Imported Upstream version 1.60.0

Change-Id: Ie709530d6d5841088ceaba025cbe175a4ef43050
Signed-off-by: DongHun Kwak <dh0128.kwak@samsung.com>

127 files changed, 1812 insertions, 1720 deletions

diff --git a/boost/math/tools/big_constant.hpp b/boost/math/tools/big_constant.hpp
index ff136337e1..4386609989 100644
--- a/boost/math/tools/big_constant.hpp
+++ b/boost/math/tools/big_constant.hpp
@@ -37,12 +37,12 @@ typedef long double largest_float;
 #endif
 
 template <class T>
-inline BOOST_CONSTEXPR_OR_CONST T make_big_value(largest_float v, const char*, mpl::true_ const&, mpl::false_ const&)
+inline BOOST_CONSTEXPR_OR_CONST T make_big_value(largest_float v, const char*, mpl::true_ const&, mpl::false_ const&) BOOST_MATH_NOEXCEPT(T)
 {
    return static_cast<T>(v);
 }
 template <class T>
-inline BOOST_CONSTEXPR_OR_CONST T make_big_value(largest_float v, const char*, mpl::true_ const&, mpl::true_ const&)
+inline BOOST_CONSTEXPR_OR_CONST T make_big_value(largest_float v, const char*, mpl::true_ const&, mpl::true_ const&) BOOST_MATH_NOEXCEPT(T)
 {
    return static_cast<T>(v);
 }
@@ -54,7 +54,7 @@ inline T make_big_value(largest_float, const char* s, mpl::false_ const&, mpl::f
 }
 #endif
 template <class T>
-inline BOOST_CONSTEXPR const char* make_big_value(largest_float, const char* s, mpl::false_ const&, mpl::true_ const&)
+inline BOOST_MATH_CONSTEXPR const char* make_big_value(largest_float, const char* s, mpl::false_ const&, mpl::true_ const&) BOOST_MATH_NOEXCEPT(T)
 {
    return s;
 }
diff --git a/boost/math/tools/config.hpp b/boost/math/tools/config.hpp
index e88f578db7..ffd0ab43a6 100644
--- a/boost/math/tools/config.hpp
+++ b/boost/math/tools/config.hpp
@@ -11,6 +11,7 @@
 #endif
 
 #include <boost/config.hpp>
+#include <boost/predef.h>
 #include <boost/cstdint.hpp> // for boost::uintmax_t
 #include <boost/detail/workaround.hpp>
 #include <boost/type_traits/is_integral.hpp>
@@ -183,14 +184,20 @@
 //
 #ifdef BOOST_MSVC
 #  define BOOST_MATH_POLY_METHOD 2
+#  define BOOST_MATH_RATIONAL_METHOD 1
 #elif defined(BOOST_INTEL)
 #  define BOOST_MATH_POLY_METHOD 2
-#  define BOOST_MATH_RATIONAL_METHOD 2
+#  define BOOST_MATH_RATIONAL_METHOD 1
 #elif defined(__GNUC__)
+#if __GNUC__ < 4
 #  define BOOST_MATH_POLY_METHOD 3
 #  define BOOST_MATH_RATIONAL_METHOD 3
 #  define BOOST_MATH_INT_TABLE_TYPE(RT, IT) RT
 #  define BOOST_MATH_INT_VALUE_SUFFIX(RV, SUF) RV##.0L
+#else
+#  define BOOST_MATH_POLY_METHOD 3
+#  define BOOST_MATH_RATIONAL_METHOD 1
+#endif
 #endif
 
 #if defined(BOOST_NO_LONG_LONG) && !defined(BOOST_MATH_INT_TABLE_TYPE)
@@ -199,20 +206,54 @@
 #endif
 
 //
+// constexpr support, early GCC implementations can't cope so disable
+// constexpr for them:
+//
+#if !defined(__clang) && defined(__GNUC__)
+#if (__GNUC__ * 100 + __GNUC_MINOR__) < 490
+#  define BOOST_MATH_DISABLE_CONSTEXPR
+#endif
+#endif
+
+#ifdef BOOST_MATH_DISABLE_CONSTEXPR
+#  define BOOST_MATH_CONSTEXPR
+#else
+#  define BOOST_MATH_CONSTEXPR BOOST_CONSTEXPR
+#endif
+
+//
+// noexcept support:
+//
+#ifndef BOOST_NO_CXX11_NOEXCEPT
+#ifndef BOOST_NO_CXX11_HDR_TYPE_TRAITS
+#include <type_traits>
+#  define BOOST_MATH_NOEXCEPT(T) noexcept(std::is_floating_point<T>::value)
+#  define BOOST_MATH_IS_FLOAT(T) (std::is_floating_point<T>::value)
+#else
+#include <boost/type_traits/is_floating_point.hpp>
+#  define BOOST_MATH_NOEXCEPT(T) noexcept(boost::is_floating_point<T>::value)
+#  define BOOST_MATH_IS_FLOAT(T) (boost::is_floating_point<T>::value)
+#endif
+#else
+#  define BOOST_MATH_NOEXCEPT(T)
+#  define BOOST_MATH_IS_FLOAT(T) false
+#endif
+
+//
 // The maximum order of polynomial that will be evaluated 
 // via an unrolled specialisation:
 //
 #ifndef BOOST_MATH_MAX_POLY_ORDER
-#  define BOOST_MATH_MAX_POLY_ORDER 17
+#  define BOOST_MATH_MAX_POLY_ORDER 20
 #endif 
 //
 // Set the method used to evaluate polynomials and rationals:
 //
 #ifndef BOOST_MATH_POLY_METHOD
-#  define BOOST_MATH_POLY_METHOD 1
+#  define BOOST_MATH_POLY_METHOD 2
 #endif 
 #ifndef BOOST_MATH_RATIONAL_METHOD
-#  define BOOST_MATH_RATIONAL_METHOD 0
+#  define BOOST_MATH_RATIONAL_METHOD 1
 #endif 
 //
 // decide whether to store constants as integers or reals:
@@ -224,7 +265,19 @@
 #  define BOOST_MATH_INT_VALUE_SUFFIX(RV, SUF) RV##SUF
 #endif
 //
-// Test whether to support __float128:
+// Test whether to support __float128, if we don't have quadmath.h then this can't currently work:
+//
+#ifndef BOOST_MATH_USE_FLOAT128
+#ifdef __has_include
+#if ! __has_include("quadmath.h")
+#define BOOST_MATH_DISABLE_FLOAT128
+#endif
+#elif !defined(BOOST_ARCH_X86)
+#define BOOST_MATH_DISABLE_FLOAT128
+#endif
+#endif
+//
+// And then the actual configuration:
 //
 #if defined(_GLIBCXX_USE_FLOAT128) && defined(BOOST_GCC) && !defined(__STRICT_ANSI__) \
    && !defined(BOOST_MATH_DISABLE_FLOAT128) || defined(BOOST_MATH_USE_FLOAT128)
@@ -296,13 +349,13 @@ namespace tools
 {
 
 template <class T>
-inline T max BOOST_PREVENT_MACRO_SUBSTITUTION(T a, T b, T c)
+inline T max BOOST_PREVENT_MACRO_SUBSTITUTION(T a, T b, T c) BOOST_MATH_NOEXCEPT(T)
 {
    return (std::max)((std::max)(a, b), c);
 }
 
 template <class T>
-inline T max BOOST_PREVENT_MACRO_SUBSTITUTION(T a, T b, T c, T d)
+inline T max BOOST_PREVENT_MACRO_SUBSTITUTION(T a, T b, T c, T d) BOOST_MATH_NOEXCEPT(T)
 {
    return (std::max)((std::max)(a, b), (std::max)(c, d));
 }
@@ -310,7 +363,7 @@ inline T max BOOST_PREVENT_MACRO_SUBSTITUTION(T a, T b, T c, T d)
 } // namespace tools
 
 template <class T>
-void suppress_unused_variable_warning(const T&)
+void suppress_unused_variable_warning(const T&) BOOST_MATH_NOEXCEPT(T)
 {
 }
 
