2) * pow(cy, -3));
+  BOOST_CHECK_EQUAL(z.derivative(2, 2), 2 * (6) * pow(cy, -4));
+  BOOST_CHECK_EQUAL(z.derivative(2, 3), 2 * (-24) * pow(cy, -5));
+  BOOST_CHECK_EQUAL(z.derivative(2, 4), 2 * (120) * pow(cy, -6));
+  for (auto j : boost::irange(n + 1)) {
+    BOOST_CHECK_EQUAL(z.derivative(3, j), 0.0);
+  }
+
+  auto x1 = make_fvar<T, m>(cx);
+  auto z1 = x1 / cy;
+  BOOST_CHECK_EQUAL(z1.derivative(0), cx / cy);
+  BOOST_CHECK_EQUAL(z1.derivative(1), 1 / cy);
+  BOOST_CHECK_EQUAL(z1.derivative(2), 0.0);
+  BOOST_CHECK_EQUAL(z1.derivative(3), 0.0);
+  auto y2 = make_fvar<T, m, n>(cy);
+  auto z2 = cx / y2;
+  BOOST_CHECK_EQUAL(z2.derivative(0, 0), cx / cy);
+  BOOST_CHECK_EQUAL(z2.derivative(0, 1), -cx / pow(cy, 2));
+  BOOST_CHECK_EQUAL(z2.derivative(0, 2), 2 * cx / pow(cy, 3));
+  BOOST_CHECK_EQUAL(z2.derivative(0, 3), -6 * cx / pow(cy, 4));
+  BOOST_CHECK_EQUAL(z2.derivative(0, 4), 24 * cx / pow(cy, 5));
+  for (auto i : boost::irange(std::size_t(1), m + 1)) {
+    for (auto j : boost::irange(n + 1)) {
+      BOOST_CHECK_EQUAL(z2.derivative(i, j), 0.0);
+    }
+  }
+
+  const auto z3 = y / x;
+  BOOST_CHECK_EQUAL(z3.derivative(0, 0), cy / cx);
+  BOOST_CHECK_EQUAL(z3.derivative(0, 1), 1 / cx);
+  BOOST_CHECK_EQUAL(z3.derivative(1, 0), -cy / pow(cx, 2));
+  BOOST_CHECK_EQUAL(z3.derivative(1, 1), -1 / pow(cx, 2));
+  BOOST_CHECK_EQUAL(z3.derivative(2, 0), 2 * cy / pow(cx, 3));
+  BOOST_CHECK_EQUAL(z3.derivative(2, 1), 2 / pow(cx, 3));
+  BOOST_CHECK_EQUAL(z3.derivative(3, 0), -6 * cy / pow(cx, 4));
+  BOOST_CHECK_EQUAL(z3.derivative(3, 1), -6 / pow(cx, 4));
+  for (auto i : boost::irange(m + 1)) {
+    for (auto j : boost::irange(std::size_t(2), n + 1)) {
+      BOOST_CHECK_EQUAL(z3.derivative(i, j), 0.0);
+    }
+  }
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(equality, T, all_float_types) {
+  constexpr std::size_t m = 3;
+  constexpr std::size_t n = 4;
+  const T cx = 10.0;
+  const T cy = 10.0;
+  const auto x = make_fvar<T, m>(cx);
+  const auto y = make_fvar<T, 0, n>(cy);
+  BOOST_CHECK_EQUAL(x, y);
+  BOOST_CHECK_EQUAL(x, cy);
+  BOOST_CHECK_EQUAL(cx, y);
+  BOOST_CHECK_EQUAL(cy, x);
+  BOOST_CHECK_EQUAL(y, cx);
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(inequality, T, all_float_types) {
+  constexpr std::size_t m = 3;
+  constexpr std::size_t n = 4;
+  const T cx = 10.0;
+  const T cy = 11.0;
+  const auto x = make_fvar<T, m>(cx);
+  const auto y = make_fvar<T, 0, n>(cy);
+  BOOST_CHECK_NE(x, y);
+  BOOST_CHECK_NE(x, cy);
+  BOOST_CHECK_NE(cx, y);
+  BOOST_CHECK_NE(cy, x);
+  BOOST_CHECK_NE(y, cx);
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(less_than_or_equal_to, T, all_float_types) {
+  constexpr std::size_t m = 3;
+  constexpr std::size_t n = 4;
+  const T cx = 10.0;
+  const T cy = 11.0;
+  const auto x = make_fvar<T, m>(cx);
+  const auto y = make_fvar<T, 0, n>(cy);
+  BOOST_CHECK_LE(x, y);
+  BOOST_CHECK_LE(x, y - 1);
+  BOOST_CHECK_LT(x, y);
+  BOOST_CHECK_LE(x, cy);
+  BOOST_CHECK_LE(x, cy - 1);
+  BOOST_CHECK_LT(x, cy);
+  BOOST_CHECK_LE(cx, y);
+  BOOST_CHECK_LE(cx, y - 1);
+  BOOST_CHECK_LT(cx, y);
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(greater_than_or_equal_to, T, all_float_types) {
+  constexpr std::size_t m = 3;
+  constexpr std::size_t n = 4;
+  const T cx = 11.0;
+  const T cy = 10.0;
+  const auto x = make_fvar<T, m>(cx);
+  const auto y = make_fvar<T, 0, n>(cy);
+  BOOST_CHECK_GE(x, y);
+  BOOST_CHECK_GE(x, y + 1);
+  BOOST_CHECK_GT(x, y);
+  BOOST_CHECK_GE(x, cy);
+  BOOST_CHECK_GE(x, cy + 1);
+  BOOST_CHECK_GT(x, cy);
+  BOOST_CHECK_GE(cx, y);
+  BOOST_CHECK_GE(cx, y + 1);
+  BOOST_CHECK_GT(cx, y);
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(fabs_test, T, all_float_types) {
+  using bmp::fabs;
+  using detail::fabs;
+  using std::fabs;
+  constexpr std::size_t m = 3;
+  const T cx = 11.0;
+  const auto x = make_fvar<T, m>(cx);
+  auto a = fabs(x);
+  BOOST_CHECK_EQUAL(a.derivative(0), fabs(cx));
+  BOOST_CHECK_EQUAL(a.derivative(1), 1.0);
+  BOOST_CHECK_EQUAL(a.derivative(2), 0.0);
+  BOOST_CHECK_EQUAL(a.derivative(3), 0.0);
+  a = fabs(-x);
+  BOOST_CHECK_EQUAL(a.derivative(0), fabs(cx));
+  BOOST_CHECK_EQUAL(a.derivative(1), 1.0); // fabs(-x) = fabs(x)
+  BOOST_CHECK_EQUAL(a.derivative(2), 0.0);
+  BOOST_CHECK_EQUAL(a.derivative(3), 0.0);
+  const auto xneg = make_fvar<T, m>(-cx);
+  a = fabs(xneg);
+  BOOST_CHECK_EQUAL(a.derivative(0), fabs(cx));
+  BOOST_CHECK_EQUAL(a.derivative(1), -1.0);
+  BOOST_CHECK_EQUAL(a.derivative(2), 0.0);
+  BOOST_CHECK_EQUAL(a.derivative(3), 0.0);
+  const auto zero = make_fvar<T, m>(0);
+  a = fabs(zero);
+  for (auto i : boost::irange(m + 1)) {
+    BOOST_CHECK_EQUAL(a.derivative(i), 0.0);
+  }
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(ceil_and_floor, T, all_float_types) {
+  using bmp::ceil;
+  using bmp::floor;
+  using std::ceil;
+  using std::floor;
+  constexpr std::size_t m = 3;
+  T tests[]{-1.5, 0.0, 1.5};
+  for (T &test : tests) {
+    const auto x = make_fvar<T, m>(test);
+    auto c = ceil(x);
+    auto f = floor(x);
+    BOOST_CHECK_EQUAL(c.derivative(0), ceil(test));
+    BOOST_CHECK_EQUAL(f.derivative(0), floor(test));
+    for (auto i : boost::irange(std::size_t(1), m + 1)) {
+      BOOST_CHECK_EQUAL(c.derivative(i), 0.0);
+      BOOST_CHECK_EQUAL(f.derivative(i), 0.0);
+    }
+  }
+}
+
+BOOST_AUTO_TEST_SUITE_END()
diff --git a/libs/math/test/test_autodiff_2.cpp b/libs/math/test/test_autodiff_2.cpp
new file mode 100644
index 0000000000..378a9bb16d
--- /dev/null
+++ b/libs/math/test/test_autodiff_2.cpp
@@ -0,0 +1,512 @@
+//           Copyright Matthew Pulver 2018 - 2019.
+// Distributed under the Boost Software License, Version 1.0.
+//      (See accompanying file LICENSE_1_0.txt or copy at
+//           https://www.boost.org/LICENSE_1_0.txt)
+
+#include "test_autodiff.hpp"
+
+BOOST_AUTO_TEST_SUITE(test_autodiff_2)
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(one_over_one_plus_x_squared, T, all_float_types) {
+  constexpr std::size_t m = 4;
+  const T cx(1);
+  auto f = make_fvar<T, m>(cx);
+  // f = 1 / ((f *= f) += 1);
+  f *= f;
+  f += T(1);
+  f = f.inverse();
+  BOOST_CHECK_EQUAL(f.derivative(0u), 0.5);
+  BOOST_CHECK_EQUAL(f.derivative(1u), -0.5);
+  BOOST_CHECK_EQUAL(f.derivative(2u), 0.5);
+  BOOST_CHECK_EQUAL(f.derivative(3u), 0);
+  BOOST_CHECK_EQUAL(f.derivative(4u), -3);
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(exp_test, T, all_float_types) {
+  using std::exp;
+  constexpr std::size_t m = 4;
+  const T cx = 2.0;
+  const auto x = make_fvar<T, m>(cx);
+  auto y = exp(x);
+  for (auto i : boost::irange(m + 1)) {
+    // std::cout.precision(100);
+    // std::cout << "y.derivative("<<i<<") = " << y.derivative(i) << ",
+    // std::exp(cx) = " << std::exp(cx) << std::endl;
+    BOOST_CHECK_CLOSE_FRACTION(y.derivative(i), exp(cx),
+                               std::numeric_limits<T>::epsilon());
+  }
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(pow, T, bin_float_types) {
+  const T eps = 201 * std::numeric_limits<T>::epsilon(); // percent
+  using std::log;
+  using std::pow;
+  constexpr std::size_t m = 5;
+  constexpr std::size_t n = 4;
+  const T cx = 2.0;
+  const T cy = 3.0;
+  const auto x = make_fvar<T, m>(cx);
+  const auto y = make_fvar<T, m, n>(cy);
+  auto z0 = pow(x, cy);
+  BOOST_CHECK_EQUAL(z0.derivative(0u), pow(cx, cy));
+  BOOST_CHECK_EQUAL(z0.derivative(1u), cy * pow(cx, cy - 1));
+  BOOST_CHECK_EQUAL(z0.derivative(2u), cy * (cy - 1) * pow(cx, cy - 2));
+  BOOST_CHECK_EQUAL(z0.derivative(3u),
+                    cy * (cy - 1) * (cy - 2) * pow(cx, cy - 3));
+  BOOST_CHECK_EQUAL(z0.derivative(4u), 0u);
+  BOOST_CHECK_EQUAL(z0.derivative(5u), 0u);
+  auto z1 = pow(cx, y);
+  BOOST_CHECK_CLOSE(z1.derivative(0u, 0u), pow(cx, cy), eps);
+  for (auto j : boost::irange(std::size_t(1), n + 1)) {
+    BOOST_CHECK_CLOSE(z1.derivative(0u, j), pow(log(cx), j) * pow(cx, cy), eps);
+  }
+
+  for (auto i : boost::irange(std::size_t(1), m + 1)) {
+    for (auto j : boost::irange(n + 1)) {
+      BOOST_CHECK_EQUAL(z1.derivative(i, j), 0);
+    }
+  }
+
+  const auto z2 = pow(x, y);
+
+  for (auto j : boost::irange(n + 1)) {
+    BOOST_CHECK_CLOSE(z2.derivative(0u, j), pow(cx, cy) * pow(log(cx), j), eps);
+  }
+  for (auto j : boost::irange(n + 1)) {
+    BOOST_CHECK_CLOSE(z2.derivative(1u, j),
+                      pow(cx, cy - 1) * pow(log(cx), static_cast<int>(j) - 1) *
+                          (cy * log(cx) + j),
+                      eps);
+  }
+  BOOST_CHECK_CLOSE(z2.derivative(2u, 0u), pow(cx, cy - 2) * cy * (cy - 1),
+                    eps);
+  BOOST_CHECK_CLOSE(z2.derivative(2u, 1u),
+                    pow(cx, cy - 2) * (cy * (cy - 1) * log(cx) + 2 * cy - 1),
+                    eps);
+  for (auto j : boost::irange(std::size_t(2u), n + 1)) {
+    BOOST_CHECK_CLOSE(z2.derivative(2u, j),
+                      pow(cx, cy - 2) * pow(log(cx), j - 2) *
+                          (j * (2 * cy - 1) * log(cx) + (j - 1) * j +
+                           (cy - 1) * cy * pow(log(cx), 2)),
+                      eps);
+  }
+  BOOST_CHECK_CLOSE(z2.derivative(2u, 4u),
+                    pow(cx, cy - 2) * pow(log(cx), 2) *
+                        (4 * (2 * cy - 1) * log(cx) + (4 - 1) * 4 +
+                         (cy - 1) * cy * pow(log(cx), 2)),
+                    eps);
+}
+
+// TODO Tests around x=0 or y=0: pow(x,y)
+BOOST_AUTO_TEST_CASE_TEMPLATE(pow2, T, bin_float_types) {
+  const T eps = 4000 * std::numeric_limits<T>::epsilon(); // percent
+  using std::pow;
+  constexpr std::size_t m = 5;
+  constexpr std::size_t n = 5;
+  const T cx = 2;
+  const T cy = 5 / 2.0;
+  const auto x = make_fvar<T, m>(cx);
+  const auto y = make_fvar<T, 0, n>(cy);
+  const auto z = pow(x, y);
+  using namespace boost::math::constants;
+  // Mathematica: Export["pow.csv", Flatten@Table[ Simplify@D[x^y,{x,i},{y,j}]
+  // /. {x->2, y->5/2},
+  //                    { i, 0, 5 }, { j, 0, 5 } ] ]
+  // sed -rf pow.sed < pow.csv
+  // with pow.sed script:
+  // s/Log\[2\]\^([0-9]+)/pow(ln_two<T>(),\1)/g
+  // s/Log\[2\]/ln_two<T>()/g
+  // s/Sqrt\[2\]/root_two<T>()/g
+  // s/[0-9]\/[0-9]+/\0.0/g
+  // s/^"/static_cast<T>(/
+  // s/"$/),/
+  const T mathematica[]{
+      static_cast<T>(4 * root_two<T>()),
+      static_cast<T>(4 * root_two<T>() * ln_two<T>()),
+      static_cast<T>(4 * root_two<T>() * pow(ln_two<T>(), 2)),
+      static_cast<T>(4 * root_two<T>() * pow(ln_two<T>(), 3)),
+      static_cast<T>(4 * root_two<T>() * pow(ln_two<T>(), 4)),
+      static_cast<T>(4 * root_two<T>() * pow(ln_two<T>(), 5)),
+      static_cast<T>(5 * root_two<T>()),
+      static_cast<T>(2 * root_two<T>() * (1 + (5 * ln_two<T>()) / 2)),
+      static_cast<T>(2 * root_two<T>() * ln_two<T>() *
+                     (2 + (5 * ln_two<T>()) / 2)),
+      static_cast<T>(2 * root_two<T>() * pow(ln_two<T>(), 2) *
+                     (3 + (5 * ln_two<T>()) / 2)),
+      static_cast<T>(2 * root_two<T>() * pow(ln_two<T>(), 3) *
+                     (4 + (5 * ln_two<T>()) / 2)),
+      static_cast<T>(2 * root_two<T>() * pow(ln_two<T>(), 4) *
+                     (5 + (5 * ln_two<T>()) / 2)),
+      static_cast<T>(15 / (2 * root_two<T>())),
+      static_cast<T>(root_two<T>() * (4 + (15 * ln_two<T>()) / 4)),
+      static_cast<T>(root_two<T>() *
+                     (2 + 8 * ln_two<T>() + (15 * pow(ln_two<T>(), 2)) / 4)),
+      static_cast<T>(root_two<T>() * ln_two<T>() *
+                     (6 + 12 * ln_two<T>() + (15 * pow(ln_two<T>(), 2)) / 4)),
+      static_cast<T>(root_two<T>() * pow(ln_two<T>(), 2) *
+                     (12 + 16 * ln_two<T>() + (15 * pow(ln_two<T>(), 2)) / 4)),
+      static_cast<T>(root_two<T>() * pow(ln_two<T>(), 3) *
+                     (20 + 20 * ln_two<T>() + (15 * pow(ln_two<T>(), 2)) / 4)),
+      static_cast<T>(15 / (8 * root_two<T>())),
+      static_cast<T>((23 / 4.0 + (15 * ln_two<T>()) / 8) / root_two<T>()),
+      static_cast<T>(
+          (9 + (23 * ln_two<T>()) / 2 + (15 * pow(ln_two<T>(), 2)) / 8) /
+          root_two<T>()),
+      static_cast<T>((6 + 27 * ln_two<T>() + (69 * pow(ln_two<T>(), 2)) / 4 +
+                      (15 * pow(ln_two<T>(), 3)) / 8) /
+                     root_two<T>()),
+      static_cast<T>(
+          (ln_two<T>() * (24 + 54 * ln_two<T>() + 23 * pow(ln_two<T>(), 2) +
+                          (15 * pow(ln_two<T>(), 3)) / 8)) /
+          root_two<T>()),
+      static_cast<T>((pow(ln_two<T>(), 2) *
+                      (60 + 90 * ln_two<T>() + (115 * pow(ln_two<T>(), 2)) / 4 +
+                       (15 * pow(ln_two<T>(), 3)) / 8)) /
+                     root_two<T>()),
+      static_cast<T>(-15 / (32 * root_two<T>())),
+      static_cast<T>((-1 - (15 * ln_two<T>()) / 16) / (2 * root_two<T>())),
+      static_cast<T>((7 - 2 * ln_two<T>() - (15 * pow(ln_two<T>(), 2)) / 16) /
+                     (2 * root_two<T>())),
+      static_cast<T>((24 + 21 * ln_two<T>() - 3 * pow(ln_two<T>(), 2) -
+                      (15 * pow(ln_two<T>(), 3)) / 16) /
+                     (2 * root_two<T>())),
+      static_cast<T>((24 + 96 * ln_two<T>() + 42 * pow(ln_two<T>(), 2) -
+                      4 * pow(ln_two<T>(), 3) -
+                      (15 * pow(ln_two<T>(), 4)) / 16) /
+                     (2 * root_two<T>())),
+      static_cast<T>(
+          (ln_two<T>() *
+           (120 + 240 * ln_two<T>() + 70 * pow(ln_two<T>(), 2) -
+            5 * pow(ln_two<T>(), 3) - (15 * pow(ln_two<T>(), 4)) / 16)) /
+          (2 * root_two<T>())),
+      static_cast<T>(45 / (128 * root_two<T>())),
+      static_cast<T>((9 / 16.0 + (45 * ln_two<T>()) / 32) /
+                     (4 * root_two<T>())),
+      static_cast<T>((-25 / 2.0 + (9 * ln_two<T>()) / 8 +
+                      (45 * pow(ln_two<T>(), 2)) / 32) /
+                     (4 * root_two<T>())),
+      static_cast<T>((-15 - (75 * ln_two<T>()) / 2 +
+                      (27 * pow(ln_two<T>(), 2)) / 16 +
+                      (45 * pow(ln_two<T>(), 3)) / 32) /
+                     (4 * root_two<T>())),
+      static_cast<T>((60 - 60 * ln_two<T>() - 75 * pow(ln_two<T>(), 2) +
+                      (9 * pow(ln_two<T>(), 3)) / 4 +
+                      (45 * pow(ln_two<T>(), 4)) / 32) /
+                     (4 * root_two<T>())),
+      static_cast<T>((120 + 300 * ln_two<T>() - 150 * pow(ln_two<T>(), 2) -
+                      125 * pow(ln_two<T>(), 3) +
+                      (45 * pow(ln_two<T>(), 4)) / 16 +
+                      (45 * pow(ln_two<T>(), 5)) / 32) /
+                     (4 * root_two<T>()))};
+  std::size_t k = 0;
+  for (auto i : boost::irange(m + 1)) {
+    for (auto j : boost::irange(n + 1)) {
+      BOOST_CHECK_CLOSE(z.derivative(i, j), mathematica[k++], eps);
+    }
+  }
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(sqrt_test, T, all_float_types) {
+  using std::pow;
+  using std::sqrt;
+  constexpr std::size_t m = 5;
+  const T cx = 4.0;
+  auto x = make_fvar<T, m>(cx);
+  auto y = sqrt(x);
+  BOOST_CHECK_CLOSE_FRACTION(y.derivative(0u), sqrt(cx),
+                             std::numeric_limits<T>::epsilon());
+  BOOST_CHECK_CLOSE_FRACTION(y.derivative(1u), 0.5 * pow(cx, -0.5),
+                             std::numeric_limits<T>::epsilon());
+  BOOST_CHECK_CLOSE_FRACTION(y.derivative(2u), -0.5 * 0.5 * pow(cx, -1.5),
+                             std::numeric_limits<T>::epsilon());
+  BOOST_CHECK_CLOSE_FRACTION(y.derivative(3u), 0.5 * 0.5 * 1.5 * pow(cx, -2.5),
+                             std::numeric_limits<T>::epsilon());
+  BOOST_CHECK_CLOSE_FRACTION(y.derivative(4u),
+                             -0.5 * 0.5 * 1.5 * 2.5 * pow(cx, -3.5),
+                             std::numeric_limits<T>::epsilon());
+  BOOST_CHECK_CLOSE_FRACTION(y.derivative(5u),
+                             0.5 * 0.5 * 1.5 * 2.5 * 3.5 * pow(cx, -4.5),
+                             std::numeric_limits<T>::epsilon());
+  x = make_fvar<T, m>(0);
+  y = sqrt(x);
+  // std::cout << "sqrt(0) = " << y << std::endl; // (0,inf,-inf,inf,-inf,inf)
+  BOOST_CHECK_EQUAL(y.derivative(0u), 0);
+  for (auto i : boost::irange(std::size_t(1), m + 1)) {
+    BOOST_CHECK_EQUAL(y.derivative(i), (i % 2 == 1 ? 1 : -1) *
+                                           std::numeric_limits<T>::infinity());
+  }
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(log_test, T, all_float_types) {
+  using std::log;
+  using std::pow;
+  constexpr std::size_t m = 5;
+  const T cx = 2.0;
+  auto x = make_fvar<T, m>(cx);
+  auto y = log(x);
+  BOOST_CHECK_CLOSE_FRACTION(y.derivative(0u), log(cx),
+                             std::numeric_limits<T>::epsilon());
+  BOOST_CHECK_CLOSE_FRACTION(y.derivative(1u), 1 / cx,
+                             std::numeric_limits<T>::epsilon());
+  BOOST_CHECK_CLOSE_FRACTION(y.derivative(2u), -1 / pow(cx, 2),
+                             std::numeric_limits<T>::epsilon());
+  BOOST_CHECK_CLOSE_FRACTION(y.derivative(3u), 2 / pow(cx, 3),
+                             std::numeric_limits<T>::epsilon());
+  BOOST_CHECK_CLOSE_FRACTION(y.derivative(4u), -6 / pow(cx, 4),
+                             std::numeric_limits<T>::epsilon());
+  BOOST_CHECK_CLOSE_FRACTION(y.derivative(5u), 24 / pow(cx, 5),
+                             std::numeric_limits<T>::epsilon());
+  x = make_fvar<T, m>(0);
+  y = log(x);
+  // std::cout << "log(0) = " << y << std::endl; // log(0) =
+  // depth(1)(-inf,inf,-inf,inf,-inf,inf)
+  for (auto i : boost::irange(m + 1)) {
+    BOOST_CHECK_EQUAL(y.derivative(i), (i % 2 == 1 ? 1 : -1) *
+                                           std::numeric_limits<T>::infinity());
+  }
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(ylogx, T, all_float_types) {
+  using std::log;
+  using std::pow;
+  const T eps = 100 * std::numeric_limits<T>::epsilon(); // percent
+  constexpr std::size_t m = 5;
+  constexpr std::size_t n = 4;
+  const T cx = 2.0;
+  const T cy = 3.0;
+  const auto x = make_fvar<T, m>(cx);
+  const auto y = make_fvar<T, m, n>(cy);
+  auto z = y * log(x);
+  BOOST_CHECK_EQUAL(z.derivative(0u, 0u), cy * log(cx));
+  BOOST_CHECK_EQUAL(z.derivative(0u, 1u), log(cx));
+  BOOST_CHECK_EQUAL(z.derivative(0u, 2u), 0);
+  BOOST_CHECK_EQUAL(z.derivative(0u, 3u), 0);
+  BOOST_CHECK_EQUAL(z.derivative(0u, 4u), 0);
+  for (auto i : boost::irange(1u, static_cast<unsigned>(m + 1))) {
+    BOOST_CHECK_CLOSE(z.derivative(i, 0u),
+                      pow(-1, i - 1) * boost::math::factorial<T>(i - 1) * cy /
+                          pow(cx, i),
+                      eps);
+    BOOST_CHECK_CLOSE(
+        z.derivative(i, 1u),
+        pow(-1, i - 1) * boost::math::factorial<T>(i - 1) / pow(cx, i), eps);
+    for (auto j : boost::irange(std::size_t(2), n + 1)) {
+      BOOST_CHECK_EQUAL(z.derivative(i, j), 0u);
+    }
+  }
+  auto z1 = exp(z);
+  // RHS is confirmed by
+  // https://www.wolframalpha.com/input/?i=D%5Bx%5Ey,%7Bx,2%7D,%7By,4%7D%5D+%2F.+%7Bx-%3E2.0,+y-%3E3.0%7D
+  BOOST_CHECK_CLOSE(z1.derivative(2u, 4u),
+                    pow(cx, cy - 2) * pow(log(cx), 2) *
+                        (4 * (2 * cy - 1) * log(cx) + (4 - 1) * 4 +
+                         (cy - 1) * cy * pow(log(cx), 2)),
+                    eps);
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(frexp_test, T, all_float_types) {
+  using std::exp2;
+  using std::frexp;
+  constexpr std::size_t m = 3;
+  const T cx = 3.5;
+  const auto x = make_fvar<T, m>(cx);
+  int exp, testexp;
+  auto y = frexp(x, &exp);
+  BOOST_CHECK_EQUAL(y.derivative(0u), frexp(cx, &testexp));
+  BOOST_CHECK_EQUAL(exp, testexp);
+  BOOST_CHECK_EQUAL(y.derivative(1u), exp2(-exp));
+  BOOST_CHECK_EQUAL(y.derivative(2u), 0);
+  BOOST_CHECK_EQUAL(y.derivative(3u), 0);
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(ldexp_test, T, all_float_types) {
+  BOOST_MATH_STD_USING
+  using boost::multiprecision::ldexp;
+  constexpr auto m = 3u;
+  const T cx = 3.5;
+  const auto x = make_fvar<T, m>(cx);
+  constexpr auto exponent = 3;
+  auto y = ldexp(x, exponent);
+  BOOST_CHECK_EQUAL(y.derivative(0u), ldexp(cx, exponent));
+  BOOST_CHECK_EQUAL(y.derivative(1u), exp2(exponent));
+  BOOST_CHECK_EQUAL(y.derivative(2u), 0);
+  BOOST_CHECK_EQUAL(y.derivative(3u), 0);
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(cos_and_sin, T, bin_float_types) {
+  using std::cos;
+  using std::sin;
+  const T eps = 200 * std::numeric_limits<T>::epsilon(); // percent
+  constexpr std::size_t m = 5;
+  const T cx = boost::math::constants::third_pi<T>();
+  const auto x = make_fvar<T, m>(cx);
+  auto cos5 = cos(x);
+  BOOST_CHECK_CLOSE(cos5.derivative(0u), cos(cx), eps);
+  BOOST_CHECK_CLOSE(cos5.derivative(1u), -sin(cx), eps);
+  BOOST_CHECK_CLOSE(cos5.derivative(2u), -cos(cx), eps);
+  BOOST_CHECK_CLOSE(cos5.derivative(3u), sin(cx), eps);
+  BOOST_CHECK_CLOSE(cos5.derivative(4u), cos(cx), eps);
+  BOOST_CHECK_CLOSE(cos5.derivative(5u), -sin(cx), eps);
+  auto sin5 = sin(x);
+  BOOST_CHECK_CLOSE(sin5.derivative(0u), sin(cx), eps);
+  BOOST_CHECK_CLOSE(sin5.derivative(1u), cos(cx), eps);
+  BOOST_CHECK_CLOSE(sin5.derivative(2u), -sin(cx), eps);
+  BOOST_CHECK_CLOSE(sin5.derivative(3u), -cos(cx), eps);
+  BOOST_CHECK_CLOSE(sin5.derivative(4u), sin(cx), eps);
+  BOOST_CHECK_CLOSE(sin5.derivative(5u), cos(cx), eps);
+  // Test Order = 0 for codecov
+  auto cos0 = cos(make_fvar<T, 0>(cx));
+  BOOST_CHECK_CLOSE(cos0.derivative(0u), cos(cx), eps);
+  auto sin0 = sin(make_fvar<T, 0>(cx));
+  BOOST_CHECK_CLOSE(sin0.derivative(0u), sin(cx), eps);
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(acos_test, T, bin_float_types) {
+  const T eps = 300 * std::numeric_limits<T>::epsilon(); // percent
+  using std::acos;
+  using std::pow;
+  using std::sqrt;
+  constexpr std::size_t m = 5;
+  const T cx = 0.5;
+  auto x = make_fvar<T, m>(cx);
+  auto y = acos(x);
+  BOOST_CHECK_CLOSE(y.derivative(0u), acos(cx), eps);
+  BOOST_CHECK_CLOSE(y.derivative(1u), -1 / sqrt(1 - cx * cx), eps);
+  BOOST_CHECK_CLOSE(y.derivative(2u), -cx / pow(1 - cx * cx, 1.5), eps);
+  BOOST_CHECK_CLOSE(y.derivative(3u),
+                    -(2 * cx * cx + 1) / pow(1 - cx * cx, 2.5), eps);
+  BOOST_CHECK_CLOSE(y.derivative(4u),
+                    -3 * cx * (2 * cx * cx + 3) / pow(1 - cx * cx, 3.5), eps);
+  BOOST_CHECK_CLOSE(y.derivative(5u),
+                    -(24 * (cx * cx + 3) * cx * cx + 9) / pow(1 - cx * cx, 4.5),
+                    eps);
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(acosh_test, T, bin_float_types) {
+  const T eps = 300 * std::numeric_limits<T>::epsilon(); // percent
+  using boost::math::acosh;
+  constexpr std::size_t m = 5;
+  const T cx = 2;
+  auto x = make_fvar<T, m>(cx);
+  auto y = acosh(x);
+  // BOOST_CHECK_EQUAL(y.derivative(0) == acosh(cx)); // FAILS! acosh(2) is
+  // overloaded for integral types
+  BOOST_CHECK_CLOSE(y.derivative(0u), acosh(static_cast<T>(x)), eps);
+  BOOST_CHECK_CLOSE(y.derivative(1u),
+                    1 / boost::math::constants::root_three<T>(), eps);
+  BOOST_CHECK_CLOSE(y.derivative(2u),
+                    -2 / (3 * boost::math::constants::root_three<T>()), eps);
+  BOOST_CHECK_CLOSE(y.derivative(3u),
+                    1 / boost::math::constants::root_three<T>(), eps);
+  BOOST_CHECK_CLOSE(y.derivative(4u),
+                    -22 / (9 * boost::math::constants::root_three<T>()), eps);
+  BOOST_CHECK_CLOSE(y.derivative(5u),
+                    227 / (27 * boost::math::constants::root_three<T>()),
+                    2 * eps);
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(asin_test, T, bin_float_types) {
+  const T eps = 300 * std::numeric_limits<T>::epsilon(); // percent
+  using std::asin;
+  using std::pow;
+  using std::sqrt;
+  constexpr std::size_t m = 5;
+  const T cx = 0.5;
+  auto x = make_fvar<T, m>(cx);
+  auto y = asin(x);
+  BOOST_CHECK_CLOSE(y.derivative(0u), asin(static_cast<T>(x)), eps);
+  BOOST_CHECK_CLOSE(y.derivative(1u), 1 / sqrt(1 - cx * cx), eps);
+  BOOST_CHECK_CLOSE(y.derivative(2u), cx / pow(1 - cx * cx, 1.5), eps);
+  BOOST_CHECK_CLOSE(y.derivative(3u), (2 * cx * cx + 1) / pow(1 - cx * cx, 2.5),
+                    eps);
+  BOOST_CHECK_CLOSE(y.derivative(4u),
+                    3 * cx * (2 * cx * cx + 3) / pow(1 - cx * cx, 3.5), eps);
+  BOOST_CHECK_CLOSE(y.derivative(5u),
+                    (24 * (cx * cx + 3) * cx * cx + 9) / pow(1 - cx * cx, 4.5),
+                    eps);
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(asin_infinity, T, all_float_types) {
+  const T eps = 100 * std::numeric_limits<T>::epsilon(); // percent
+  constexpr std::size_t m = 5;
+  auto x = make_fvar<T, m>(1);
+  auto y = asin(x);
+  // std::cout << "asin(1) = " << y << std::endl; //
+  // depth(1)(1.5707963267949,inf,inf,-nan,-nan,-nan)
+  BOOST_CHECK_CLOSE(y.derivative(0u), boost::math::constants::half_pi<T>(),
+                    eps); // MacOS is not exact
+  BOOST_CHECK_EQUAL(y.derivative(1u), std::numeric_limits<T>::infinity());
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(asin_derivative, T, bin_float_types) {
+  const T eps = 300 * std::numeric_limits<T>::epsilon(); // percent
+  using std::pow;
+  using std::sqrt;
+  constexpr std::size_t m = 4;
+  const T cx(0.5);
+  auto x = make_fvar<T, m>(cx);
+  auto y = T(1) - x * x;
+  BOOST_CHECK_EQUAL(y.derivative(0u), 1 - cx * cx);
+  BOOST_CHECK_EQUAL(y.derivative(1u), -2 * cx);
+  BOOST_CHECK_EQUAL(y.derivative(2u), -2);
+  BOOST_CHECK_EQUAL(y.derivative(3u), 0);
+  BOOST_CHECK_EQUAL(y.derivative(4u), 0);
+  y = sqrt(y);
+  BOOST_CHECK_EQUAL(y.derivative(0u), sqrt(1 - cx * cx));
+  BOOST_CHECK_CLOSE(y.derivative(1u), -cx / sqrt(1 - cx * cx), eps);
+  BOOST_CHECK_CLOSE(y.derivative(2u), -1 / pow(1 - cx * cx, 1.5), eps);
+  BOOST_CHECK_CLOSE(y.derivative(3u), -3 * cx / pow(1 - cx * cx, 2.5), eps);
+  BOOST_CHECK_CLOSE(y.derivative(4u),
+                    -(12 * cx * cx + 3) / pow(1 - cx * cx, 3.5), eps);
+  y = y.inverse(); // asin'(x) = 1 / sqrt(1-x*x).
+  BOOST_CHECK_CLOSE(y.derivative(0u), 1 / sqrt(1 - cx * cx), eps);
+  BOOST_CHECK_CLOSE(y.derivative(1u), cx / pow(1 - cx * cx, 1.5), eps);
+  BOOST_CHECK_CLOSE(y.derivative(2u), (2 * cx * cx + 1) / pow(1 - cx * cx, 2.5),
+                    eps);
+  BOOST_CHECK_CLOSE(y.derivative(3u),
+                    3 * cx * (2 * cx * cx + 3) / pow(1 - cx * cx, 3.5), eps);
+  BOOST_CHECK_CLOSE(y.derivative(4u),
+                    (24 * (cx * cx + 3) * cx * cx + 9) / pow(1 - cx * cx, 4.5),
+                    eps);
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(asinh_test, T, bin_float_types) {
+  const T eps = 300 * std::numeric_limits<T>::epsilon(); // percent
+  using boost::math::asinh;
+  constexpr std::size_t m = 5;
+  const T cx = 1;
+  auto x = make_fvar<T, m>(cx);
+  auto y = asinh(x);
+  BOOST_CHECK_CLOSE(y.derivative(0u), asinh(static_cast<T>(x)), eps);
+  BOOST_CHECK_CLOSE(y.derivative(1u), 1 / boost::math::constants::root_two<T>(),
+                    eps);
+  BOOST_CHECK_CLOSE(y.derivative(2u),
+                    -1 / (2 * boost::math::constants::root_two<T>()), eps);
+  BOOST_CHECK_CLOSE(y.derivative(3u),
+                    1 / (4 * boost::math::constants::root_two<T>()), eps);
+  BOOST_CHECK_CLOSE(y.derivative(4u),
+                    3 / (8 * boost::math::constants::root_two<T>()), eps);
+  BOOST_CHECK_CLOSE(y.derivative(5u),
+                    -39 / (16 * boost::math::constants::root_two<T>()), eps);
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(atan2_function, T, all_float_types) {
+  using test_constants = test_constants_t<T>;
+  static constexpr auto m = test_constants::order;
+
+  test_detail::RandomSample<T> x_sampler{-2000, 2000};
+  test_detail::RandomSample<T> y_sampler{-2000, 2000};
+
+  for (auto i : boost::irange(test_constants::n_samples)) {
+    std::ignore = i;
+    auto x = x_sampler.next();
+    auto y = y_sampler.next();
+
+    auto autodiff_v = atan2(make_fvar<T, m>(x), make_fvar<T, m>(y));
+    auto anchor_v = atan2(x, y);
+    BOOST_CHECK_CLOSE(autodiff_v, anchor_v,
+                      5000 * test_constants::pct_epsilon());
+  }
+}
+
+BOOST_AUTO_TEST_SUITE_END()
diff --git a/libs/math/test/test_autodiff_3.cpp b/libs/math/test/test_autodiff_3.cpp
new file mode 100644
index 0000000000..a83bcc88b0
--- /dev/null
+++ b/libs/math/test/test_autodiff_3.cpp
@@ -0,0 +1,343 @@
+//           Copyright Matthew Pulver 2018 - 2019.
+// Distributed under the Boost Software License, Version 1.0.
+//      (See accompanying file LICENSE_1_0.txt or copy at
+//           https://www.boost.org/LICENSE_1_0.txt)
+
+#include "test_autodiff.hpp"
+#include <boost/utility/identity_type.hpp>
+
+BOOST_AUTO_TEST_SUITE(test_autodiff_3)
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(atanh_test, T, all_float_types) {
+  const T eps = 3000 * test_constants_t<T>::pct_epsilon(); // percent
+  constexpr unsigned m = 5;
+  const T cx = 0.5;
+  auto x = make_fvar<T, m>(cx);
+  auto y = atanh(x);
+  // BOOST_CHECK_EQUAL(y.derivative(0) , atanh(cx)); // fails due to overload
+  BOOST_CHECK_CLOSE(y.derivative(0u), atanh(static_cast<T>(x)), eps);
+  BOOST_CHECK_CLOSE(y.derivative(1u), static_cast<T>(4) / 3, eps);
+  BOOST_CHECK_CLOSE(y.derivative(2u), static_cast<T>(16) / 9, eps);
+  BOOST_CHECK_CLOSE(y.derivative(3u), static_cast<T>(224) / 27, eps);
+  BOOST_CHECK_CLOSE(y.derivative(4u), static_cast<T>(1280) / 27, eps);
+  BOOST_CHECK_CLOSE(y.derivative(5u), static_cast<T>(31232) / 81, eps);
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(atan_test, T, all_float_types) {
+  BOOST_MATH_STD_USING
+  using namespace boost;
+
+  const T cx = 1.0;
+  constexpr unsigned m = 5;
+  const auto x = make_fvar<T, m>(cx);
+  auto y = atan(x);
+  const auto eps = boost::math::tools::epsilon<T>();
+  BOOST_CHECK_CLOSE(y.derivative(0u), boost::math::constants::pi<T>() / 4, eps);
+  BOOST_CHECK_CLOSE(y.derivative(1u), T(0.5), eps);
+  BOOST_CHECK_CLOSE(y.derivative(2u), T(-0.5), eps);
+  BOOST_CHECK_CLOSE(y.derivative(3u), T(0.5), eps);
+  BOOST_CHECK_CLOSE(y.derivative(4u), T(0), eps);
+  BOOST_CHECK_CLOSE(y.derivative(5u), T(-3), eps);
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(erf_test, T, all_float_types) {
+  BOOST_MATH_STD_USING
+  using namespace boost;
+
+  const T eps = 300 * 100 * boost::math::tools::epsilon<T>(); // percent
+  const T cx = 1.0;
+  constexpr unsigned m = 5;
+  const auto x = make_fvar<T, m>(cx);
+  auto y = erf(x);
+  BOOST_CHECK_CLOSE(y.derivative(0u), erf(static_cast<T>(x)), eps);
+  BOOST_CHECK_CLOSE(
+      y.derivative(1u),
+      T(2) / (math::constants::e<T>() * math::constants::root_pi<T>()), eps);
+  BOOST_CHECK_CLOSE(
+      y.derivative(2u),