diff --git a/boost/math/tools/detail/polynomial_horner1_10.hpp b/boost/math/tools/detail/polynomial_horner1_10.hpp
index b13d6a3887..48cf9e39b3 100644
--- a/boost/math/tools/detail/polynomial_horner1_10.hpp
+++ b/boost/math/tools/detail/polynomial_horner1_10.hpp
@@ -12,67 +12,67 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*)
+inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((a[7] * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((a[8] * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<10>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<10>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((a[9] * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
diff --git a/boost/math/tools/detail/polynomial_horner1_11.hpp b/boost/math/tools/detail/polynomial_horner1_11.hpp
index f0cf67e959..e52595429e 100644
--- a/boost/math/tools/detail/polynomial_horner1_11.hpp
+++ b/boost/math/tools/detail/polynomial_horner1_11.hpp
@@ -12,73 +12,73 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*)
+inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((a[7] * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((a[8] * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<10>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<10>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((a[9] * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<11>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<11>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((a[10] * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
diff --git a/boost/math/tools/detail/polynomial_horner1_12.hpp b/boost/math/tools/detail/polynomial_horner1_12.hpp
index 03b974ceca..10cd178975 100644
--- a/boost/math/tools/detail/polynomial_horner1_12.hpp
+++ b/boost/math/tools/detail/polynomial_horner1_12.hpp
@@ -12,79 +12,79 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*)
+inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((a[7] * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((a[8] * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<10>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<10>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((a[9] * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<11>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<11>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((a[10] * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<12>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<12>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((((a[11] * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
diff --git a/boost/math/tools/detail/polynomial_horner1_13.hpp b/boost/math/tools/detail/polynomial_horner1_13.hpp
index b947f542c3..90fa9ec43d 100644
--- a/boost/math/tools/detail/polynomial_horner1_13.hpp
+++ b/boost/math/tools/detail/polynomial_horner1_13.hpp
@@ -12,85 +12,85 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*)
+inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((a[7] * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((a[8] * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<10>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<10>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((a[9] * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<11>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<11>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((a[10] * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<12>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<12>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((((a[11] * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<13>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<13>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((((a[12] * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
diff --git a/boost/math/tools/detail/polynomial_horner1_14.hpp b/boost/math/tools/detail/polynomial_horner1_14.hpp
index 8374e38904..389c8063b0 100644
--- a/boost/math/tools/detail/polynomial_horner1_14.hpp
+++ b/boost/math/tools/detail/polynomial_horner1_14.hpp
@@ -12,91 +12,91 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*)
+inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((a[7] * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((a[8] * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<10>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<10>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((a[9] * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<11>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<11>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((a[10] * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<12>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<12>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((((a[11] * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<13>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<13>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((((a[12] * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<14>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<14>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((((((a[13] * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
diff --git a/boost/math/tools/detail/polynomial_horner1_15.hpp b/boost/math/tools/detail/polynomial_horner1_15.hpp
index ebfa463601..d196a41603 100644
--- a/boost/math/tools/detail/polynomial_horner1_15.hpp
+++ b/boost/math/tools/detail/polynomial_horner1_15.hpp
@@ -12,97 +12,97 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*)
+inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((a[7] * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((a[8] * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<10>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<10>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((a[9] * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<11>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<11>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((a[10] * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<12>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<12>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((((a[11] * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<13>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<13>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((((a[12] * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<14>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<14>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((((((a[13] * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<15>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<15>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((((((a[14] * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
diff --git a/boost/math/tools/detail/polynomial_horner1_16.hpp b/boost/math/tools/detail/polynomial_horner1_16.hpp
index 60eb4dc675..fa48c6614c 100644
--- a/boost/math/tools/detail/polynomial_horner1_16.hpp
+++ b/boost/math/tools/detail/polynomial_horner1_16.hpp
@@ -12,103 +12,103 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*)
+inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((a[7] * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((a[8] * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<10>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<10>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((a[9] * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<11>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<11>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((a[10] * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<12>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<12>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((((a[11] * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<13>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<13>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((((a[12] * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<14>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<14>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((((((a[13] * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<15>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<15>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((((((a[14] * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<16>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<16>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((((((((a[15] * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
diff --git a/boost/math/tools/detail/polynomial_horner1_17.hpp b/boost/math/tools/detail/polynomial_horner1_17.hpp
index 6233f1b07b..4575aeac7b 100644
--- a/boost/math/tools/detail/polynomial_horner1_17.hpp
+++ b/boost/math/tools/detail/polynomial_horner1_17.hpp
@@ -12,109 +12,109 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*)
+inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((a[7] * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((a[8] * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<10>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<10>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((a[9] * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<11>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<11>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((a[10] * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<12>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<12>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((((a[11] * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<13>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<13>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((((a[12] * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<14>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<14>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((((((a[13] * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<15>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<15>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((((((a[14] * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<16>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<16>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((((((((a[15] * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<17>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<17>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((((((((a[16] * x + a[15]) * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
diff --git a/boost/math/tools/detail/polynomial_horner1_18.hpp b/boost/math/tools/detail/polynomial_horner1_18.hpp
index 2a06def44b..95dd400416 100644
--- a/boost/math/tools/detail/polynomial_horner1_18.hpp
+++ b/boost/math/tools/detail/polynomial_horner1_18.hpp
@@ -12,115 +12,115 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*)
+inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((a[7] * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((a[8] * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<10>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<10>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((a[9] * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<11>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<11>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((a[10] * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<12>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<12>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((((a[11] * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<13>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<13>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((((a[12] * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<14>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<14>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((((((a[13] * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<15>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<15>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((((((a[14] * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<16>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<16>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((((((((a[15] * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<17>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<17>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((((((((a[16] * x + a[15]) * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<18>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<18>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((((((((((a[17] * x + a[16]) * x + a[15]) * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
diff --git a/boost/math/tools/detail/polynomial_horner1_19.hpp b/boost/math/tools/detail/polynomial_horner1_19.hpp
index 8f0da8b219..6d73eb8ffc 100644
--- a/boost/math/tools/detail/polynomial_horner1_19.hpp
+++ b/boost/math/tools/detail/polynomial_horner1_19.hpp
@@ -12,121 +12,121 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*)
+inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((a[7] * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((a[8] * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<10>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<10>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((a[9] * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<11>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<11>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((a[10] * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<12>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<12>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((((a[11] * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<13>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<13>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((((a[12] * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<14>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<14>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((((((a[13] * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<15>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<15>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((((((a[14] * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<16>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<16>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((((((((a[15] * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<17>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<17>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((((((((a[16] * x + a[15]) * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<18>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<18>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((((((((((a[17] * x + a[16]) * x + a[15]) * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<19>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<19>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((((((((((a[18] * x + a[17]) * x + a[16]) * x + a[15]) * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
diff --git a/boost/math/tools/detail/polynomial_horner1_2.hpp b/boost/math/tools/detail/polynomial_horner1_2.hpp
index a0b10d5ee5..85640edf67 100644
--- a/boost/math/tools/detail/polynomial_horner1_2.hpp
+++ b/boost/math/tools/detail/polynomial_horner1_2.hpp
@@ -12,19 +12,19 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*)
+inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
diff --git a/boost/math/tools/detail/polynomial_horner1_20.hpp b/boost/math/tools/detail/polynomial_horner1_20.hpp
index d1a886dd76..f8b7f34384 100644
--- a/boost/math/tools/detail/polynomial_horner1_20.hpp
+++ b/boost/math/tools/detail/polynomial_horner1_20.hpp
@@ -12,127 +12,127 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*)
+inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((a[7] * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((a[8] * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<10>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<10>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((a[9] * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<11>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<11>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((a[10] * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<12>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<12>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((((a[11] * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<13>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<13>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((((a[12] * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<14>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<14>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((((((a[13] * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<15>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<15>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((((((a[14] * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<16>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<16>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((((((((a[15] * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<17>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<17>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((((((((a[16] * x + a[15]) * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<18>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<18>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((((((((((a[17] * x + a[16]) * x + a[15]) * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<19>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<19>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((((((((((a[18] * x + a[17]) * x + a[16]) * x + a[15]) * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<20>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<20>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((((((((((((a[19] * x + a[18]) * x + a[17]) * x + a[16]) * x + a[15]) * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
diff --git a/boost/math/tools/detail/polynomial_horner1_3.hpp b/boost/math/tools/detail/polynomial_horner1_3.hpp
index 715a69aee0..c0ad4660e9 100644
--- a/boost/math/tools/detail/polynomial_horner1_3.hpp
+++ b/boost/math/tools/detail/polynomial_horner1_3.hpp
@@ -12,25 +12,25 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*)
+inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
diff --git a/boost/math/tools/detail/polynomial_horner1_4.hpp b/boost/math/tools/detail/polynomial_horner1_4.hpp
index d74b7a6386..27ad74eb95 100644
--- a/boost/math/tools/detail/polynomial_horner1_4.hpp
+++ b/boost/math/tools/detail/polynomial_horner1_4.hpp
@@ -12,31 +12,31 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*)
+inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
diff --git a/boost/math/tools/detail/polynomial_horner1_5.hpp b/boost/math/tools/detail/polynomial_horner1_5.hpp
index bb66e6c41d..5cfafb4052 100644
--- a/boost/math/tools/detail/polynomial_horner1_5.hpp
+++ b/boost/math/tools/detail/polynomial_horner1_5.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*)
+inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
diff --git a/boost/math/tools/detail/polynomial_horner1_6.hpp b/boost/math/tools/detail/polynomial_horner1_6.hpp
index a29c2710e8..f7f4bee480 100644
--- a/boost/math/tools/detail/polynomial_horner1_6.hpp
+++ b/boost/math/tools/detail/polynomial_horner1_6.hpp
@@ -12,43 +12,43 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*)
+inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
diff --git a/boost/math/tools/detail/polynomial_horner1_7.hpp b/boost/math/tools/detail/polynomial_horner1_7.hpp
index 093ab89b02..c612822fc0 100644
--- a/boost/math/tools/detail/polynomial_horner1_7.hpp
+++ b/boost/math/tools/detail/polynomial_horner1_7.hpp
@@ -12,49 +12,49 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*)
+inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
diff --git a/boost/math/tools/detail/polynomial_horner1_8.hpp b/boost/math/tools/detail/polynomial_horner1_8.hpp
index a3d329a37b..5d9b453b9d 100644
--- a/boost/math/tools/detail/polynomial_horner1_8.hpp
+++ b/boost/math/tools/detail/polynomial_horner1_8.hpp
@@ -12,55 +12,55 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*)
+inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((a[7] * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
diff --git a/boost/math/tools/detail/polynomial_horner1_9.hpp b/boost/math/tools/detail/polynomial_horner1_9.hpp
index e90f578d04..84977fd13b 100644
--- a/boost/math/tools/detail/polynomial_horner1_9.hpp
+++ b/boost/math/tools/detail/polynomial_horner1_9.hpp
@@ -12,61 +12,61 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*)
+inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((a[7] * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((a[8] * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
diff --git a/boost/math/tools/detail/polynomial_horner2_10.hpp b/boost/math/tools/detail/polynomial_horner2_10.hpp
index 7c4101f465..f10c5d0492 100644
--- a/boost/math/tools/detail/polynomial_horner2_10.hpp
+++ b/boost/math/tools/detail/polynomial_horner2_10.hpp
@@ -12,72 +12,72 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*)
+inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((a[4] * x2 + a[2]) * x2 + a[0] + (a[3] * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[5] * x2 + a[3]) * x2 + a[1]) * x + (a[4] * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((a[5] * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((a[7] * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((a[8] * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + (((a[7] * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<10>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<10>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((a[9] * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + (((a[8] * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
diff --git a/boost/math/tools/detail/polynomial_horner2_11.hpp b/boost/math/tools/detail/polynomial_horner2_11.hpp
index bebd1e6483..757357addf 100644
--- a/boost/math/tools/detail/polynomial_horner2_11.hpp
+++ b/boost/math/tools/detail/polynomial_horner2_11.hpp
@@ -12,79 +12,79 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*)
+inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((a[4] * x2 + a[2]) * x2 + a[0] + (a[3] * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[5] * x2 + a[3]) * x2 + a[1]) * x + (a[4] * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((a[5] * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((a[7] * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((a[8] * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + (((a[7] * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<10>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<10>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((a[9] * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + (((a[8] * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<11>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<11>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((a[10] * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((((a[9] * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
diff --git a/boost/math/tools/detail/polynomial_horner2_12.hpp b/boost/math/tools/detail/polynomial_horner2_12.hpp
index c4da24ac88..e0fc8a9df7 100644
--- a/boost/math/tools/detail/polynomial_horner2_12.hpp
+++ b/boost/math/tools/detail/polynomial_horner2_12.hpp
@@ -12,86 +12,86 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*)
+inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((a[4] * x2 + a[2]) * x2 + a[0] + (a[3] * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[5] * x2 + a[3]) * x2 + a[1]) * x + (a[4] * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((a[5] * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((a[7] * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((a[8] * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + (((a[7] * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<10>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<10>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((a[9] * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + (((a[8] * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<11>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<11>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((a[10] * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((((a[9] * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<12>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<12>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((a[11] * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((((a[10] * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
diff --git a/boost/math/tools/detail/polynomial_horner2_13.hpp b/boost/math/tools/detail/polynomial_horner2_13.hpp
index 5d7dddc5b5..c13a0a7cc2 100644
--- a/boost/math/tools/detail/polynomial_horner2_13.hpp
+++ b/boost/math/tools/detail/polynomial_horner2_13.hpp
@@ -12,93 +12,93 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*)
+inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((a[4] * x2 + a[2]) * x2 + a[0] + (a[3] * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[5] * x2 + a[3]) * x2 + a[1]) * x + (a[4] * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((a[5] * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((a[7] * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((a[8] * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + (((a[7] * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<10>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<10>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((a[9] * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + (((a[8] * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<11>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<11>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((a[10] * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((((a[9] * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<12>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<12>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((a[11] * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((((a[10] * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<13>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<13>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((a[12] * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + (((((a[11] * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
diff --git a/boost/math/tools/detail/polynomial_horner2_14.hpp b/boost/math/tools/detail/polynomial_horner2_14.hpp
index 21a5a37903..ccc6e7d8da 100644
--- a/boost/math/tools/detail/polynomial_horner2_14.hpp
+++ b/boost/math/tools/detail/polynomial_horner2_14.hpp
@@ -12,100 +12,100 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*)
+inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((a[4] * x2 + a[2]) * x2 + a[0] + (a[3] * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[5] * x2 + a[3]) * x2 + a[1]) * x + (a[4] * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((a[5] * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((a[7] * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((a[8] * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + (((a[7] * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<10>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<10>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((a[9] * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + (((a[8] * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<11>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<11>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((a[10] * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((((a[9] * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<12>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<12>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((a[11] * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((((a[10] * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<13>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<13>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((a[12] * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + (((((a[11] * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<14>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<14>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((((a[13] * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + (((((a[12] * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
diff --git a/boost/math/tools/detail/polynomial_horner2_15.hpp b/boost/math/tools/detail/polynomial_horner2_15.hpp
index 7b41214466..a409ba7fdb 100644
--- a/boost/math/tools/detail/polynomial_horner2_15.hpp
+++ b/boost/math/tools/detail/polynomial_horner2_15.hpp
@@ -12,107 +12,107 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*)
+inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((a[4] * x2 + a[2]) * x2 + a[0] + (a[3] * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[5] * x2 + a[3]) * x2 + a[1]) * x + (a[4] * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((a[5] * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((a[7] * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((a[8] * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + (((a[7] * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<10>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<10>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((a[9] * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + (((a[8] * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<11>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<11>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((a[10] * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((((a[9] * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<12>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<12>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((a[11] * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((((a[10] * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<13>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<13>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((a[12] * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + (((((a[11] * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<14>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<14>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((((a[13] * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + (((((a[12] * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<15>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<15>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((((a[14] * x2 + a[12]) * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((((((a[13] * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
diff --git a/boost/math/tools/detail/polynomial_horner2_16.hpp b/boost/math/tools/detail/polynomial_horner2_16.hpp
index aa3763ad65..a69c1a3619 100644
--- a/boost/math/tools/detail/polynomial_horner2_16.hpp
+++ b/boost/math/tools/detail/polynomial_horner2_16.hpp
@@ -12,114 +12,114 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*)
+inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((a[4] * x2 + a[2]) * x2 + a[0] + (a[3] * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[5] * x2 + a[3]) * x2 + a[1]) * x + (a[4] * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((a[5] * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((a[7] * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((a[8] * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + (((a[7] * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<10>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<10>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((a[9] * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + (((a[8] * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<11>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<11>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((a[10] * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((((a[9] * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<12>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<12>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((a[11] * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((((a[10] * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<13>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<13>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((a[12] * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + (((((a[11] * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<14>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<14>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((((a[13] * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + (((((a[12] * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<15>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<15>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((((a[14] * x2 + a[12]) * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((((((a[13] * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<16>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<16>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((((a[15] * x2 + a[13]) * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((((((a[14] * x2 + a[12]) * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
diff --git a/boost/math/tools/detail/polynomial_horner2_17.hpp b/boost/math/tools/detail/polynomial_horner2_17.hpp
index 6ed5566d49..9e7c05d007 100644
--- a/boost/math/tools/detail/polynomial_horner2_17.hpp
+++ b/boost/math/tools/detail/polynomial_horner2_17.hpp
@@ -12,121 +12,121 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*)
+inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((a[4] * x2 + a[2]) * x2 + a[0] + (a[3] * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[5] * x2 + a[3]) * x2 + a[1]) * x + (a[4] * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((a[5] * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((a[7] * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((a[8] * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + (((a[7] * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<10>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<10>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((a[9] * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + (((a[8] * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<11>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<11>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((a[10] * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((((a[9] * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<12>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<12>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((a[11] * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((((a[10] * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<13>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<13>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((a[12] * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + (((((a[11] * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<14>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<14>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((((a[13] * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + (((((a[12] * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<15>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<15>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((((a[14] * x2 + a[12]) * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((((((a[13] * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<16>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<16>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((((a[15] * x2 + a[13]) * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((((((a[14] * x2 + a[12]) * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<17>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<17>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((((a[16] * x2 + a[14]) * x2 + a[12]) * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + (((((((a[15] * x2 + a[13]) * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
diff --git a/boost/math/tools/detail/polynomial_horner2_18.hpp b/boost/math/tools/detail/polynomial_horner2_18.hpp
index 02c72b8227..1ea0e052c0 100644
--- a/boost/math/tools/detail/polynomial_horner2_18.hpp
+++ b/boost/math/tools/detail/polynomial_horner2_18.hpp
@@ -12,128 +12,128 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*)
+inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((a[4] * x2 + a[2]) * x2 + a[0] + (a[3] * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[5] * x2 + a[3]) * x2 + a[1]) * x + (a[4] * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((a[5] * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((a[7] * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((a[8] * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + (((a[7] * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<10>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<10>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((a[9] * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + (((a[8] * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<11>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<11>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((a[10] * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((((a[9] * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<12>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<12>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((a[11] * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((((a[10] * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<13>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<13>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((a[12] * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + (((((a[11] * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<14>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<14>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((((a[13] * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + (((((a[12] * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<15>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<15>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((((a[14] * x2 + a[12]) * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((((((a[13] * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<16>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<16>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((((a[15] * x2 + a[13]) * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((((((a[14] * x2 + a[12]) * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<17>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<17>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((((a[16] * x2 + a[14]) * x2 + a[12]) * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + (((((((a[15] * x2 + a[13]) * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<18>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<18>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((((((a[17] * x2 + a[15]) * x2 + a[13]) * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + (((((((a[16] * x2 + a[14]) * x2 + a[12]) * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
diff --git a/boost/math/tools/detail/polynomial_horner2_19.hpp b/boost/math/tools/detail/polynomial_horner2_19.hpp
index 6e36ace904..45c125c871 100644
--- a/boost/math/tools/detail/polynomial_horner2_19.hpp
+++ b/boost/math/tools/detail/polynomial_horner2_19.hpp
@@ -12,135 +12,135 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*)
+inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((a[4] * x2 + a[2]) * x2 + a[0] + (a[3] * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[5] * x2 + a[3]) * x2 + a[1]) * x + (a[4] * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((a[5] * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((a[7] * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((a[8] * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + (((a[7] * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<10>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<10>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((a[9] * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + (((a[8] * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<11>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<11>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((a[10] * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((((a[9] * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<12>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<12>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((a[11] * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((((a[10] * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<13>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<13>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((a[12] * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + (((((a[11] * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<14>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<14>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((((a[13] * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + (((((a[12] * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<15>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<15>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((((a[14] * x2 + a[12]) * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((((((a[13] * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<16>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<16>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((((a[15] * x2 + a[13]) * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((((((a[14] * x2 + a[12]) * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<17>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<17>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((((a[16] * x2 + a[14]) * x2 + a[12]) * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + (((((((a[15] * x2 + a[13]) * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<18>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<18>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((((((a[17] * x2 + a[15]) * x2 + a[13]) * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + (((((((a[16] * x2 + a[14]) * x2 + a[12]) * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<19>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<19>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((((((a[18] * x2 + a[16]) * x2 + a[14]) * x2 + a[12]) * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((((((((a[17] * x2 + a[15]) * x2 + a[13]) * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
diff --git a/boost/math/tools/detail/polynomial_horner2_2.hpp b/boost/math/tools/detail/polynomial_horner2_2.hpp
index e2a4e7faef..20da483c33 100644
--- a/boost/math/tools/detail/polynomial_horner2_2.hpp
+++ b/boost/math/tools/detail/polynomial_horner2_2.hpp
@@ -12,31 +12,31 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*)
+inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
diff --git a/boost/math/tools/detail/polynomial_horner2_20.hpp b/boost/math/tools/detail/polynomial_horner2_20.hpp
index e394b6b325..956c6dba4f 100644
--- a/boost/math/tools/detail/polynomial_horner2_20.hpp
+++ b/boost/math/tools/detail/polynomial_horner2_20.hpp
@@ -12,142 +12,142 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*)
+inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((a[4] * x2 + a[2]) * x2 + a[0] + (a[3] * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[5] * x2 + a[3]) * x2 + a[1]) * x + (a[4] * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((a[5] * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((a[7] * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((a[8] * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + (((a[7] * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<10>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<10>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((a[9] * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + (((a[8] * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<11>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<11>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((a[10] * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((((a[9] * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<12>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<12>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((a[11] * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((((a[10] * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<13>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<13>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((a[12] * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + (((((a[11] * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<14>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<14>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((((a[13] * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + (((((a[12] * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<15>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<15>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((((a[14] * x2 + a[12]) * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((((((a[13] * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<16>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<16>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((((a[15] * x2 + a[13]) * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((((((a[14] * x2 + a[12]) * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<17>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<17>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((((a[16] * x2 + a[14]) * x2 + a[12]) * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + (((((((a[15] * x2 + a[13]) * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<18>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<18>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((((((a[17] * x2 + a[15]) * x2 + a[13]) * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + (((((((a[16] * x2 + a[14]) * x2 + a[12]) * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<19>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<19>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((((((a[18] * x2 + a[16]) * x2 + a[14]) * x2 + a[12]) * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((((((((a[17] * x2 + a[15]) * x2 + a[13]) * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<20>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<20>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((((((a[19] * x2 + a[17]) * x2 + a[15]) * x2 + a[13]) * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((((((((a[18] * x2 + a[16]) * x2 + a[14]) * x2 + a[12]) * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
diff --git a/boost/math/tools/detail/polynomial_horner2_3.hpp b/boost/math/tools/detail/polynomial_horner2_3.hpp
index 187b86c1ce..58b290c7c9 100644
--- a/boost/math/tools/detail/polynomial_horner2_3.hpp
+++ b/boost/math/tools/detail/polynomial_horner2_3.hpp
@@ -12,31 +12,31 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*)
+inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
diff --git a/boost/math/tools/detail/polynomial_horner2_4.hpp b/boost/math/tools/detail/polynomial_horner2_4.hpp
index 84badc365a..74f969b749 100644
--- a/boost/math/tools/detail/polynomial_horner2_4.hpp
+++ b/boost/math/tools/detail/polynomial_horner2_4.hpp
@@ -12,31 +12,31 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*)
+inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
diff --git a/boost/math/tools/detail/polynomial_horner2_5.hpp b/boost/math/tools/detail/polynomial_horner2_5.hpp
index 287b4be08e..134cbc8ef9 100644
--- a/boost/math/tools/detail/polynomial_horner2_5.hpp
+++ b/boost/math/tools/detail/polynomial_horner2_5.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*)
+inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((a[4] * x2 + a[2]) * x2 + a[0] + (a[3] * x2 + a[1]) * x);
diff --git a/boost/math/tools/detail/polynomial_horner2_6.hpp b/boost/math/tools/detail/polynomial_horner2_6.hpp
index 3662d44f93..7cb75d75c8 100644
--- a/boost/math/tools/detail/polynomial_horner2_6.hpp
+++ b/boost/math/tools/detail/polynomial_horner2_6.hpp
@@ -12,44 +12,44 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*)
+inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((a[4] * x2 + a[2]) * x2 + a[0] + (a[3] * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[5] * x2 + a[3]) * x2 + a[1]) * x + (a[4] * x2 + a[2]) * x2 + a[0]);
diff --git a/boost/math/tools/detail/polynomial_horner2_7.hpp b/boost/math/tools/detail/polynomial_horner2_7.hpp
index 78ed0df54d..327639deb6 100644
--- a/boost/math/tools/detail/polynomial_horner2_7.hpp
+++ b/boost/math/tools/detail/polynomial_horner2_7.hpp
@@ -12,51 +12,51 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*)
+inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((a[4] * x2 + a[2]) * x2 + a[0] + (a[3] * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[5] * x2 + a[3]) * x2 + a[1]) * x + (a[4] * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((a[5] * x2 + a[3]) * x2 + a[1]) * x);
diff --git a/boost/math/tools/detail/polynomial_horner2_8.hpp b/boost/math/tools/detail/polynomial_horner2_8.hpp
index ac8e941180..2145ad6dcd 100644
--- a/boost/math/tools/detail/polynomial_horner2_8.hpp
+++ b/boost/math/tools/detail/polynomial_horner2_8.hpp
@@ -12,58 +12,58 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*)
+inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((a[4] * x2 + a[2]) * x2 + a[0] + (a[3] * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[5] * x2 + a[3]) * x2 + a[1]) * x + (a[4] * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((a[5] * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((a[7] * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
diff --git a/boost/math/tools/detail/polynomial_horner2_9.hpp b/boost/math/tools/detail/polynomial_horner2_9.hpp
index e1a3d17eca..08f6336e49 100644
--- a/boost/math/tools/detail/polynomial_horner2_9.hpp
+++ b/boost/math/tools/detail/polynomial_horner2_9.hpp
@@ -12,65 +12,65 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*)
+inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((a[4] * x2 + a[2]) * x2 + a[0] + (a[3] * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[5] * x2 + a[3]) * x2 + a[1]) * x + (a[4] * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((a[5] * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((a[7] * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((a[8] * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + (((a[7] * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
diff --git a/boost/math/tools/detail/polynomial_horner3_10.hpp b/boost/math/tools/detail/polynomial_horner3_10.hpp
index 69736d7118..05ad20cc30 100644
--- a/boost/math/tools/detail/polynomial_horner3_10.hpp
+++ b/boost/math/tools/detail/polynomial_horner3_10.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*)
+inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -55,7 +55,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -70,7 +70,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -87,7 +87,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -106,7 +106,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -127,7 +127,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<10>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<10>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
diff --git a/boost/math/tools/detail/polynomial_horner3_11.hpp b/boost/math/tools/detail/polynomial_horner3_11.hpp
index 273ed535cc..9f8628e750 100644
--- a/boost/math/tools/detail/polynomial_horner3_11.hpp
+++ b/boost/math/tools/detail/polynomial_horner3_11.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*)
+inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -55,7 +55,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -70,7 +70,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -87,7 +87,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -106,7 +106,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -127,7 +127,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<10>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<10>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -150,7 +150,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<10>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<11>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<11>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
diff --git a/boost/math/tools/detail/polynomial_horner3_12.hpp b/boost/math/tools/detail/polynomial_horner3_12.hpp
index 340567400b..ccb3ec4d10 100644
--- a/boost/math/tools/detail/polynomial_horner3_12.hpp
+++ b/boost/math/tools/detail/polynomial_horner3_12.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*)
+inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -55,7 +55,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -70,7 +70,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -87,7 +87,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -106,7 +106,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -127,7 +127,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<10>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<10>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -150,7 +150,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<10>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<11>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<11>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -175,7 +175,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<11>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<12>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<12>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
diff --git a/boost/math/tools/detail/polynomial_horner3_13.hpp b/boost/math/tools/detail/polynomial_horner3_13.hpp
index 849c93e54a..a8cdf2c508 100644
--- a/boost/math/tools/detail/polynomial_horner3_13.hpp
+++ b/boost/math/tools/detail/polynomial_horner3_13.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*)
+inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -55,7 +55,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -70,7 +70,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -87,7 +87,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -106,7 +106,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -127,7 +127,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<10>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<10>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -150,7 +150,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<10>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<11>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<11>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -175,7 +175,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<11>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<12>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<12>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -202,7 +202,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<12>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<13>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<13>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
diff --git a/boost/math/tools/detail/polynomial_horner3_14.hpp b/boost/math/tools/detail/polynomial_horner3_14.hpp
index f5ac1df9d1..5eb4ef1f28 100644
--- a/boost/math/tools/detail/polynomial_horner3_14.hpp
+++ b/boost/math/tools/detail/polynomial_horner3_14.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*)
+inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -55,7 +55,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -70,7 +70,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -87,7 +87,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -106,7 +106,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -127,7 +127,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<10>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<10>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -150,7 +150,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<10>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<11>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<11>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -175,7 +175,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<11>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<12>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<12>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -202,7 +202,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<12>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<13>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<13>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -231,7 +231,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<13>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<14>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<14>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
diff --git a/boost/math/tools/detail/polynomial_horner3_15.hpp b/boost/math/tools/detail/polynomial_horner3_15.hpp
index b57af7e3dc..7e8edcd8aa 100644
--- a/boost/math/tools/detail/polynomial_horner3_15.hpp
+++ b/boost/math/tools/detail/polynomial_horner3_15.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*)
+inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -55,7 +55,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -70,7 +70,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -87,7 +87,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -106,7 +106,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -127,7 +127,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<10>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<10>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -150,7 +150,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<10>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<11>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<11>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -175,7 +175,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<11>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<12>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<12>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -202,7 +202,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<12>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<13>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<13>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -231,7 +231,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<13>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<14>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<14>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -262,7 +262,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<14>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<15>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<15>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
diff --git a/boost/math/tools/detail/polynomial_horner3_16.hpp b/boost/math/tools/detail/polynomial_horner3_16.hpp
index 1fc8560a21..58bea1581f 100644
--- a/boost/math/tools/detail/polynomial_horner3_16.hpp
+++ b/boost/math/tools/detail/polynomial_horner3_16.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*)
+inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -55,7 +55,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -70,7 +70,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -87,7 +87,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -106,7 +106,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -127,7 +127,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<10>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<10>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -150,7 +150,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<10>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<11>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<11>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -175,7 +175,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<11>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<12>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<12>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -202,7 +202,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<12>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<13>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<13>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -231,7 +231,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<13>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<14>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<14>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -262,7 +262,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<14>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<15>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<15>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -295,7 +295,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<15>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<16>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<16>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
diff --git a/boost/math/tools/detail/polynomial_horner3_17.hpp b/boost/math/tools/detail/polynomial_horner3_17.hpp
index 4a0d0aa472..007b8a4918 100644
--- a/boost/math/tools/detail/polynomial_horner3_17.hpp
+++ b/boost/math/tools/detail/polynomial_horner3_17.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*)
+inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -55,7 +55,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -70,7 +70,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -87,7 +87,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -106,7 +106,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -127,7 +127,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<10>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<10>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -150,7 +150,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<10>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<11>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<11>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -175,7 +175,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<11>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<12>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<12>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -202,7 +202,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<12>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<13>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<13>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -231,7 +231,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<13>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<14>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<14>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -262,7 +262,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<14>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<15>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<15>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -295,7 +295,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<15>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<16>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<16>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -330,7 +330,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<16>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<17>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<17>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
diff --git a/boost/math/tools/detail/polynomial_horner3_18.hpp b/boost/math/tools/detail/polynomial_horner3_18.hpp
index 899117d2f9..68935adba1 100644
--- a/boost/math/tools/detail/polynomial_horner3_18.hpp
+++ b/boost/math/tools/detail/polynomial_horner3_18.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*)
+inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -55,7 +55,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -70,7 +70,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -87,7 +87,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -106,7 +106,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -127,7 +127,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<10>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<10>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -150,7 +150,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<10>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<11>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<11>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -175,7 +175,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<11>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<12>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<12>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -202,7 +202,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<12>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<13>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<13>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -231,7 +231,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<13>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<14>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<14>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -262,7 +262,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<14>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<15>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<15>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -295,7 +295,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<15>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<16>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<16>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -330,7 +330,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<16>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<17>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<17>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -367,7 +367,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<17>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<18>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<18>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
diff --git a/boost/math/tools/detail/polynomial_horner3_19.hpp b/boost/math/tools/detail/polynomial_horner3_19.hpp
index 7c4f728419..acffba6b47 100644
--- a/boost/math/tools/detail/polynomial_horner3_19.hpp
+++ b/boost/math/tools/detail/polynomial_horner3_19.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*)
+inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -55,7 +55,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -70,7 +70,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -87,7 +87,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -106,7 +106,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -127,7 +127,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<10>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<10>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -150,7 +150,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<10>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<11>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<11>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -175,7 +175,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<11>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<12>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<12>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -202,7 +202,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<12>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<13>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<13>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -231,7 +231,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<13>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<14>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<14>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -262,7 +262,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<14>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<15>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<15>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -295,7 +295,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<15>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<16>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<16>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -330,7 +330,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<16>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<17>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<17>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -367,7 +367,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<17>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<18>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<18>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -406,7 +406,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<18>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<19>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<19>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
diff --git a/boost/math/tools/detail/polynomial_horner3_2.hpp b/boost/math/tools/detail/polynomial_horner3_2.hpp
index 372630cfd9..6b8d9a71f8 100644
--- a/boost/math/tools/detail/polynomial_horner3_2.hpp
+++ b/boost/math/tools/detail/polynomial_horner3_2.hpp
@@ -12,31 +12,31 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*)
+inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
diff --git a/boost/math/tools/detail/polynomial_horner3_20.hpp b/boost/math/tools/detail/polynomial_horner3_20.hpp
index b20e0d5fe1..b3a170c095 100644
--- a/boost/math/tools/detail/polynomial_horner3_20.hpp
+++ b/boost/math/tools/detail/polynomial_horner3_20.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*)
+inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -55,7 +55,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -70,7 +70,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -87,7 +87,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -106,7 +106,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -127,7 +127,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<10>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<10>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -150,7 +150,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<10>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<11>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<11>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -175,7 +175,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<11>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<12>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<12>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -202,7 +202,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<12>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<13>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<13>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -231,7 +231,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<13>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<14>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<14>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -262,7 +262,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<14>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<15>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<15>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -295,7 +295,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<15>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<16>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<16>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -330,7 +330,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<16>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<17>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<17>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -367,7 +367,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<17>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<18>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<18>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -406,7 +406,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<18>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<19>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<19>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -447,7 +447,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<19>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<20>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<20>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
diff --git a/boost/math/tools/detail/polynomial_horner3_3.hpp b/boost/math/tools/detail/polynomial_horner3_3.hpp
index cc6b1a9351..05fe88fccc 100644
--- a/boost/math/tools/detail/polynomial_horner3_3.hpp
+++ b/boost/math/tools/detail/polynomial_horner3_3.hpp
@@ -12,31 +12,31 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*)
+inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
diff --git a/boost/math/tools/detail/polynomial_horner3_4.hpp b/boost/math/tools/detail/polynomial_horner3_4.hpp
index 74192f0c90..b98d6f678d 100644
--- a/boost/math/tools/detail/polynomial_horner3_4.hpp
+++ b/boost/math/tools/detail/polynomial_horner3_4.hpp
@@ -12,31 +12,31 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*)
+inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
diff --git a/boost/math/tools/detail/polynomial_horner3_5.hpp b/boost/math/tools/detail/polynomial_horner3_5.hpp
index 73d1900998..12e639cef3 100644
--- a/boost/math/tools/detail/polynomial_horner3_5.hpp
+++ b/boost/math/tools/detail/polynomial_horner3_5.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*)
+inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
diff --git a/boost/math/tools/detail/polynomial_horner3_6.hpp b/boost/math/tools/detail/polynomial_horner3_6.hpp
index da02574866..b645cb5bbc 100644
--- a/boost/math/tools/detail/polynomial_horner3_6.hpp
+++ b/boost/math/tools/detail/polynomial_horner3_6.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*)
+inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -55,7 +55,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
diff --git a/boost/math/tools/detail/polynomial_horner3_7.hpp b/boost/math/tools/detail/polynomial_horner3_7.hpp
index d45a622278..3df4b5b4ef 100644
--- a/boost/math/tools/detail/polynomial_horner3_7.hpp
+++ b/boost/math/tools/detail/polynomial_horner3_7.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*)
+inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -55,7 +55,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -70,7 +70,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
diff --git a/boost/math/tools/detail/polynomial_horner3_8.hpp b/boost/math/tools/detail/polynomial_horner3_8.hpp
index d0198bf345..9a49d2555e 100644
--- a/boost/math/tools/detail/polynomial_horner3_8.hpp
+++ b/boost/math/tools/detail/polynomial_horner3_8.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*)
+inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -55,7 +55,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -70,7 +70,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -87,7 +87,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
diff --git a/boost/math/tools/detail/polynomial_horner3_9.hpp b/boost/math/tools/detail/polynomial_horner3_9.hpp
index b3e0b19970..3507d37604 100644
--- a/boost/math/tools/detail/polynomial_horner3_9.hpp
+++ b/boost/math/tools/detail/polynomial_horner3_9.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*)
+inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -55,7 +55,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<5>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -70,7 +70,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<6>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -87,7 +87,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<7>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -106,7 +106,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<8>*)
 }
 