+      T(-4) / (math::constants::e<T>() * math::constants::root_pi<T>()), eps);
+  BOOST_CHECK_CLOSE(
+      y.derivative(3u),
+      T(4) / (math::constants::e<T>() * math::constants::root_pi<T>()), eps);
+  BOOST_CHECK_CLOSE(
+      y.derivative(4u),
+      T(8) / (math::constants::e<T>() * math::constants::root_pi<T>()), eps);
+  BOOST_CHECK_CLOSE(
+      y.derivative(5u),
+      T(-40) / (math::constants::e<T>() * math::constants::root_pi<T>()), eps);
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(sinc_test, T, bin_float_types) {
+  BOOST_MATH_STD_USING
+  const T eps = 20000 * boost::math::tools::epsilon<T>(); // percent
+  const T cx = 1;
+  constexpr unsigned m = 5;
+  auto x = make_fvar<T, m>(cx);
+  auto y = sinc(x);
+  BOOST_CHECK_CLOSE(y.derivative(0u), sin(cx), eps);
+  BOOST_CHECK_CLOSE(y.derivative(1u), cos(cx) - sin(cx), eps);
+  BOOST_CHECK_CLOSE(y.derivative(2u), sin(cx) - 2 * cos(cx), eps);
+  BOOST_CHECK_CLOSE(y.derivative(3u), T(5) * cos(cx) - T(3) * sin(cx), eps);
+  BOOST_CHECK_CLOSE(y.derivative(4u), T(13) * sin(cx) - T(20) * cos(cx), eps);
+  BOOST_CHECK_CLOSE(y.derivative(5u), T(101) * cos(cx) - T(65) * sin(cx), eps);
+  // Test at x = 0
+  auto y2 = sinc(make_fvar<T, 10>(0));
+  BOOST_CHECK_CLOSE(y2.derivative(0u), T(1), eps);
+  BOOST_CHECK_CLOSE(y2.derivative(1u), T(0), eps);
+  BOOST_CHECK_CLOSE(y2.derivative(2u), -cx / T(3), eps);
+  BOOST_CHECK_CLOSE(y2.derivative(3u), T(0), eps);
+  BOOST_CHECK_CLOSE(y2.derivative(4u), cx / T(5), eps);
+  BOOST_CHECK_CLOSE(y2.derivative(5u), T(0), eps);
+  BOOST_CHECK_CLOSE(y2.derivative(6u), -cx / T(7), eps);
+  BOOST_CHECK_CLOSE(y2.derivative(7u), T(0), eps);
+  BOOST_CHECK_CLOSE(y2.derivative(8u), cx / T(9), eps);
+  BOOST_CHECK_CLOSE(y2.derivative(9u), T(0), eps);
+  BOOST_CHECK_CLOSE(y2.derivative(10u), -cx / T(11), eps);
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(sinh_and_cosh, T, bin_float_types) {
+  BOOST_MATH_STD_USING
+  const T eps = 300 * boost::math::tools::epsilon<T>(); // percent
+  const T cx = 1;
+  constexpr unsigned m = 5;
+  auto x = make_fvar<T, m>(cx);
+  auto s = sinh(x);
+  auto c = cosh(x);
+  BOOST_CHECK_CLOSE(s.derivative(0u), sinh(static_cast<T>(x)), eps);
+  BOOST_CHECK_CLOSE(c.derivative(0u), cosh(static_cast<T>(x)), eps);
+  for (auto i : boost::irange(m + 1)) {
+    BOOST_CHECK_CLOSE(s.derivative(i), static_cast<T>(i % 2 == 1 ? c : s), eps);
+    BOOST_CHECK_CLOSE(c.derivative(i), static_cast<T>(i % 2 == 1 ? s : c), eps);
+  }
+}
+
+#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
+BOOST_AUTO_TEST_CASE_TEMPLATE(tanh_test, T, all_float_types) {
+  using bmp::fabs;
+  using bmp::tanh;
+  using detail::fabs;
+  using detail::tanh;
+  using std::fabs;
+  using std::tanh;
+  constexpr std::array<const char *, 6> tanh_derivatives{
+      {"0."
+       "76159415595576488811945828260479359041276859725793655159681050012195324"
+       "457663848345894752167367671442190275970155",
+       "0."
+       "41997434161402606939449673904170144491718672823077095471331144024458989"
+       "95240483056156940088623187260",
+       "-0."
+       "63970000844922450018849176930384395321921136306079914494299856318702069"
+       "34885434644440069533372017992",
+       "0."
+       "62162668077129626310653042872222339967572411755445418563968706335816206"
+       "22188951465548376863495698762",
+       "0."
+       "66509104475050167773507148092106234992757132833203125448814929383096463"
+       "47626843278089998045994094537",
+       "-5."
+       "55689355847371979760458290231697200987383372116293456019531342394708989"
+       "7942786231796317250984197038"}};
+  const T cx = 1;
+  constexpr std::size_t m = 5;
+  auto x = make_fvar<T, m>(cx);
+  auto t = tanh(x);
+  for (auto i : boost::irange(tanh_derivatives.size())) {
+    BOOST_TEST_WARN(isNearZero(t.derivative(i) -
+                               boost::lexical_cast<T>(tanh_derivatives[i])));
+  }
+}
+#endif
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(tan_test, T, bin_float_types) {
+  BOOST_MATH_STD_USING
+  const T eps = 800 * boost::math::tools::epsilon<T>(); // percent
+  const T cx = boost::math::constants::third_pi<T>();
+  const T root_three = boost::math::constants::root_three<T>();
+  constexpr unsigned m = 5;
+  const auto x = make_fvar<T, m>(cx);
+  auto y = tan(x);
+  BOOST_CHECK_CLOSE(y.derivative(0u), root_three, eps);
+  BOOST_CHECK_CLOSE(y.derivative(1u), T(4), eps);
+  BOOST_CHECK_CLOSE(y.derivative(2u), T(8) * root_three, eps);
+  BOOST_CHECK_CLOSE(y.derivative(3u), T(80), eps);
+  BOOST_CHECK_CLOSE(y.derivative(4u), T(352) * root_three, eps);
+  BOOST_CHECK_CLOSE(y.derivative(5u), T(5824), eps);
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(fmod_test, T, bin_float_types) {
+  BOOST_MATH_STD_USING
+  constexpr unsigned m = 3;
+  const T cx = 3.25;
+  const T cy = 0.5;
+  auto x = make_fvar<T, m>(cx);
+  auto y = fmod(x, autodiff_fvar<T, m>(cy));
+  BOOST_CHECK_EQUAL(y.derivative(0u), T(0.25));
+  BOOST_CHECK_EQUAL(y.derivative(1u), T(1));
+  BOOST_CHECK_EQUAL(y.derivative(2u), T(0));
+  BOOST_CHECK_EQUAL(y.derivative(3u), T(0));
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(round_and_trunc, T, all_float_types) {
+  BOOST_MATH_STD_USING
+  constexpr unsigned m = 3;
+  const T cx = 3.25;
+  auto x = make_fvar<T, m>(cx);
+  auto y = round(x);
+  BOOST_CHECK_EQUAL(y.derivative(0u), round(cx));
+  BOOST_CHECK_EQUAL(y.derivative(1u), T(0));
+  BOOST_CHECK_EQUAL(y.derivative(2u), T(0));
+  BOOST_CHECK_EQUAL(y.derivative(3u), T(0));
+  y = trunc(x);
+  BOOST_CHECK_EQUAL(y.derivative(0u), trunc(cx));
+  BOOST_CHECK_EQUAL(y.derivative(1u), T(0));
+  BOOST_CHECK_EQUAL(y.derivative(2u), T(0));
+  BOOST_CHECK_EQUAL(y.derivative(3u), T(0));
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(iround_and_itrunc, T, all_float_types) {
+  BOOST_MATH_STD_USING
+  using namespace boost::math;
+  constexpr unsigned m = 3;
+  const T cx = 3.25;
+  auto x = make_fvar<T, m>(cx);
+  int y = iround(x);
+  BOOST_CHECK_EQUAL(y, iround(cx));
+  y = itrunc(x);
+  BOOST_CHECK_EQUAL(y, itrunc(cx));
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(lambert_w0_test, T, all_float_types) {
+  const T eps = 1000 * boost::math::tools::epsilon<T>(); // percent
+  constexpr unsigned m = 10;
+  const T cx = 3;
+  // Mathematica: N[Table[D[ProductLog[x], {x, n}], {n, 0, 10}] /. x -> 3, 52]
+  constexpr std::array<const char *, m + 1> answers{
+      {"1.049908894964039959988697070552897904589466943706341",
+       "0.1707244807388472968312949774415522047470762509741737",
+       "-0.04336545501146252734105411312976167858858970875797718",
+       "0.02321456264324789334313200360870492961288748451791104",
+       "-0.01909049778427783072663170526188353869136655225133878",
+       "0.02122935002563637629500975949987796094687564718834156",
+       "-0.02979093848448877259041971538394953658978044986784643",
+       "0.05051290266216717699803334605370337985567016837482099",
+       "-0.1004503154972645060971099914384090562800544486549660",
+       "0.2292464437392250211967939182075930820454464472006425",
+       "-0.5905839053125614593682763387470654123192290838719517"}};
+  auto x = make_fvar<T, m>(cx);
+  auto y = lambert_w0(x);
+  for (auto i : boost::irange(m + 1)) {
+    const T answer = boost::lexical_cast<T>(answers[i]);
+    BOOST_CHECK_CLOSE(y.derivative(i), answer, eps);
+  }
+  // const T cx0 = -1 / boost::math::constants::e<T>();
+  // auto edge = lambert_w0(make_fvar<T,m>(cx0));
+  // std::cout << "edge = " << edge << std::endl;
+  // edge = depth(1)(-1,inf,-inf,inf,-inf,inf,-inf,inf,-inf,inf,-inf)
+  // edge = depth(1)(-1,inf,-inf,inf,-inf,inf,-inf,inf,-inf,inf,-inf)
+  // edge =
+  // depth(1)(-1,3.68935e+19,-9.23687e+57,4.62519e+96,-2.89497e+135,2.02945e+174,-1.52431e+213,1.19943e+252,-9.75959e+290,8.14489e+329,-6.93329e+368)
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(digamma_test, T, all_float_types) {
+  const T eps = 1000 * boost::math::tools::epsilon<T>(); // percent
+  constexpr unsigned m = 10;
+  const T cx = 3;
+  // Mathematica: N[Table[PolyGamma[n, 3], {n, 0, 10}], 52]
+  constexpr std::array<const char *, m + 1> answers{
+    {"0.9227843350984671393934879099175975689578406640600764"
+    ,"0.3949340668482264364724151666460251892189499012067984"
+    ,"-0.1541138063191885707994763230228999815299725846809978"
+    ,"0.1189394022668291490960221792470074166485057115123614"
+    ,"-0.1362661234408782319527716749688200333699420680459075"
+    ,"0.2061674381338967657421515749104633482180988039424274"
+    ,"-0.3864797149844353246542358918536669119017636069718686"
+    ,"0.8623752376394704685736020836084249051623848752441025"
+    ,"-2.228398747634885327823655450854278779627928241914664"
+    ,"6.536422382626807143525565747764891144367614117601463"
+    ,"-21.4366066287129906188428320541054572790340793874298"}};
+  auto x = make_fvar<T, m>(cx);
+  auto y = digamma(x);
+  for (auto i : boost::irange(m + 1)) {
+    const T answer = boost::lexical_cast<T>(answers[i]);
+    BOOST_CHECK_CLOSE(y.derivative(i), answer, eps);
+  }
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(lgamma_test, T, all_float_types) {
+  const T eps = 1000 * boost::math::tools::epsilon<T>(); // percent
+  constexpr unsigned m = 10;
+  const T cx = 3;
+  // Mathematica: N[Table[D[LogGamma[x],{x,n}] /. x->3, {n, 0, 10}], 52]
+  constexpr std::array<const char *, m + 1> answers{
+    {"0.6931471805599453094172321214581765680755001343602553"
+    ,"0.9227843350984671393934879099175975689578406640600764"
+    ,"0.3949340668482264364724151666460251892189499012067984"
+    ,"-0.1541138063191885707994763230228999815299725846809978"
+    ,"0.1189394022668291490960221792470074166485057115123614"
+    ,"-0.1362661234408782319527716749688200333699420680459075"
+    ,"0.2061674381338967657421515749104633482180988039424274"
+    ,"-0.3864797149844353246542358918536669119017636069718686"
+    ,"0.8623752376394704685736020836084249051623848752441025"
+    ,"-2.228398747634885327823655450854278779627928241914664"
+    ,"6.536422382626807143525565747764891144367614117601463"}};
+  auto x = make_fvar<T, m>(cx);
+  auto y = lgamma(x);
+  for (auto i : boost::irange(m + 1)) {
+    const T answer = boost::lexical_cast<T>(answers[i]);
+    BOOST_CHECK_CLOSE(y.derivative(i), answer, eps);
+  }
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(tgamma_test, T, all_float_types) {
+  const T eps = 1000 * boost::math::tools::epsilon<T>(); // percent
+  constexpr unsigned m = 10;
+  const T cx = 3;
+  // Mathematica: N[Table[D[Gamma[x],{x,n}] /. x->3, {n, 0, 10}], 52]
+  constexpr std::array<const char *, m + 1> answers{
+    {"2.0"
+    ,"1.845568670196934278786975819835195137915681328120153"
+    ,"2.492929991902693057942510065508124245503778067273315"
+    ,"3.449965013523673365279327178241708777509009968597547"
+    ,"5.521798578098737512443417699412265532987916790978887"
+    ,"8.845805593922864253981346455183370214190789096412155"
+    ,"15.86959874461221647760760269963155031595848150772695"
+    ,"27.46172054213435946038727460195592342721862288816812"
+    ,"54.64250508485402729556251663145824730270508661240771"
+    ,"96.08542140594972502872131946513104238293824803599579"
+    ,"222.0936743583156040996433943128676567542497584689499"}};
+  auto x = make_fvar<T, m>(cx);
+  auto y = tgamma(x);
+  for (auto i : boost::irange(m + 1)) {
+    const T answer = boost::lexical_cast<T>(answers[i]);
+    BOOST_CHECK_CLOSE(y.derivative(i), answer, eps);
+  }
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(tgamma2_test, T, all_float_types) {
+  //const T eps = 5000 * boost::math::tools::epsilon<T>(); // ok for non-multiprecision
+  const T eps = 500000 * boost::math::tools::epsilon<T>(); // percent
+  constexpr unsigned m = 10;
+  const T cx = -1.5;
+  // Mathematica: N[Table[D[Gamma[x],{x,n}] /. x->-3/2, {n, 0, 10}], 52]
+  constexpr std::array<const char *, m + 1> answers{
+    {"2.363271801207354703064223311121526910396732608163183"
+    ,"1.661750260668596505586468565464938761014714509096807"
+    ,"23.33417984355457252918927856618603412638766668207679"
+    ,"47.02130025080143055642555842335081335790754507072526"
+    ,"1148.336052788822231948472800239024335856568111484074"
+    ,"3831.214710988836934569706027888431190714054814541186"
+    ,"138190.9008816865362698874238213771413807566436072179"
+    ,"644956.0066517306036921195893233874126907491308967028"
+    ,"3.096453684470713902448094810299787572782887316764214e7"
+    ,"1.857893143852025058151037296906468662709947415219451e8"
+    ,"1.114762466163487983067783853825224537320312784955935e10"}};
+  auto x = make_fvar<T, m>(cx);
+  auto y = tgamma(x);
+  for (auto i : boost::irange(m + 1)) {
+    const T answer = boost::lexical_cast<T>(answers[i]);
+    BOOST_CHECK_CLOSE(y.derivative(i), answer, eps);
+  }
+}
+
+BOOST_AUTO_TEST_SUITE_END()
diff --git a/libs/math/test/test_autodiff_4.cpp b/libs/math/test/test_autodiff_4.cpp
new file mode 100644
index 0000000000..842d7e4716
--- /dev/null
+++ b/libs/math/test/test_autodiff_4.cpp
@@ -0,0 +1,194 @@
+//           Copyright Matthew Pulver 2018 - 2019.
+// Distributed under the Boost Software License, Version 1.0.
+//      (See accompanying file LICENSE_1_0.txt or copy at
+//           https://www.boost.org/LICENSE_1_0.txt)
+
+#include "test_autodiff.hpp"
+
+BOOST_AUTO_TEST_SUITE(test_autodiff_4)
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(lround_llround_lltrunc_truncl, T,
+                              all_float_types) {
+  using boost::math::llround;
+  using boost::math::lltrunc;
+  using boost::math::lround;
+  using boost::multiprecision::llround;
+  using boost::multiprecision::lltrunc;
+  using boost::multiprecision::lround;
+  using detail::llround;
+  using detail::lltrunc;
+  using detail::lround;
+  using detail::truncl;
+  using std::truncl;
+
+  constexpr std::size_t m = 3;
+  const auto &cx = static_cast<T>(3.25);
+  auto x = make_fvar<T, m>(cx);
+  auto yl = lround(x);
+  BOOST_CHECK_EQUAL(yl, lround(cx));
+  auto yll = llround(x);
+  BOOST_CHECK_EQUAL(yll, llround(cx));
+  BOOST_CHECK_EQUAL(lltrunc(cx), lltrunc(x));
+
+#ifndef BOOST_NO_CXX17_IF_CONSTEXPR
+  if constexpr (!bmp::is_number<T>::value &&
+                !bmp::is_number_expression<T>::value) {
+    BOOST_CHECK_EQUAL(truncl(x), truncl(cx));
+  }
+#endif
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(equality, T, all_float_types) {
+  BOOST_MATH_STD_USING
+  using boost::math::epsilon_difference;
+  using boost::math::fpclassify;
+  using boost::math::ulp;
+  using std::fpclassify;
+
+  constexpr std::size_t m = 3;
+  // check zeros
+  {
+    auto x = make_fvar<T, m>(0.0);
+    auto y = T(-0.0);
+    BOOST_CHECK_EQUAL(x.derivative(0u), y);
+  }
+}
+
+#if defined(BOOST_AUTODIFF_TESTING_INCLUDE_MULTIPRECISION)
+BOOST_AUTO_TEST_CASE_TEMPLATE(multiprecision, T, multiprecision_float_types) {
+  using boost::multiprecision::fabs;
+  using detail::fabs;
+  using std::fabs;
+
+  const T eps = 3000 * std::numeric_limits<T>::epsilon();
+  constexpr std::size_t Nw = 3;
+  constexpr std::size_t Nx = 2;
+  constexpr std::size_t Ny = 4;
+  constexpr std::size_t Nz = 3;
+  const auto w = make_fvar<T, Nw>(11);
+  const auto x = make_fvar<T, 0, Nx>(12);
+  const auto y = make_fvar<T, 0, 0, Ny>(13);
+  const auto z = make_fvar<T, 0, 0, 0, Nz>(14);
+  const auto v =
+      mixed_partials_f(w, x, y, z); // auto = autodiff_fvar<T,Nw,Nx,Ny,Nz>
+  // Calculated from Mathematica symbolic differentiation.
+  const T answer = boost::lexical_cast<T>(
+      "1976.3196007477977177798818752904187209081211892187"
+      "5499076582535951111845769110560421820940516423255314");
+  // BOOST_CHECK_CLOSE(v.derivative(Nw,Nx,Ny,Nz), answer, eps); // Doesn't work
+  // for cpp_dec_float
+  const T relative_error =
+      static_cast<T>(fabs(v.derivative(Nw, Nx, Ny, Nz) / answer - 1));
+  BOOST_CHECK_LT(relative_error, eps);
+}
+#endif
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(acosh_hpp, T, all_float_types) {
+  using boost::math::acosh;
+  using test_constants = test_constants_t<T>;
+  static constexpr auto m = test_constants::order;
+
+  test_detail::RandomSample<T> x_sampler{1, 100};
+  for (auto i : boost::irange(test_constants::n_samples)) {
+    std::ignore = i;
+    auto x = x_sampler.next();
+    auto autodiff_v = acosh(make_fvar<T, m>(x));
+    auto anchor_v = acosh(x);
+    BOOST_CHECK_CLOSE(autodiff_v.derivative(0u), anchor_v,
+                      1e3 * test_constants::pct_epsilon());
+  }
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(asinh_hpp, T, all_float_types) {
+  using boost::math::asinh;
+  using test_constants = test_constants_t<T>;
+  static constexpr auto m = test_constants::order;
+
+  test_detail::RandomSample<T> x_sampler{-100, 100};
+  for (auto i : boost::irange(test_constants::n_samples)) {
+    std::ignore = i;
+    auto x = x_sampler.next();
+
+    auto autodiff_v = asinh(make_fvar<T, m>(x));
+    auto anchor_v = asinh(x);
+    BOOST_CHECK_CLOSE(autodiff_v.derivative(0u), anchor_v,
+                      1e3 * test_constants::pct_epsilon());
+  }
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(atanh_hpp, T, all_float_types) {
+  using boost::math::nextafter;
+  using std::nextafter;
+
+  using boost::math::atanh;
+  using test_constants = test_constants_t<T>;
+  static constexpr auto m = test_constants::order;
+
+  test_detail::RandomSample<T> x_sampler{-1, 1};
+  for (auto i : boost::irange(test_constants::n_samples)) {
+    std::ignore = i;
+    auto x = nextafter(x_sampler.next(), T(0));
+
+    auto autodiff_v = atanh(make_fvar<T, m>(x));
+    auto anchor_v = atanh(x);
+    BOOST_CHECK_CLOSE(autodiff_v.derivative(0u), anchor_v,
+                      1e3 * test_constants::pct_epsilon());
+  }
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(atan_hpp, T, all_float_types) {
+  using boost::math::float_prior;
+  using boost::math::fpclassify;
+  using boost::math::signbit;
+  using boost::math::differentiation::detail::atan;
+  using boost::multiprecision::atan;
+  using boost::multiprecision::fabs;
+  using boost::multiprecision::fpclassify;
+  using boost::multiprecision::signbit;
+  using detail::fabs;
+  using std::atan;
+  using std::fabs;
+
+  using test_constants = test_constants_t<T>;
+  static constexpr auto m = test_constants::order;
+
+  test_detail::RandomSample<T> x_sampler{-1, 1};
+  for (auto i : boost::irange(test_constants::n_samples)) {
+    std::ignore = i;
+    auto x = T(1);
+    while (fpclassify(T(fabs(x) - 1)) == FP_ZERO) {
+      x = x_sampler.next();
+    }
+
+    auto autodiff_v = atan(make_fvar<T, m>(x));
+    auto anchor_v = atan(x);
+    BOOST_CHECK_CLOSE(autodiff_v.derivative(0u), anchor_v,
+                      1e3 * test_constants::pct_epsilon());
+  }
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(bernoulli_hpp, T, all_float_types) {
+
+  using boost::multiprecision::min;
+  using std::min;
+  using test_constants = test_constants_t<T>;
+  static constexpr auto m = test_constants::order;
+
+  for (auto i : boost::irange(test_constants::n_samples)) {
+    {
+      auto autodiff_v = boost::math::bernoulli_b2n<autodiff_fvar<T, m>>(i);
+      auto anchor_v = boost::math::bernoulli_b2n<T>(i);
+      BOOST_CHECK_CLOSE(autodiff_v.derivative(0u), anchor_v,
+                        50 * test_constants::pct_epsilon());
+    }
+    {
+      auto i_ = (min)(19, i);
+      auto autodiff_v = boost::math::tangent_t2n<autodiff_fvar<T, m>>(i_);
+      auto anchor_v = boost::math::tangent_t2n<T>(i_);
+      BOOST_CHECK_CLOSE(autodiff_v.derivative(0u), anchor_v,
+                        50 * test_constants::pct_epsilon());
+    }
+  }
+}
+
+BOOST_AUTO_TEST_SUITE_END()
diff --git a/libs/math/test/test_autodiff_5.cpp b/libs/math/test/test_autodiff_5.cpp
new file mode 100644
index 0000000000..614630cacf
--- /dev/null
+++ b/libs/math/test/test_autodiff_5.cpp
@@ -0,0 +1,120 @@
+//           Copyright Matthew Pulver 2018 - 2019.
+// Distributed under the Boost Software License, Version 1.0.
+//      (See accompanying file LICENSE_1_0.txt or copy at
+//           https://www.boost.org/LICENSE_1_0.txt)
+
+#include "test_autodiff.hpp"
+
+BOOST_AUTO_TEST_SUITE(test_autodiff_5)
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(binomial_hpp, T, all_float_types) {
+  using boost::multiprecision::min;
+  using std::fabs;
+  using std::min;
+
+  using test_constants = test_constants_t<T>;
+  static constexpr auto m = test_constants::order;
+  test_detail::RandomSample<unsigned> n_sampler{0u, 30u};
+  test_detail::RandomSample<unsigned> r_sampler{0u, 30u};
+
+  for (auto i : boost::irange(test_constants::n_samples)) {
+    std::ignore = i;
+    auto n = n_sampler.next();
+    auto r = n == 0 ? 0 : (min)(r_sampler.next(), n - 1);
+
+    // This is a hard function to test for type float due to a specialization of
+    // boost::math::binomial_coefficient
+    auto autodiff_v =
+        std::is_same<T, float>::value
+            ? make_fvar<T, m>(boost::math::binomial_coefficient<T>(n, r))
+            : boost::math::binomial_coefficient<T>(n, r);
+    auto anchor_v = boost::math::binomial_coefficient<T>(n, r);
+    BOOST_CHECK_EQUAL(autodiff_v.derivative(0u), anchor_v);
+  }
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(cbrt_hpp, T, all_float_types) {
+  using test_constants = test_constants_t<T>;
+  static constexpr auto m = test_constants::order;
+  test_detail::RandomSample<T> x_sampler{-2000, 2000};
+  for (auto i : boost::irange(test_constants::n_samples)) {
+    std::ignore = i;
+    auto x = x_sampler.next();
+    BOOST_CHECK_CLOSE(boost::math::cbrt(make_fvar<T, m>(x)).derivative(0u),
+                      boost::math::cbrt(x), 50 * test_constants::pct_epsilon());
+  }
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(chebyshev_hpp, T, all_float_types) {
+  using test_constants = test_constants_t<T>;
+  static constexpr auto m = test_constants::order;
+  {
+    test_detail::RandomSample<unsigned> n_sampler{0u, 10u};
+    test_detail::RandomSample<T> x_sampler{-2, 2};
+    for (auto i : boost::irange(test_constants::n_samples)) {
+      std::ignore = i;
+      auto n = n_sampler.next();
+      auto x = x_sampler.next();
+      BOOST_CHECK_CLOSE(
+          boost::math::chebyshev_t(n, make_fvar<T, m>(x)).derivative(0u),
+          boost::math::chebyshev_t(n, x), 40 * test_constants::pct_epsilon());
+
+      BOOST_CHECK_CLOSE(
+          boost::math::chebyshev_u(n, make_fvar<T, m>(x)).derivative(0u),
+          boost::math::chebyshev_u(n, x), 40 * test_constants::pct_epsilon());
+
+      BOOST_CHECK_CLOSE(
+          boost::math::chebyshev_t_prime(n, make_fvar<T, m>(x)).derivative(0u),
+          boost::math::chebyshev_t_prime(n, x),
+          40 * test_constants::pct_epsilon());
+
+      /*/usr/include/boost/math/special_functions/chebyshev.hpp:164:40: error:
+       cannot convert
+       boost::math::differentiation::autodiff_v1::detail::fvar<double, 3> to
+       double in return
+       BOOST_CHECK_EQUAL(boost::math::chebyshev_clenshaw_recurrence(c.data(),c.size(),make_fvar<T,m>(0.20))
+       ,
+       boost::math::chebyshev_clenshaw_recurrence(c.data(),c.size(),static_cast<T>(0.20)));*/
+      /*try {
+        std::array<T, 4> c0{{14.2, -13.7, 82.3, 96}};
+        BOOST_CHECK_CLOSE(boost::math::chebyshev_clenshaw_recurrence(c0.data(),
+      c0.size(), make_fvar<T,m>(x)),
+                                     boost::math::chebyshev_clenshaw_recurrence(c0.data(),
+      c0.size(), x), 10*test_constants::pct_epsilon()); } catch (...) {
+        std::rethrow_exception(std::exception_ptr(std::current_exception()));
+      }*/
+    }
+  }
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(cospi_hpp, T, all_float_types) {
+  using test_constants = test_constants_t<T>;
+  static constexpr auto m = test_constants::order;
+  test_detail::RandomSample<T> x_sampler{-2000, 2000};
+  for (auto i : boost::irange(test_constants::n_samples)) {
+    std::ignore = i;
+    auto x = x_sampler.next();
+    BOOST_CHECK_CLOSE(boost::math::cos_pi(make_fvar<T, m>(x)).derivative(0u),
+                      boost::math::cos_pi(x), test_constants::pct_epsilon());
+  }
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(digamma_hpp, T, all_float_types) {
+
+  using boost::math::nextafter;
+  using std::nextafter;
+
+  using test_constants = test_constants_t<T>;
+  static constexpr auto m = test_constants::order;
+  test_detail::RandomSample<T> x_sampler{-1, 2000};
+  for (auto i : boost::irange(test_constants::n_samples)) {
+    std::ignore = i;
+    auto x = nextafter(x_sampler.next(), ((std::numeric_limits<T>::max))());
+    auto autodiff_v = boost::math::digamma(make_fvar<T, m>(x));
+    auto anchor_v = boost::math::digamma(x);
+    BOOST_CHECK_CLOSE(autodiff_v.derivative(0u), anchor_v,
+                      1e4 * test_constants::pct_epsilon());
+  }
+}
+
+BOOST_AUTO_TEST_SUITE_END()
diff --git a/libs/math/test/test_autodiff_6.cpp b/libs/math/test/test_autodiff_6.cpp
new file mode 100644
index 0000000000..770ca229d5
--- /dev/null
+++ b/libs/math/test/test_autodiff_6.cpp
@@ -0,0 +1,280 @@
+//           Copyright Matthew Pulver 2018 - 2019.
+// Distributed under the Boost Software License, Version 1.0.
+//      (See accompanying file LICENSE_1_0.txt or copy at
+//           https://www.boost.org/LICENSE_1_0.txt)
+
+#include "test_autodiff.hpp"
+
+BOOST_AUTO_TEST_SUITE(test_autodiff_6)
+
+/*********************************************************************************************************************
+ * special functions tests
+ *********************************************************************************************************************/
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(ellint_1_hpp, T, all_float_types) {
+  using test_constants = test_constants_t<T>;
+  static constexpr auto m = test_constants::order;
+  test_detail::RandomSample<T> k_sampler{T{-1}, T{1}};
+  test_detail::RandomSample<T> phi_sampler{-boost::math::constants::two_pi<T>(),
+                                           boost::math::constants::two_pi<T>()};
+  for (auto i : boost::irange(test_constants::n_samples)) {
+    std::ignore = i;
+    auto k = k_sampler.next();
+    auto phi = phi_sampler.next();
+    BOOST_CHECK_CLOSE(boost::math::ellint_1(make_fvar<T, m>(k)).derivative(0u),
+                      boost::math::ellint_1(k),
+                      2.5e3 * test_constants::pct_epsilon());
+    BOOST_CHECK_CLOSE(
+        boost::math::ellint_1(make_fvar<T, m>(k), make_fvar<T, m>(phi))
+            .derivative(0u),
+        boost::math::ellint_1(k, phi), 1e4 * test_constants::pct_epsilon());
+  }
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(ellint_2_hpp, T, all_float_types) {
+  using test_constants = test_constants_t<T>;
+  static constexpr auto m = test_constants::order;
+  test_detail::RandomSample<T> k_sampler{-1, 1};
+  test_detail::RandomSample<T> phi_sampler{-boost::math::constants::two_pi<T>(),
+                                           boost::math::constants::two_pi<T>()};
+  for (auto i : boost::irange(test_constants::n_samples)) {
+    std::ignore = i;
+    auto k = k_sampler.next();
+    auto phi = phi_sampler.next();
+    BOOST_CHECK_CLOSE(boost::math::ellint_2(make_fvar<T, m>(k)).derivative(0u),
+                      boost::math::ellint_2(k),
+                      2.5e3 * test_constants::pct_epsilon());
+    BOOST_CHECK_CLOSE(
+        boost::math::ellint_2(make_fvar<T, m>(k), make_fvar<T, m>(phi))
+            .derivative(0u),
+        boost::math::ellint_2(k, phi), 2.5e3 * test_constants::pct_epsilon());
+  }
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(ellint_3_hpp, T, all_float_types) {
+  using boost::math::nextafter;
+  using boost::multiprecision::nextafter;
+
+  using boost::math::differentiation::detail::sin;
+  using boost::multiprecision::min;
+  using std::min;
+  using std::sin;
+
+  using test_constants = test_constants_t<T>;
+  static constexpr auto m = test_constants::order;
+  test_detail::RandomSample<T> k_sampler{-1, 1};
+  test_detail::RandomSample<T> n_sampler{-2000, 2000};
+  test_detail::RandomSample<T> phi_sampler{-boost::math::constants::two_pi<T>(),
+                                           boost::math::constants::two_pi<T>()};
+  for (auto i : boost::irange(test_constants::n_samples)) {
+    std::ignore = i;
+    auto k = k_sampler.next();
+    auto phi = phi_sampler.next();
+    auto n = (min)((min)(n_sampler.next(), T(1) / (sin(phi) * sin(phi))),
+                   nextafter(T(1), T(0)));
+    BOOST_CHECK_CLOSE(boost::math::ellint_3(make_fvar<T, m>(k),
+                                            make_fvar<T, m>(n),
+                                            make_fvar<T, m>(phi))
+                          .derivative(0u),
+                      boost::math::ellint_3(k, n, phi),
+                      2.5e3 * test_constants::pct_epsilon());
+  }
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(ellint_d_hpp, T, all_float_types) {
+  using test_constants = test_constants_t<T>;
+  static constexpr auto m = test_constants::order;
+  test_detail::RandomSample<T> k_sampler{-1, 1};
+  test_detail::RandomSample<T> phi_sampler{-boost::math::constants::two_pi<T>(),
+                                           boost::math::constants::two_pi<T>()};
+  for (auto i : boost::irange(test_constants::n_samples)) {
+    std::ignore = i;
+    auto k = k_sampler.next();
+    auto phi = phi_sampler.next();
+    BOOST_CHECK_CLOSE(boost::math::ellint_d(make_fvar<T, m>(k)).derivative(0u),
+                      boost::math::ellint_d(k),
+                      2.5e3 * test_constants::pct_epsilon());
+    BOOST_CHECK_CLOSE(
+        boost::math::ellint_d(make_fvar<T, m>(k), make_fvar<T, m>(phi))
+            .derivative(0u),
+        boost::math::ellint_d(k, phi), 2.5e3 * test_constants::pct_epsilon());
+  }
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(ellint_rf_hpp, T, all_float_types) {
+
+  using boost::math::tools::max;
+  using std::max;
+
+  using boost::math::nextafter;
+  using std::nextafter;
+
+  using test_constants = test_constants_t<T>;
+  static constexpr auto m = test_constants::order;
+
+  test_detail::RandomSample<T> x_sampler{0, 2000};
+  test_detail::RandomSample<T> y_sampler{0, 2000};
+  test_detail::RandomSample<T> z_sampler{0, 2000};
+  for (auto i : boost::irange(test_constants::n_samples)) {
+    std::ignore = i;
+    auto x = nextafter(x_sampler.next(), ((std::numeric_limits<T>::max))());
+    auto y = nextafter(y_sampler.next(), ((std::numeric_limits<T>::max))());
+    auto z = nextafter(z_sampler.next(), ((std::numeric_limits<T>::max))());