 template <class T, class V>
-inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<9>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
diff --git a/boost/math/tools/detail/rational_horner1_10.hpp b/boost/math/tools/detail/rational_horner1_10.hpp
index 919ba6d09f..e670853869 100644
--- a/boost/math/tools/detail/rational_horner1_10.hpp
+++ b/boost/math/tools/detail/rational_horner1_10.hpp
@@ -12,19 +12,19 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*)
+inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
@@ -36,7 +36,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
@@ -48,7 +48,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
@@ -60,7 +60,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((b[4] * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -72,7 +72,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((b[5] * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -84,7 +84,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((b[6] * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -96,7 +96,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<8>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((((((a[7] * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((b[7] * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -108,7 +108,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<9>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((((((((a[8] * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((b[8] * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -120,7 +120,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<10>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((((((((a[9] * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((b[9] * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
diff --git a/boost/math/tools/detail/rational_horner1_11.hpp b/boost/math/tools/detail/rational_horner1_11.hpp
index e17bfbc723..65e17598ff 100644
--- a/boost/math/tools/detail/rational_horner1_11.hpp
+++ b/boost/math/tools/detail/rational_horner1_11.hpp
@@ -12,19 +12,19 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*)
+inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
@@ -36,7 +36,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
@@ -48,7 +48,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
@@ -60,7 +60,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((b[4] * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -72,7 +72,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((b[5] * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -84,7 +84,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((b[6] * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -96,7 +96,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<8>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((((((a[7] * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((b[7] * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -108,7 +108,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<9>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((((((((a[8] * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((b[8] * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -120,7 +120,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<10>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((((((((a[9] * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((b[9] * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -132,7 +132,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<11>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((((((((((a[10] * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((b[10] * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
diff --git a/boost/math/tools/detail/rational_horner1_12.hpp b/boost/math/tools/detail/rational_horner1_12.hpp
index 67b430a990..de33af0e07 100644
--- a/boost/math/tools/detail/rational_horner1_12.hpp
+++ b/boost/math/tools/detail/rational_horner1_12.hpp
@@ -12,19 +12,19 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*)
+inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
@@ -36,7 +36,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
@@ -48,7 +48,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
@@ -60,7 +60,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((b[4] * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -72,7 +72,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((b[5] * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -84,7 +84,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((b[6] * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -96,7 +96,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<8>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((((((a[7] * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((b[7] * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -108,7 +108,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<9>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((((((((a[8] * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((b[8] * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -120,7 +120,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<10>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((((((((a[9] * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((b[9] * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -132,7 +132,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<11>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((((((((((a[10] * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((b[10] * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -144,7 +144,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<12>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((((((((((a[11] * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((((b[11] * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
diff --git a/boost/math/tools/detail/rational_horner1_13.hpp b/boost/math/tools/detail/rational_horner1_13.hpp
index 33ae67523c..ed4ac1af8b 100644
--- a/boost/math/tools/detail/rational_horner1_13.hpp
+++ b/boost/math/tools/detail/rational_horner1_13.hpp
@@ -12,19 +12,19 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*)
+inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
@@ -36,7 +36,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
@@ -48,7 +48,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
@@ -60,7 +60,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((b[4] * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -72,7 +72,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((b[5] * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -84,7 +84,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((b[6] * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -96,7 +96,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<8>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((((((a[7] * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((b[7] * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -108,7 +108,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<9>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((((((((a[8] * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((b[8] * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -120,7 +120,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<10>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((((((((a[9] * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((b[9] * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -132,7 +132,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<11>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((((((((((a[10] * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((b[10] * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -144,7 +144,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<12>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((((((((((a[11] * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((((b[11] * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -156,7 +156,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<13>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<13>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((((((((((((a[12] * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((((b[12] * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
diff --git a/boost/math/tools/detail/rational_horner1_14.hpp b/boost/math/tools/detail/rational_horner1_14.hpp
index 0c5f1884c6..a3222f8212 100644
--- a/boost/math/tools/detail/rational_horner1_14.hpp
+++ b/boost/math/tools/detail/rational_horner1_14.hpp
@@ -12,19 +12,19 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*)
+inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
@@ -36,7 +36,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
@@ -48,7 +48,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
@@ -60,7 +60,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((b[4] * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -72,7 +72,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((b[5] * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -84,7 +84,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((b[6] * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -96,7 +96,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<8>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((((((a[7] * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((b[7] * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -108,7 +108,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<9>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((((((((a[8] * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((b[8] * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -120,7 +120,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<10>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((((((((a[9] * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((b[9] * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -132,7 +132,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<11>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((((((((((a[10] * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((b[10] * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -144,7 +144,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<12>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((((((((((a[11] * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((((b[11] * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -156,7 +156,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<13>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<13>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((((((((((((a[12] * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((((b[12] * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -168,7 +168,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<14>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<14>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((((((((((((a[13] * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((((((b[13] * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
diff --git a/boost/math/tools/detail/rational_horner1_15.hpp b/boost/math/tools/detail/rational_horner1_15.hpp
index 848190761f..c8cd691573 100644
--- a/boost/math/tools/detail/rational_horner1_15.hpp
+++ b/boost/math/tools/detail/rational_horner1_15.hpp
@@ -12,19 +12,19 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*)
+inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
@@ -36,7 +36,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
@@ -48,7 +48,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
@@ -60,7 +60,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((b[4] * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -72,7 +72,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((b[5] * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -84,7 +84,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((b[6] * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -96,7 +96,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<8>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((((((a[7] * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((b[7] * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -108,7 +108,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<9>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((((((((a[8] * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((b[8] * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -120,7 +120,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<10>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((((((((a[9] * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((b[9] * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -132,7 +132,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<11>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((((((((((a[10] * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((b[10] * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -144,7 +144,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<12>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((((((((((a[11] * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((((b[11] * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -156,7 +156,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<13>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<13>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((((((((((((a[12] * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((((b[12] * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -168,7 +168,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<14>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<14>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((((((((((((a[13] * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((((((b[13] * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -180,7 +180,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<15>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<15>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((((((((((((((a[14] * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((((((b[14] * x + b[13]) * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
diff --git a/boost/math/tools/detail/rational_horner1_16.hpp b/boost/math/tools/detail/rational_horner1_16.hpp
index e0661f8b3e..8003c82db7 100644
--- a/boost/math/tools/detail/rational_horner1_16.hpp
+++ b/boost/math/tools/detail/rational_horner1_16.hpp
@@ -12,19 +12,19 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*)
+inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
@@ -36,7 +36,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
@@ -48,7 +48,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
@@ -60,7 +60,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((b[4] * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -72,7 +72,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((b[5] * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -84,7 +84,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((b[6] * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -96,7 +96,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<8>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((((((a[7] * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((b[7] * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -108,7 +108,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<9>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((((((((a[8] * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((b[8] * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -120,7 +120,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<10>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((((((((a[9] * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((b[9] * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -132,7 +132,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<11>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((((((((((a[10] * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((b[10] * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -144,7 +144,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<12>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((((((((((a[11] * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((((b[11] * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -156,7 +156,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<13>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<13>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((((((((((((a[12] * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((((b[12] * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -168,7 +168,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<14>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<14>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((((((((((((a[13] * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((((((b[13] * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -180,7 +180,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<15>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<15>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((((((((((((((a[14] * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((((((b[14] * x + b[13]) * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -192,7 +192,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<16>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<16>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((((((((((((((a[15] * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((((((((b[15] * x + b[14]) * x + b[13]) * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
diff --git a/boost/math/tools/detail/rational_horner1_17.hpp b/boost/math/tools/detail/rational_horner1_17.hpp
index f123da4c95..294c3f175d 100644
--- a/boost/math/tools/detail/rational_horner1_17.hpp
+++ b/boost/math/tools/detail/rational_horner1_17.hpp
@@ -12,19 +12,19 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*)
+inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
@@ -36,7 +36,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
@@ -48,7 +48,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
@@ -60,7 +60,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((b[4] * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -72,7 +72,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((b[5] * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -84,7 +84,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((b[6] * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -96,7 +96,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<8>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((((((a[7] * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((b[7] * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -108,7 +108,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<9>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((((((((a[8] * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((b[8] * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -120,7 +120,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<10>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((((((((a[9] * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((b[9] * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -132,7 +132,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<11>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((((((((((a[10] * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((b[10] * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -144,7 +144,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<12>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((((((((((a[11] * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((((b[11] * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -156,7 +156,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<13>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<13>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((((((((((((a[12] * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((((b[12] * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -168,7 +168,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<14>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<14>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((((((((((((a[13] * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((((((b[13] * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -180,7 +180,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<15>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<15>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((((((((((((((a[14] * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((((((b[14] * x + b[13]) * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -192,7 +192,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<16>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<16>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((((((((((((((a[15] * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((((((((b[15] * x + b[14]) * x + b[13]) * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -204,7 +204,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<17>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<17>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((((((((((((((((a[16] * x + a[15]) * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((((((((b[16] * x + b[15]) * x + b[14]) * x + b[13]) * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
diff --git a/boost/math/tools/detail/rational_horner1_18.hpp b/boost/math/tools/detail/rational_horner1_18.hpp
index 718ace87fc..1a48bba097 100644
--- a/boost/math/tools/detail/rational_horner1_18.hpp
+++ b/boost/math/tools/detail/rational_horner1_18.hpp
@@ -12,19 +12,19 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*)
+inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
@@ -36,7 +36,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
@@ -48,7 +48,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
@@ -60,7 +60,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((b[4] * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -72,7 +72,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((b[5] * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -84,7 +84,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((b[6] * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -96,7 +96,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<8>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((((((a[7] * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((b[7] * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -108,7 +108,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<9>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((((((((a[8] * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((b[8] * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -120,7 +120,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<10>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((((((((a[9] * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((b[9] * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -132,7 +132,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<11>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((((((((((a[10] * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((b[10] * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -144,7 +144,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<12>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((((((((((a[11] * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((((b[11] * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -156,7 +156,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<13>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<13>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((((((((((((a[12] * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((((b[12] * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -168,7 +168,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<14>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<14>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((((((((((((a[13] * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((((((b[13] * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -180,7 +180,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<15>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<15>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((((((((((((((a[14] * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((((((b[14] * x + b[13]) * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -192,7 +192,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<16>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<16>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((((((((((((((a[15] * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((((((((b[15] * x + b[14]) * x + b[13]) * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -204,7 +204,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<17>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<17>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((((((((((((((((a[16] * x + a[15]) * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((((((((b[16] * x + b[15]) * x + b[14]) * x + b[13]) * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -216,7 +216,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<18>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<18>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((((((((((((((((a[17] * x + a[16]) * x + a[15]) * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((((((((((b[17] * x + b[16]) * x + b[15]) * x + b[14]) * x + b[13]) * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
diff --git a/boost/math/tools/detail/rational_horner1_19.hpp b/boost/math/tools/detail/rational_horner1_19.hpp
index c849ba8c06..12fd75cf1b 100644
--- a/boost/math/tools/detail/rational_horner1_19.hpp
+++ b/boost/math/tools/detail/rational_horner1_19.hpp
@@ -12,19 +12,19 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*)
+inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
@@ -36,7 +36,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
@@ -48,7 +48,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
@@ -60,7 +60,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((b[4] * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -72,7 +72,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((b[5] * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -84,7 +84,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((b[6] * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -96,7 +96,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<8>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((((((a[7] * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((b[7] * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -108,7 +108,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<9>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((((((((a[8] * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((b[8] * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -120,7 +120,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<10>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((((((((a[9] * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((b[9] * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -132,7 +132,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<11>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((((((((((a[10] * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((b[10] * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -144,7 +144,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<12>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((((((((((a[11] * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((((b[11] * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -156,7 +156,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<13>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<13>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((((((((((((a[12] * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((((b[12] * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -168,7 +168,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<14>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<14>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((((((((((((a[13] * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((((((b[13] * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -180,7 +180,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<15>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<15>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((((((((((((((a[14] * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((((((b[14] * x + b[13]) * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -192,7 +192,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<16>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<16>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((((((((((((((a[15] * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((((((((b[15] * x + b[14]) * x + b[13]) * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -204,7 +204,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<17>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<17>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((((((((((((((((a[16] * x + a[15]) * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((((((((b[16] * x + b[15]) * x + b[14]) * x + b[13]) * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -216,7 +216,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<18>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<18>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((((((((((((((((a[17] * x + a[16]) * x + a[15]) * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((((((((((b[17] * x + b[16]) * x + b[15]) * x + b[14]) * x + b[13]) * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -228,7 +228,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<19>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<19>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((((((((((((((((((a[18] * x + a[17]) * x + a[16]) * x + a[15]) * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((((((((((b[18] * x + b[17]) * x + b[16]) * x + b[15]) * x + b[14]) * x + b[13]) * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
diff --git a/boost/math/tools/detail/rational_horner1_2.hpp b/boost/math/tools/detail/rational_horner1_2.hpp
index 87e41ab3f9..c838f2a2cd 100644
--- a/boost/math/tools/detail/rational_horner1_2.hpp
+++ b/boost/math/tools/detail/rational_horner1_2.hpp
@@ -12,19 +12,19 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*)
+inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
diff --git a/boost/math/tools/detail/rational_horner1_20.hpp b/boost/math/tools/detail/rational_horner1_20.hpp
index e05eaaa89b..3ee3e966e6 100644
--- a/boost/math/tools/detail/rational_horner1_20.hpp
+++ b/boost/math/tools/detail/rational_horner1_20.hpp
@@ -12,19 +12,19 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*)
+inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
@@ -36,7 +36,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
@@ -48,7 +48,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
@@ -60,7 +60,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((b[4] * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -72,7 +72,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((b[5] * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -84,7 +84,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((b[6] * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -96,7 +96,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<8>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((((((a[7] * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((b[7] * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -108,7 +108,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<9>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((((((((a[8] * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((b[8] * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -120,7 +120,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<10>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((((((((a[9] * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((b[9] * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -132,7 +132,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<11>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((((((((((a[10] * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((b[10] * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -144,7 +144,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<12>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((((((((((a[11] * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((((b[11] * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -156,7 +156,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<13>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<13>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((((((((((((a[12] * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((((b[12] * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -168,7 +168,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<14>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<14>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((((((((((((a[13] * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((((((b[13] * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -180,7 +180,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<15>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<15>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((((((((((((((a[14] * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((((((b[14] * x + b[13]) * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -192,7 +192,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<16>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<16>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((((((((((((((a[15] * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((((((((b[15] * x + b[14]) * x + b[13]) * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -204,7 +204,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<17>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<17>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((((((((((((((((a[16] * x + a[15]) * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((((((((b[16] * x + b[15]) * x + b[14]) * x + b[13]) * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -216,7 +216,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<18>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<18>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((((((((((((((((a[17] * x + a[16]) * x + a[15]) * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((((((((((b[17] * x + b[16]) * x + b[15]) * x + b[14]) * x + b[13]) * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -228,7 +228,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<19>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<19>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((((((((((((((((((a[18] * x + a[17]) * x + a[16]) * x + a[15]) * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((((((((((b[18] * x + b[17]) * x + b[16]) * x + b[15]) * x + b[14]) * x + b[13]) * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -240,7 +240,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<20>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<20>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((((((((((((((((((a[19] * x + a[18]) * x + a[17]) * x + a[16]) * x + a[15]) * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((((((((((((b[19] * x + b[18]) * x + b[17]) * x + b[16]) * x + b[15]) * x + b[14]) * x + b[13]) * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
diff --git a/boost/math/tools/detail/rational_horner1_3.hpp b/boost/math/tools/detail/rational_horner1_3.hpp
index ac1b785e93..034ead3f66 100644
--- a/boost/math/tools/detail/rational_horner1_3.hpp
+++ b/boost/math/tools/detail/rational_horner1_3.hpp
@@ -12,19 +12,19 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*)
+inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
@@ -36,7 +36,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
diff --git a/boost/math/tools/detail/rational_horner1_4.hpp b/boost/math/tools/detail/rational_horner1_4.hpp
index eeced600f4..de2972f4c4 100644
--- a/boost/math/tools/detail/rational_horner1_4.hpp
+++ b/boost/math/tools/detail/rational_horner1_4.hpp
@@ -12,19 +12,19 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*)
+inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
@@ -36,7 +36,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
@@ -48,7 +48,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
diff --git a/boost/math/tools/detail/rational_horner1_5.hpp b/boost/math/tools/detail/rational_horner1_5.hpp
index 0479f66376..a59ff114d1 100644
--- a/boost/math/tools/detail/rational_horner1_5.hpp
+++ b/boost/math/tools/detail/rational_horner1_5.hpp
@@ -12,19 +12,19 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*)
+inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
@@ -36,7 +36,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
@@ -48,7 +48,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
@@ -60,7 +60,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((b[4] * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
diff --git a/boost/math/tools/detail/rational_horner1_6.hpp b/boost/math/tools/detail/rational_horner1_6.hpp
index db259968ee..c5000c5db4 100644
--- a/boost/math/tools/detail/rational_horner1_6.hpp
+++ b/boost/math/tools/detail/rational_horner1_6.hpp
@@ -12,19 +12,19 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*)
+inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
@@ -36,7 +36,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
@@ -48,7 +48,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
@@ -60,7 +60,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((b[4] * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -72,7 +72,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((b[5] * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
diff --git a/boost/math/tools/detail/rational_horner1_7.hpp b/boost/math/tools/detail/rational_horner1_7.hpp
index b431fe91ef..bc860f3bf7 100644
--- a/boost/math/tools/detail/rational_horner1_7.hpp
+++ b/boost/math/tools/detail/rational_horner1_7.hpp
@@ -12,19 +12,19 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*)
+inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
@@ -36,7 +36,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
@@ -48,7 +48,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
@@ -60,7 +60,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((b[4] * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -72,7 +72,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((b[5] * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -84,7 +84,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((b[6] * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
diff --git a/boost/math/tools/detail/rational_horner1_8.hpp b/boost/math/tools/detail/rational_horner1_8.hpp
index 5a04a7a343..69368978b6 100644
--- a/boost/math/tools/detail/rational_horner1_8.hpp
+++ b/boost/math/tools/detail/rational_horner1_8.hpp
@@ -12,19 +12,19 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*)
+inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
@@ -36,7 +36,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
@@ -48,7 +48,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
@@ -60,7 +60,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((b[4] * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -72,7 +72,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((b[5] * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -84,7 +84,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((b[6] * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -96,7 +96,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<8>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((((((a[7] * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((b[7] * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
diff --git a/boost/math/tools/detail/rational_horner1_9.hpp b/boost/math/tools/detail/rational_horner1_9.hpp
index 4b5465fc4a..0aafea15fd 100644
--- a/boost/math/tools/detail/rational_horner1_9.hpp
+++ b/boost/math/tools/detail/rational_horner1_9.hpp
@@ -12,19 +12,19 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*)
+inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
@@ -36,7 +36,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
@@ -48,7 +48,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
@@ -60,7 +60,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((b[4] * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -72,7 +72,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((b[5] * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -84,7 +84,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((b[6] * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -96,7 +96,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<8>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>((((((((a[7] * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((b[7] * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -108,7 +108,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<9>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
      return static_cast<V>(((((((((a[8] * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((b[8] * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
diff --git a/boost/math/tools/detail/rational_horner2_10.hpp b/boost/math/tools/detail/rational_horner2_10.hpp
index e26d2d934f..127777bc2a 100644
--- a/boost/math/tools/detail/rational_horner2_10.hpp
+++ b/boost/math/tools/detail/rational_horner2_10.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*)
+inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -58,7 +58,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -74,7 +74,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -90,7 +90,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<8>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -106,7 +106,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<9>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -122,7 +122,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<10>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
diff --git a/boost/math/tools/detail/rational_horner2_11.hpp b/boost/math/tools/detail/rational_horner2_11.hpp
index c05e697197..53983ed4ad 100644
--- a/boost/math/tools/detail/rational_horner2_11.hpp
+++ b/boost/math/tools/detail/rational_horner2_11.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*)
+inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -58,7 +58,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -74,7 +74,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -90,7 +90,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<8>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -106,7 +106,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<9>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -122,7 +122,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<10>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -138,7 +138,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<11>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
diff --git a/boost/math/tools/detail/rational_horner2_12.hpp b/boost/math/tools/detail/rational_horner2_12.hpp
index 4ee3734001..4ad0856b06 100644
--- a/boost/math/tools/detail/rational_horner2_12.hpp
+++ b/boost/math/tools/detail/rational_horner2_12.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*)
+inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -58,7 +58,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -74,7 +74,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -90,7 +90,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<8>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -106,7 +106,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<9>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -122,7 +122,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<10>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -138,7 +138,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<11>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -154,7 +154,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<12>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
diff --git a/boost/math/tools/detail/rational_horner2_13.hpp b/boost/math/tools/detail/rational_horner2_13.hpp
index 37977a111d..5f9303d0c3 100644
--- a/boost/math/tools/detail/rational_horner2_13.hpp
+++ b/boost/math/tools/detail/rational_horner2_13.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*)
+inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -58,7 +58,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -74,7 +74,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -90,7 +90,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<8>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -106,7 +106,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<9>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -122,7 +122,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<10>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -138,7 +138,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<11>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -154,7 +154,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<12>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -170,7 +170,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<13>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<13>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
diff --git a/boost/math/tools/detail/rational_horner2_14.hpp b/boost/math/tools/detail/rational_horner2_14.hpp
index 78edfbbe1b..dc512f393f 100644
--- a/boost/math/tools/detail/rational_horner2_14.hpp
+++ b/boost/math/tools/detail/rational_horner2_14.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*)
+inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -58,7 +58,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -74,7 +74,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -90,7 +90,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<8>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -106,7 +106,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<9>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -122,7 +122,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<10>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -138,7 +138,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<11>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -154,7 +154,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<12>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -170,7 +170,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<13>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<13>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -186,7 +186,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<14>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<14>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
diff --git a/boost/math/tools/detail/rational_horner2_15.hpp b/boost/math/tools/detail/rational_horner2_15.hpp
index 3cf4ef56a0..cf084e8be0 100644
--- a/boost/math/tools/detail/rational_horner2_15.hpp
+++ b/boost/math/tools/detail/rational_horner2_15.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*)
+inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -58,7 +58,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -74,7 +74,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -90,7 +90,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<8>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -106,7 +106,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<9>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -122,7 +122,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<10>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -138,7 +138,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<11>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -154,7 +154,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<12>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -170,7 +170,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<13>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<13>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -186,7 +186,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<14>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<14>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -202,7 +202,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<15>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<15>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
diff --git a/boost/math/tools/detail/rational_horner2_16.hpp b/boost/math/tools/detail/rational_horner2_16.hpp
index 3936a1ba4b..3d13db2553 100644
--- a/boost/math/tools/detail/rational_horner2_16.hpp
+++ b/boost/math/tools/detail/rational_horner2_16.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*)
+inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -58,7 +58,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -74,7 +74,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -90,7 +90,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<8>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -106,7 +106,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<9>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -122,7 +122,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<10>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -138,7 +138,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<11>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -154,7 +154,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<12>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -170,7 +170,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<13>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<13>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -186,7 +186,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<14>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<14>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -202,7 +202,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<15>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<15>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -218,7 +218,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<16>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<16>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
diff --git a/boost/math/tools/detail/rational_horner2_17.hpp b/boost/math/tools/detail/rational_horner2_17.hpp
index 4d253b9593..3adf4053bd 100644
--- a/boost/math/tools/detail/rational_horner2_17.hpp
+++ b/boost/math/tools/detail/rational_horner2_17.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*)
+inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -58,7 +58,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -74,7 +74,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -90,7 +90,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<8>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -106,7 +106,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<9>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -122,7 +122,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<10>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -138,7 +138,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<11>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -154,7 +154,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<12>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -170,7 +170,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<13>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<13>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -186,7 +186,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<14>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<14>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -202,7 +202,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<15>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<15>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -218,7 +218,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<16>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<16>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -234,7 +234,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<17>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<17>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
diff --git a/boost/math/tools/detail/rational_horner2_18.hpp b/boost/math/tools/detail/rational_horner2_18.hpp
index 6c213ecfb0..607609fd8e 100644
--- a/boost/math/tools/detail/rational_horner2_18.hpp
+++ b/boost/math/tools/detail/rational_horner2_18.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*)
+inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -58,7 +58,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -74,7 +74,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -90,7 +90,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<8>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -106,7 +106,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<9>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -122,7 +122,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<10>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -138,7 +138,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<11>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -154,7 +154,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<12>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -170,7 +170,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<13>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<13>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -186,7 +186,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<14>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<14>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -202,7 +202,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<15>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<15>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -218,7 +218,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<16>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<16>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -234,7 +234,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<17>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<17>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -250,7 +250,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<18>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<18>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
diff --git a/boost/math/tools/detail/rational_horner2_19.hpp b/boost/math/tools/detail/rational_horner2_19.hpp
index 88e0b9ff01..bc324c3be3 100644
--- a/boost/math/tools/detail/rational_horner2_19.hpp
+++ b/boost/math/tools/detail/rational_horner2_19.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*)
+inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -58,7 +58,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -74,7 +74,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -90,7 +90,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<8>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -106,7 +106,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<9>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -122,7 +122,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<10>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -138,7 +138,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<11>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -154,7 +154,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<12>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -170,7 +170,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<13>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<13>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -186,7 +186,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<14>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<14>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -202,7 +202,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<15>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<15>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -218,7 +218,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<16>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<16>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -234,7 +234,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<17>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<17>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -250,7 +250,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<18>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<18>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -266,7 +266,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<19>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<19>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
diff --git a/boost/math/tools/detail/rational_horner2_2.hpp b/boost/math/tools/detail/rational_horner2_2.hpp
index 35b5abb354..95ec0251d5 100644
--- a/boost/math/tools/detail/rational_horner2_2.hpp
+++ b/boost/math/tools/detail/rational_horner2_2.hpp
@@ -12,31 +12,31 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*)
+inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
diff --git a/boost/math/tools/detail/rational_horner2_20.hpp b/boost/math/tools/detail/rational_horner2_20.hpp
index dc73fdd58e..cf1211b61f 100644
--- a/boost/math/tools/detail/rational_horner2_20.hpp
+++ b/boost/math/tools/detail/rational_horner2_20.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*)
+inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -58,7 +58,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -74,7 +74,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -90,7 +90,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<8>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -106,7 +106,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<9>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -122,7 +122,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<10>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -138,7 +138,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<11>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -154,7 +154,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<12>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -170,7 +170,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<13>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<13>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -186,7 +186,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<14>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<14>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -202,7 +202,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<15>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<15>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -218,7 +218,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<16>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<16>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -234,7 +234,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<17>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<17>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -250,7 +250,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<18>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<18>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -266,7 +266,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<19>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<19>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -282,7 +282,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<20>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<20>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
diff --git a/boost/math/tools/detail/rational_horner2_3.hpp b/boost/math/tools/detail/rational_horner2_3.hpp
index 8838ac13e6..9ce437b41f 100644
--- a/boost/math/tools/detail/rational_horner2_3.hpp
+++ b/boost/math/tools/detail/rational_horner2_3.hpp
@@ -12,31 +12,31 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*)
+inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
diff --git a/boost/math/tools/detail/rational_horner2_4.hpp b/boost/math/tools/detail/rational_horner2_4.hpp
index 5fe5ada83b..00543ede85 100644
--- a/boost/math/tools/detail/rational_horner2_4.hpp
+++ b/boost/math/tools/detail/rational_horner2_4.hpp
@@ -12,31 +12,31 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*)
+inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
diff --git a/boost/math/tools/detail/rational_horner2_5.hpp b/boost/math/tools/detail/rational_horner2_5.hpp
index 48b8498bc7..d117b66633 100644
--- a/boost/math/tools/detail/rational_horner2_5.hpp
+++ b/boost/math/tools/detail/rational_horner2_5.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*)
+inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
diff --git a/boost/math/tools/detail/rational_horner2_6.hpp b/boost/math/tools/detail/rational_horner2_6.hpp
index 83631eaf51..c431d16344 100644
--- a/boost/math/tools/detail/rational_horner2_6.hpp
+++ b/boost/math/tools/detail/rational_horner2_6.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*)
+inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -58,7 +58,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
diff --git a/boost/math/tools/detail/rational_horner2_7.hpp b/boost/math/tools/detail/rational_horner2_7.hpp
index 3ed86eafcd..2104302472 100644
--- a/boost/math/tools/detail/rational_horner2_7.hpp
+++ b/boost/math/tools/detail/rational_horner2_7.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*)
+inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -58,7 +58,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -74,7 +74,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
diff --git a/boost/math/tools/detail/rational_horner2_8.hpp b/boost/math/tools/detail/rational_horner2_8.hpp
index f8b36ece4a..fd98289b99 100644
--- a/boost/math/tools/detail/rational_horner2_8.hpp
+++ b/boost/math/tools/detail/rational_horner2_8.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*)
+inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -58,7 +58,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -74,7 +74,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -90,7 +90,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<8>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
diff --git a/boost/math/tools/detail/rational_horner2_9.hpp b/boost/math/tools/detail/rational_horner2_9.hpp
index 88cc4e5fcf..1081ab2f8b 100644
--- a/boost/math/tools/detail/rational_horner2_9.hpp
+++ b/boost/math/tools/detail/rational_horner2_9.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*)
+inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -58,7 +58,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -74,7 +74,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -90,7 +90,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<8>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -106,7 +106,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<9>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
diff --git a/boost/math/tools/detail/rational_horner3_10.hpp b/boost/math/tools/detail/rational_horner3_10.hpp
index 019ffdacc3..7da05875f3 100644
--- a/boost/math/tools/detail/rational_horner3_10.hpp
+++ b/boost/math/tools/detail/rational_horner3_10.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*)
+inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -80,7 +80,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -126,7 +126,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -180,7 +180,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<8>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -242,7 +242,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<9>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -312,7 +312,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<10>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
diff --git a/boost/math/tools/detail/rational_horner3_11.hpp b/boost/math/tools/detail/rational_horner3_11.hpp
index 13ce3134ae..df971197a3 100644
--- a/boost/math/tools/detail/rational_horner3_11.hpp
+++ b/boost/math/tools/detail/rational_horner3_11.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*)
+inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -80,7 +80,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -126,7 +126,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -180,7 +180,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<8>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -242,7 +242,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<9>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -312,7 +312,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<10>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -390,7 +390,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<11>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
diff --git a/boost/math/tools/detail/rational_horner3_12.hpp b/boost/math/tools/detail/rational_horner3_12.hpp
index 634140bd0d..668f76684f 100644
--- a/boost/math/tools/detail/rational_horner3_12.hpp
+++ b/boost/math/tools/detail/rational_horner3_12.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*)
+inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -80,7 +80,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -126,7 +126,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -180,7 +180,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<8>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -242,7 +242,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<9>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -312,7 +312,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<10>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -390,7 +390,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<11>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -476,7 +476,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<12>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
diff --git a/boost/math/tools/detail/rational_horner3_13.hpp b/boost/math/tools/detail/rational_horner3_13.hpp
index 0b4974a501..b0b4c2ac58 100644
--- a/boost/math/tools/detail/rational_horner3_13.hpp
+++ b/boost/math/tools/detail/rational_horner3_13.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*)
+inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -80,7 +80,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -126,7 +126,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -180,7 +180,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<8>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -242,7 +242,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<9>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -312,7 +312,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<10>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -390,7 +390,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<11>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -476,7 +476,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<12>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -570,7 +570,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<13>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<13>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
diff --git a/boost/math/tools/detail/rational_horner3_14.hpp b/boost/math/tools/detail/rational_horner3_14.hpp
index 63f4e95963..92035ef806 100644
--- a/boost/math/tools/detail/rational_horner3_14.hpp
+++ b/boost/math/tools/detail/rational_horner3_14.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*)
+inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -80,7 +80,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -126,7 +126,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -180,7 +180,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<8>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -242,7 +242,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<9>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -312,7 +312,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<10>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -390,7 +390,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<11>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -476,7 +476,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<12>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -570,7 +570,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<13>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<13>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -672,7 +672,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<14>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<14>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
diff --git a/boost/math/tools/detail/rational_horner3_15.hpp b/boost/math/tools/detail/rational_horner3_15.hpp
index c13500f130..9536ecd844 100644
--- a/boost/math/tools/detail/rational_horner3_15.hpp
+++ b/boost/math/tools/detail/rational_horner3_15.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*)
+inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -80,7 +80,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -126,7 +126,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -180,7 +180,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<8>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -242,7 +242,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<9>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -312,7 +312,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<10>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -390,7 +390,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<11>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -476,7 +476,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<12>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -570,7 +570,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<13>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<13>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -672,7 +672,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<14>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<14>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -782,7 +782,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<15>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<15>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
diff --git a/boost/math/tools/detail/rational_horner3_16.hpp b/boost/math/tools/detail/rational_horner3_16.hpp
index b1c89774f8..7ccf8f6e7a 100644
--- a/boost/math/tools/detail/rational_horner3_16.hpp
+++ b/boost/math/tools/detail/rational_horner3_16.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*)
+inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -80,7 +80,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -126,7 +126,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -180,7 +180,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<8>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -242,7 +242,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<9>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -312,7 +312,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<10>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -390,7 +390,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<11>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -476,7 +476,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<12>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -570,7 +570,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<13>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<13>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -672,7 +672,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<14>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<14>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -782,7 +782,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<15>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<15>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -900,7 +900,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<16>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<16>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
diff --git a/boost/math/tools/detail/rational_horner3_17.hpp b/boost/math/tools/detail/rational_horner3_17.hpp
index 9c3498ec24..1a35c47397 100644
--- a/boost/math/tools/detail/rational_horner3_17.hpp
+++ b/boost/math/tools/detail/rational_horner3_17.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*)
+inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -80,7 +80,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -126,7 +126,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -180,7 +180,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<8>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -242,7 +242,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<9>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -312,7 +312,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<10>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -390,7 +390,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<11>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -476,7 +476,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<12>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -570,7 +570,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<13>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<13>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -672,7 +672,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<14>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<14>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -782,7 +782,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<15>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<15>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -900,7 +900,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<16>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<16>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -1026,7 +1026,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<17>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<17>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
diff --git a/boost/math/tools/detail/rational_horner3_18.hpp b/boost/math/tools/detail/rational_horner3_18.hpp
index 5401e9f3a2..8a1c16eb2f 100644
--- a/boost/math/tools/detail/rational_horner3_18.hpp
+++ b/boost/math/tools/detail/rational_horner3_18.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*)
+inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -80,7 +80,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -126,7 +126,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -180,7 +180,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<8>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -242,7 +242,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<9>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -312,7 +312,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<10>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -390,7 +390,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<11>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -476,7 +476,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<12>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -570,7 +570,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<13>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<13>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -672,7 +672,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<14>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<14>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -782,7 +782,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<15>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<15>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -900,7 +900,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<16>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<16>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -1026,7 +1026,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<17>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<17>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -1160,7 +1160,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<18>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<18>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
diff --git a/boost/math/tools/detail/rational_horner3_19.hpp b/boost/math/tools/detail/rational_horner3_19.hpp
index c111b68f1e..15d16bafc3 100644
--- a/boost/math/tools/detail/rational_horner3_19.hpp
+++ b/boost/math/tools/detail/rational_horner3_19.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*)
+inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -80,7 +80,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -126,7 +126,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -180,7 +180,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<8>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -242,7 +242,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<9>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -312,7 +312,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<10>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -390,7 +390,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<11>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -476,7 +476,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<12>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -570,7 +570,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<13>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<13>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -672,7 +672,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<14>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<14>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -782,7 +782,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<15>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<15>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -900,7 +900,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<16>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<16>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -1026,7 +1026,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<17>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<17>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -1160,7 +1160,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<18>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<18>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -1302,7 +1302,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<19>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<19>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
diff --git a/boost/math/tools/detail/rational_horner3_2.hpp b/boost/math/tools/detail/rational_horner3_2.hpp
index 35b5abb354..95ec0251d5 100644
--- a/boost/math/tools/detail/rational_horner3_2.hpp
+++ b/boost/math/tools/detail/rational_horner3_2.hpp
@@ -12,31 +12,31 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*)
+inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
diff --git a/boost/math/tools/detail/rational_horner3_20.hpp b/boost/math/tools/detail/rational_horner3_20.hpp
index 7bee9b110a..78233214d8 100644
--- a/boost/math/tools/detail/rational_horner3_20.hpp
+++ b/boost/math/tools/detail/rational_horner3_20.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*)
+inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -80,7 +80,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -126,7 +126,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -180,7 +180,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<8>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -242,7 +242,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<9>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -312,7 +312,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<10>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -390,7 +390,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<11>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -476,7 +476,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<12>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -570,7 +570,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<13>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<13>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -672,7 +672,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<14>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<14>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -782,7 +782,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<15>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<15>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -900,7 +900,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<16>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<16>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -1026,7 +1026,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<17>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<17>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -1160,7 +1160,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<18>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<18>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -1302,7 +1302,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<19>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<19>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -1452,7 +1452,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<20>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<20>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
diff --git a/boost/math/tools/detail/rational_horner3_3.hpp b/boost/math/tools/detail/rational_horner3_3.hpp
index 8838ac13e6..9ce437b41f 100644
--- a/boost/math/tools/detail/rational_horner3_3.hpp
+++ b/boost/math/tools/detail/rational_horner3_3.hpp
@@ -12,31 +12,31 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*)
+inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
diff --git a/boost/math/tools/detail/rational_horner3_4.hpp b/boost/math/tools/detail/rational_horner3_4.hpp
index 5fe5ada83b..00543ede85 100644
--- a/boost/math/tools/detail/rational_horner3_4.hpp
+++ b/boost/math/tools/detail/rational_horner3_4.hpp
@@ -12,31 +12,31 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*)
+inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
diff --git a/boost/math/tools/detail/rational_horner3_5.hpp b/boost/math/tools/detail/rational_horner3_5.hpp
index 23a606855b..35dce45a80 100644
--- a/boost/math/tools/detail/rational_horner3_5.hpp
+++ b/boost/math/tools/detail/rational_horner3_5.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*)
+inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
diff --git a/boost/math/tools/detail/rational_horner3_6.hpp b/boost/math/tools/detail/rational_horner3_6.hpp
index 186167d614..b9361ba07a 100644
--- a/boost/math/tools/detail/rational_horner3_6.hpp
+++ b/boost/math/tools/detail/rational_horner3_6.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*)
+inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -80,7 +80,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
diff --git a/boost/math/tools/detail/rational_horner3_7.hpp b/boost/math/tools/detail/rational_horner3_7.hpp
index e08dce62d7..92b00b3a15 100644
--- a/boost/math/tools/detail/rational_horner3_7.hpp
+++ b/boost/math/tools/detail/rational_horner3_7.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*)
+inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -80,7 +80,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -126,7 +126,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
diff --git a/boost/math/tools/detail/rational_horner3_8.hpp b/boost/math/tools/detail/rational_horner3_8.hpp
index 3ceb717439..197b6c0550 100644
--- a/boost/math/tools/detail/rational_horner3_8.hpp
+++ b/boost/math/tools/detail/rational_horner3_8.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*)
+inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -80,7 +80,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -126,7 +126,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -180,7 +180,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<8>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
diff --git a/boost/math/tools/detail/rational_horner3_9.hpp b/boost/math/tools/detail/rational_horner3_9.hpp
index 94dab4c0db..5aad957c37 100644
--- a/boost/math/tools/detail/rational_horner3_9.hpp
+++ b/boost/math/tools/detail/rational_horner3_9.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*)
+inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -80,7 +80,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -126,7 +126,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -180,7 +180,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<8>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
@@ -242,7 +242,7 @@ inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::
 }
 