+
+    BOOST_CHECK_CLOSE(
+        boost::math::ellint_rf(make_fvar<T, m>(x), make_fvar<T, m>(y),
+                               make_fvar<T, m>(z))
+            .derivative(0u),
+        boost::math::ellint_rf(x, y, z), 2.5e3 * test_constants::pct_epsilon());
+  }
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(ellint_rc_hpp, T, all_float_types) {
+  using boost::math::fpclassify;
+  using boost::math::nextafter;
+  using boost::math::signbit;
+  using boost::math::tools::max;
+  using boost::multiprecision::fpclassify;
+  using boost::multiprecision::signbit;
+  using std::max;
+  using std::nextafter;
+
+  using test_constants = test_constants_t<T>;
+  static constexpr auto m = test_constants::order;
+  test_detail::RandomSample<T> x_sampler{0, 2000};
+  test_detail::RandomSample<T> y_sampler{0, 2000};
+  for (auto i : boost::irange(test_constants::n_samples)) {
+    std::ignore = i;
+    auto x = x_sampler.next();
+    auto y = T(0);
+    while (fpclassify(T(y)) == FP_ZERO) {
+      y = (max)(y_sampler.next(),
+                nextafter(T(0), T(signbit(y) ? -1 : 1) *
+                                    ((std::numeric_limits<T>::max))()));
+    }
+
+    BOOST_CHECK_CLOSE(
+        boost::math::ellint_rc(make_fvar<T, m>(x), make_fvar<T, m>(y))
+            .derivative(0u),
+        boost::math::ellint_rc(x, y), 2.5e3 * test_constants::pct_epsilon());
+  }
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(ellint_rj_hpp, T, all_float_types) {
+  using boost::math::fpclassify;
+  using boost::math::nextafter;
+  using boost::math::signbit;
+  using boost::math::tools::max;
+  using boost::multiprecision::fpclassify;
+  using boost::multiprecision::signbit;
+
+  using std::max;
+  using std::nextafter;
+
+  using test_constants = test_constants_t<T>;
+  static constexpr auto m = test_constants::order;
+
+  test_detail::RandomSample<T> x_sampler{0, 2000};
+  test_detail::RandomSample<T> y_sampler{0, 2000};
+  test_detail::RandomSample<T> z_sampler{0, 2000};
+  test_detail::RandomSample<T> p_sampler{-2000, 2000};
+
+  for (auto i : boost::irange(test_constants::n_samples)) {
+    std::ignore = i;
+    auto x = x_sampler.next();
+    auto y = (x != 0 ? 1 : 0) + y_sampler.next();
+    auto z = ((x == 0 || y == 0) ? 1 : 0) + z_sampler.next();
+    auto p = T(0);
+
+    while (fpclassify(T(p)) == FP_ZERO) {
+      p = (max)(p_sampler.next(),
+                nextafter(T(0), T(signbit(p) ? -1 : 1) *
+                                    ((std::numeric_limits<T>::max))()));
+    }
+    BOOST_CHECK_CLOSE(
+        boost::math::ellint_rj(make_fvar<T, m>(x), make_fvar<T, m>(y),
+                               make_fvar<T, m>(z), make_fvar<T, m>(p))
+            .derivative(0u),
+        boost::math::ellint_rj(x, y, z, p),
+        2.5e3 * test_constants::pct_epsilon());
+  }
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(ellint_rd_hpp, T, all_float_types) {
+  using test_constants = test_constants_t<T>;
+  static constexpr auto m = test_constants::order;
+  test_detail::RandomSample<T> x_sampler{0, 2000};
+  test_detail::RandomSample<T> y_sampler{0, 2000};
+  test_detail::RandomSample<T> z_sampler{0, 2000};
+  for (auto i : boost::irange(test_constants::n_samples)) {
+    std::ignore = i;
+    auto x = x_sampler.next();
+    auto y = (x == 0 ? 1 : 0) + y_sampler.next();
+    auto z = z_sampler.next();
+    BOOST_CHECK_CLOSE(
+        boost::math::ellint_rd(make_fvar<T, m>(x), make_fvar<T, m>(y),
+                               make_fvar<T, m>(z))
+            .derivative(0u),
+        boost::math::ellint_rd(x, y, z), 2.5e3 * test_constants::pct_epsilon());
+  }
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(ellint_rg_hpp, T, all_float_types) {
+
+  using boost::math::nextafter;
+  using std::nextafter;
+
+  using test_constants = test_constants_t<T>;
+  static constexpr auto m = test_constants::order;
+  test_detail::RandomSample<T> x_sampler{0, 2000};
+  test_detail::RandomSample<T> y_sampler{0, 2000};
+  test_detail::RandomSample<T> z_sampler{0, 2000};
+
+  for (auto i : boost::irange(test_constants::n_samples)) {
+    std::ignore = i;
+    auto x = nextafter(x_sampler.next(), ((std::numeric_limits<T>::max))());
+    auto y = nextafter(y_sampler.next(), ((std::numeric_limits<T>::max))());
+    auto z = z_sampler.next();
+    BOOST_CHECK_CLOSE(
+        boost::math::ellint_rg(make_fvar<T, m>(x), make_fvar<T, m>(y),
+                               make_fvar<T, m>(z))
+            .derivative(0u),
+        boost::math::ellint_rg(x, y, z), 50 * test_constants::pct_epsilon());
+  }
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(erf_hpp, T, all_float_types) {
+  using test_constants = test_constants_t<T>;
+  static constexpr auto m = test_constants::order;
+  test_detail::RandomSample<T> x_sampler{-2000, 2000};
+  for (auto i : boost::irange(test_constants::n_samples)) {
+    std::ignore = i;
+    auto x = x_sampler.next();
+
+    BOOST_CHECK(isNearZero(erf(make_fvar<T, m>(x)).derivative(0u) -
+                           boost::math::erf(x)));
+    BOOST_CHECK(isNearZero(erfc(make_fvar<T, m>(x)).derivative(0u) -
+                           boost::math::erfc(x)));
+  }
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(expint_hpp, T, all_float_types) {
+  using test_constants = test_constants_t<T>;
+  static constexpr auto m = test_constants::order;
+  test_detail::RandomSample<T> x_sampler{1, 83};
+  for (auto n :
+       boost::irange(1u, static_cast<unsigned>(test_constants::n_samples))) {
+    auto x = x_sampler.next();
+    BOOST_CHECK_CLOSE(boost::math::expint(n, make_fvar<T, m>(x)).derivative(0u),
+                      boost::math::expint(n, x),
+                      200 * test_constants::pct_epsilon());
+
+    for (auto y : {-1, 1}) {
+      BOOST_CHECK_CLOSE(
+          boost::math::expint(make_fvar<T, m>(x * y)).derivative(0u),
+          boost::math::expint(x * y), 200 * test_constants::pct_epsilon());
+    }
+  }
+}
+
+BOOST_AUTO_TEST_SUITE_END()
diff --git a/libs/math/test/test_autodiff_7.cpp b/libs/math/test/test_autodiff_7.cpp
new file mode 100644
index 0000000000..c41d806ae4
--- /dev/null
+++ b/libs/math/test/test_autodiff_7.cpp
@@ -0,0 +1,67 @@
+//           Copyright Matthew Pulver 2018 - 2019.
+// Distributed under the Boost Software License, Version 1.0.
+//      (See accompanying file LICENSE_1_0.txt or copy at
+//           https://www.boost.org/LICENSE_1_0.txt)
+
+#include "test_autodiff.hpp"
+
+BOOST_AUTO_TEST_SUITE(test_autodiff_7)
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(expm1_hpp, T, all_float_types) {
+  using boost::math::differentiation::detail::log;
+  using boost::multiprecision::log;
+  using std::log;
+  using test_constants = test_constants_t<T>;
+  static constexpr auto m = test_constants::order;
+  test_detail::RandomSample<T> x_sampler{-log(T(2000)), log(T(2000))};
+  for (auto i : boost::irange(test_constants::n_samples)) {
+    std::ignore = i;
+    auto x = x_sampler.next();
+    BOOST_CHECK_CLOSE(boost::math::expm1(make_fvar<T, m>(x)).derivative(0u),
+                      boost::math::expm1(x),
+                      50 * test_constants::pct_epsilon());
+  }
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(fpclassify_hpp, T, all_float_types) {
+  using boost::math::fpclassify;
+  using boost::math::isfinite;
+  using boost::math::isinf;
+  using boost::math::isnan;
+  using boost::math::isnormal;
+  using boost::multiprecision::fpclassify;
+  using boost::multiprecision::isfinite;
+  using boost::multiprecision::isinf;
+  using boost::multiprecision::isnan;
+  using boost::multiprecision::isnormal;
+
+  using test_constants = test_constants_t<T>;
+  static constexpr auto m = test_constants::order;
+  test_detail::RandomSample<T> x_sampler{-1000, 1000};
+  for (auto i : boost::irange(test_constants::n_samples)) {
+    std::ignore = i;
+
+    BOOST_CHECK_EQUAL(fpclassify(make_fvar<T, m>(0)), FP_ZERO);
+    BOOST_CHECK_EQUAL(fpclassify(make_fvar<T, m>(10)), FP_NORMAL);
+    BOOST_CHECK_EQUAL(
+        fpclassify(make_fvar<T, m>(std::numeric_limits<T>::infinity())),
+        FP_INFINITE);
+    BOOST_CHECK_EQUAL(
+        fpclassify(make_fvar<T, m>(std::numeric_limits<T>::quiet_NaN())),
+        FP_NAN);
+    if (std::numeric_limits<T>::has_denorm != std::denorm_absent) {
+      BOOST_CHECK_EQUAL(
+          fpclassify(make_fvar<T, m>(std::numeric_limits<T>::denorm_min())),
+          FP_SUBNORMAL);
+    }
+
+    BOOST_CHECK(isfinite(make_fvar<T, m>(0)));
+    BOOST_CHECK(isnormal(make_fvar<T, m>((std::numeric_limits<T>::min)())));
+    BOOST_CHECK(
+        !isnormal(make_fvar<T, m>(std::numeric_limits<T>::denorm_min())));
+    BOOST_CHECK(isinf(make_fvar<T, m>(std::numeric_limits<T>::infinity())));
+    BOOST_CHECK(isnan(make_fvar<T, m>(std::numeric_limits<T>::quiet_NaN())));
+  }
+}
+
+BOOST_AUTO_TEST_SUITE_END()
diff --git a/libs/math/test/test_autodiff_8.cpp b/libs/math/test/test_autodiff_8.cpp
new file mode 100644
index 0000000000..4afab08783
--- /dev/null
+++ b/libs/math/test/test_autodiff_8.cpp
@@ -0,0 +1,506 @@
+//           Copyright Matthew Pulver 2018 - 2019.
+// Distributed under the Boost Software License, Version 1.0.
+//      (See accompanying file LICENSE_1_0.txt or copy at
+//           https://www.boost.org/LICENSE_1_0.txt)
+
+#include "test_autodiff.hpp"
+
+BOOST_AUTO_TEST_SUITE(test_autodiff_8)
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(hermite_hpp, T, all_float_types) {
+  using test_constants = test_constants_t<T>;
+  static constexpr auto m = test_constants::order;
+  test_detail::RandomSample<T> x_sampler{-200, 200};
+  for (auto i : boost::irange(14u)) {
+    auto x = x_sampler.next();
+    auto autodiff_v = boost::math::hermite(i, make_fvar<T, m>(x));
+    auto anchor_v = boost::math::hermite(i, x);
+    BOOST_CHECK(isNearZero(autodiff_v.derivative(0u) - anchor_v));
+  }
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(heuman_lambda_hpp, T, all_float_types) {
+  using test_constants = test_constants_t<T>;
+  static constexpr auto m = test_constants::order;
+  test_detail::RandomSample<T> x_sampler{-1, 1};
+  test_detail::RandomSample<T> phi_sampler{-boost::math::constants::two_pi<T>(),
+                                           boost::math::constants::two_pi<T>()};
+  for (auto i : boost::irange(test_constants::n_samples)) {
+    std::ignore = i;
+    auto x = x_sampler.next();
+    auto phi = phi_sampler.next();
+    auto autodiff_v =
+        boost::math::heuman_lambda(make_fvar<T, m>(x), make_fvar<T, m>(phi));
+    auto anchor_v = boost::math::heuman_lambda(x, phi);
+    BOOST_CHECK(isNearZero(autodiff_v.derivative(0u) - anchor_v));
+  }
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(hypot_hpp, T, all_float_types) {
+  using test_constants = test_constants_t<T>;
+  static constexpr auto m = test_constants::order;
+  test_detail::RandomSample<T> x_sampler{-2000, 2000};
+  test_detail::RandomSample<T> y_sampler{-2000, 2000};
+  for (auto i : boost::irange(test_constants::n_samples)) {
+    std::ignore = i;
+    auto x = x_sampler.next();
+    auto y = y_sampler.next();
+    auto autodiff_v =
+        boost::math::hypot(make_fvar<T, m>(x), make_fvar<T, m>(y));
+    auto anchor_v = boost::math::hypot(x, y);
+    BOOST_CHECK(isNearZero(autodiff_v.derivative(0u) - anchor_v));
+  }
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(jacobi_elliptic_hpp, T, all_float_types) {
+  using test_constants = test_constants_t<T>;
+  static constexpr auto m = test_constants::order;
+  test_detail::RandomSample<T> k_sampler{0, 1};
+  test_detail::RandomSample<T> theta_sampler{-100, 100};
+  for (auto i : boost::irange(test_constants::n_samples)) {
+    std::ignore = i;
+    auto k = k_sampler.next();
+    auto theta = theta_sampler.next();
+    BOOST_CHECK(isNearZero(
+        boost::math::jacobi_cd(make_fvar<T, m>(k), make_fvar<T, m>(theta))
+            .derivative(0u) -
+        boost::math::jacobi_cd(k, theta)));
+    BOOST_CHECK(isNearZero(
+        boost::math::jacobi_cn(make_fvar<T, m>(k), make_fvar<T, m>(theta))
+            .derivative(0u) -
+        boost::math::jacobi_cn(k, theta)));
+    BOOST_CHECK(isNearZero(
+        boost::math::jacobi_cs(make_fvar<T, m>(k), make_fvar<T, m>(theta))
+            .derivative(0u) -
+        boost::math::jacobi_cs(k, theta)));
+    BOOST_CHECK(isNearZero(
+        boost::math::jacobi_dc(make_fvar<T, m>(k), make_fvar<T, m>(theta))
+            .derivative(0u) -
+        boost::math::jacobi_dc(k, theta)));
+    BOOST_CHECK(isNearZero(
+        boost::math::jacobi_dn(make_fvar<T, m>(k), make_fvar<T, m>(theta))
+            .derivative(0u) -
+        boost::math::jacobi_dn(k, theta)));
+    BOOST_CHECK(isNearZero(
+        boost::math::jacobi_ds(make_fvar<T, m>(k), make_fvar<T, m>(theta))
+            .derivative(0u) -
+        boost::math::jacobi_ds(k, theta)));
+    BOOST_CHECK(isNearZero(
+        boost::math::jacobi_nc(make_fvar<T, m>(k), make_fvar<T, m>(theta))
+            .derivative(0u) -
+        boost::math::jacobi_nc(k, theta)));
+    BOOST_CHECK(isNearZero(
+        boost::math::jacobi_nd(make_fvar<T, m>(k), make_fvar<T, m>(theta))
+            .derivative(0u) -
+        boost::math::jacobi_nd(k, theta)));
+    BOOST_CHECK(isNearZero(
+        boost::math::jacobi_ns(make_fvar<T, m>(k), make_fvar<T, m>(theta))
+            .derivative(0u) -
+        boost::math::jacobi_ns(k, theta)));
+    BOOST_CHECK(isNearZero(
+        boost::math::jacobi_sc(make_fvar<T, m>(k), make_fvar<T, m>(theta))
+            .derivative(0u) -
+        boost::math::jacobi_sc(k, theta)));
+    BOOST_CHECK(isNearZero(
+        boost::math::jacobi_sd(make_fvar<T, m>(k), make_fvar<T, m>(theta))
+            .derivative(0u) -
+        boost::math::jacobi_sd(k, theta)));
+    BOOST_CHECK(isNearZero(
+        boost::math::jacobi_sn(make_fvar<T, m>(k), make_fvar<T, m>(theta))
+            .derivative(0u) -
+        boost::math::jacobi_sn(k, theta)));
+  }
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(jacobi_zeta_hpp, T, all_float_types) {
+  using test_constants = test_constants_t<T>;
+  static constexpr auto m = test_constants::order;
+  test_detail::RandomSample<T> x_sampler{-1, 1};
+  test_detail::RandomSample<T> phi_sampler{-boost::math::constants::two_pi<T>(),
+                                           boost::math::constants::two_pi<T>()};
+  for (auto i : boost::irange(test_constants::n_samples)) {
+    std::ignore = i;
+    auto x = x_sampler.next();
+    auto phi = phi_sampler.next();
+    BOOST_CHECK(isNearZero(
+        boost::math::jacobi_zeta(make_fvar<T, m>(x), make_fvar<T, m>(phi))
+            .derivative(0u) -
+        boost::math::jacobi_zeta(x, phi)));
+  }
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(laguerre_hpp, T, all_float_types) {
+  using boost::multiprecision::min;
+  using std::min;
+
+  using test_constants = test_constants_t<T>;
+  static constexpr auto m = test_constants::order;
+  test_detail::RandomSample<unsigned> n_sampler{1, 50};
+  test_detail::RandomSample<unsigned> r_sampler{0, 50};
+  test_detail::RandomSample<T> x_sampler{0, 50};
+
+  for (auto i : boost::irange(test_constants::n_samples)) {
+    std::ignore = i;
+    auto n = n_sampler.next();
+    auto r = (min)(n - 1, r_sampler.next());
+    auto x = x_sampler.next();
+
+    {
+      auto autodiff_v = boost::math::laguerre(n, make_fvar<T, m>(x));
+      auto anchor_v = boost::math::laguerre(n, x);
+      BOOST_CHECK(isNearZero(autodiff_v.derivative(0u) - anchor_v));
+    }
+    {
+      auto autodiff_v = boost::math::laguerre(n, r, make_fvar<T, m>(x));
+      auto anchor_v = boost::math::laguerre(n, r, x);
+      BOOST_CHECK(isNearZero(autodiff_v.derivative(0u) - anchor_v));
+    }
+  }
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(lambert_w_hpp, T, all_float_types) {
+  using boost::math::nextafter;
+  using boost::math::tools::max;
+  using boost::multiprecision::fabs;
+  using boost::multiprecision::min;
+  using detail::fabs;
+  using std::fabs;
+  using std::max;
+  using std::min;
+  using std::nextafter;
+
+  using promoted_t = promote<T, double>;
+  using test_constants = test_constants_t<T>;
+  static constexpr auto m = test_constants::order;
+  test_detail::RandomSample<T> x_sampler{static_cast<T>(-1 / std::exp(-1)),
+                                         ((std::numeric_limits<T>::max))()};
+  for (auto i : boost::irange(test_constants::n_samples)) {
+    std::ignore = i;
+    auto x = x_sampler.next();
+    {
+      auto x_ = (min<T>)(static_cast<T>(((max<promoted_t>))(
+                             -exp(promoted_t(-1)), promoted_t(x))),
+                         ((std::numeric_limits<T>::max))());
+      {
+        auto autodiff_v = boost::math::lambert_w0(make_fvar<T, m>(x_));
+        auto anchor_v = boost::math::lambert_w0(x_);
+        BOOST_CHECK(isNearZero(autodiff_v.derivative(0u) - anchor_v));
+      }
+      {
+        auto autodiff_v = boost::math::lambert_w0_prime(make_fvar<T, m>(x_));
+        auto anchor_v = boost::math::lambert_w0_prime(x_);
+        BOOST_CHECK(isNearZero(autodiff_v.derivative(0u) - anchor_v));
+      }
+    }
+
+    {
+      auto x_ = nextafter(
+          static_cast<T>(nextafter(
+              ((max))(static_cast<promoted_t>(-exp(-1)), -fabs(promoted_t(x))),
+              ((std::numeric_limits<promoted_t>::max))())),
+          ((std::numeric_limits<T>::max))());
+      x_ = (max)(static_cast<T>(-0.36), x_);
+      BOOST_CHECK(isNearZero(
+          boost::math::lambert_wm1(make_fvar<T, m>(x_)).derivative(0u) -
+          boost::math::lambert_wm1(x_)));
+      BOOST_CHECK(isNearZero(
+          boost::math::lambert_wm1_prime(make_fvar<T, m>(x_)).derivative(0u) -
+          boost::math::lambert_wm1_prime(x_)));
+    }
+  }
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(log1p_hpp, T, all_float_types) {
+  using boost::math::log1p;
+  using boost::multiprecision::log1p;
+
+  using test_constants = test_constants_t<T>;
+  static constexpr auto m = test_constants::order;
+  test_detail::RandomSample<T> x_sampler{-1, 2000};
+  for (auto i : boost::irange(test_constants::n_samples)) {
+    std::ignore = i;
+    auto x = x_sampler.next();
+    BOOST_CHECK(
+        isNearZero(log1p(make_fvar<T, m>(x)).derivative(0u) - log1p(x)));
+  }
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(next_hpp, T, all_float_types) {
+  using boost::math::float_advance;
+  using boost::math::float_distance;
+  using boost::math::float_next;
+  using boost::math::float_prior;
+  using boost::math::nextafter;
+  using boost::multiprecision::nextafter;
+
+  using test_constants = test_constants_t<T>;
+  static constexpr auto m = test_constants::order;
+  for (auto i : boost::irange(test_constants::n_samples)) {
+    const auto j = static_cast<T>(i);
+    auto fvar_j = make_fvar<T, m>(j);
+    BOOST_CHECK(isNearZero(float_next(fvar_j).derivative(0u) - float_next(j)));
+    BOOST_CHECK(
+        isNearZero(float_prior(fvar_j).derivative(0u) - float_prior(j)));
+
+    BOOST_CHECK(isNearZero(
+        nextafter(fvar_j, make_fvar<T, m>(static_cast<T>(1))).derivative(0u) -
+        nextafter(j, static_cast<T>(1))));
+    BOOST_CHECK(
+        isNearZero(nextafter(fvar_j, make_fvar<T, m>(static_cast<T>(i + 2))) -
+                   nextafter(j, static_cast<T>(i + 2))));
+    BOOST_CHECK(
+        isNearZero(nextafter(fvar_j, make_fvar<T, m>(static_cast<T>(i + 1)))
+                       .derivative(0u) -
+                   nextafter(j, static_cast<T>(i + 2))));
+    BOOST_CHECK(isNearZero(
+        nextafter(fvar_j, make_fvar<T, m>(static_cast<T>(-1))).derivative(0u) -
+        nextafter(j, static_cast<T>(-1))));
+    BOOST_CHECK(isNearZero(
+        nextafter(fvar_j, make_fvar<T, m>(static_cast<T>(-1 * (i + 2))))
+            .derivative(0u) -
+        nextafter(j, -1 * static_cast<T>(i + 2))));
+
+    BOOST_CHECK(isNearZero(
+        nextafter(fvar_j, make_fvar<T, m>(static_cast<T>(-1 * (i + 1))))
+            .derivative(0u) -
+        nextafter(j, -1 * static_cast<T>(i + 2))));
+
+    BOOST_CHECK(isNearZero(nextafter(fvar_j, fvar_j) - fvar_j));
+
+    BOOST_CHECK(isNearZero(float_advance(fvar_j, 1).derivative(0u) -
+                           float_advance(j, 1)));
+    BOOST_CHECK(isNearZero(float_advance(fvar_j, i + 2).derivative(0u) -
+                           float_advance(j, i + 2)));
+    BOOST_CHECK(isNearZero(
+        float_advance(fvar_j, i + 1).derivative(0u) -
+        float_advance(float_advance(fvar_j, i + 2), -1).derivative(0u)));
+
+    BOOST_CHECK(isNearZero(float_advance(fvar_j, -1).derivative(0u) -
+                           float_advance(j, -1)));
+
+    BOOST_CHECK(isNearZero(
+        float_advance(fvar_j, -i - 1).derivative(0u) -
+        float_advance(float_advance(fvar_j, -i - 2), 1).derivative(0u)));
+
+    BOOST_CHECK(isNearZero(float_advance(fvar_j, 0) - fvar_j));
+
+    BOOST_CHECK(isNearZero(float_distance(fvar_j, j).derivative(0u) -
+                           static_cast<T>(0)));
+    BOOST_CHECK(
+        isNearZero(float_distance(float_next(fvar_j), fvar_j).derivative(0u) -
+                   ((make_fvar<T, m>(-1))).derivative(0u)));
+    BOOST_CHECK(
+        isNearZero(float_distance(float_prior(fvar_j), fvar_j).derivative(0u) -
+                   (make_fvar<T, m>(1)).derivative(0u)));
+  }
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(owens_t_hpp, T, bin_float_types) {
+  BOOST_MATH_STD_USING;
+  using test_constants = test_constants_t<T>;
+  static constexpr auto m = test_constants::order;
+  test_detail::RandomSample<T> h_sampler{-2000, 2000};
+  test_detail::RandomSample<T> a_sampler{-2000, 2000};
+  for (auto i : boost::irange(test_constants::n_samples)) {
+    std::ignore = i;
+    auto h = h_sampler.next();
+    auto a = a_sampler.next();
+    auto autodiff_v =
+        boost::math::owens_t(make_fvar<T, m>(h), make_fvar<T, m>(a));
+    auto anchor_v = boost::math::owens_t(h, a);
+    BOOST_CHECK(isNearZero(autodiff_v.derivative(0u) - anchor_v));
+  }
+}
+
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(pow_hpp, T, all_float_types) {
+  using test_constants = test_constants_t<T>;
+  static constexpr auto m = test_constants::order;
+  for (auto i : boost::irange(10)) {
+    BOOST_CHECK_CLOSE(
+        boost::math::pow<0>(make_fvar<T, m>(static_cast<T>(i))).derivative(0u),
+        boost::math::pow<0>(static_cast<T>(i)), test_constants::pct_epsilon());
+    BOOST_CHECK_CLOSE(
+        boost::math::pow<1>(make_fvar<T, m>(static_cast<T>(i))).derivative(0u),
+        boost::math::pow<1>(static_cast<T>(i)), test_constants::pct_epsilon());
+    BOOST_CHECK_CLOSE(
+        boost::math::pow<2>(make_fvar<T, m>(static_cast<T>(i))).derivative(0u),
+        boost::math::pow<2>(static_cast<T>(i)), test_constants::pct_epsilon());
+    BOOST_CHECK_CLOSE(
+        boost::math::pow<3>(make_fvar<T, m>(static_cast<T>(i))).derivative(0u),
+        boost::math::pow<3>(static_cast<T>(i)), test_constants::pct_epsilon());
+    BOOST_CHECK_CLOSE(
+        boost::math::pow<4>(make_fvar<T, m>(static_cast<T>(i))).derivative(0u),
+        boost::math::pow<4>(static_cast<T>(i)), test_constants::pct_epsilon());
+    BOOST_CHECK_CLOSE(
+        boost::math::pow<5>(make_fvar<T, m>(static_cast<T>(i))).derivative(0u),
+        boost::math::pow<5>(static_cast<T>(i)), test_constants::pct_epsilon());
+    BOOST_CHECK_CLOSE(
+        boost::math::pow<6>(make_fvar<T, m>(static_cast<T>(i))).derivative(0u),
+        boost::math::pow<6>(static_cast<T>(i)), test_constants::pct_epsilon());
+    BOOST_CHECK_CLOSE(
+        boost::math::pow<7>(make_fvar<T, m>(static_cast<T>(i))).derivative(0u),
+        boost::math::pow<7>(static_cast<T>(i)), test_constants::pct_epsilon());
+    BOOST_CHECK_CLOSE(
+        boost::math::pow<8>(make_fvar<T, m>(static_cast<T>(i))).derivative(0u),
+        boost::math::pow<8>(static_cast<T>(i)), test_constants::pct_epsilon());
+    BOOST_CHECK_CLOSE(
+        boost::math::pow<9>(make_fvar<T, m>(static_cast<T>(i))).derivative(0u),
+        boost::math::pow<9>(static_cast<T>(i)), test_constants::pct_epsilon());
+  }
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(polygamma_hpp, T, all_float_types) {
+  using test_constants = test_constants_t<T>;
+  static constexpr auto m = test_constants::order;
+  test_detail::RandomSample<T> x_sampler{0, 2000};
+  for (auto i : boost::irange(test_constants::n_samples)) {
+    auto x = x_sampler.next();
+    try {
+      auto autodiff_v = boost::math::polygamma(i, make_fvar<T, m>(x));
+      auto anchor_v = boost::math::polygamma(i, x);
+      BOOST_CHECK(isNearZero(autodiff_v.derivative(0u) - anchor_v));
+    } catch (const std::overflow_error &) {
+      std::cout << "Overflow Error thrown with inputs i: " << i << " x: " << x
+                << std::endl;
+      BOOST_CHECK_THROW(boost::math::polygamma(i, make_fvar<T, m>(x)),
+                        boost::wrapexcept<std::overflow_error>);
+      BOOST_CHECK_THROW(boost::math::polygamma(i, x),
+                        boost::wrapexcept<std::overflow_error>);
+    }
+  }
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(powm1_hpp, T, all_float_types) {
+  using boost::math::tools::max;
+  using boost::multiprecision::max;
+  using std::max;
+
+  using boost::multiprecision::log;
+  using detail::log;
+  using std::log;
+
+  using boost::multiprecision::min;
+  using std::min;
+
+  using boost::multiprecision::sqrt;
+  using detail::sqrt;
+  using std::sqrt;
+
+  using boost::math::nextafter;
+  using boost::multiprecision::nextafter;
+
+  using test_constants = test_constants_t<T>;
+  static constexpr auto m = test_constants::order;
+  test_detail::RandomSample<T> x_sampler{0, 2000};
+  for (auto i : boost::irange(test_constants::n_samples)) {
+    std::ignore = i;
+    auto x = ((max))(x_sampler.next(),
+                     boost::math::nextafter(static_cast<T>(0),
+                                            ((std::numeric_limits<T>::max))()));
+
+    auto y =
+        ((min))(x_sampler.next(),
+                log(sqrt(((std::numeric_limits<T>::max))()) + 1) / log(x + 1));
+    auto autodiff_v =
+        boost::math::powm1(make_fvar<T, m>(x), make_fvar<T, m>(y));
+    auto anchor_v = boost::math::powm1(x, y);
+    BOOST_CHECK(isNearZero(autodiff_v.derivative(0u) - anchor_v));
+  }
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(sin_pi_hpp, T, all_float_types) {
+  using test_constants = test_constants_t<T>;
+  static constexpr auto m = test_constants::order;
+  test_detail::RandomSample<T> x_sampler{-2000, 2000};
+  for (auto i : boost::irange(test_constants::n_samples)) {
+    std::ignore = i;
+    auto x = x_sampler.next();
+    BOOST_CHECK(
+        isNearZero(boost::math::sin_pi(make_fvar<T, m>(x)).derivative(0u) -
+                   boost::math::sin_pi(x)));
+  }
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(sinhc_hpp, T, all_float_types) {
+  using test_constants = test_constants_t<T>;
+  static constexpr auto m = test_constants::order;
+  test_detail::RandomSample<T> x_sampler{ -80, 80 };
+  for (auto i : boost::irange(test_constants::n_samples)) {
+    std::ignore = i;
+    auto x = x_sampler.next();
+    if (x != 0) {
+      auto autodiff_v = boost::math::sinhc_pi(make_fvar<T, m>(x));
+      auto anchor_v = boost::math::sinhc_pi(x);
+      BOOST_CHECK_CLOSE(autodiff_v.derivative(0u), anchor_v,
+                        50 * test_constants::pct_epsilon());
+    }
+  }
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(spherical_harmonic_hpp, T, all_float_types) {
+  using test_constants = test_constants_t<T>;
+  static constexpr auto m = test_constants::order;
+  test_detail::RandomSample<T> theta_sampler{0,
+                                             boost::math::constants::pi<T>()};
+  test_detail::RandomSample<T> phi_sampler{0,
+                                           boost::math::constants::two_pi<T>()};
+  test_detail::RandomSample<int> r_sampler{0, test_constants::n_samples};
+  for (auto n : boost::irange(
+           1u, static_cast<unsigned>(test_constants::n_samples) + 1u)) {
+    auto theta = theta_sampler.next();
+    auto phi = phi_sampler.next();
+    auto r = (std::min)(static_cast<int>(n) - 1, r_sampler.next());
+    {
+      auto autodiff_v = boost::math::spherical_harmonic(
+          n, r, make_fvar<T, m>(theta), make_fvar<T, m>(phi));
+      auto anchor_v = boost::math::spherical_harmonic(n, r, theta, phi);
+      BOOST_CHECK(
+          isNearZero(autodiff_v.real().derivative(0u) - anchor_v.real()));
+      BOOST_CHECK(
+          isNearZero(autodiff_v.imag().derivative(0u) - anchor_v.imag()));
+    }
+
+    {
+      auto autodiff_v = boost::math::spherical_harmonic_r(
+          n, r, make_fvar<T, m>(theta), make_fvar<T, m>(phi));
+      auto anchor_v = boost::math::spherical_harmonic_r(n, r, theta, phi);
+      BOOST_CHECK(isNearZero(autodiff_v.derivative(0u) - anchor_v));
+    }
+
+    {
+      auto autodiff_v = boost::math::spherical_harmonic_i(
+          n, r, make_fvar<T, m>(theta), make_fvar<T, m>(phi));
+      auto anchor_v = boost::math::spherical_harmonic_i(n, r, theta, phi);
+      BOOST_CHECK(isNearZero(autodiff_v.derivative(0u) - anchor_v));
+    }
+  }
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(sqrt1pm1_hpp, T, all_float_types) {
+  using test_constants = test_constants_t<T>;
+  static constexpr auto m = test_constants::order;
+  test_detail::RandomSample<T> x_sampler{-1, 2000};
+  for (auto i : boost::irange(test_constants::n_samples)) {
+    std::ignore = i;
+    auto x = x_sampler.next();
+    BOOST_CHECK(
+        isNearZero(boost::math::sqrt1pm1(make_fvar<T, m>(x)).derivative(0u) -
+                   boost::math::sqrt1pm1(x)));
+  }
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(trigamma_hpp, T, all_float_types) {
+  using test_constants = test_constants_t<T>;
+  static constexpr auto m = test_constants::order;
+  test_detail::RandomSample<T> x_sampler{0, 2000};
+  for (auto i : boost::irange(test_constants::n_samples)) {
+    std::ignore = i;
+    auto x = x_sampler.next();
+    BOOST_CHECK(
+        isNearZero(boost::math::trigamma(make_fvar<T, m>(x)).derivative(0u) -
+                   boost::math::trigamma(x)));
+  }
+}
+
+BOOST_AUTO_TEST_SUITE_END()
diff --git a/libs/math/test/test_cstdfloat.cpp b/libs/math/test/test_cstdfloat.cpp
index 2ce3c5fdc7..28d64416a8 100644
--- a/libs/math/test/test_cstdfloat.cpp
+++ b/libs/math/test/test_cstdfloat.cpp
@@ -13,7 +13,7 @@
 #include <iomanip>
 #include <sstream>
 #include <string>
-#include <boost/math/cstdfloat/cstdfloat_types.hpp>
+#include <boost/cstdfloat.hpp>
 
 #ifdef _MSC_VER
 #  pragma warning(disable : 4127) // conditional expression is constant.
@@ -24,6 +24,12 @@
 #define BOOST_TEST_MAIN
 #include <boost/test/unit_test.hpp> // Boost.Test
 #include <boost/test/floating_point_comparison.hpp>
+#include <boost/scoped_array.hpp>
+
+//
+// We need to define an iostream operator for __float128 in order to
+// compile this test:
+//
 
 //
 // DESCRIPTION:
@@ -49,6 +55,20 @@
 // the functionality of <cmath>, I/O stream operations, and <complex>
 // functions for boost::float128_t.
 
+// For some reason the (x != x) check fails on Mingw:
+#if !defined(__MINGW64__)
+#define TEST_CSTDFLOAT_SANITY_CHECK_NAN(the_digits)                                                  \
+  {                                                                                                  \
+    using std::sqrt;                                                                                 \
+    const float_type x = sqrt(float_type(test_cstdfloat::minus_one));                                \
+    const bool the_nan_test = (   std::numeric_limits<float_type>::has_quiet_NaN                     \
+                               && (x != x));                                                         \
+    BOOST_CHECK_EQUAL( the_nan_test, true );                                                         \
+  }  
+#else
+#define TEST_CSTDFLOAT_SANITY_CHECK_NAN(the_digits)                                                  
+#endif
+
 #define TEST_CSTDFLOAT_SANITY_CHECK(the_digits)                                                      \
 void sanity_check_##the_digits##_func()                                                              \
 {                                                                                                    \
@@ -83,13 +103,7 @@ void sanity_check_##the_digits##_func()
                                && (x == std::numeric_limits<float_type>::infinity()));               \
     BOOST_CHECK_EQUAL( the_inf_test, true );                                                         \
   }                                                                                                  \
-  {                                                                                                  \
-    using std::sqrt;                                                                                 \
-    const float_type x = sqrt(float_type(test_cstdfloat::minus_one));                                \
-    const bool the_nan_test = (   std::numeric_limits<float_type>::has_quiet_NaN                     \
-                               && (x != x));                                                         \
-    BOOST_CHECK_EQUAL( the_nan_test, true );                                                         \
-  }                                                                                                  \
+  TEST_CSTDFLOAT_SANITY_CHECK_NAN(the_digits)\
   {                                                                                                  \
     const bool the_lim_test =                                                                        \
       (std::numeric_limits<boost::floatmax_t>::digits >= std::numeric_limits<float_type>::digits);   \
@@ -99,72 +113,450 @@ void sanity_check_##the_digits##_func()
 