 template <class T, class U, class V>
-inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<9>*)
+inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if(x <= 1)
    {
diff --git a/boost/math/tools/fraction.hpp b/boost/math/tools/fraction.hpp
index b245ddd2a3..a787c603f3 100644
--- a/boost/math/tools/fraction.hpp
+++ b/boost/math/tools/fraction.hpp
@@ -33,11 +33,11 @@ namespace detail
        typedef typename Gen::result_type result_type;
        typedef typename Gen::result_type value_type;
 
-       static result_type a(const value_type&)
+       static result_type a(const value_type&) BOOST_MATH_NOEXCEPT(value_type)
        {
           return 1;
        }
-       static result_type b(const value_type& v)
+       static result_type b(const value_type& v) BOOST_MATH_NOEXCEPT(value_type)
        {
           return v;
        }
@@ -49,11 +49,11 @@ namespace detail
        typedef typename Gen::result_type value_type;
        typedef typename value_type::first_type result_type;
 
-       static result_type a(const value_type& v)
+       static result_type a(const value_type& v) BOOST_MATH_NOEXCEPT(value_type)
        {
           return v.first;
        }
-       static result_type b(const value_type& v)
+       static result_type b(const value_type& v) BOOST_MATH_NOEXCEPT(value_type)
        {
           return v.second;
        }
@@ -85,7 +85,8 @@ namespace detail
 // Note that the first a0 returned by generator Gen is disarded.
 //
 template <class Gen, class U>
-inline typename detail::fraction_traits<Gen>::result_type continued_fraction_b(Gen& g, const U& factor, boost::uintmax_t& max_terms)
+inline typename detail::fraction_traits<Gen>::result_type continued_fraction_b(Gen& g, const U& factor, boost::uintmax_t& max_terms) 
+      BOOST_NOEXCEPT_IF(BOOST_MATH_IS_FLOAT(typename detail::fraction_traits<Gen>::result_type) && noexcept(std::declval<Gen>()()))
 {
    BOOST_MATH_STD_USING // ADL of std names
 
@@ -126,6 +127,7 @@ inline typename detail::fraction_traits<Gen>::result_type continued_fraction_b(G
 
 template <class Gen, class U>
 inline typename detail::fraction_traits<Gen>::result_type continued_fraction_b(Gen& g, const U& factor)
+   BOOST_NOEXCEPT_IF(BOOST_MATH_IS_FLOAT(typename detail::fraction_traits<Gen>::result_type) && noexcept(std::declval<Gen>()()))
 {
    boost::uintmax_t max_terms = (std::numeric_limits<boost::uintmax_t>::max)();
    return continued_fraction_b(g, factor, max_terms);
@@ -133,6 +135,7 @@ inline typename detail::fraction_traits<Gen>::result_type continued_fraction_b(G
 
 template <class Gen>
 inline typename detail::fraction_traits<Gen>::result_type continued_fraction_b(Gen& g, int bits)
+   BOOST_NOEXCEPT_IF(BOOST_MATH_IS_FLOAT(typename detail::fraction_traits<Gen>::result_type) && noexcept(std::declval<Gen>()()))
 {
    BOOST_MATH_STD_USING // ADL of std names
 
@@ -146,6 +149,7 @@ inline typename detail::fraction_traits<Gen>::result_type continued_fraction_b(G
 
 template <class Gen>
 inline typename detail::fraction_traits<Gen>::result_type continued_fraction_b(Gen& g, int bits, boost::uintmax_t& max_terms)
+   BOOST_NOEXCEPT_IF(BOOST_MATH_IS_FLOAT(typename detail::fraction_traits<Gen>::result_type) && noexcept(std::declval<Gen>()()))
 {
    BOOST_MATH_STD_USING // ADL of std names
 
@@ -172,6 +176,7 @@ inline typename detail::fraction_traits<Gen>::result_type continued_fraction_b(G
 //
 template <class Gen, class U>
 inline typename detail::fraction_traits<Gen>::result_type continued_fraction_a(Gen& g, const U& factor, boost::uintmax_t& max_terms)
+   BOOST_NOEXCEPT_IF(BOOST_MATH_IS_FLOAT(typename detail::fraction_traits<Gen>::result_type) && noexcept(std::declval<Gen>()()))
 {
    BOOST_MATH_STD_USING // ADL of std names
 
@@ -213,6 +218,7 @@ inline typename detail::fraction_traits<Gen>::result_type continued_fraction_a(G
 
 template <class Gen, class U>
 inline typename detail::fraction_traits<Gen>::result_type continued_fraction_a(Gen& g, const U& factor)
+   BOOST_NOEXCEPT_IF(BOOST_MATH_IS_FLOAT(typename detail::fraction_traits<Gen>::result_type) && noexcept(std::declval<Gen>()()))
 {
    boost::uintmax_t max_iter = (std::numeric_limits<boost::uintmax_t>::max)();
    return continued_fraction_a(g, factor, max_iter);
@@ -220,6 +226,7 @@ inline typename detail::fraction_traits<Gen>::result_type continued_fraction_a(G
 
 template <class Gen>
 inline typename detail::fraction_traits<Gen>::result_type continued_fraction_a(Gen& g, int bits)
+   BOOST_NOEXCEPT_IF(BOOST_MATH_IS_FLOAT(typename detail::fraction_traits<Gen>::result_type) && noexcept(std::declval<Gen>()()))
 {
    BOOST_MATH_STD_USING // ADL of std names
 
@@ -234,6 +241,7 @@ inline typename detail::fraction_traits<Gen>::result_type continued_fraction_a(G
 
 template <class Gen>
 inline typename detail::fraction_traits<Gen>::result_type continued_fraction_a(Gen& g, int bits, boost::uintmax_t& max_terms)
+   BOOST_NOEXCEPT_IF(BOOST_MATH_IS_FLOAT(typename detail::fraction_traits<Gen>::result_type) && noexcept(std::declval<Gen>()()))
 {
    BOOST_MATH_STD_USING // ADL of std names
 
diff --git a/boost/math/tools/minima.hpp b/boost/math/tools/minima.hpp
index 3dc5356f3e..b76dabe3f6 100644
--- a/boost/math/tools/minima.hpp
+++ b/boost/math/tools/minima.hpp
@@ -21,6 +21,7 @@ namespace boost{ namespace math{ namespace tools{
 
 template <class F, class T>
 std::pair<T, T> brent_find_minima(F f, T min, T max, int bits, boost::uintmax_t& max_iter)
+   BOOST_NOEXCEPT_IF(BOOST_MATH_IS_FLOAT(T) && noexcept(std::declval<F>()(std::declval<T>())))
 {
    BOOST_MATH_STD_USING
    bits = (std::min)(policies::digits<T, policies::policy<> >() / 2, bits);
@@ -138,6 +139,7 @@ std::pair<T, T> brent_find_minima(F f, T min, T max, int bits, boost::uintmax_t&
 
 template <class F, class T>
 inline std::pair<T, T> brent_find_minima(F f, T min, T max, int digits)
+   BOOST_NOEXCEPT_IF(BOOST_MATH_IS_FLOAT(T) && noexcept(std::declval<F>()(std::declval<T>())))
 {
    boost::uintmax_t m = (std::numeric_limits<boost::uintmax_t>::max)();
    return brent_find_minima(f, min, max, digits, m);
diff --git a/boost/math/tools/precision.hpp b/boost/math/tools/precision.hpp
index ed146c458f..9631fc2eb6 100644
--- a/boost/math/tools/precision.hpp
+++ b/boost/math/tools/precision.hpp
@@ -39,7 +39,7 @@ namespace tools
 // See  Conceptual Requirements for Real Number Types.
 
 template <class T>
-inline int digits(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(T))
+inline BOOST_MATH_CONSTEXPR int digits(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(T)) BOOST_NOEXCEPT
 {
 #ifndef BOOST_NO_LIMITS_COMPILE_TIME_CONSTANTS
    BOOST_STATIC_ASSERT( ::std::numeric_limits<T>::is_specialized);
@@ -54,7 +54,7 @@ inline int digits(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(T))
 }
 
 template <class T>
-inline T max_value(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE(T))
+inline BOOST_MATH_CONSTEXPR T max_value(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE(T))  BOOST_MATH_NOEXCEPT(T)
 {
 #ifndef BOOST_NO_LIMITS_COMPILE_TIME_CONSTANTS
    BOOST_STATIC_ASSERT( ::std::numeric_limits<T>::is_specialized);
@@ -66,7 +66,7 @@ inline T max_value(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE(T))
 // -max_value<double> = -1.79769e+308, max_value<double> = 1.79769e+308.
 
 template <class T>
-inline T min_value(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE(T))
+inline BOOST_MATH_CONSTEXPR T min_value(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE(T)) BOOST_MATH_NOEXCEPT(T)
 {
 #ifndef BOOST_NO_LIMITS_COMPILE_TIME_CONSTANTS
    BOOST_STATIC_ASSERT( ::std::numeric_limits<T>::is_specialized);
@@ -86,13 +86,13 @@ namespace detail{
 // For type float first:
 //
 template <class T>
-inline T log_max_value(const mpl::int_<128>& BOOST_MATH_APPEND_EXPLICIT_TEMPLATE_TYPE(T))
+inline BOOST_MATH_CONSTEXPR T log_max_value(const mpl::int_<128>& BOOST_MATH_APPEND_EXPLICIT_TEMPLATE_TYPE(T)) BOOST_MATH_NOEXCEPT(T)
 {
    return 88.0f;
 }
 
 template <class T>
-inline T log_min_value(const mpl::int_<128>& BOOST_MATH_APPEND_EXPLICIT_TEMPLATE_TYPE(T))
+inline BOOST_MATH_CONSTEXPR T log_min_value(const mpl::int_<128>& BOOST_MATH_APPEND_EXPLICIT_TEMPLATE_TYPE(T)) BOOST_MATH_NOEXCEPT(T)
 {
    return -87.0f;
 }
@@ -100,13 +100,13 @@ inline T log_min_value(const mpl::int_<128>& BOOST_MATH_APPEND_EXPLICIT_TEMPLATE
 // Now double:
 //
 template <class T>
-inline T log_max_value(const mpl::int_<1024>& BOOST_MATH_APPEND_EXPLICIT_TEMPLATE_TYPE(T))
+inline BOOST_MATH_CONSTEXPR T log_max_value(const mpl::int_<1024>& BOOST_MATH_APPEND_EXPLICIT_TEMPLATE_TYPE(T)) BOOST_MATH_NOEXCEPT(T)
 {
    return 709.0;
 }
 
 template <class T>
-inline T log_min_value(const mpl::int_<1024>& BOOST_MATH_APPEND_EXPLICIT_TEMPLATE_TYPE(T))
+inline BOOST_MATH_CONSTEXPR T log_min_value(const mpl::int_<1024>& BOOST_MATH_APPEND_EXPLICIT_TEMPLATE_TYPE(T)) BOOST_MATH_NOEXCEPT(T)
 {
    return -708.0;
 }
@@ -114,13 +114,13 @@ inline T log_min_value(const mpl::int_<1024>& BOOST_MATH_APPEND_EXPLICIT_TEMPLAT
 // 80 and 128-bit long doubles:
 //
 template <class T>
-inline T log_max_value(const mpl::int_<16384>& BOOST_MATH_APPEND_EXPLICIT_TEMPLATE_TYPE(T))
+inline BOOST_MATH_CONSTEXPR T log_max_value(const mpl::int_<16384>& BOOST_MATH_APPEND_EXPLICIT_TEMPLATE_TYPE(T)) BOOST_MATH_NOEXCEPT(T)
 {
    return 11356.0L;
 }
 
 template <class T>
-inline T log_min_value(const mpl::int_<16384>& BOOST_MATH_APPEND_EXPLICIT_TEMPLATE_TYPE(T))
+inline BOOST_MATH_CONSTEXPR T log_min_value(const mpl::int_<16384>& BOOST_MATH_APPEND_EXPLICIT_TEMPLATE_TYPE(T)) BOOST_MATH_NOEXCEPT(T)
 {
    return -11355.0L;
 }
@@ -128,17 +128,12 @@ inline T log_min_value(const mpl::int_<16384>& BOOST_MATH_APPEND_EXPLICIT_TEMPLA
 template <class T>
 inline T log_max_value(const mpl::int_<0>& BOOST_MATH_APPEND_EXPLICIT_TEMPLATE_TYPE(T))
 {
-#ifndef BOOST_NO_LIMITS_COMPILE_TIME_CONSTANTS
-   BOOST_STATIC_ASSERT( ::std::numeric_limits<T>::is_specialized);
-#else
-   BOOST_ASSERT(::std::numeric_limits<T>::is_specialized);
-#endif
    BOOST_MATH_STD_USING
 #ifdef __SUNPRO_CC
-   static const T m = (std::numeric_limits<T>::max)();
+   static const T m = boost::math::tools::max_value<T>();
    static const T val = log(m);
 #else
-   static const T val = log((std::numeric_limits<T>::max)());
+   static const T val = log(boost::math::tools::max_value<T>());
 #endif
    return val;
 }
@@ -146,30 +141,25 @@ inline T log_max_value(const mpl::int_<0>& BOOST_MATH_APPEND_EXPLICIT_TEMPLATE_T
 template <class T>
 inline T log_min_value(const mpl::int_<0>& BOOST_MATH_APPEND_EXPLICIT_TEMPLATE_TYPE(T))
 {
-#ifndef BOOST_NO_LIMITS_COMPILE_TIME_CONSTANTS
-   BOOST_STATIC_ASSERT( ::std::numeric_limits<T>::is_specialized);
-#else
-   BOOST_ASSERT(::std::numeric_limits<T>::is_specialized);
-#endif
    BOOST_MATH_STD_USING
 #ifdef __SUNPRO_CC
-   static const T m = (std::numeric_limits<T>::min)();
+   static const T m = boost::math::tools::min_value<T>();
    static const T val = log(m);
 #else
-   static const T val = log((std::numeric_limits<T>::min)());
+   static const T val = log(boost::math::tools::min_value<T>());
 #endif
    return val;
 }
 
 template <class T>
-inline T epsilon(const mpl::true_& BOOST_MATH_APPEND_EXPLICIT_TEMPLATE_TYPE(T))
+inline BOOST_MATH_CONSTEXPR T epsilon(const mpl::true_& BOOST_MATH_APPEND_EXPLICIT_TEMPLATE_TYPE(T)) BOOST_MATH_NOEXCEPT(T)
 {
    return std::numeric_limits<T>::epsilon();
 }
 
 #if defined(__GNUC__) && ((LDBL_MANT_DIG == 106) || (__LDBL_MANT_DIG__ == 106))
 template <>
-inline long double epsilon<long double>(const mpl::true_& BOOST_MATH_APPEND_EXPLICIT_TEMPLATE_TYPE(long double))
+inline BOOST_MATH_CONSTEXPR long double epsilon<long double>(const mpl::true_& BOOST_MATH_APPEND_EXPLICIT_TEMPLATE_TYPE(long double)) BOOST_MATH_NOEXCEPT(long double)
 {
    // numeric_limits on Darwin (and elsewhere) tells lies here:
    // the issue is that long double on a few platforms is
@@ -195,6 +185,27 @@ inline T epsilon(const mpl::false_& BOOST_MATH_APPEND_EXPLICIT_TEMPLATE_TYPE(T))
    return eps;
 }
 
+template <class T>
+struct log_limit_traits
+{
+   typedef typename mpl::if_c<
+      (std::numeric_limits<T>::radix == 2) &&
+      (std::numeric_limits<T>::max_exponent == 128
+         || std::numeric_limits<T>::max_exponent == 1024
+         || std::numeric_limits<T>::max_exponent == 16384),
+      mpl::int_<(std::numeric_limits<T>::max_exponent > INT_MAX ? INT_MAX : static_cast<int>(std::numeric_limits<T>::max_exponent))>,
+      mpl::int_<0>
+   >::type tag_type;
+   BOOST_STATIC_CONSTANT(bool, value = tag_type::value ? true : false);
+   BOOST_STATIC_ASSERT(::std::numeric_limits<T>::is_specialized || (value == 0));
+};
+
+template <class T, bool b> struct log_limit_noexcept_traits_imp : public log_limit_traits<T> {};
+template <class T> struct log_limit_noexcept_traits_imp<T, false> : public boost::integral_constant<bool, false> {};
+
+template <class T>
+struct log_limit_noexcept_traits : public log_limit_noexcept_traits_imp<T, BOOST_MATH_IS_FLOAT(T)> {};
+
 } // namespace detail
 