 namespace test_cstdfloat
 {
-  int zero;
-  int minus_one;
-
-  #if defined(BOOST_FLOATMAX_C)
-  BOOST_CONSTEXPR_OR_CONST int has_floatmax_t = 1;
-  #else
-  BOOST_CONSTEXPR_OR_CONST int has_floatmax_t = 0;
-  #endif
-
-  #if defined(BOOST_FLOAT16_C)
-  TEST_CSTDFLOAT_SANITY_CHECK(16)
-  #endif
-
-  #if defined(BOOST_FLOAT32_C)
-  TEST_CSTDFLOAT_SANITY_CHECK(32)
-  #endif
-
-  #if defined(BOOST_FLOAT64_C)
-  TEST_CSTDFLOAT_SANITY_CHECK(64)
-  #endif
-
-  #if defined(BOOST_FLOAT80_C)
-  TEST_CSTDFLOAT_SANITY_CHECK(80)
-  #endif
-
-  #if defined(BOOST_FLOAT128_C)
-  TEST_CSTDFLOAT_SANITY_CHECK(128)
-
-  void extend_check_128_func()
-  {
-  }
-  #endif // defined (BOOST_FLOAT128_C)
+#if defined(BOOST_FLOAT128_C)
+
+   template <class T, class U>
+   void test_less(T a, U b)
+   {
+      BOOST_CHECK(a < b);
+      BOOST_CHECK(a <= b);
+      BOOST_CHECK(!(a > b));
+      BOOST_CHECK(!(a >= b));
+      BOOST_CHECK(!(a == b));
+      BOOST_CHECK((a != b));
+
+      BOOST_CHECK(b > a);
+      BOOST_CHECK(b >= a);
+      BOOST_CHECK(!(b < a));
+      BOOST_CHECK(!(b <= a));
+      BOOST_CHECK(!(b == a));
+      BOOST_CHECK((b != a));
+
+      BOOST_CHECK(std::isless(a, b));
+      BOOST_CHECK(std::islessequal(a, b));
+      BOOST_CHECK(!std::isgreater(a, b));
+      BOOST_CHECK(!std::isgreaterequal(a, b));
+      BOOST_CHECK(std::islessgreater(a, b));
+
+      BOOST_CHECK(!std::isless(b, a));
+      BOOST_CHECK(!std::islessequal(b, a));
+      BOOST_CHECK(std::isgreater(b, a));
+      BOOST_CHECK(std::isgreaterequal(b, a));
+      BOOST_CHECK(std::islessgreater(b, a));
+   }
+   template <class T, class U>
+   void test_equal(T a, U b)
+   {
+      BOOST_CHECK(!(a < b));
+      BOOST_CHECK(a <= b);
+      BOOST_CHECK(!(a > b));
+      BOOST_CHECK((a >= b));
+      BOOST_CHECK((a == b));
+      BOOST_CHECK(!(a != b));
+
+      BOOST_CHECK(!(b > a));
+      BOOST_CHECK(b >= a);
+      BOOST_CHECK(!(b < a));
+      BOOST_CHECK((b <= a));
+      BOOST_CHECK((b == a));
+      BOOST_CHECK(!(b != a));
+
+      BOOST_CHECK(!std::isless(a, b));
+      BOOST_CHECK(std::islessequal(a, b));
+      BOOST_CHECK(!std::isgreater(a, b));
+      BOOST_CHECK(std::isgreaterequal(a, b));
+      BOOST_CHECK(!std::islessgreater(a, b));
+
+      BOOST_CHECK(!std::isless(b, a));
+      BOOST_CHECK(std::islessequal(b, a));
+      BOOST_CHECK(!std::isgreater(b, a));
+      BOOST_CHECK(std::isgreaterequal(b, a));
+      BOOST_CHECK(!std::islessgreater(b, a));
+   }
+   template <class T, class U>
+   void test_unordered(T a, U b)
+   {
+      BOOST_CHECK(!(a < b));
+      BOOST_CHECK(!(a <= b));
+      BOOST_CHECK(!(a > b));
+      BOOST_CHECK(!(a >= b));
+      BOOST_CHECK(!(a == b));
+      BOOST_CHECK((a != b));
+
+      BOOST_CHECK(!(b > a));
+      BOOST_CHECK(!(b >= a));
+      BOOST_CHECK(!(b < a));
+      BOOST_CHECK(!(b <= a));
+      BOOST_CHECK(!(b == a));
+      BOOST_CHECK((b != a));
+
+      BOOST_CHECK(!std::isless(a, b));
+      BOOST_CHECK(!std::islessequal(a, b));
+      BOOST_CHECK(!std::isgreater(a, b));
+      BOOST_CHECK(!std::isgreaterequal(a, b));
+      BOOST_CHECK(!std::islessgreater(a, b));
+
+      BOOST_CHECK(!std::isless(b, a));
+      BOOST_CHECK(!std::islessequal(b, a));
+      BOOST_CHECK(!std::isgreater(b, a));
+      BOOST_CHECK(!std::isgreaterequal(b, a));
+      BOOST_CHECK(!std::islessgreater(b, a));
+   }
+
+   template <class T>
+   void test()
+   {
+      //
+      // Basic sanity checks for C99 functions which are just imported versions
+      // from Boost.Math.  These should still be found via ADL so no using declarations here...
+      //
+      T val = 2;
+      BOOST_CHECK(std::signbit(val) == 0);
+      BOOST_CHECK(std::signbit(val + 2) == 0);
+      val = -val;
+      BOOST_CHECK(std::signbit(val));
+      BOOST_CHECK(std::signbit(val * 2));
+
+      T s = 2;
+      val = 3;
+      BOOST_CHECK_EQUAL(std::copysign(val, s), 3);
+      BOOST_CHECK_EQUAL(std::copysign(val, s * -2), -3);
+      BOOST_CHECK_EQUAL(std::copysign(-2 * val, s), 6);
+      BOOST_CHECK_EQUAL(std::copysign(-2 * val, 2 * s), 6);
+      s = -2;
+      BOOST_CHECK_EQUAL(std::copysign(val, s), -3);
+      BOOST_CHECK_EQUAL(std::copysign(val, s * -2), 3);
+      BOOST_CHECK_EQUAL(std::copysign(-2 * val, s), -6);
+      BOOST_CHECK_EQUAL(std::copysign(-2 * val, 2 * s), -6);
+      val = -3;
+      BOOST_CHECK_EQUAL(std::copysign(val, s), -3);
+      BOOST_CHECK_EQUAL(std::copysign(val, s * -2), 3);
+      BOOST_CHECK_EQUAL(std::copysign(-2 * val, s), -6);
+      BOOST_CHECK_EQUAL(std::copysign(-2 * val, 2 * s), -6);
+      s = 0;
+      BOOST_CHECK_EQUAL(std::copysign(val, s), 3);
+      BOOST_CHECK_EQUAL(std::copysign(val, s * -2), -3);
+
+      BOOST_CHECK_EQUAL(std::copysign(-2 * val, s), 6);
+      BOOST_CHECK_EQUAL(std::copysign(-2 * val, 2 * s), 6);
+      // Things involving signed zero, need to detect it first:
+
+      val = 3;
+      BOOST_CHECK_EQUAL(std::fpclassify(val), FP_NORMAL);
+      BOOST_CHECK_EQUAL(std::fpclassify(val * 3), FP_NORMAL);
+      BOOST_CHECK(!std::isinf(val));
+      BOOST_CHECK(!std::isinf(val + 2));
+      BOOST_CHECK(!std::isnan(val));
+      BOOST_CHECK(!std::isnan(val + 2));
+      BOOST_CHECK(std::isnormal(val));
+      BOOST_CHECK(std::isnormal(val + 2));
+      val = -3;
+      BOOST_CHECK_EQUAL(std::fpclassify(val), FP_NORMAL);
+      BOOST_CHECK_EQUAL(std::fpclassify(val * 3), FP_NORMAL);
+      BOOST_CHECK(!std::isinf(val));
+      BOOST_CHECK(!std::isinf(val + 2));
+      BOOST_CHECK(!std::isnan(val));
+      BOOST_CHECK(!std::isnan(val + 2));
+      BOOST_CHECK(std::isnormal(val));
+      BOOST_CHECK(std::isnormal(val + 2));
+      val = 0;
+      BOOST_CHECK_EQUAL(std::fpclassify(val), FP_ZERO);
+      BOOST_CHECK_EQUAL(std::fpclassify(val * 3), FP_ZERO);
+      BOOST_CHECK(!std::isinf(val));
+      BOOST_CHECK(!std::isinf(val + 2));
+      BOOST_CHECK(!std::isnan(val));
+      BOOST_CHECK(!std::isnan(val + 2));
+      BOOST_CHECK(!std::isnormal(val));
+      BOOST_CHECK(!std::isnormal(val * 2));
+      BOOST_CHECK(!std::isnormal(val * -2));
+      if (std::numeric_limits<T>::has_infinity)
+      {
+         val = std::numeric_limits<T>::infinity();
+         BOOST_CHECK_EQUAL(std::fpclassify(val), FP_INFINITE);
+         BOOST_CHECK_EQUAL(std::fpclassify(val * 3), FP_INFINITE);
+         BOOST_CHECK(std::isinf(val));
+         BOOST_CHECK(std::isinf(val + 2));
+         BOOST_CHECK(!std::isnan(val));
+         BOOST_CHECK(!std::isnan(val + 2));
+         BOOST_CHECK(!std::isnormal(val));
+         BOOST_CHECK(!std::isnormal(val + 2));
+         val = -val;
+         BOOST_CHECK_EQUAL(std::fpclassify(val), FP_INFINITE);
+         BOOST_CHECK_EQUAL(std::fpclassify(val * 3), FP_INFINITE);
+         BOOST_CHECK(std::isinf(val));
+         BOOST_CHECK(std::isinf(val + 2));
+         BOOST_CHECK(!std::isnan(val));
+         BOOST_CHECK(!std::isnan(val + 2));
+         BOOST_CHECK(!std::isnormal(val));
+         BOOST_CHECK(!std::isnormal(val + 2));
+      }
+      if (std::numeric_limits<T>::has_quiet_NaN)
+      {
+         val = std::numeric_limits <T>::quiet_NaN();
+         BOOST_CHECK_EQUAL(std::fpclassify(val), FP_NAN);
+         BOOST_CHECK_EQUAL(std::fpclassify(val * 3), FP_NAN);
+         BOOST_CHECK(!std::isinf(val));
+         BOOST_CHECK(!std::isinf(val + 2));
+         BOOST_CHECK(std::isnan(val));
+         BOOST_CHECK(std::isnan(val + 2));
+         BOOST_CHECK(!std::isnormal(val));
+         BOOST_CHECK(!std::isnormal(val + 2));
+      }
+      s = 8 * std::numeric_limits<T>::epsilon();
+      val = 2.5;
+      BOOST_CHECK_CLOSE_FRACTION(std::asinh(val), T(1.6472311463710957106248586104436196635044144301932365282203100930843983757633104078778420255069424907777006132075516484778755360595913172299093829522950397895699619540523579875476513967578478619028438291006578604823887119907434Q), s);
+      BOOST_CHECK_CLOSE_FRACTION(std::acosh(val), T(1.5667992369724110786640568625804834938620823510926588639329459980122148134693922696279968499622201141051039184050936311066453565386393240356562374302417843319480223211857615778787272615171906055455922537080327062362258846337050Q), s);
+      val = 0.5;
+      BOOST_CHECK_CLOSE_FRACTION(std::atanh(val), T(0.5493061443340548456976226184612628523237452789113747258673471668187471466093044834368078774068660443939850145329789328711840021129652599105264009353836387053015813845916906835896868494221804799518712851583979557605727959588753Q), s);
+      val = 55.25;
+      BOOST_CHECK_CLOSE_FRACTION(std::cbrt(val), T(3.8087058015466360309383876359583281382991983919300128125378938779672144843676192684301168479657279498120767424724024965319869248797423276064015643361426189576415670917818313417529572608229017809069355688606687557031643655896118Q), s);
+      val = 2.75;
+      BOOST_CHECK_CLOSE_FRACTION(std::erf(val), T(0.9998993780778803631630956080249130432349352621422640655161095794654526422025908961447328296681056892975214344779300734620255391682713519265048496199034963706976420982849598189071465666866369396765001072187538732800143945532487Q), s);
+      BOOST_CHECK_CLOSE_FRACTION(std::erfc(val), T(0.0001006219221196368369043919750869567650647378577359344838904205345473577974091038552671703318943107024785655220699265379744608317286480734951503800965036293023579017150401810928534333133630603234998927812461267199856054467512Q), s);
+      val = 0.125;
+      BOOST_CHECK_CLOSE_FRACTION(std::expm1(val), T(0.1331484530668263168290072278117938725655031317451816259128200360788235778800483865139399907949417285732315270156473075657048210452584733998785564025916995261162759280700397984729320345630340659469435372721057879969170503978449Q), s);
+
+      val = 20;
+      s = 2;
+      BOOST_CHECK_EQUAL(std::fdim(val, s), 18);
+      BOOST_CHECK_EQUAL(std::fdim(s, val), 0);
+      BOOST_CHECK_EQUAL(std::fdim(val, s * 2), 16);
+      BOOST_CHECK_EQUAL(std::fdim(s * 2, val), 0);
+      BOOST_CHECK_EQUAL(std::fdim(val, 2), 18);
+      BOOST_CHECK_EQUAL(std::fdim(2, val), 0);
+
+      BOOST_CHECK_EQUAL(std::fmax(val, s), val);
+      BOOST_CHECK_EQUAL(std::fmax(s, val), val);
+      BOOST_CHECK_EQUAL(std::fmax(val * 2, s), val * 2);
+      BOOST_CHECK_EQUAL(std::fmax(val, s * 2), val);
+      BOOST_CHECK_EQUAL(std::fmax(val * 2, s * 2), val * 2);
+      BOOST_CHECK_EQUAL(std::fmin(val, s), s);
+      BOOST_CHECK_EQUAL(std::fmin(s, val), s);
+      BOOST_CHECK_EQUAL(std::fmin(val * 2, s), s);
+      BOOST_CHECK_EQUAL(std::fmin(val, s * 2), s * 2);
+      BOOST_CHECK_EQUAL(std::fmin(val * 2, s * 2), s * 2);
+
+      BOOST_CHECK_EQUAL(std::fmax(val, 2), val);
+      BOOST_CHECK_EQUAL(std::fmax(val, 2.0), val);
+      BOOST_CHECK_EQUAL(std::fmax(20, s), val);
+      BOOST_CHECK_EQUAL(std::fmax(20.0, s), val);
+      BOOST_CHECK_EQUAL(std::fmin(val, 2), s);
+      BOOST_CHECK_EQUAL(std::fmin(val, 2.0), s);
+      BOOST_CHECK_EQUAL(std::fmin(20, s), s);
+      BOOST_CHECK_EQUAL(std::fmin(20.0, s), s);
+      if (std::numeric_limits<T>::has_quiet_NaN)
+      {
+         BOOST_CHECK_EQUAL(std::fmax(val, std::numeric_limits<T>::quiet_NaN()), val);
+         BOOST_CHECK_EQUAL(std::fmax(std::numeric_limits<T>::quiet_NaN(), val), val);
+         BOOST_CHECK_EQUAL(std::fmin(val, std::numeric_limits<T>::quiet_NaN()), val);
+         BOOST_CHECK_EQUAL(std::fmin(std::numeric_limits<T>::quiet_NaN(), val), val);
+      }
+      if (std::numeric_limits<double>::has_quiet_NaN)
+      {
+         BOOST_CHECK_EQUAL(std::fmax(val, std::numeric_limits<double>::quiet_NaN()), val);
+         BOOST_CHECK_EQUAL(std::fmax(std::numeric_limits<double>::quiet_NaN(), val), val);
+         BOOST_CHECK_EQUAL(std::fmin(val, std::numeric_limits<double>::quiet_NaN()), val);
+         BOOST_CHECK_EQUAL(std::fmin(std::numeric_limits<double>::quiet_NaN(), val), val);
+      }
+
+      test_less(s, val);
+      test_less(2, val);
+      test_less(s, 20);
+      test_less(s + 0, val);
+      test_less(s, val * 1);
+      test_less(s * 1, val * 1);
+      test_less(s * 1, 20);
+      test_less(s + 2, val * 2);
+
+      test_equal(val, val);
+      test_equal(20, val);
+      test_equal(val, 20);
+      test_equal(val + 0, val);
+      test_equal(val, val * 1);
+      test_equal(val * 1, val * 1);
+      test_equal(val * 1, 20);
+      test_equal(val * 20, val * 20);
+
+      if (std::numeric_limits<T>::has_quiet_NaN)
+      {
+         s = std::numeric_limits<T>::quiet_NaN();
+         test_unordered(s, val);
+         test_unordered(s, 20);
+         test_unordered(s + 0, val);
+         test_unordered(s, val * 1);
+         test_unordered(s * 1, val * 1);
+         test_unordered(s * 1, 20);
+         test_unordered(s + 2, val * 2);
+         if (std::numeric_limits<double>::has_quiet_NaN)
+         {
+            double n = std::numeric_limits<double>::quiet_NaN();
+            test_unordered(n, val);
+         }
+      }
+
+      T tol = 8 * std::numeric_limits<T>::epsilon();
+      s = 2;
+      BOOST_CHECK_CLOSE_FRACTION(T(std::hypot(val, s)), T(20.099751242241780540438529825519152373890046940052754581145656594656982463103940762472355384907904704732599006530Q), tol);
+      BOOST_CHECK_CLOSE_FRACTION(T(std::hypot(val, 2)), T(20.099751242241780540438529825519152373890046940052754581145656594656982463103940762472355384907904704732599006530Q), tol);
+      BOOST_CHECK_CLOSE_FRACTION(T(std::hypot(val, 2.0)), T(20.099751242241780540438529825519152373890046940052754581145656594656982463103940762472355384907904704732599006530Q), tol);
+      BOOST_CHECK_CLOSE_FRACTION(T(std::hypot(20, s)), T(20.099751242241780540438529825519152373890046940052754581145656594656982463103940762472355384907904704732599006530Q), tol);
+      BOOST_CHECK_CLOSE_FRACTION(T(std::hypot(20.0, s)), T(20.099751242241780540438529825519152373890046940052754581145656594656982463103940762472355384907904704732599006530Q), tol);
+      BOOST_CHECK_CLOSE_FRACTION(T(std::hypot(val * 1, s)), T(20.099751242241780540438529825519152373890046940052754581145656594656982463103940762472355384907904704732599006530Q), tol);
+      BOOST_CHECK_CLOSE_FRACTION(T(std::hypot(val * 1, s * 1)), T(20.099751242241780540438529825519152373890046940052754581145656594656982463103940762472355384907904704732599006530Q), tol);
+      BOOST_CHECK_CLOSE_FRACTION(T(std::hypot(val * 1, 2)), T(20.099751242241780540438529825519152373890046940052754581145656594656982463103940762472355384907904704732599006530Q), tol);
+      BOOST_CHECK_CLOSE_FRACTION(T(std::hypot(val * 1, 2.0)), T(20.099751242241780540438529825519152373890046940052754581145656594656982463103940762472355384907904704732599006530Q), tol);
+      BOOST_CHECK_CLOSE_FRACTION(T(std::hypot(20, s * 1)), T(20.099751242241780540438529825519152373890046940052754581145656594656982463103940762472355384907904704732599006530Q), tol);
+      BOOST_CHECK_CLOSE_FRACTION(T(std::hypot(20.0, s * 1)), T(20.099751242241780540438529825519152373890046940052754581145656594656982463103940762472355384907904704732599006530Q), tol);
+
+      BOOST_CHECK_CLOSE_FRACTION(std::lgamma(val), T(39.339884187199494036224652394567381081691457206897853119937969989377572554993874476249340525204204720861169039582Q), tol);
+      BOOST_CHECK_CLOSE_FRACTION(std::lgamma(val + 0), T(39.339884187199494036224652394567381081691457206897853119937969989377572554993874476249340525204204720861169039582Q), tol);
+
+      BOOST_CHECK_EQUAL(std::lrint(val), 20);
+      BOOST_CHECK_EQUAL(std::lrint(val * 2), 40);
+      BOOST_CHECK_EQUAL(std::llrint(val), 20);
+      BOOST_CHECK_EQUAL(std::llrint(val * 2), 40);
+
+      val = 0.125;
+      BOOST_CHECK_CLOSE_FRACTION(std::log1p(val), T(0.117783035656383454538794109470521705068480712564733141107348638794807720528133786929641528638208114949935615070Q), tol);
+      BOOST_CHECK_CLOSE_FRACTION(std::log1p(val + 0), T(0.117783035656383454538794109470521705068480712564733141107348638794807720528133786929641528638208114949935615070Q), tol);
+      val = 20;
+      BOOST_CHECK_CLOSE_FRACTION(T(std::log2(val)), T(4.321928094887362347870319429489390175864831393024580612054756395815934776608625215850139743359370155099657371710Q), tol);
+      BOOST_CHECK_CLOSE_FRACTION(T(std::log2(val + 0)), T(4.321928094887362347870319429489390175864831393024580612054756395815934776608625215850139743359370155099657371710Q), tol);
+
+      BOOST_CHECK_EQUAL(T(std::nearbyint(val)), 20);
+      BOOST_CHECK_EQUAL(T(std::nearbyint(val + 0.25)), 20);
+      BOOST_CHECK_EQUAL(T(std::rint(val)), 20);
+      BOOST_CHECK_EQUAL(T(std::rint(val + 0.25)), 20);
+
+      BOOST_CHECK_GT(std::nextafter(val, T(200)), val);
+      BOOST_CHECK_GT(std::nextafter(val + 0, T(200)), val);
+      BOOST_CHECK_GT(std::nextafter(val + 0, T(200) + 1), val);
+      BOOST_CHECK_GT(std::nextafter(val, T(200) + 1), val);
+
+      BOOST_CHECK_GT(std::nexttoward(val, T(200)), val);
+      BOOST_CHECK_GT(std::nexttoward(val + 0, T(200)), val);
+      BOOST_CHECK_GT(std::nexttoward(val + 0, T(200) + 1), val);
+      BOOST_CHECK_GT(std::nexttoward(val, T(200) + 1), val);
+
+      val = 21;
+      s = 5;
+      BOOST_CHECK_EQUAL(T(std::remainder(val, s)), 1);
+      BOOST_CHECK_EQUAL(T(std::remainder(val, 5)), 1);
+      BOOST_CHECK_EQUAL(T(std::remainder(21, s)), 1);
+      BOOST_CHECK_EQUAL(T(std::remainder(val * 1, s)), 1);
+      BOOST_CHECK_EQUAL(T(std::remainder(val * 1, s * 1)), 1);
+      BOOST_CHECK_EQUAL(T(std::remainder(val, s * 1)), 1);
+      BOOST_CHECK_EQUAL(T(std::remainder(val * 1, 5)), 1);
+      BOOST_CHECK_EQUAL(T(std::remainder(21, s * 1)), 1);
+      int i(0);
+      BOOST_CHECK_EQUAL(T(std::remquo(val, s, &i)), 1);
+      BOOST_CHECK_EQUAL(i, 4);
+      i = 0;
+      BOOST_CHECK_EQUAL(T(std::remquo(val, 5, &i)), 1);
+      BOOST_CHECK_EQUAL(i, 4);
+      i = 0;
+      BOOST_CHECK_EQUAL(T(std::remquo(21, s, &i)), 1);
+      BOOST_CHECK_EQUAL(i, 4);
+      i = 0;
+      BOOST_CHECK_EQUAL(T(std::remquo(val * 1, s, &i)), 1);
+      BOOST_CHECK_EQUAL(i, 4);
+      i = 0;
+      BOOST_CHECK_EQUAL(T(std::remquo(val * 1, s * 1, &i)), 1);
+      BOOST_CHECK_EQUAL(i, 4);
+      i = 0;
+      BOOST_CHECK_EQUAL(T(std::remquo(val, s * 1, &i)), 1);
+      BOOST_CHECK_EQUAL(i, 4);
+      i = 0;
+      BOOST_CHECK_EQUAL(T(std::remquo(val * 1, 5, &i)), 1);
+      BOOST_CHECK_EQUAL(i, 4);
+      i = 0;
+      BOOST_CHECK_EQUAL(T(std::remquo(21, s * 1, &i)), 1);
+      BOOST_CHECK_EQUAL(i, 4);
+      i = 0;
+      val = 5.25;
+      tol = 3000;
+      BOOST_CHECK_CLOSE_FRACTION(std::tgamma(val), T(35.211611852799685705225257690531248115026311138908448314086859575901217653313145619623624570033258659272301335544Q), tol);
+      BOOST_CHECK_CLOSE_FRACTION(std::tgamma(val + 1), T(184.86096222719834995243260287528905260388813347926935364895601277348139267989401450302402899267460796117958201160Q), tol);
+
+      BOOST_CHECK_CLOSE_FRACTION(T(std::exp2(val)), T(38.054627680087074134959999057935229289375106958842157216608071191022933383261349115865003025220405558913196632792Q), tol);
+      BOOST_CHECK_CLOSE_FRACTION(T(std::exp2(val + 1)), T(76.109255360174148269919998115870458578750213917684314433216142382045866766522698231730006050440811117826393265585Q), tol);
+      val = 15;
+      BOOST_CHECK_CLOSE_FRACTION(T(std::exp2(val)), T(32768uL), tol);
+      BOOST_CHECK_CLOSE_FRACTION(T(std::exp2(val + 1)), T(65536uL), tol);
+
+      i = std::fpclassify(val) + std::isgreaterequal(val, s) + std::islessequal(val, s) + std::isnan(val) + std::isunordered(val, s)
+         + std::isfinite(val) + std::isinf(val) + std::islessgreater(val, s) + std::isnormal(val) + std::signbit(val) + std::isgreater(val, s) + std::isless(val, s);
+   }
+
+#endif
+
+   int zero;
+   int minus_one;
+
+#if defined(BOOST_FLOATMAX_C)
+   BOOST_CONSTEXPR_OR_CONST int has_floatmax_t = 1;
+#else
+   BOOST_CONSTEXPR_OR_CONST int has_floatmax_t = 0;
+#endif
+
+#if defined(BOOST_FLOAT16_C)
+   TEST_CSTDFLOAT_SANITY_CHECK(16)
+#endif
+
+#if defined(BOOST_FLOAT32_C)
+      TEST_CSTDFLOAT_SANITY_CHECK(32)
+#endif
+
+#if defined(BOOST_FLOAT64_C)
+      TEST_CSTDFLOAT_SANITY_CHECK(64)
+#endif
+
+#if defined(BOOST_FLOAT80_C)
+      TEST_CSTDFLOAT_SANITY_CHECK(80)
+#endif
+
+#if defined(BOOST_FLOAT128_C)
+      TEST_CSTDFLOAT_SANITY_CHECK(128)
+
+      void extend_check_128_func()
+   {
+      test<boost::float128_t>();
+   }
+#endif // defined (BOOST_FLOAT128_C)
 }
 
 BOOST_AUTO_TEST_CASE(test_main)
 {
-  test_cstdfloat::zero      =  0;
-  test_cstdfloat::minus_one = -1;
+   test_cstdfloat::zero = 0;
+   test_cstdfloat::minus_one = -1;
 
-  // Perform basic sanity checks that verify both the existence of the proper
-  // floating-point literal macros as well as the correct digit handling
-  // for a given floating-point typedef having specified width.
+   // Perform basic sanity checks that verify both the existence of the proper
+   // floating-point literal macros as well as the correct digit handling
+   // for a given floating-point typedef having specified width.
 
-  BOOST_CHECK_EQUAL( test_cstdfloat::has_floatmax_t, 1 );
+   BOOST_CHECK_EQUAL(test_cstdfloat::has_floatmax_t, 1);
 
-  #if defined(BOOST_FLOAT16_C)
-  test_cstdfloat::sanity_check_16_func();
-  #endif
+#if defined(BOOST_FLOAT16_C)
+   test_cstdfloat::sanity_check_16_func();
+#endif
 
-  #if defined(BOOST_FLOAT32_C)
-  test_cstdfloat::sanity_check_32_func();
-  #endif
+#if defined(BOOST_FLOAT32_C)
+   test_cstdfloat::sanity_check_32_func();
+#endif
 
-  #if defined(BOOST_FLOAT64_C)
-  test_cstdfloat::sanity_check_64_func();
-  #endif
+#if defined(BOOST_FLOAT64_C)
+   test_cstdfloat::sanity_check_64_func();
+#endif
 
-  #if defined(BOOST_FLOAT80_C)
-  test_cstdfloat::sanity_check_80_func();
-  #endif
+#if defined(BOOST_FLOAT80_C)
+   test_cstdfloat::sanity_check_80_func();
+#endif
 
-  #if defined(BOOST_FLOAT128_C)
-  test_cstdfloat::sanity_check_128_func();
+#if defined(BOOST_FLOAT128_C)
+   test_cstdfloat::sanity_check_128_func();
 
-  // Perform an extended check of boost::float128_t including
-  // a variety of functions from the C++ standard library.
-  test_cstdfloat::extend_check_128_func();
-  #endif // defined (BOOST_FLOAT128_C)
+   // Perform an extended check of boost::float128_t including
+   // a variety of functions from the C++ standard library.
+   test_cstdfloat::extend_check_128_func();
+#endif // defined (BOOST_FLOAT128_C)
 }
diff --git a/libs/math/test/test_ellint_1.hpp b/libs/math/test/test_ellint_1.hpp
index b03d0583db..0e94b324b9 100644
--- a/libs/math/test/test_ellint_1.hpp
+++ b/libs/math/test/test_ellint_1.hpp
@@ -84,7 +84,7 @@ void test_spots(T, const char* type_name)
 {
     // Function values calculated on http://functions.wolfram.com/
     // Note that Mathematica's EllipticF accepts k^2 as the second parameter.
-    static const boost::array<boost::array<typename table_type<T>::type, 3>, 19> data1 = {{
+    static const boost::array<boost::array<typename table_type<T>::type, 3>, 22> data1 = {{
         {{ SC_(0.0), SC_(0.0), SC_(0.0) }},
         {{ SC_(-10.0), SC_(0.0), SC_(-10.0) }},
         {{ SC_(-1.0), SC_(-1.0), SC_(-1.2261911708835170708130609674719067527242483502207) }},
@@ -104,6 +104,10 @@ void test_spots(T, const char* type_name)
         {{ SC_(-4.0), SC_(0.5), SC_(-4.2543274975235836861894752787874633017836785640477) }},
         {{ SC_(-6.0), SC_(0.5), SC_(-6.4588766202317746302999080620490579800463614807916) }},
         {{ SC_(-10.0), SC_(0.5), SC_(-10.697409951222544858346795279378531495869386960090) }},
+        // Some values where k is > 1:
+        {{ static_cast<typename table_type<T>::type>(2)/13, static_cast<typename table_type<T>::type>(15)/13, SC_(0.154661869446904722070471580919758948531148566762183486996920)}},
+        {{ static_cast<typename table_type<T>::type>(2)/13, static_cast<typename table_type<T>::type>(19)/13, SC_(0.155166467455029577314314021156113481657713115640002027219)}},
+        {{ static_cast<typename table_type<T>::type>(2)/13, static_cast<typename table_type<T>::type>(32)/13, SC_(0.15776272074094290829870142225970052217542486917945444918)}},
     }};
 
     do_test_ellint_f<T>(data1, type_name, "Elliptic Integral F: Mathworld Data");
@@ -131,5 +135,15 @@ void test_spots(T, const char* type_name)
 #include "ellint_k_data.ipp"
 
     do_test_ellint_k<T>(ellint_k_data, type_name, "Elliptic Integral K: Random Data");
+
+    //
+    // Test error handling:
+    //
+    BOOST_CHECK_GE(boost::math::ellint_1(T(1)), boost::math::tools::max_value<T>());
+    BOOST_CHECK_GE(boost::math::ellint_1(T(-1)), boost::math::tools::max_value<T>());
+    BOOST_CHECK_THROW(boost::math::ellint_1(T(1.0001)), std::domain_error);
+    BOOST_CHECK_THROW(boost::math::ellint_1(T(-1.0001)), std::domain_error);
+    BOOST_CHECK_THROW(boost::math::ellint_1(T(2.2), T(0.5)), std::domain_error);
+    BOOST_CHECK_THROW(boost::math::ellint_1(T(-2.2), T(0.5)), std::domain_error);
 }
 
diff --git a/libs/math/test/test_ellint_2.hpp b/libs/math/test/test_ellint_2.hpp
index 2de80fcaf0..a48e4cecb6 100644
--- a/libs/math/test/test_ellint_2.hpp
+++ b/libs/math/test/test_ellint_2.hpp
@@ -84,7 +84,7 @@ void test_spots(T, const char* type_name)
     BOOST_MATH_STD_USING
     // Function values calculated on http://functions.wolfram.com/
     // Note that Mathematica's EllipticE accepts k^2 as the second parameter.
-    static const boost::array<boost::array<typename table_type<T>::type, 3>, 10> data1 = {{
+    static const boost::array<boost::array<typename table_type<T>::type, 3>, 12> data1 = {{
         {{ SC_(0.0), SC_(0.0), SC_(0.0) }},
         {{ SC_(-10.0), SC_(0.0), SC_(-10.0) }},
         {{ SC_(-1.0), SC_(-1.0), SC_(-0.84147098480789650665250232163029899962256306079837) }},
@@ -95,6 +95,8 @@ void test_spots(T, const char* type_name)
         {{ SC_(1e+10), SC_(-0.5), SC_(9.3421545766487137036576748555295222252286528414669e9) }},
         {{ SC_(7.3786976294838206464e19) /*static_cast<T>(ldexp(T(1), 66))*/, SC_(0.390625) /*T(400) / 1024*/, SC_(7.0886102721911705466476846969992069994308167515242e19) }},
         {{ SC_(9.3536104789177786765035829293842113257979682750464e49) /*static_cast<T>(ldexp(T(1), 166))*/, SC_(0.87890625) /*T(900) / 1024*/, SC_(7.1259011068364515942912094521783688927118026465790e49) }},
+        {{ SC_(0.25), SC_(1.5), SC_(0.244087118441983436818717707617920319373286836562840) }},
+        {{ SC_(0.125), SC_(4.5), SC_(0.118076756678411098995742003403224531993649663256045) }},
     }};
 
     do_test_ellint_e2<T>(data1, type_name, "Elliptic Integral E: Mathworld Data");
@@ -128,5 +130,12 @@ void test_spots(T, const char* type_name)
        {{ SC_(0.00097656250000000000000000000000000000000000000000000), SC_(0.5), SC_(0.00097656246119489873806295171767681128826061680891539) }},{{ SC_(0.00048828125000000000000000000000000000000000000000000), SC_(0.5), SC_(0.00048828124514936177847275804383491089917731651869089) }},{{ SC_(0.00024414062500000000000000000000000000000000000000000), SC_(0.5), SC_(0.00024414062439367020469080959924292294147407037569089) }},{{ SC_(0.00012207031250000000000000000000000000000000000000000), SC_(0.5), SC_(0.00012207031242420877503577978533579671450656676021144) }},{{ SC_(0.000061035156250000000000000000000000000000000000000000), SC_(0.5), SC_(0.000061035156240526096862267116434822602398026203555135) }},{{ SC_(0.000030517578125000000000000000000000000000000000000000), SC_(0.5), SC_(0.000030517578123815762107245722156263286910312978330942) }},{{ SC_(0.000015258789062500000000000000000000000000000000000000), SC_(0.5), SC_(0.000015258789062351970263388913163340973814136929083865) }},{{ SC_(7.6293945312500000000000000000000000000000000000000e-6), SC_(0.5), SC_(7.6293945312314962829230890795991108894734462126936e-6) }},{{ SC_(3.8146972656250000000000000000000000000000000000000e-6), SC_(0.5), SC_(3.8146972656226870353653697266430602974836595561218e-6) }},{{ SC_(1.9073486328125000000000000000000000000000000000000e-6), SC_(0.5), SC_(1.9073486328122108794206707030707941437882919842603e-6) }},{{ SC_(9.5367431640625000000000000000000000000000000000000e-7), SC_(0.5), SC_(9.5367431640621385992758382186011213067376941980499e-7) }},{{ SC_(4.7683715820312500000000000000000000000000000000000e-7), SC_(0.5), SC_(4.7683715820312048249094797723177223079355575583105e-7) }},{{ SC_(2.3841857910156250000000000000000000000000000000000e-7), SC_(0.5), SC_(2.3841857910156193531136849713832334805104830239272e-7) }},{{ SC_(1.1920928955078125000000000000000000000000000000000e-7), SC_(0.5), SC_(1.1920928955078117941392106214180141285643896716624e-7) }},{{ SC_(5.9604644775390625000000000000000000000000000000000e-8), SC_(0.5), SC_(5.9604644775390616176740132767709895180494181165759e-8) }},{{ SC_(2.9802322387695312500000000000000000000000000000000e-8), SC_(0.5), SC_(2.9802322387695311397092516595963259352981751091479e-8) }},{{ SC_(1.4901161193847656250000000000000000000000000000000e-8), SC_(0.5), SC_(1.4901161193847656112136564574495392495854593212863e-8) }},{{ SC_(7.4505805969238281250000000000000000000000000000000e-9), SC_(0.5), SC_(7.4505805969238281077670705718119235956296952243088e-9) }},{{ SC_(3.7252902984619140625000000000000000000000000000000e-9), SC_(0.5), SC_(3.7252902984619140603458838214764904348802078740605e-9) }},{{ SC_(1.8626451492309570312500000000000000000000000000000e-9), SC_(0.5), SC_(1.8626451492309570309807354776845613039046039833520e-9) }},{{ SC_(9.3132257461547851562500000000000000000000000000000e-10), SC_(0.5), SC_(9.3132257461547851559134193471057016297384356039070e-10) }},{{ SC_(4.6566128730773925781250000000000000000000000000000e-10), SC_(0.5), SC_(4.6566128730773925780829274183882127037128569700108e-10) }},{{ SC_(2.3283064365386962890625000000000000000000000000000e-10), SC_(0.5), SC_(2.3283064365386962890572409272985265879639681374864e-10) }},{{ SC_(1.1641532182693481445312500000000000000000000000000e-10), SC_(0.5), SC_(1.1641532182693481445305926159123158234954916739431e-10) }},{{ SC_(5.8207660913467407226562500000000000000000000000000e-11), SC_(0.5), SC_(5.8207660913467407226554282698903947793693632351656e-11) }},{{ SC_(2.9103830456733703613281250000000000000000000000000e-11), SC_(0.5), SC_(2.9103830456733703613280222837362993474211703619812e-11) }},{{ SC_(1.4551915228366851806640625000000000000000000000000e-11), SC_(0.5), SC_(1.4551915228366851806640496604670374184276462939222e-11) }},{{ SC_(7.2759576141834259033203125000000000000000000000000e-12), SC_(0.5), SC_(7.2759576141834259033202964505837967730345578669885e-12) }},{{ SC_(3.6379788070917129516601562500000000000000000000000e-12), SC_(0.5), SC_(3.6379788070917129516601542438229745966293197333606e-12) }},{{ SC_(1.8189894035458564758300781250000000000000000000000e-12), SC_(0.5), SC_(1.8189894035458564758300778742278718245786649666697e-12) }},{{ SC_(9.0949470177292823791503906250000000000000000000000e-13), SC_(0.5), SC_(9.0949470177292823791503903115348397807233312083370e-13) }},{{ SC_(4.5474735088646411895751953125000000000000000000000e-13), SC_(0.5), SC_(4.5474735088646411895751952733168549725904164010421e-13) }},{{ SC_(2.2737367544323205947875976562500000000000000000000e-13), SC_(0.5), SC_(2.2737367544323205947875976513521068715738020501303e-13) }},{{ SC_(1.1368683772161602973937988281250000000000000000000e-13), SC_(0.5), SC_(1.1368683772161602973937988275127633589467252562663e-13) }},{{ SC_(5.6843418860808014869689941406250000000000000000000e-14), SC_(0.5), SC_(5.6843418860808014869689941398597041986834065703329e-14) }},{{ SC_(2.8421709430404007434844970703125000000000000000000e-14), SC_(0.5), SC_(2.8421709430404007434844970702168380248354258212916e-14) }},{{ SC_(1.4210854715202003717422485351562500000000000000000e-14), SC_(0.5), SC_(1.4210854715202003717422485351442922531044282276615e-14) }},{{ SC_(7.1054273576010018587112426757812500000000000000000e-15), SC_(0.5), SC_(7.1054273576010018587112426757663028163805352845768e-15) }},{{ SC_(3.5527136788005009293556213378906250000000000000000e-15), SC_(0.5), SC_(3.5527136788005009293556213378887566020475669105721e-15) }},{{ SC_(1.7763568394002504646778106689453125000000000000000e-15), SC_(0.5), SC_(1.7763568394002504646778106689450789502559458638215e-15) }},{{ SC_(8.8817841970012523233890533447265625000000000000000e-16), SC_(0.5), SC_(8.8817841970012523233890533447262705628199323297769e-16) }},{{ SC_(4.4408920985006261616945266723632812500000000000000e-16), SC_(0.5), SC_(4.4408920985006261616945266723632447578524915412221e-16) }},{{ SC_(2.2204460492503130808472633361816406250000000000000e-16), SC_(0.5), SC_(2.2204460492503130808472633361816360634815614426528e-16) }},{{ SC_(1.1102230246251565404236316680908203125000000000000e-16), SC_(0.5), SC_(1.1102230246251565404236316680908197423101951803316e-16) }},{{ SC_(5.5511151231257827021181583404541015625000000000000e-17), SC_(0.5), SC_(5.5511151231257827021181583404541008497627439754145e-17) }},{{ SC_(2.7755575615628913510590791702270507812500000000000e-17), SC_(0.5), SC_(2.7755575615628913510590791702270506921578429969268e-17) }},{{ SC_(1.3877787807814456755295395851135253906250000000000e-17), SC_(0.5), SC_(1.3877787807814456755295395851135253794884803746159e-17) }},{{ SC_(6.9388939039072283776476979255676269531250000000000e-18), SC_(0.5), SC_(6.9388939039072283776476979255676269392043504682698e-18) }},{{ SC_(3.4694469519536141888238489627838134765625000000000e-18), SC_(0.5), SC_(3.4694469519536141888238489627838134748224188085337e-18) }},{{ SC_(1.7347234759768070944119244813919067382812500000000e-18), SC_(0.5), SC_(1.7347234759768070944119244813919067380637398510667e-18) }},{{ SC_(8.6736173798840354720596224069595336914062500000000e-19), SC_(0.5), SC_(8.6736173798840354720596224069595336911343623138334e-19) }},{{ SC_(4.3368086899420177360298112034797668457031250000000e-19), SC_(0.5), SC_(4.3368086899420177360298112034797668456691390392292e-19) }},{{ SC_(2.1684043449710088680149056017398834228515625000000e-19), SC_(0.5), SC_(2.1684043449710088680149056017398834228473142549036e-19) }},{{ SC_(1.0842021724855044340074528008699417114257812500000e-19), SC_(0.5), SC_(1.0842021724855044340074528008699417114252502193630e-19) }},{{ SC_(5.4210108624275221700372640043497085571289062500000e-20), SC_(0.5), SC_(5.4210108624275221700372640043497085571282424617037e-20) }},{{ SC_(2.7105054312137610850186320021748542785644531250000e-20), SC_(0.5), SC_(2.7105054312137610850186320021748542785643701514630e-20) }},{{ SC_(1.3552527156068805425093160010874271392822265625000e-20), SC_(0.5), SC_(1.3552527156068805425093160010874271392822161908079e-20) }},{{ SC_(6.7762635780344027125465800054371356964111328125000e-21), SC_(0.5), SC_(6.7762635780344027125465800054371356964111198478848e-21) }},{{ SC_(3.3881317890172013562732900027185678482055664062500e-21), SC_(0.5), SC_(3.3881317890172013562732900027185678482055647856731e-21) }},{{ SC_(1.6940658945086006781366450013592839241027832031250e-21), SC_(0.5), SC_(1.6940658945086006781366450013592839241027830005529e-21) }},{{ SC_(8.4703294725430033906832250067964196205139160156250e-22), SC_(0.5), SC_(8.4703294725430033906832250067964196205139157624099e-22) }},{{ SC_(4.2351647362715016953416125033982098102569580078125e-22), SC_(0.5), SC_(4.2351647362715016953416125033982098102569579761606e-22) }},{{ SC_(2.1175823681357508476708062516991049051284790039062e-22), SC_(0.5), SC_(2.1175823681357508476708062516991049051284789999498e-22) }},{{ SC_(1.0587911840678754238354031258495524525642395019531e-22), SC_(0.5), SC_(1.0587911840678754238354031258495524525642395014586e-22) }},{{ SC_(5.2939559203393771191770156292477622628211975097656e-23), SC_(0.5), SC_(5.2939559203393771191770156292477622628211975091474e-23) }},{{ SC_(2.6469779601696885595885078146238811314105987548828e-23), SC_(0.5), SC_(2.6469779601696885595885078146238811314105987548055e-23) }},{{ SC_(1.3234889800848442797942539073119405657052993774414e-23), SC_(0.5), SC_(1.3234889800848442797942539073119405657052993774317e-23) }},{{ SC_(6.6174449004242213989712695365597028285264968872070e-24), SC_(0.5), SC_(6.6174449004242213989712695365597028285264968871950e-24) }},{{ SC_(3.3087224502121106994856347682798514142632484436035e-24), SC_(0.5), SC_(3.3087224502121106994856347682798514142632484436020e-24) }},{{ SC_(1.6543612251060553497428173841399257071316242218018e-24), SC_(0.5), SC_(1.6543612251060553497428173841399257071316242218016e-24) }},{{ SC_(8.2718061255302767487140869206996285356581211090088e-25), SC_(0.5), SC_(8.2718061255302767487140869206996285356581211090086e-25) }},{{ SC_(4.1359030627651383743570434603498142678290605545044e-25), SC_(0.5), SC_(4.1359030627651383743570434603498142678290605545044e-25) }}
     } };
     do_test_ellint_e2<T>(small_angles, type_name, "Elliptic Integral E: Small Angles");
+    //
+    // Test error handling:
+    //
+    BOOST_CHECK_EQUAL(boost::math::ellint_2(T(1)), T(1));
+    BOOST_CHECK_EQUAL(boost::math::ellint_2(T(-1)), T(1));
+    BOOST_CHECK_THROW(boost::math::ellint_2(T(1.5)), std::domain_error);
+    BOOST_CHECK_THROW(boost::math::ellint_2(T(-1.5)), std::domain_error);
 }
 