 #ifdef BOOST_MSVC
@@ -203,19 +214,10 @@ inline T epsilon(const mpl::false_& BOOST_MATH_APPEND_EXPLICIT_TEMPLATE_TYPE(T))
 #endif
 
 template <class T>
-inline T log_max_value(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE(T))
+inline BOOST_MATH_CONSTEXPR T log_max_value(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE(T)) BOOST_NOEXCEPT_IF(detail::log_limit_noexcept_traits<T>::value)
 {
 #ifndef BOOST_NO_LIMITS_COMPILE_TIME_CONSTANTS
-   typedef typename mpl::if_c<
-      (std::numeric_limits<T>::radix == 2) &&
-      (std::numeric_limits<T>::max_exponent == 128
-      || std::numeric_limits<T>::max_exponent == 1024
-      || std::numeric_limits<T>::max_exponent == 16384),
-      mpl::int_<(std::numeric_limits<T>::max_exponent > INT_MAX ? INT_MAX : static_cast<int>(std::numeric_limits<T>::max_exponent))>,
-      mpl::int_<0>
-   >::type tag_type;
-   BOOST_STATIC_ASSERT( ::std::numeric_limits<T>::is_specialized);
-   return detail::log_max_value<T>(tag_type());
+   return detail::log_max_value<T>(typename detail::log_limit_traits<T>::tag_type());
 #else
    BOOST_ASSERT(::std::numeric_limits<T>::is_specialized);
    BOOST_MATH_STD_USING
@@ -225,20 +227,10 @@ inline T log_max_value(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE(T))
 }
 
 template <class T>
-inline T log_min_value(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE(T))
+inline BOOST_MATH_CONSTEXPR T log_min_value(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE(T)) BOOST_NOEXCEPT_IF(detail::log_limit_noexcept_traits<T>::value)
 {
 #ifndef BOOST_NO_LIMITS_COMPILE_TIME_CONSTANTS
-   typedef typename mpl::if_c<
-      (std::numeric_limits<T>::radix == 2) &&
-      (std::numeric_limits<T>::max_exponent == 128
-      || std::numeric_limits<T>::max_exponent == 1024
-      || std::numeric_limits<T>::max_exponent == 16384),
-      mpl::int_<(std::numeric_limits<T>::max_exponent > INT_MAX ? INT_MAX : static_cast<int>(std::numeric_limits<T>::max_exponent))>,
-      mpl::int_<0>
-   >::type tag_type;
-
-   BOOST_STATIC_ASSERT( ::std::numeric_limits<T>::is_specialized);
-   return detail::log_min_value<T>(tag_type());
+   return detail::log_min_value<T>(typename detail::log_limit_traits<T>::tag_type());
 #else
    BOOST_ASSERT(::std::numeric_limits<T>::is_specialized);
    BOOST_MATH_STD_USING
@@ -252,7 +244,7 @@ inline T log_min_value(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE(T))
 #endif
 
 template <class T>
-inline T epsilon(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(T))
+inline BOOST_MATH_CONSTEXPR T epsilon(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(T)) BOOST_MATH_NOEXCEPT(T)
 {
 #ifndef BOOST_NO_LIMITS_COMPILE_TIME_CONSTANTS
    return detail::epsilon<T>(mpl::bool_< ::std::numeric_limits<T>::is_specialized>());
@@ -266,25 +258,25 @@ inline T epsilon(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(T))
 namespace detail{
 
 template <class T>
-inline T root_epsilon_imp(const mpl::int_<24>&)
+inline BOOST_MATH_CONSTEXPR T root_epsilon_imp(const mpl::int_<24>&) BOOST_MATH_NOEXCEPT(T)
 {
    return static_cast<T>(0.00034526698300124390839884978618400831996329879769945L);
 }
 
 template <class T>
-inline T root_epsilon_imp(const T*, const mpl::int_<53>&)
+inline BOOST_MATH_CONSTEXPR T root_epsilon_imp(const T*, const mpl::int_<53>&) BOOST_MATH_NOEXCEPT(T)
 {
    return static_cast<T>(0.1490116119384765625e-7L);
 }
 
 template <class T>
-inline T root_epsilon_imp(const T*, const mpl::int_<64>&)
+inline BOOST_MATH_CONSTEXPR T root_epsilon_imp(const T*, const mpl::int_<64>&) BOOST_MATH_NOEXCEPT(T)
 {
    return static_cast<T>(0.32927225399135962333569506281281311031656150598474e-9L);
 }
 
 template <class T>
-inline T root_epsilon_imp(const T*, const mpl::int_<113>&)
+inline BOOST_MATH_CONSTEXPR T root_epsilon_imp(const T*, const mpl::int_<113>&) BOOST_MATH_NOEXCEPT(T)
 {
    return static_cast<T>(0.1387778780781445675529539585113525390625e-16L);
 }
@@ -298,25 +290,25 @@ inline T root_epsilon_imp(const T*, const Tag&)
 }
 
 template <class T>
-inline T cbrt_epsilon_imp(const mpl::int_<24>&)
+inline BOOST_MATH_CONSTEXPR T cbrt_epsilon_imp(const mpl::int_<24>&) BOOST_MATH_NOEXCEPT(T)
 {
    return static_cast<T>(0.0049215666011518482998719164346805794944150447839903L);
 }
 
 template <class T>
-inline T cbrt_epsilon_imp(const T*, const mpl::int_<53>&)
+inline BOOST_MATH_CONSTEXPR T cbrt_epsilon_imp(const T*, const mpl::int_<53>&) BOOST_MATH_NOEXCEPT(T)
 {
    return static_cast<T>(6.05545445239333906078989272793696693569753008995e-6L);
 }
 
 template <class T>
-inline T cbrt_epsilon_imp(const T*, const mpl::int_<64>&)
+inline BOOST_MATH_CONSTEXPR T cbrt_epsilon_imp(const T*, const mpl::int_<64>&) BOOST_MATH_NOEXCEPT(T)
 {
    return static_cast<T>(4.76837158203125e-7L);
 }
 
 template <class T>
-inline T cbrt_epsilon_imp(const T*, const mpl::int_<113>&)
+inline BOOST_MATH_CONSTEXPR T cbrt_epsilon_imp(const T*, const mpl::int_<113>&) BOOST_MATH_NOEXCEPT(T)
 {
    return static_cast<T>(5.7749313854154005630396773604745549542403508090496e-12L);
 }
@@ -330,25 +322,25 @@ inline T cbrt_epsilon_imp(const T*, const Tag&)
 }
 
 template <class T>
-inline T forth_root_epsilon_imp(const T*, const mpl::int_<24>&)
+inline BOOST_MATH_CONSTEXPR T forth_root_epsilon_imp(const T*, const mpl::int_<24>&) BOOST_MATH_NOEXCEPT(T)
 {
    return static_cast<T>(0.018581361171917516667460937040007436176452688944747L);
 }
 
 template <class T>
-inline T forth_root_epsilon_imp(const T*, const mpl::int_<53>&)
+inline BOOST_MATH_CONSTEXPR T forth_root_epsilon_imp(const T*, const mpl::int_<53>&) BOOST_MATH_NOEXCEPT(T)
 {
    return static_cast<T>(0.0001220703125L);
 }
 
 template <class T>
-inline T forth_root_epsilon_imp(const T*, const mpl::int_<64>&)
+inline BOOST_MATH_CONSTEXPR T forth_root_epsilon_imp(const T*, const mpl::int_<64>&) BOOST_MATH_NOEXCEPT(T)
 {
    return static_cast<T>(0.18145860519450699870567321328132261891067079047605e-4L);
 }
 
 template <class T>
-inline T forth_root_epsilon_imp(const T*, const mpl::int_<113>&)
+inline BOOST_MATH_CONSTEXPR T forth_root_epsilon_imp(const T*, const mpl::int_<113>&) BOOST_MATH_NOEXCEPT(T)
 {
    return static_cast<T>(0.37252902984619140625e-8L);
 }
@@ -361,27 +353,31 @@ inline T forth_root_epsilon_imp(const T*, const Tag&)
    return r_eps;
 }
 
+template <class T>
+struct root_epsilon_traits
+{
+   typedef mpl::int_< (::std::numeric_limits<T>::radix == 2) ? std::numeric_limits<T>::digits : 0> tag_type;
+   BOOST_STATIC_CONSTANT(bool, has_noexcept = (tag_type::value == 113) || (tag_type::value == 64) || (tag_type::value == 53) || (tag_type::value == 24));
+};
+
 }
 
 template <class T>
-inline T root_epsilon()
+inline BOOST_MATH_CONSTEXPR T root_epsilon() BOOST_NOEXCEPT_IF(BOOST_MATH_IS_FLOAT(T) && detail::root_epsilon_traits<T>::has_noexcept)
 {
-   typedef mpl::int_< (::std::numeric_limits<T>::radix == 2) ? std::numeric_limits<T>::digits : 0> tag_type;
-   return detail::root_epsilon_imp(static_cast<T const*>(0), tag_type());
+   return detail::root_epsilon_imp(static_cast<T const*>(0), typename detail::root_epsilon_traits<T>::tag_type());
 }
 
 template <class T>
-inline T cbrt_epsilon()
+inline BOOST_MATH_CONSTEXPR T cbrt_epsilon() BOOST_NOEXCEPT_IF(BOOST_MATH_IS_FLOAT(T) && detail::root_epsilon_traits<T>::has_noexcept)
 {
-   typedef mpl::int_< (::std::numeric_limits<T>::radix == 2) ? std::numeric_limits<T>::digits : 0> tag_type;
-   return detail::cbrt_epsilon_imp(static_cast<T const*>(0), tag_type());
+   return detail::cbrt_epsilon_imp(static_cast<T const*>(0), typename detail::root_epsilon_traits<T>::tag_type());
 }
 
 template <class T>
-inline T forth_root_epsilon()
+inline BOOST_MATH_CONSTEXPR T forth_root_epsilon() BOOST_NOEXCEPT_IF(BOOST_MATH_IS_FLOAT(T) && detail::root_epsilon_traits<T>::has_noexcept)
 {
-   typedef mpl::int_< (::std::numeric_limits<T>::radix == 2) ? std::numeric_limits<T>::digits : 0> tag_type;
-   return detail::forth_root_epsilon_imp(static_cast<T const*>(0), tag_type());
+   return detail::forth_root_epsilon_imp(static_cast<T const*>(0), typename detail::root_epsilon_traits<T>::tag_type());
 }
 
 } // namespace tools
diff --git a/boost/math/tools/promotion.hpp b/boost/math/tools/promotion.hpp
index b3ad204077..494d7f99e2 100644
--- a/boost/math/tools/promotion.hpp
+++ b/boost/math/tools/promotion.hpp
@@ -86,13 +86,20 @@ namespace boost
 
         typedef typename mpl::if_<
           typename mpl::and_<is_floating_point<T1P>, is_floating_point<T2P> >::type, // both T1P and T2P are floating-point?
-          typename mpl::if_< typename mpl::or_<is_same<long double, T1P>, is_same<long double, T2P> >::type, // either long double?
-            long double, // then result type is long double.
-            typename mpl::if_< typename mpl::or_<is_same<double, T1P>, is_same<double, T2P> >::type, // either double?
-            double, // result type is double.
-          float // else result type is float.
-          >::type
-          >::type,
+#ifdef BOOST_MATH_USE_FLOAT128
+           typename mpl::if_< typename mpl::or_<is_same<__float128, T1P>, is_same<__float128, T2P> >::type, // either long double?
+            __float128,
+#endif
+             typename mpl::if_< typename mpl::or_<is_same<long double, T1P>, is_same<long double, T2P> >::type, // either long double?
+               long double, // then result type is long double.
+               typename mpl::if_< typename mpl::or_<is_same<double, T1P>, is_same<double, T2P> >::type, // either double?
+                  double, // result type is double.
+                  float // else result type is float.
+             >::type
+#ifdef BOOST_MATH_USE_FLOAT128
+             >::type
+#endif
+             >::type,
           // else one or the other is a user-defined type:
           typename mpl::if_< typename mpl::and_<mpl::not_<is_floating_point<T2P> >, ::boost::is_convertible<T1P, T2P> >, T2P, T1P>::type>::type type;
       }; // promote_arg2
diff --git a/boost/math/tools/rational.hpp b/boost/math/tools/rational.hpp
index accffeaf26..d8bd4a73aa 100644
--- a/boost/math/tools/rational.hpp
+++ b/boost/math/tools/rational.hpp
@@ -168,12 +168,12 @@ namespace boost{ namespace math{ namespace tools{
 // Forward declaration to keep two phase lookup happy:
 //
 template <class T, class U>
-U evaluate_polynomial(const T* poly, U const& z, std::size_t count);
+U evaluate_polynomial(const T* poly, U const& z, std::size_t count) BOOST_MATH_NOEXCEPT(U);
 
 namespace detail{
 
 template <class T, class V, class Tag>
-inline V evaluate_polynomial_c_imp(const T* a, const V& val, const Tag*)
+inline V evaluate_polynomial_c_imp(const T* a, const V& val, const Tag*) BOOST_MATH_NOEXCEPT(V)
 {
    return evaluate_polynomial(a, val, Tag::value);
 }
@@ -186,7 +186,7 @@ inline V evaluate_polynomial_c_imp(const T* a, const V& val, const Tag*)
 // the loop expanded versions above:
 //
 template <class T, class U>
-inline U evaluate_polynomial(const T* poly, U const& z, std::size_t count)
+inline U evaluate_polynomial(const T* poly, U const& z, std::size_t count) BOOST_MATH_NOEXCEPT(U)
 {
    BOOST_ASSERT(count > 0);
    U sum = static_cast<U>(poly[count - 1]);
@@ -202,14 +202,14 @@ inline U evaluate_polynomial(const T* poly, U const& z, std::size_t count)
 // implementations above:
 //
 template <std::size_t N, class T, class V>
-inline V evaluate_polynomial(const T(&a)[N], const V& val)
+inline V evaluate_polynomial(const T(&a)[N], const V& val) BOOST_MATH_NOEXCEPT(V)
 {
    typedef mpl::int_<N> tag_type;
    return detail::evaluate_polynomial_c_imp(static_cast<const T*>(a), val, static_cast<tag_type const*>(0));
 }
 
 template <std::size_t N, class T, class V>
-inline V evaluate_polynomial(const boost::array<T,N>& a, const V& val)
+inline V evaluate_polynomial(const boost::array<T,N>& a, const V& val) BOOST_MATH_NOEXCEPT(V)
 {
    typedef mpl::int_<N> tag_type;
    return detail::evaluate_polynomial_c_imp(static_cast<const T*>(a.data()), val, static_cast<tag_type const*>(0));
@@ -218,19 +218,19 @@ inline V evaluate_polynomial(const boost::array<T,N>& a, const V& val)
 // Even polynomials are trivial: just square the argument!
 //
 template <class T, class U>
-inline U evaluate_even_polynomial(const T* poly, U z, std::size_t count)
+inline U evaluate_even_polynomial(const T* poly, U z, std::size_t count) BOOST_MATH_NOEXCEPT(U)
 {
    return evaluate_polynomial(poly, U(z*z), count);
 }
 
 template <std::size_t N, class T, class V>
-inline V evaluate_even_polynomial(const T(&a)[N], const V& z)
+inline V evaluate_even_polynomial(const T(&a)[N], const V& z) BOOST_MATH_NOEXCEPT(V)
 {
    return evaluate_polynomial(a, V(z*z));
 }
 
 template <std::size_t N, class T, class V>
-inline V evaluate_even_polynomial(const boost::array<T,N>& a, const V& z)
+inline V evaluate_even_polynomial(const boost::array<T,N>& a, const V& z) BOOST_MATH_NOEXCEPT(V)
 {
    return evaluate_polynomial(a, V(z*z));
 }
@@ -238,32 +238,32 @@ inline V evaluate_even_polynomial(const boost::array<T,N>& a, const V& z)
 // Odd polynomials come next:
 //
 template <class T, class U>
-inline U evaluate_odd_polynomial(const T* poly, U z, std::size_t count)
+inline U evaluate_odd_polynomial(const T* poly, U z, std::size_t count) BOOST_MATH_NOEXCEPT(U)
 {
    return poly[0] + z * evaluate_polynomial(poly+1, U(z*z), count-1);
 }
 
 template <std::size_t N, class T, class V>
-inline V evaluate_odd_polynomial(const T(&a)[N], const V& z)
+inline V evaluate_odd_polynomial(const T(&a)[N], const V& z) BOOST_MATH_NOEXCEPT(V)
 {
    typedef mpl::int_<N-1> tag_type;
    return a[0] + z * detail::evaluate_polynomial_c_imp(static_cast<const T*>(a) + 1, V(z*z), static_cast<tag_type const*>(0));
 }
 