diff --git a/libs/math/test/test_ellint_3.hpp b/libs/math/test/test_ellint_3.hpp
index bac1058445..770b08cdc2 100644
--- a/libs/math/test/test_ellint_3.hpp
+++ b/libs/math/test/test_ellint_3.hpp
@@ -87,7 +87,7 @@ void test_spots(T, const char* type_name)
 {
     BOOST_MATH_STD_USING
     // function values calculated on http://functions.wolfram.com/
-    static const boost::array<boost::array<typename table_type<T>::type, 4>, 65> data1 = {{
+    static const boost::array<boost::array<typename table_type<T>::type, 4>, 70> data1 = {{
         {{ SC_(1.0), SC_(-1.0), SC_(0.0), SC_(-1.557407724654902230506974807458360173087) }},
         {{ SC_(0.0), SC_(-4.0), SC_(0.4), SC_(-4.153623371196831087495427530365430979011) }},
         {{ SC_(0.0), SC_(8.0), SC_(-0.6), SC_(8.935930619078575123490612395578518914416) }},
@@ -166,6 +166,12 @@ void test_spots(T, const char* type_name)
         { { SC_(-1.0), SC_(0.0), SC_(0.5), SC_(0.0) } },
         { { SC_(100.0), SC_(0.0), SC_(0.5), SC_(0.0) } },
         { { SC_(-100.0), SC_(0.0), SC_(0.5), SC_(0.0) } },
+        // cases where |k| > 1:
+        {{ SC_(1.015625), SC_(0.125), SC_(2.5), SC_(0.12780840244950364924992513047014683502850891674019968726)}},
+        {{ SC_(1.015625), SC_(0.125), SC_(4.5), SC_(0.133468341825478826487248053944106425799790398297092314041)}},
+        {{ SC_(-1.015625), SC_(0.125), SC_(4.5), SC_(0.131998693459801470974303284674812630138938285546080214149)}},
+        {{ SC_(-1.015625), SC_(-0.125), SC_(4.5), SC_(-0.13199869345980147097430328467481263013893828554608021414)}},
+        {{ SC_(-1.015625), SC_(-0.125), SC_(1.5), SC_(-0.12508193549646497011359938978158598001227028251706394704)}},
     } };
 
     do_test_ellint_pi3<T>(data1, type_name, "Elliptic Integral PI: Mathworld Data");
@@ -207,7 +213,7 @@ void test_spots(T, const char* type_name)
     do_test_ellint_pi2<T>(ellint_pi2_data, type_name, "Complete Elliptic Integral PI: Random Data");
 
     // Special cases, exceptions etc:
-    BOOST_MATH_CHECK_THROW(boost::math::ellint_3(T(1.0001), T(-1), T(0)), std::domain_error);
+    BOOST_MATH_CHECK_THROW(boost::math::ellint_3(T(2.1), T(-1), T(0.5)), std::domain_error);
     BOOST_MATH_CHECK_THROW(boost::math::ellint_3(T(0.5), T(20), T(1.5)), std::domain_error);
     BOOST_MATH_CHECK_THROW(boost::math::ellint_3(T(1.0001), T(-1)), std::domain_error);
     BOOST_MATH_CHECK_THROW(boost::math::ellint_3(T(0.5), T(1)), std::domain_error);
diff --git a/libs/math/test/test_ellint_d.hpp b/libs/math/test/test_ellint_d.hpp
index 96582645f0..55d26cb78c 100644
--- a/libs/math/test/test_ellint_d.hpp
+++ b/libs/math/test/test_ellint_d.hpp
@@ -84,7 +84,7 @@ void test_spots(T, const char* type_name)
     BOOST_MATH_STD_USING
     // Function values calculated on http://functions.wolfram.com/
     // Note that Mathematica's EllipticE accepts k^2 as the second parameter.
-    static const boost::array<boost::array<T, 3>, 10> data1 = {{
+    static const boost::array<boost::array<T, 3>, 11> data1 = {{
        { { SC_(0.5), SC_(0.5), SC_(0.040348098248931543984282958654503585) } },
         {{ SC_(0), SC_(0.5), SC_(0) }},
         { { SC_(1), SC_(0.5), SC_(0.28991866293419922467977188008516755) } },
@@ -93,6 +93,7 @@ void test_spots(T, const char* type_name)
         { { SC_(-1), T(0.5), SC_(-0.28991866293419922467977188008516755) } },
         { { SC_(-10), T(0.5), SC_(-5.2996914501577855803123384771117708) } },
         { { SC_(10), SC_(-0.5), SC_(5.2996914501577855803123384771117708) } },
+        { { SC_(0.125), SC_(1.5), SC_(0.000655956467603362564458676111698495009248974444516843) } },
     }};
 
     do_test_ellint_d2<T>(data1, type_name, "Elliptic Integral E: Mathworld Data");
diff --git a/libs/math/test/test_roots.cpp b/libs/math/test/test_roots.cpp
index b26b91f634..73a81ccbae 100644
--- a/libs/math/test/test_roots.cpp
+++ b/libs/math/test/test_roots.cpp
@@ -49,27 +49,28 @@
 template <class T, class Policy>
 struct ibeta_roots_1   // for first order algorithms
 {
-   ibeta_roots_1(T _a, T _b, T t, bool inv = false)
-      : a(_a), b(_b), target(t), invert(inv) {}
+   ibeta_roots_1(T _a, T _b, T t, bool inv = false, bool neg = false)
+      : a(_a), b(_b), target(t), invert(inv), neg(neg) {}
 
    T operator()(const T& x)
    {
-      return boost::math::detail::ibeta_imp(a, b, x, Policy(), invert, true) - target;
+      return boost::math::detail::ibeta_imp(a, b, (neg ? -x : x), Policy(), invert, true) - target;
    }
 private:
    T a, b, target;
-   bool invert;
+   bool invert, neg;
 };
 
 template <class T, class Policy>
 struct ibeta_roots_2   // for second order algorithms
 {
-   ibeta_roots_2(T _a, T _b, T t, bool inv = false)
-      : a(_a), b(_b), target(t), invert(inv) {}
+   ibeta_roots_2(T _a, T _b, T t, bool inv = false, bool neg = false)
+      : a(_a), b(_b), target(t), invert(inv), neg(neg) {}
 
-   boost::math::tuple<T, T> operator()(const T& x)
+   boost::math::tuple<T, T> operator()(const T& xx)
    {
       typedef typename boost::math::lanczos::lanczos<T, Policy>::type L;
+      T x = neg ? -xx : xx;
       T f = boost::math::detail::ibeta_imp(a, b, x, Policy(), invert, true) - target;
       T f1 = invert ?
          -boost::math::detail::ibeta_power_terms(b, a, 1 - x, x, L(), true, Policy())
@@ -83,22 +84,23 @@ struct ibeta_roots_2   // for second order algorithms
       if(f1 == 0)
          f1 = (invert ? -1 : 1) * boost::math::tools::min_value<T>() * 64;
 
-      return boost::math::make_tuple(f, f1);
+      return boost::math::make_tuple(f, neg ? -f1 : f1);
    }
 private:
    T a, b, target;
-   bool invert;
+   bool invert, neg;
 };
 
 template <class T, class Policy>
 struct ibeta_roots_3   // for third order algorithms
 {
-   ibeta_roots_3(T _a, T _b, T t, bool inv = false)
-      : a(_a), b(_b), target(t), invert(inv) {}
+   ibeta_roots_3(T _a, T _b, T t, bool inv = false, bool neg = false)
+      : a(_a), b(_b), target(t), invert(inv), neg(neg) {}
 
-   boost::math::tuple<T, T, T> operator()(const T& x)
+   boost::math::tuple<T, T, T> operator()(const T& xx)
    {
       typedef typename boost::math::lanczos::lanczos<T, Policy>::type L;
+      T x = neg ? -xx : xx;
       T f = boost::math::detail::ibeta_imp(a, b, x, Policy(), invert, true) - target;
       T f1 = invert ?
                -boost::math::detail::ibeta_power_terms(b, a, 1 - x, x, L(), true, Policy())
@@ -115,11 +117,16 @@ struct ibeta_roots_3   // for third order algorithms
       if(f1 == 0)
          f1 = (invert ? -1 : 1) * boost::math::tools::min_value<T>() * 64;
 
+      if (neg)
+      {
+         f1 = -f1;
+      }
+
       return boost::math::make_tuple(f, f1, f2);
    }
 private:
    T a, b, target;
-   bool invert;
+   bool invert, neg;
 };
 
 double inverse_ibeta_bisect(double a, double b, double z)
@@ -154,6 +161,38 @@ double inverse_ibeta_bisect(double a, double b, double z)
    return boost::math::tools::bisect(ibeta_roots_1<double, pol>(a, b, z, invert), min, max, tol).first;
 }
 
+double inverse_ibeta_bisect_neg(double a, double b, double z)
+{
+   typedef boost::math::policies::policy<> pol;
+   bool invert = false;
+   int bits = std::numeric_limits<double>::digits;
+
+   //
+   // special cases, we need to have these because there may be other
+   // possible answers:
+   //
+   if(z == 1) return 1;
+   if(z == 0) return 0;
+
+   //
+   // We need a good estimate of the error in the incomplete beta function
+   // so that we don't set the desired precision too high.  Assume that 3-bits
+   // are lost each time the arguments increase by a factor of 10:
+   //
+   using namespace std;
+   int bits_lost = static_cast<int>(ceil(log10((std::max)(a, b)) * 3));
+   if(bits_lost < 0)
+      bits_lost = 3;
+   else
+      bits_lost += 3;
+   int precision = bits - bits_lost;
+
+   double min = -1;
+   double max = 0;
+   boost::math::tools::eps_tolerance<double> tol(precision);
+   return -boost::math::tools::bisect(ibeta_roots_1<double, pol>(a, b, z, invert, true), min, max, tol).first;
+}
+
 double inverse_ibeta_newton(double a, double b, double z)
 {
    double guess = 0.5;
@@ -185,6 +224,37 @@ double inverse_ibeta_newton(double a, double b, double z)
    return boost::math::tools::newton_raphson_iterate(ibeta_roots_2<double, boost::math::policies::policy<> >(a, b, z, invert), guess, min, max, precision);
 }
 
+double inverse_ibeta_newton_neg(double a, double b, double z)
+{
+   double guess = 0.5;
+   bool invert = false;
+   int bits = std::numeric_limits<double>::digits;
+
+   //
+   // special cases, we need to have these because there may be other
+   // possible answers:
+   //
+   if(z == 1) return 1;
+   if(z == 0) return 0;
+
+   //
+   // We need a good estimate of the error in the incomplete beta function
+   // so that we don't set the desired precision too high.  Assume that 3-bits
+   // are lost each time the arguments increase by a factor of 10:
+   //
+   using namespace std;
+   int bits_lost = static_cast<int>(ceil(log10((std::max)(a, b)) * 3));
+   if(bits_lost < 0)
+      bits_lost = 3;
+   else
+      bits_lost += 3;
+   int precision = bits - bits_lost;
+
+   double min = -1;
+   double max = 0;
+   return -boost::math::tools::newton_raphson_iterate(ibeta_roots_2<double, boost::math::policies::policy<> >(a, b, z, invert, true), -guess, min, max, precision);
+}
+
 double inverse_ibeta_halley(double a, double b, double z)
 {
    double guess = 0.5;
@@ -216,6 +286,37 @@ double inverse_ibeta_halley(double a, double b, double z)
    return boost::math::tools::halley_iterate(ibeta_roots_3<double, boost::math::policies::policy<> >(a, b, z, invert), guess, min, max, precision);
 }
 
+double inverse_ibeta_halley_neg(double a, double b, double z)
+{
+   double guess = -0.5;
+   bool invert = false;
+   int bits = std::numeric_limits<double>::digits;
+
+   //
+   // special cases, we need to have these because there may be other
+   // possible answers:
+   //
+   if(z == 1) return 1;
+   if(z == 0) return 0;
+
+   //
+   // We need a good estimate of the error in the incomplete beta function
+   // so that we don't set the desired precision too high.  Assume that 3-bits
+   // are lost each time the arguments increase by a factor of 10:
+   //
+   using namespace std;
+   int bits_lost = static_cast<int>(ceil(log10((std::max)(a, b)) * 3));
+   if(bits_lost < 0)
+      bits_lost = 3;
+   else
+      bits_lost += 3;
+   int precision = bits - bits_lost;
+
+   double min = -1;
+   double max = 0;
+   return -boost::math::tools::halley_iterate(ibeta_roots_3<double, boost::math::policies::policy<> >(a, b, z, invert, true), guess, min, max, precision);
+}
+
 double inverse_ibeta_schroder(double a, double b, double z)
 {
    double guess = 0.5;
@@ -269,9 +370,12 @@ void test_inverses(const T& data)
       if(data[i][5] == 0)
       {
          BOOST_CHECK_EQUAL(inverse_ibeta_halley(Real(data[i][0]), Real(data[i][1]), Real(data[i][5])), value_type(0));
+         BOOST_CHECK_EQUAL(inverse_ibeta_halley_neg(Real(data[i][0]), Real(data[i][1]), Real(data[i][5])), value_type(0));
          BOOST_CHECK_EQUAL(inverse_ibeta_schroder(Real(data[i][0]), Real(data[i][1]), Real(data[i][5])), value_type(0));
          BOOST_CHECK_EQUAL(inverse_ibeta_newton(Real(data[i][0]), Real(data[i][1]), Real(data[i][5])), value_type(0));
+         BOOST_CHECK_EQUAL(inverse_ibeta_newton_neg(Real(data[i][0]), Real(data[i][1]), Real(data[i][5])), value_type(0));
          BOOST_CHECK_EQUAL(inverse_ibeta_bisect(Real(data[i][0]), Real(data[i][1]), Real(data[i][5])), value_type(0));
+         BOOST_CHECK_EQUAL(inverse_ibeta_bisect_neg(Real(data[i][0]), Real(data[i][1]), Real(data[i][5])), value_type(0));
       }
       else if((1 - data[i][5] > 0.001)
          && (fabs(data[i][5]) > 2 * boost::math::tools::min_value<value_type>())
@@ -279,19 +383,29 @@ void test_inverses(const T& data)
       {
          value_type inv = inverse_ibeta_halley(Real(data[i][0]), Real(data[i][1]), Real(data[i][5]));
          BOOST_CHECK_CLOSE_EX(Real(data[i][2]), inv, precision, i);
+         inv = inverse_ibeta_halley_neg(Real(data[i][0]), Real(data[i][1]), Real(data[i][5]));
+         BOOST_ASSERT(boost::math::isfinite(inv));
+         BOOST_CHECK_CLOSE_EX(Real(data[i][2]), inv, precision, i);
          inv = inverse_ibeta_schroder(Real(data[i][0]), Real(data[i][1]), Real(data[i][5]));
          BOOST_CHECK_CLOSE_EX(Real(data[i][2]), inv, precision, i);
          inv = inverse_ibeta_newton(Real(data[i][0]), Real(data[i][1]), Real(data[i][5]));
          BOOST_CHECK_CLOSE_EX(Real(data[i][2]), inv, precision, i);
+         inv = inverse_ibeta_newton_neg(Real(data[i][0]), Real(data[i][1]), Real(data[i][5]));
+         BOOST_CHECK_CLOSE_EX(Real(data[i][2]), inv, precision, i);
          inv = inverse_ibeta_bisect(Real(data[i][0]), Real(data[i][1]), Real(data[i][5]));
          BOOST_CHECK_CLOSE_EX(Real(data[i][2]), inv, precision, i);
+         inv = inverse_ibeta_bisect_neg(Real(data[i][0]), Real(data[i][1]), Real(data[i][5]));
+         BOOST_CHECK_CLOSE_EX(Real(data[i][2]), inv, precision, i);
       }
       else if(1 == data[i][5])
       {
          BOOST_CHECK_EQUAL(inverse_ibeta_halley(Real(data[i][0]), Real(data[i][1]), Real(data[i][5])), value_type(1));
+         BOOST_CHECK_EQUAL(inverse_ibeta_halley_neg(Real(data[i][0]), Real(data[i][1]), Real(data[i][5])), value_type(1));
          BOOST_CHECK_EQUAL(inverse_ibeta_schroder(Real(data[i][0]), Real(data[i][1]), Real(data[i][5])), value_type(1));
          BOOST_CHECK_EQUAL(inverse_ibeta_newton(Real(data[i][0]), Real(data[i][1]), Real(data[i][5])), value_type(1));
+         BOOST_CHECK_EQUAL(inverse_ibeta_newton_neg(Real(data[i][0]), Real(data[i][1]), Real(data[i][5])), value_type(1));
          BOOST_CHECK_EQUAL(inverse_ibeta_bisect(Real(data[i][0]), Real(data[i][1]), Real(data[i][5])), value_type(1));
+         BOOST_CHECK_EQUAL(inverse_ibeta_bisect_neg(Real(data[i][0]), Real(data[i][1]), Real(data[i][5])), value_type(1));
       }
 
    }
diff --git a/libs/math/test/test_vector_barycentric_rational.cpp b/libs/math/test/test_vector_barycentric_rational.cpp
new file mode 100644
index 0000000000..6250fa8979
--- /dev/null
+++ b/libs/math/test/test_vector_barycentric_rational.cpp
@@ -0,0 +1,385 @@
+// Copyright Nick Thompson, 2019
+// Use, modification and distribution are subject to the
+// Boost Software License, Version 1.0.
+// (See accompanying file LICENSE_1_0.txt
+// or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+#define BOOST_TEST_MODULE vector_barycentric_rational
+
+#include <cmath>
+#include <random>
+#include <array>
+#include <Eigen/Dense>
+#include <boost/numeric/ublas/vector.hpp>
+#include <boost/random/uniform_real_distribution.hpp>
+#include <boost/type_index.hpp>
+#include <boost/test/included/unit_test.hpp>
+#include <boost/test/floating_point_comparison.hpp>
+#include <boost/math/interpolators/barycentric_rational.hpp>
+#include <boost/math/interpolators/vector_barycentric_rational.hpp>
+
+using std::sqrt;
+using std::abs;
+using std::numeric_limits;
+
+template<class Real>
+void test_agreement_with_1d()
+{
+    std::cout << "Testing with 1D interpolation on type "
+              << boost::typeindex::type_id<Real>().pretty_name()  << "\n";
+    std::mt19937 gen(4723);
+    boost::random::uniform_real_distribution<Real> dis(0.1f, 1);
+    std::vector<Real> t(100);
+    std::vector<Eigen::Vector2d> y(100);
+    t[0] = dis(gen);
+    y[0][0] = dis(gen);
+    y[0][1] = dis(gen);
+    for (size_t i = 1; i < t.size(); ++i)
+    {
+        t[i] = t[i-1] + dis(gen);
+        y[i][0] = dis(gen);
+        y[i][1] = dis(gen);
+    }
+
+    std::vector<Eigen::Vector2d> y_copy = y;
+    std::vector<Real> t_copy = t;
+    std::vector<Real> t_copy0 = t;
+    std::vector<Real> t_copy1 = t;
+
+    std::vector<Real> y_copy0(y.size());
+    std::vector<Real> y_copy1(y.size());
+    for (size_t i = 0; i < y.size(); ++i) {
+        y_copy0[i] = y[i][0];
+        y_copy1[i] = y[i][1];
+    }
+
+    boost::random::uniform_real_distribution<Real> dis2(t[0], t[t.size()-1]);
+    boost::math::vector_barycentric_rational<decltype(t), decltype(y)> interpolator(std::move(t), std::move(y));
+    boost::math::barycentric_rational<Real> scalar_interpolator0(std::move(t_copy0), std::move(y_copy0));
+    boost::math::barycentric_rational<Real> scalar_interpolator1(std::move(t_copy1), std::move(y_copy1));
+
+
+    Eigen::Vector2d z;
+
+    size_t samples = 0;
+    while (samples++ < 1000)
+    {
+        Real t = dis2(gen);
+        interpolator(z, t);
+        BOOST_CHECK_CLOSE(z[0], scalar_interpolator0(t), 2*numeric_limits<Real>::epsilon());
+        BOOST_CHECK_CLOSE(z[1], scalar_interpolator1(t), 2*numeric_limits<Real>::epsilon());
+    }
+}
+
+
+template<class Real>
+void test_interpolation_condition_eigen()
+{
+    std::cout << "Testing interpolation condition for barycentric interpolation on Eigen vectors of type "
+              << boost::typeindex::type_id<Real>().pretty_name()  << "\n";
+    std::mt19937 gen(4723);
+    boost::random::uniform_real_distribution<Real> dis(0.1f, 1);
+    std::vector<Real> t(100);
+    std::vector<Eigen::Vector2d> y(100);
+    t[0] = dis(gen);
+    y[0][0] = dis(gen);
+    y[0][1] = dis(gen);
+    for (size_t i = 1; i < t.size(); ++i)
+    {
+        t[i] = t[i-1] + dis(gen);
+        y[i][0] = dis(gen);
+        y[i][1] = dis(gen);
+    }
+
+    std::vector<Eigen::Vector2d> y_copy = y;
+    std::vector<Real> t_copy = t;
+    boost::math::vector_barycentric_rational<decltype(t), decltype(y)> interpolator(std::move(t), std::move(y));
+
+    Eigen::Vector2d z;
+    for (size_t i = 0; i < t_copy.size(); ++i)
+    {
+        interpolator(z, t_copy[i]);
+        BOOST_CHECK_CLOSE(z[0], y_copy[i][0], 100*numeric_limits<Real>::epsilon());
+        BOOST_CHECK_CLOSE(z[1], y_copy[i][1], 100*numeric_limits<Real>::epsilon());
+    }
+}
+
+template<class Real>
+void test_interpolation_condition_std_array()
+{
+    std::cout << "Testing interpolation condition for barycentric interpolation on std::array vectors of type "
+              << boost::typeindex::type_id<Real>().pretty_name()  << "\n";
+    std::mt19937 gen(4723);
+    boost::random::uniform_real_distribution<Real> dis(0.1f, 1);
+    std::vector<Real> t(100);
+    std::vector<std::array<Real, 2>> y(100);
+    t[0] = dis(gen);
+    y[0][0] = dis(gen);
+    y[0][1] = dis(gen);
+    for (size_t i = 1; i < t.size(); ++i)
+    {
+        t[i] = t[i-1] + dis(gen);
+        y[i][0] = dis(gen);
+        y[i][1] = dis(gen);
+    }
+
+    std::vector<std::array<Real, 2>> y_copy = y;
+    std::vector<Real> t_copy = t;
+    boost::math::vector_barycentric_rational<decltype(t), decltype(y)> interpolator(std::move(t), std::move(y));
+
+    std::array<Real, 2> z;
+    for (size_t i = 0; i < t_copy.size(); ++i)
+    {
+        interpolator(z, t_copy[i]);
+        BOOST_CHECK_CLOSE(z[0], y_copy[i][0], 100*numeric_limits<Real>::epsilon());
+        BOOST_CHECK_CLOSE(z[1], y_copy[i][1], 100*numeric_limits<Real>::epsilon());
+    }
+}
+
+
+template<class Real>
+void test_interpolation_condition_ublas()
+{
+    std::cout << "Testing interpolation condition for barycentric interpolation ublas vectors of type "
+              << boost::typeindex::type_id<Real>().pretty_name()  << "\n";
+    std::mt19937 gen(4723);
+    boost::random::uniform_real_distribution<Real> dis(0.1f, 1);
+    std::vector<Real> t(100);
+    std::vector<boost::numeric::ublas::vector<Real>> y(100);
+    t[0] = dis(gen);
+    y[0].resize(2);
+    y[0][0] = dis(gen);
+    y[0][1] = dis(gen);
+    for (size_t i = 1; i < t.size(); ++i)
+    {
+        t[i] = t[i-1] + dis(gen);
+        y[i].resize(2);
+        y[i][0] = dis(gen);
+        y[i][1] = dis(gen);
+    }
+
+    std::vector<Real> t_copy = t;
+    std::vector<boost::numeric::ublas::vector<Real>> y_copy = y;
+
+    boost::math::vector_barycentric_rational<decltype(t), decltype(y)> interpolator(std::move(t), std::move(y));
+
+    boost::numeric::ublas::vector<Real> z(2);
+    for (size_t i = 0; i < t_copy.size(); ++i)
+    {
+        interpolator(z, t_copy[i]);
+        BOOST_CHECK_CLOSE(z[0], y_copy[i][0], 100*numeric_limits<Real>::epsilon());
+        BOOST_CHECK_CLOSE(z[1], y_copy[i][1], 100*numeric_limits<Real>::epsilon());
+    }
+}
+
+template<class Real>
+void test_interpolation_condition_high_order()
+{
+    std::cout << "Testing interpolation condition in high order for barycentric interpolation on type " << boost::typeindex::type_id<Real>().pretty_name()  << "\n";
+    std::mt19937 gen(5);
+    boost::random::uniform_real_distribution<Real> dis(0.1f, 1);
+    std::vector<Real> t(100);
+    std::vector<Eigen::Vector2d> y(100);
+    t[0] = dis(gen);
+    y[0][0] = dis(gen);
+    y[0][1] = dis(gen);
+    for (size_t i = 1; i < t.size(); ++i)
+    {
+        t[i] = t[i-1] + dis(gen);
+        y[i][0] = dis(gen);
+        y[i][1] = dis(gen);
+    }
+
+    std::vector<Eigen::Vector2d> y_copy = y;
+    std::vector<Real> t_copy = t;
+    boost::math::vector_barycentric_rational<decltype(t), decltype(y)> interpolator(std::move(t), std::move(y), 5);
+
+    Eigen::Vector2d z;
+    for (size_t i = 0; i < t_copy.size(); ++i)
+    {
+        interpolator(z, t_copy[i]);
+        BOOST_CHECK_CLOSE(z[0], y_copy[i][0], 100*numeric_limits<Real>::epsilon());
+        BOOST_CHECK_CLOSE(z[1], y_copy[i][1], 100*numeric_limits<Real>::epsilon());
+    }
+}
+
+
+template<class Real>
+void test_constant_eigen()
+{
+    std::cout << "Testing that constants are interpolated correctly using barycentric interpolation on Eigen vectors of type "
+              << boost::typeindex::type_id<Real>().pretty_name() << "\n";
+
+    std::mt19937 gen(6);
+    boost::random::uniform_real_distribution<Real> dis(0.1f, 1);
+    std::vector<Real> t(100);
+    std::vector<Eigen::Vector2d> y(100);
+    t[0] = dis(gen);
+    Real constant0 = dis(gen);
+    Real constant1 = dis(gen);
+    y[0][0] = constant0;
+    y[0][1] = constant1;
+    for (size_t i = 1; i < t.size(); ++i)
+    {
+        t[i] = t[i-1] + dis(gen);
+        y[i][0] = constant0;
+        y[i][1] = constant1;
+    }
+
+    std::vector<Eigen::Vector2d> y_copy = y;
+    std::vector<Real> t_copy = t;
+    boost::math::vector_barycentric_rational<decltype(t), decltype(y)> interpolator(std::move(t), std::move(y));
+
+    Eigen::Vector2d z;
+    for (size_t i = 0; i < t_copy.size(); ++i)
+    {
+        // Don't evaluate the constant at x[i]; that's already tested in the interpolation condition test.
+        Real t = t_copy[i] + dis(gen);
+        z = interpolator(t);
+        BOOST_CHECK_CLOSE(z[0], constant0, 100*sqrt(numeric_limits<Real>::epsilon()));
+        BOOST_CHECK_CLOSE(z[1], constant1, 100*sqrt(numeric_limits<Real>::epsilon()));
+        Eigen::Vector2d zprime = interpolator.prime(t);
+        Real zero_0 = zprime[0];
+        Real zero_1 = zprime[1];
+        BOOST_CHECK_SMALL(zero_0, sqrt(numeric_limits<Real>::epsilon()));
+        BOOST_CHECK_SMALL(zero_1, sqrt(numeric_limits<Real>::epsilon()));
+    }
+}
+
+
+template<class Real>
+void test_constant_std_array()
+{
+    std::cout << "Testing that constants are interpolated correctly using barycentric interpolation on std::array vectors of type "
+              << boost::typeindex::type_id<Real>().pretty_name() << "\n";
+
+    std::mt19937 gen(6);
+    boost::random::uniform_real_distribution<Real> dis(0.1f, 1);
+    std::vector<Real> t(100);
+    std::vector<std::array<Real, 2>> y(100);
+    t[0] = dis(gen);
+    Real constant0 = dis(gen);
+    Real constant1 = dis(gen);
+    y[0][0] = constant0;
+    y[0][1] = constant1;
+    for (size_t i = 1; i < t.size(); ++i)
+    {
+        t[i] = t[i-1] + dis(gen);
+        y[i][0] = constant0;
+        y[i][1] = constant1;
+    }
+
+    std::vector<std::array<Real,2>> y_copy = y;
+    std::vector<Real> t_copy = t;
+    boost::math::vector_barycentric_rational<decltype(t), decltype(y)> interpolator(std::move(t), std::move(y));
+
+    std::array<Real, 2> z;
+    for (size_t i = 0; i < t_copy.size(); ++i)
+    {
+        // Don't evaluate the constant at x[i]; that's already tested in the interpolation condition test.
+        Real t = t_copy[i] + dis(gen);
+        z = interpolator(t);
+        BOOST_CHECK_CLOSE(z[0], constant0, 100*sqrt(numeric_limits<Real>::epsilon()));
+        BOOST_CHECK_CLOSE(z[1], constant1, 100*sqrt(numeric_limits<Real>::epsilon()));
+        std::array<Real, 2> zprime = interpolator.prime(t);
+        Real zero_0 = zprime[0];
+        Real zero_1 = zprime[1];
+        BOOST_CHECK_SMALL(zero_0, sqrt(numeric_limits<Real>::epsilon()));
+        BOOST_CHECK_SMALL(zero_1, sqrt(numeric_limits<Real>::epsilon()));
+    }
+}
+
+
+template<class Real>
+void test_constant_high_order()
+{
+    std::cout << "Testing that constants are interpolated correctly using barycentric interpolation on type " << boost::typeindex::type_id<Real>().pretty_name() << "\n";
+
+    std::mt19937 gen(6);
+    boost::random::uniform_real_distribution<Real> dis(0.1f, 1);
+    std::vector<Real> t(100);
+    std::vector<Eigen::Vector2d> y(100);
+    t[0] = dis(gen);
+    Real constant0 = dis(gen);
+    Real constant1 = dis(gen);
+    y[0][0] = constant0;
+    y[0][1] = constant1;
+    for (size_t i = 1; i < t.size(); ++i)
+    {
+        t[i] = t[i-1] + dis(gen);
+        y[i][0] = constant0;
+        y[i][1] = constant1;
+    }
+
+    std::vector<Eigen::Vector2d> y_copy = y;
+    std::vector<Real> t_copy = t;
+    boost::math::vector_barycentric_rational<decltype(t), decltype(y)> interpolator(std::move(t), std::move(y), 5);
+
+    Eigen::Vector2d z;
+    for (size_t i = 0; i < t_copy.size(); ++i)
+    {
+        // Don't evaluate the constant at x[i]; that's already tested in the interpolation condition test.
+        Real t = t_copy[i] + dis(gen);
+        z = interpolator(t);
+        BOOST_CHECK_CLOSE(z[0], constant0, 100*sqrt(numeric_limits<Real>::epsilon()));
+        BOOST_CHECK_CLOSE(z[1], constant1, 100*sqrt(numeric_limits<Real>::epsilon()));
+        Eigen::Vector2d zprime = interpolator.prime(t);
+        Real zero_0 = zprime[0];
+        Real zero_1 = zprime[1];
+        BOOST_CHECK_SMALL(zero_0, sqrt(numeric_limits<Real>::epsilon()));
+        BOOST_CHECK_SMALL(zero_1, sqrt(numeric_limits<Real>::epsilon()));
+    }
+}
+
+
+template<class Real>
+void test_weights()
+{
+    std::cout << "Testing weights are calculated correctly using barycentric interpolation on type " << boost::typeindex::type_id<Real>().pretty_name() << "\n";
+
+    std::mt19937 gen(9);
+    boost::random::uniform_real_distribution<Real> dis(0.005, 0.01);
+    std::vector<Real> t(100);
+    std::vector<Eigen::Vector2d> y(100);
+    t[0] = dis(gen);
+    y[0][0] = dis(gen);
+    y[0][1] = dis(gen);
+    for (size_t i = 1; i < t.size(); ++i)
+    {
+        t[i] = t[i-1] + dis(gen);
+        y[i][0] = dis(gen);
+        y[i][1] = dis(gen);
+    }
+
+    std::vector<Eigen::Vector2d> y_copy = y;
+    std::vector<Real> t_copy = t;
+    boost::math::detail::vector_barycentric_rational_imp<decltype(t), decltype(y)> interpolator(std::move(t), std::move(y), 1);
+
+    for (size_t i = 1; i < t_copy.size() - 1; ++i)
+    {
+        Real w = interpolator.weight(i);
+        Real w_expect = 1/(t_copy[i] - t_copy[i - 1]) + 1/(t_copy[i+1] - t_copy[i]);
+        if (i % 2 == 0)
+        {
+            BOOST_CHECK_CLOSE(w, -w_expect, 0.00001);
+        }
+        else
+        {
+            BOOST_CHECK_CLOSE(w, w_expect, 0.00001);
+        }
+    }
+}
+
+
+BOOST_AUTO_TEST_CASE(vector_barycentric_rational)
+{
+    test_weights<double>();
+    test_constant_eigen<double>();
+    test_constant_std_array<double>();
+    test_constant_high_order<double>();
+    test_interpolation_condition_eigen<double>();
+    test_interpolation_condition_ublas<double>();
+    test_interpolation_condition_std_array<double>();
+    test_interpolation_condition_high_order<double>();
+    test_agreement_with_1d<double>();
+}
diff --git a/libs/math/test/univariate_statistics_test.cpp b/libs/math/test/univariate_statistics_test.cpp
index a2db405c70..181da0153c 100644
--- a/libs/math/test/univariate_statistics_test.cpp
+++ b/libs/math/test/univariate_statistics_test.cpp
@@ -124,6 +124,17 @@ void test_integer_mean()
     BOOST_TEST(abs(m1 - m2) < tol*abs(m1));
 }
 
+template<class RandomAccessContainer>
+auto naive_mean(RandomAccessContainer const & v)
+{
+    typename RandomAccessContainer::value_type sum = 0;
+    for (auto & x : v)
+    {
+        sum += x;
+    }
+    return sum/v.size();
+}
+
 template<class Real>
 void test_mean()
 {
@@ -172,6 +183,23 @@ void test_mean()
     }
     Real m2 = boost::math::tools::mean(v);
     BOOST_TEST(abs(m1 - m2) < tol*abs(m1));
+
+    // Stress test:
+    for (size_t i = 1; i < 30; ++i)
+    {
+        v = generate_random_vector<Real>(i, 12803);
+        auto naive_ = naive_mean(v);
+        auto higham_ = boost::math::tools::mean(v);
+        if (abs(higham_ - naive_) >= 100*tol*abs(naive_))
+        {
+            std::cout << std::hexfloat;
+            std::cout << "Terms = " << v.size() << "\n";
+            std::cout << "higham = " << higham_ << "\n";
+            std::cout << "naive_ = " << naive_ << "\n";
+        }
+        BOOST_TEST(abs(higham_ - naive_) < 100*tol*abs(naive_));
+    }
+
 }
 
 template<class Complex>
diff --git a/libs/math/test/whittaker_shannon_test.cpp b/libs/math/test/whittaker_shannon_test.cpp
new file mode 100644
index 0000000000..7bf24647bf
--- /dev/null
+++ b/libs/math/test/whittaker_shannon_test.cpp
@@ -0,0 +1,142 @@
+/*
+ * Copyright Nick Thompson, 2019
+ * Use, modification and distribution are subject to the
+ * Boost Software License, Version 1.0. (See accompanying file
+ * LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#include "math_unit_test.hpp"
+#include <numeric>
+#include <utility>
+#include <random>
+#include <boost/core/demangle.hpp>
+#include <boost/math/interpolators/whittaker_shannon.hpp>
+#ifdef BOOST_HAS_FLOAT128
+#include <boost/multiprecision/float128.hpp>
+using boost::multiprecision::float128;
+#endif
+
+using boost::math::interpolators::whittaker_shannon;
+
+template<class Real>
+void test_trivial()
+{
+    Real t0 = 0;
+    Real h = Real(1)/Real(16);
+    std::vector<Real> v{1.5};
+    std::vector<Real> v_copy = v;
+    auto ws = whittaker_shannon<decltype(v)>(std::move(v), t0, h);
+
+
+    Real expected = 0;
+    if(!CHECK_MOLLIFIED_CLOSE(expected, ws.prime(0), 10*std::numeric_limits<Real>::epsilon())) {
+        std::cerr << "  Problem occured at abscissa " << 0 << "\n";
+    }
+
+    expected = -v_copy[0]/h;
+    if(!CHECK_MOLLIFIED_CLOSE(expected, ws.prime(h), 10*std::numeric_limits<Real>::epsilon())) {
+        std::cerr << "  Problem occured at abscissa " << 0 << "\n";
+    }
+}
+
+template<class Real>
+void test_knots()
+{
+    Real t0 = 0;
+    Real h = Real(1)/Real(16);
+    size_t n = 512;
+    std::vector<Real> v(n);
+    std::mt19937 gen(323723);
+    std::uniform_real_distribution<Real> dis(1.0, 2.0);
+
+    for(size_t i = 0;  i < n; ++i) {
+      v[i] = static_cast<Real>(dis(gen));
+    }
+    auto ws = whittaker_shannon<decltype(v)>(std::move(v), t0, h);
+
+    size_t i = 0;
+    while (i < n) {
+      Real t = t0 + i*h;
+      Real expected = ws[i];
+      Real computed = ws(t);
+      CHECK_ULP_CLOSE(expected, computed, 16);
+      ++i;
+    }
+}
+
+template<class Real>
+void test_bump()
+{
+    using std::exp;
+    using std::abs;
+    using std::sqrt;
+    auto bump = [](Real x) { if (abs(x) >= 1) { return Real(0); } return exp(-Real(1)/(Real(1)-x*x)); };
+
+    auto bump_prime = [&bump](Real x) { Real z = 1-x*x; return -2*x*bump(x)/(z*z); };
+
+    Real t0 = -1;
+    size_t n = 2049;
+    Real h = Real(2)/Real(n-1);
+
+    std::vector<Real> v(n);
+    for(size_t i = 0; i < n; ++i) {
+        Real t = t0 + i*h;
+        v[i] = bump(t);
+    }
+
+
+    std::vector<Real> v_copy = v;
+    auto ws = whittaker_shannon<decltype(v)>(std::move(v), t0, h);
+
+    // Test the knots:
+    for(size_t i = v_copy.size()/4; i < 3*v_copy.size()/4; ++i) {
+        Real t = t0 + i*h;
+        Real expected = v_copy[i];
+        Real computed = ws(t);
+        if(!CHECK_MOLLIFIED_CLOSE(expected, computed, 10*std::numeric_limits<Real>::epsilon())) {
+            std::cerr << "  Problem occured at abscissa " << t << "\n";
+        }
+
+        Real expected_prime = bump_prime(t);
+        Real computed_prime = ws.prime(t);
+        if(!CHECK_MOLLIFIED_CLOSE(expected_prime, computed_prime, 1000*std::numeric_limits<Real>::epsilon())) {
+            std::cerr << "  Problem occured at abscissa " << t << "\n";
+        }
+
+    }
+
+    std::mt19937 gen(323723);
+    std::uniform_real_distribution<long double> dis(-0.85, 0.85);
+
+    size_t i = 0;
+    while (i++ < 1000)
+    {
+        Real t = static_cast<Real>(dis(gen));
+        Real expected = bump(t);
+        Real computed = ws(t);
+        if(!CHECK_MOLLIFIED_CLOSE(expected, computed, 10*std::numeric_limits<Real>::epsilon())) {
+            std::cerr << "  Problem occured at abscissa " << t << "\n";
+        }
+
+        Real expected_prime = bump_prime(t);
+        Real computed_prime = ws.prime(t);
+        if(!CHECK_MOLLIFIED_CLOSE(expected_prime, computed_prime, sqrt(std::numeric_limits<Real>::epsilon()))) {
+            std::cerr << "  Problem occured at abscissa " << t << "\n";
+        }
+    }
+}
+
+
+int main()
+{
+    test_knots<float>();
+    test_knots<double>();
+    test_knots<long double>();
+
+    test_bump<double>();
+    test_bump<long double>();
+
+    test_trivial<float>();
+    test_trivial<double>();
+    return boost::math::test::report_errors();
+}
diff --git a/libs/math/tools/lambert_w_errors_graph.cpp b/libs/math/tools/lambert_w_errors_graph.cpp
new file mode 100644
index 0000000000..45baa200ce
--- /dev/null
+++ b/libs/math/tools/lambert_w_errors_graph.cpp
@@ -0,0 +1,262 @@
+// Copyright Paul A. Bristow 2017, 2018
+// Copyright John Z. Maddock 2017
+
+// Distributed under the Boost Software License, Version 1.0.
+// (See accompanying file LICENSE_1_0.txt or
+//  copy at http ://www.boost.org/LICENSE_1_0.txt).
+
+/*! \brief Graph showing differences of Lambert W function double from nearest representable values.
+
+\details
+
+*/
+
+#include <boost/math/special_functions/lambert_w.hpp>
+using boost::math::lambert_w0;
+using boost::math::lambert_wm1;
+#include <boost/math/special_functions.hpp>
+using boost::math::isfinite;
+#include <boost/svg_plot/svg_2d_plot.hpp>
+using namespace boost::svg;
+
+// For higher precision computation of Lambert W.
+#include <boost/multiprecision/cpp_bin_float.hpp>
+#include <boost/math/special_functions/next.hpp> // For float_distance.
+using boost::math::float_distance;
+
+#include <iostream>
+// using std::cout;
+// using std::endl;
+#include <exception>
+#include <stdexcept>
+#include <string>
+#include <array>
+#include <vector>
+#include <utility>
+using std::pair;
+#include <map>
+using std::map;
+#include <set>
+using std::multiset;
+#include <limits>
+using std::numeric_limits;
+#include <cmath> // exp
+
+/*!
+*/
+
+
+int main()
+{
+  try
+  {
+    std::cout << "Lambert W errors graph." << std::endl;
+    using boost::multiprecision::cpp_bin_float_50; 
+    using boost::multiprecision::cpp_bin_float_quad; 
+
+    typedef cpp_bin_float_quad HPT; // High precision type.
+
+    using boost::math::float_distance;
+    using boost::math::policies::precision;
+    using boost::math::policies::digits10;
+    using boost::math::policies::digits2;
+    using boost::math::policies::policy;
+
+    std::cout.precision(std::numeric_limits<double>::max_digits10);
+
+    //[lambert_w_graph_1
+
+    //] [/lambert_w_graph_1]
+    {
+      std::map<const double, double> w0s;   // Lambert W0 branch values, default double precision, digits2 = 53.
+      std::map<const double, double> w0s_50;   // Lambert W0 branch values digits2 = 50.
+
+      int max_distance = 0;
+      int total_distance = 0;
+      int count = 0;
+      const int bits = 7;
+      double min_z = -0.367879; // Close to singularity at -0.3678794411714423215955237701614608727 -exp(-1)
+      //double min_z = 0.06; // Above 0.05 switch point.
+      double max_z = 99.99;
+      double step_z = 0.05;
+
+      for (HPT z = min_z; z < max_z; z += step_z)
+      {
+        double zd = static_cast<double>(z);
+        double w0d = lambert_w0(zd); // double result from same default.
+        HPT w0_best = lambert_w0<HPT>(z);
+        double w0_best_d = static_cast<double>(w0_best); // reference result.
+       // w0s[zd] = (w0d - w0_best_d); // absolute difference.
+        // w0s[z] = 100 * (w0 - w0_best) / w0_best; // difference relative % .
+        w0s[zd] = float_distance<double>(w0d, w0_best_d); // difference in bits.
+        double fd = float_distance<double>(w0d, w0_best_d);
+        int distance = static_cast<int>(fd);
+        int abs_distance = abs(distance);
+
+         // std::cout << count << " " << zd << " " << w0d << " " << w0_best_d
+         //   << ", Difference = " << w0d - w0_best_d << ", % = " << (w0d - w0_best_d) / w0d << ", Distance = " << distance << std::endl;
+
+        total_distance += abs_distance;
+        if (abs_distance > max_distance)
+        {
+          max_distance = abs_distance;
+        }
+        count++;
+      } // for z
+      std::cout << "points " << count << std::endl;
+      std::cout.precision(3);
+      std::cout << "max distance " << max_distance << ", total distances = " << total_distance
+        << ", mean distance " << (float)total_distance / count << std::endl;
+
+      typedef std::map<const double, double>::const_iterator Map_Iterator;
+
+   /* for (std::map<const double, double>::const_iterator it = w0s.begin(); it != w0s.end(); ++it)
+      {
+        std::cout  << " " << *(it) << "\n";
+      }
+  */
+      svg_2d_plot data_plot_0; // <-0.368, -46> <-0.358, -4> <-0.348, 1>...
+
+      data_plot_0.title("Lambert W0 function differences from 'best' for double.")
+        .title_font_size(11)
+        .x_size(400)
+        .y_size(200)
+        .legend_on(false)
+        //.legend_font_weight(1)
+        .x_label("z")
+        .y_label("W0 difference (bits)")
+        //.x_label_on(true)
+        //.y_label_on(true)
+        //.xy_values_on(false)
+        .x_range(-1, 100.)
+        .y_range(-4., +4.)
+        .x_major_interval(10.)
+        .y_major_interval(2.)
+        .x_major_grid_on(true)
+        .y_major_grid_on(true)
+        .x_label_font_size(9)
+        .y_label_font_size(9)
+        //.x_values_on(true)
+        //.y_values_on(true)
+        .y_values_rotation(horizontal)
+        //.plot_window_on(true)
+        .x_values_precision(3)
+        .y_values_precision(3)
+        .coord_precision(3) // Needed to avoid stepping on curves.
+        //.coord_precision(4) // Needed to avoid stepping on curves.
+        .copyright_holder("Paul A. Bristow")
+        .copyright_date("2018")
+        //.background_border_color(black);
+        ;
+
+
+      data_plot_0.plot(w0s, "W0 branch").line_color(red).shape(none).line_on(true).bezier_on(false).line_width(0.2);
+      //data_plot.plot(wm1s, "W-1 branch").line_color(blue).shape(none).line_on(true).bezier_on(false).line_width(1);
+      data_plot_0.write("./lambert_w0_errors_graph");
+
+    } // end W0 branch plot.
+    { // Repeat for Lambert W-1 branch.
+
+      std::map<const double, double> wm1s;   // Lambert W-1 branch values.
+      std::map<const double, double> wm1s_50;   // Lambert Wm1 branch values digits2 = 50.
+
+      int max_distance = 0;
+      int total_distance = 0;
+      int count = 0;
+      const int bits = 7;
+      double min_z = -0.367879; // Close to singularity at -0.3678794411714423215955237701614608727 -exp(-1)
+                                //double min_z = 0.06; // Above 0.05 switch point.
+      double max_z = -0.0001;
+      double step_z = 0.001;
+
+      for (HPT z = min_z; z < max_z; z += step_z)
+      {
+        if (z > max_z)
+        {
+          break;
+        }
+        double zd = static_cast<double>(z);
+        double wm1d = lambert_wm1(zd); // double result from same default.
+        HPT wm1_best = lambert_wm1<HPT>(z);
+        double wm1_best_d = static_cast<double>(wm1_best); // reference result.
+                                                         // wm1s[zd] = (wm1d - wm1_best_d); // absolute difference.
+                                                         // wm1s[z] = 100 * (wm1 - wm1_best) / wm1_best; // difference relative % .
+        wm1s[zd] = float_distance<double>(wm1d, wm1_best_d); // difference in bits.
+        double fd = float_distance<double>(wm1d, wm1_best_d);
+        int distance = static_cast<int>(fd);
+        int abs_distance = abs(distance);
+
+         //std::cout << count << " " << zd << " " << wm1d << " " << wm1_best_d
+         //  << ", Difference = " << wm1d - wm1_best_d << ", % = " << (wm1d - wm1_best_d) / wm1d << ", Distance = " << distance << std::endl;
+
+        total_distance += abs_distance;
+        if (abs_distance > max_distance)
+        {
+          max_distance = abs_distance;
+        }
+        count++;
+
+      } // for z
+      std::cout << "points " << count << std::endl;
+      std::cout.precision(3);
+      std::cout << "max distance " << max_distance << ", total distances = " << total_distance
+        << ", mean distance " << (float)total_distance / count << std::endl;
+
+      typedef std::map<const double, double>::const_iterator Map_Iterator;
+
+      /* for (std::map<const double, double>::const_iterator it = wm1s.begin(); it != wm1s.end(); ++it)
+      {
+      std::cout  << " " << *(it) << "\n";
+      }
+      */
+      svg_2d_plot data_plot_m1; // <-0.368, -46> <-0.358, -4> <-0.348, 1>...
+
+      data_plot_m1.title("Lambert W-1 function differences from 'best' for double.")
+        .title_font_size(11)
+        .x_size(400)
+        .y_size(200)
+        .legend_on(false)
+        //.legend_font_weight(1)
+        .x_label("z")
+        .y_label("W-1 difference (bits)")
+        .x_range(-0.39, +0.0001)
+        .y_range(-4., +4.)
+        .x_major_interval(0.1)
+        .y_major_interval(2.)
+        .x_major_grid_on(true)
+        .y_major_grid_on(true)
+        .x_label_font_size(9)
+        .y_label_font_size(9)
+        //.x_values_on(true)
+        //.y_values_on(true)
+        .y_values_rotation(horizontal)
+        //.plot_window_on(true)
+        .x_values_precision(3)
+        .y_values_precision(3)
+        .coord_precision(3) // Needed to avoid stepping on curves.
+                            //.coord_precision(4) // Needed to avoid stepping on curves.
+        .copyright_holder("Paul A. Bristow")
+        .copyright_date("2018")
+        //.background_border_color(black);
+        ;
+        data_plot_m1.plot(wm1s, "W-1 branch").line_color(darkblue).shape(none).line_on(true).bezier_on(false).line_width(0.2);
+        data_plot_m1.write("./lambert_wm1_errors_graph");
+    }
+  }
+  catch (std::exception& ex)
+  {
+    std::cout << ex.what() << std::endl;
+  }
+}  // int main()
+
+   /*
+   //[lambert_w_errors_graph_1_output
+   Lambert W errors graph.
+   points 2008
+   max distance 46, total distances = 717, mean distance 0.357
+
+   points 368
+   max distance 23, total distances = 329, mean distance 0.894
+
+   //] [/lambert_w_errors_graph_1_output]
+   */
author	DongHun Kwak <dh0128.kwak@samsung.com>	2019-12-05 15:24:45 +0900
committer	DongHun Kwak <dh0128.kwak@samsung.com>	2019-12-05 15:24:45 +0900
commit	5ce1cfc2525b06c0a9e38531813781de0281c96d (patch)
tree	19cc66c6cf6396db288813b2558cc350f1deede2 /libs/math
parent	3c1df2168531ad5580076ae08d529054689aeedd (diff)
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