 template <std::size_t N, class T, class V>
-inline V evaluate_odd_polynomial(const boost::array<T,N>& a, const V& z)
+inline V evaluate_odd_polynomial(const boost::array<T,N>& a, const V& z) BOOST_MATH_NOEXCEPT(V)
 {
    typedef mpl::int_<N-1> tag_type;
    return a[0] + z * detail::evaluate_polynomial_c_imp(static_cast<const T*>(a.data()) + 1, V(z*z), static_cast<tag_type const*>(0));
 }
 
 template <class T, class U, class V>
-V evaluate_rational(const T* num, const U* denom, const V& z_, std::size_t count);
+V evaluate_rational(const T* num, const U* denom, const V& z_, std::size_t count) BOOST_MATH_NOEXCEPT(V);
 
 namespace detail{
 
 template <class T, class U, class V, class Tag>
-inline V evaluate_rational_c_imp(const T* num, const U* denom, const V& z, const Tag*)
+inline V evaluate_rational_c_imp(const T* num, const U* denom, const V& z, const Tag*) BOOST_MATH_NOEXCEPT(V)
 {
    return boost::math::tools::evaluate_rational(num, denom, z, Tag::value);
 }
@@ -278,7 +278,7 @@ inline V evaluate_rational_c_imp(const T* num, const U* denom, const V& z, const
 // in our Lanczos code for example.
 //
 template <class T, class U, class V>
-V evaluate_rational(const T* num, const U* denom, const V& z_, std::size_t count)
+V evaluate_rational(const T* num, const U* denom, const V& z_, std::size_t count) BOOST_MATH_NOEXCEPT(V)
 {
    V z(z_);
    V s1, s2;
@@ -311,13 +311,13 @@ V evaluate_rational(const T* num, const U* denom, const V& z_, std::size_t count
 }
 
 template <std::size_t N, class T, class U, class V>
-inline V evaluate_rational(const T(&a)[N], const U(&b)[N], const V& z)
+inline V evaluate_rational(const T(&a)[N], const U(&b)[N], const V& z) BOOST_MATH_NOEXCEPT(V)
 {
    return detail::evaluate_rational_c_imp(a, b, z, static_cast<const mpl::int_<N>*>(0));
 }
 
 template <std::size_t N, class T, class U, class V>
-inline V evaluate_rational(const boost::array<T,N>& a, const boost::array<U,N>& b, const V& z)
+inline V evaluate_rational(const boost::array<T,N>& a, const boost::array<U,N>& b, const V& z) BOOST_MATH_NOEXCEPT(V)
 {
    return detail::evaluate_rational_c_imp(a.data(), b.data(), z, static_cast<mpl::int_<N>*>(0));
 }
diff --git a/boost/math/tools/real_cast.hpp b/boost/math/tools/real_cast.hpp
index 9b854e3014..873e60259b 100644
--- a/boost/math/tools/real_cast.hpp
+++ b/boost/math/tools/real_cast.hpp
@@ -6,6 +6,8 @@
 #ifndef BOOST_MATH_TOOLS_REAL_CAST_HPP
 #define BOOST_MATH_TOOLS_REAL_CAST_HPP
 
+#include <boost/math/tools/config.hpp>
+
 #ifdef _MSC_VER
 #pragma once
 #endif
@@ -15,7 +17,7 @@ namespace boost{ namespace math
   namespace tools
   {
     template <class To, class T>
-    inline To real_cast(T t)
+    inline BOOST_MATH_CONSTEXPR To real_cast(T t) BOOST_NOEXCEPT_IF(BOOST_MATH_IS_FLOAT(T) && BOOST_MATH_IS_FLOAT(To))
     {
        return static_cast<To>(t);
     }
diff --git a/boost/math/tools/roots.hpp b/boost/math/tools/roots.hpp
index 2442f5c2d1..25300fee38 100644
--- a/boost/math/tools/roots.hpp
+++ b/boost/math/tools/roots.hpp
@@ -36,9 +36,49 @@ namespace boost{ namespace math{ namespace tools{
 
 namespace detail{
 
+namespace dummy{
+
+   template<int n, class T>
+   typename T::value_type get(const T&) BOOST_MATH_NOEXCEPT(T);
+}
+
+template <class Tuple, class T>
+void unpack_tuple(const Tuple& t, T& a, T& b) BOOST_MATH_NOEXCEPT(T)
+{
+   using dummy::get;
+   // Use ADL to find the right overload for get:
+   a = get<0>(t);
+   b = get<1>(t);
+}
 template <class Tuple, class T>
-inline void unpack_0(const Tuple& t, T& val)
-{ val = boost::math::get<0>(t); }
+void unpack_tuple(const Tuple& t, T& a, T& b, T& c) BOOST_MATH_NOEXCEPT(T)
+{
+   using dummy::get;
+   // Use ADL to find the right overload for get:
+   a = get<0>(t);
+   b = get<1>(t);
+   c = get<2>(t);
+}
+
+template <class Tuple, class T>
+inline void unpack_0(const Tuple& t, T& val) BOOST_MATH_NOEXCEPT(T)
+{
+   using dummy::get;
+   // Rely on ADL to find the correct overload of get:
+   val = get<0>(t); 
+}
+
+template <class T, class U, class V>
+inline void unpack_tuple(const std::pair<T, U>& p, V& a, V& b) BOOST_MATH_NOEXCEPT(T)
+{
+   a = p.first;
+   b = p.second;
+}
+template <class T, class U, class V>
+inline void unpack_0(const std::pair<T, U>& p, V& a) BOOST_MATH_NOEXCEPT(T)
+{
+   a = p.first;
+}
 
 template <class F, class T>
 void handle_zero_derivative(F f,
@@ -48,7 +88,7 @@ void handle_zero_derivative(F f,
                             T& result,
                             T& guess,
                             const T& min,
-                            const T& max)
+                            const T& max) BOOST_NOEXCEPT_IF(BOOST_MATH_IS_FLOAT(T) && noexcept(std::declval<F>()(std::declval<T>())))
 {
    if(last_f0 == 0)
    {
@@ -94,14 +134,20 @@ void handle_zero_derivative(F f,
 } // namespace
 
 template <class F, class T, class Tol, class Policy>
-std::pair<T, T> bisect(F f, T min, T max, Tol tol, boost::uintmax_t& max_iter, const Policy& pol)
+std::pair<T, T> bisect(F f, T min, T max, Tol tol, boost::uintmax_t& max_iter, const Policy& pol) BOOST_NOEXCEPT_IF(policies::is_noexcept_error_policy<Policy>::value && BOOST_MATH_IS_FLOAT(T) && noexcept(std::declval<F>()(std::declval<T>())))
 {
    T fmin = f(min);
    T fmax = f(max);
    if(fmin == 0)
+   {
+      max_iter = 2;
       return std::make_pair(min, min);
+   }
    if(fmax == 0)
+   {
+      max_iter = 2;
       return std::make_pair(max, max);
+   }
 
    //
    // Error checking:
@@ -168,20 +214,21 @@ std::pair<T, T> bisect(F f, T min, T max, Tol tol, boost::uintmax_t& max_iter, c
 }
 
 template <class F, class T, class Tol>
-inline std::pair<T, T> bisect(F f, T min, T max, Tol tol, boost::uintmax_t& max_iter)
+inline std::pair<T, T> bisect(F f, T min, T max, Tol tol, boost::uintmax_t& max_iter)  BOOST_NOEXCEPT_IF(policies::is_noexcept_error_policy<policies::policy<> >::value && BOOST_MATH_IS_FLOAT(T) && noexcept(std::declval<F>()(std::declval<T>())))
 {
    return bisect(f, min, max, tol, max_iter, policies::policy<>());
 }
 
 template <class F, class T, class Tol>
-inline std::pair<T, T> bisect(F f, T min, T max, Tol tol)
+inline std::pair<T, T> bisect(F f, T min, T max, Tol tol) BOOST_NOEXCEPT_IF(policies::is_noexcept_error_policy<policies::policy<> >::value && BOOST_MATH_IS_FLOAT(T) && noexcept(std::declval<F>()(std::declval<T>())))
 {
    boost::uintmax_t m = (std::numeric_limits<boost::uintmax_t>::max)();
    return bisect(f, min, max, tol, m, policies::policy<>());
 }
 
+
 template <class F, class T>
-T newton_raphson_iterate(F f, T guess, T min, T max, int digits, boost::uintmax_t& max_iter)
+T newton_raphson_iterate(F f, T guess, T min, T max, int digits, boost::uintmax_t& max_iter) BOOST_NOEXCEPT_IF(BOOST_MATH_IS_FLOAT(T) && noexcept(std::declval<F>()(std::declval<T>())))
 {
    BOOST_MATH_STD_USING
 
@@ -189,7 +236,7 @@ T newton_raphson_iterate(F f, T guess, T min, T max, int digits, boost::uintmax_
    T result = guess;
 
    T factor = static_cast<T>(ldexp(1.0, 1 - digits));
-   T delta = 1;
+   T delta = tools::max_value<T>();
    T delta1 = tools::max_value<T>();
    T delta2 = tools::max_value<T>();
 
@@ -199,7 +246,8 @@ T newton_raphson_iterate(F f, T guess, T min, T max, int digits, boost::uintmax_
       last_f0 = f0;
       delta2 = delta1;
       delta1 = delta;
-      boost::math::tie(f0, f1) = f(result);
+      detail::unpack_tuple(f(result), f0, f1);
+      --count;
       if(0 == f0)
          break;
       if(f1 == 0)
@@ -243,7 +291,7 @@ T newton_raphson_iterate(F f, T guess, T min, T max, int digits, boost::uintmax_
          max = guess;
       else
          min = guess;
-   }while(--count && (fabs(result * factor) < fabs(delta)));
+   }while(count && (fabs(result * factor) < fabs(delta)));
 
    max_iter -= count;
 
@@ -262,213 +310,208 @@ T newton_raphson_iterate(F f, T guess, T min, T max, int digits, boost::uintmax_
 }
 
 template <class F, class T>
-inline T newton_raphson_iterate(F f, T guess, T min, T max, int digits)
+inline T newton_raphson_iterate(F f, T guess, T min, T max, int digits) BOOST_NOEXCEPT_IF(BOOST_MATH_IS_FLOAT(T) && noexcept(std::declval<F>()(std::declval<T>())))
 {
    boost::uintmax_t m = (std::numeric_limits<boost::uintmax_t>::max)();
    return newton_raphson_iterate(f, guess, min, max, digits, m);
 }
 
-template <class F, class T>
-T halley_iterate(F f, T guess, T min, T max, int digits, boost::uintmax_t& max_iter)
-{
-   BOOST_MATH_STD_USING
+namespace detail{
 
-   T f0(0), f1, f2;
-   T result = guess;
+   struct halley_step
+   {
+      template <class T>
+      static T step(const T& /*x*/, const T& f0, const T& f1, const T& f2) BOOST_NOEXCEPT_IF(BOOST_MATH_IS_FLOAT(T))
+      {
+         using std::fabs;
+         T denom = 2 * f0;
+         T num = 2 * f1 - f0 * (f2 / f1);
+         T delta;
 
-   T factor = static_cast<T>(ldexp(1.0, 1 - digits));
-   T delta = (std::max)(T(10000000 * guess), T(10000000));  // arbitarily large delta
-   T last_f0 = 0;
-   T delta1 = delta;
-   T delta2 = delta;
+         BOOST_MATH_INSTRUMENT_VARIABLE(denom);
+         BOOST_MATH_INSTRUMENT_VARIABLE(num);
 
-   bool out_of_bounds_sentry = false;
+         if((fabs(num) < 1) && (fabs(denom) >= fabs(num) * tools::max_value<T>()))
+         {
+            // possible overflow, use Newton step:
+            delta = f0 / f1;
+         }
+         else
+            delta = denom / num;
+         return delta;
+      }
+   };
+
+   template <class Stepper, class F, class T>
+   T second_order_root_finder(F f, T guess, T min, T max, int digits, boost::uintmax_t& max_iter) BOOST_NOEXCEPT_IF(BOOST_MATH_IS_FLOAT(T) && noexcept(std::declval<F>()(std::declval<T>())))
+   {
+      BOOST_MATH_STD_USING
+
+         T f0(0), f1, f2;
+      T result = guess;
+
+      T factor = static_cast<T>(ldexp(1.0, 1 - digits));
+      T delta = (std::max)(T(10000000 * guess), T(10000000));  // arbitarily large delta
+      T last_f0 = 0;
+      T delta1 = delta;
+      T delta2 = delta;
+
+      bool out_of_bounds_sentry = false;
 
 #ifdef BOOST_MATH_INSTRUMENT
-   std::cout << "Halley iteration, limit = " << factor << std::endl;
+      std::cout << "Second order root iteration, limit = " << factor << std::endl;
 #endif
 
-   boost::uintmax_t count(max_iter);
+      boost::uintmax_t count(max_iter);
 
-   do{
-      last_f0 = f0;
-      delta2 = delta1;
-      delta1 = delta;
-      boost::math::tie(f0, f1, f2) = f(result);
+      do{
+         last_f0 = f0;
+         delta2 = delta1;
+         delta1 = delta;
+         detail::unpack_tuple(f(result), f0, f1, f2);
+         --count;
 
-      BOOST_MATH_INSTRUMENT_VARIABLE(f0);
-      BOOST_MATH_INSTRUMENT_VARIABLE(f1);
-      BOOST_MATH_INSTRUMENT_VARIABLE(f2);
-      
-      if(0 == f0)
-         break;
-      if(f1 == 0)
-      {
-         // Oops zero derivative!!!
+         BOOST_MATH_INSTRUMENT_VARIABLE(f0);
+         BOOST_MATH_INSTRUMENT_VARIABLE(f1);
+         BOOST_MATH_INSTRUMENT_VARIABLE(f2);
+
+         if(0 == f0)
+            break;
+         if(f1 == 0)
+         {
+            // Oops zero derivative!!!
 #ifdef BOOST_MATH_INSTRUMENT
-         std::cout << "Halley iteration, zero derivative found" << std::endl;
+            std::cout << "Second order root iteration, zero derivative found" << std::endl;
 #endif
-         detail::handle_zero_derivative(f, last_f0, f0, delta, result, guess, min, max);
-      }
-      else
-      {
-         if(f2 != 0)
+            detail::handle_zero_derivative(f, last_f0, f0, delta, result, guess, min, max);
+         }
+         else
          {
-            T denom = 2 * f0;
-            T num = 2 * f1 - f0 * (f2 / f1);
-
-            BOOST_MATH_INSTRUMENT_VARIABLE(denom);
-            BOOST_MATH_INSTRUMENT_VARIABLE(num);
-
-            if((fabs(num) < 1) && (fabs(denom) >= fabs(num) * tools::max_value<T>()))
+            if(f2 != 0)
             {
-               // possible overflow, use Newton step:
-               delta = f0 / f1;
+               delta = Stepper::step(result, f0, f1, f2);
+               if(delta * f1 / f0 < 0)
+               {
+                  // Oh dear, we have a problem as Newton and Halley steps
+                  // disagree about which way we should move.  Probably
+                  // there is cancelation error in the calculation of the
+                  // Halley step, or else the derivatives are so small
+                  // that their values are basically trash.  We will move
+                  // in the direction indicated by a Newton step, but
+                  // by no more than twice the current guess value, otherwise
+                  // we can jump way out of bounds if we're not careful.
+                  // See https://svn.boost.org/trac/boost/ticket/8314.
+                  delta = f0 / f1;
+                  if(fabs(delta) > 2 * fabs(guess))
+                     delta = (delta < 0 ? -1 : 1) * 2 * fabs(guess);
+               }
             }
             else
-               delta = denom / num;
-            if(delta * f1 / f0 < 0)
-            {
-               // Oh dear, we have a problem as Newton and Halley steps
-               // disagree about which way we should move.  Probably
-               // there is cancelation error in the calculation of the
-               // Halley step, or else the derivatives are so small
-               // that their values are basically trash.  We will move
-               // in the direction indicated by a Newton step, but
-               // by no more than twice the current guess value, otherwise
-               // we can jump way out of bounds if we're not careful.
-               // See https://svn.boost.org/trac/boost/ticket/8314.
                delta = f0 / f1;
-               if(fabs(delta) > 2 * fabs(guess))
-                  delta = (delta < 0 ? -1 : 1) * 2 * fabs(guess);
-            }
          }
-         else
-            delta = f0 / f1;
-      }
 #ifdef BOOST_MATH_INSTRUMENT
-      std::cout << "Halley iteration, delta = " << delta << std::endl;
+         std::cout << "Second order root iteration, delta = " << delta << std::endl;
 #endif
-      T convergence = fabs(delta / delta2);
-      if((convergence > 0.8) && (convergence < 2))
-      {
-         // last two steps haven't converged, try bisection:
-         delta = (delta > 0) ? (result - min) / 2 : (result - max) / 2;
-         if(fabs(delta) > result)
-            delta = sign(delta) * result; // protect against huge jumps!
-         // reset delta2 so that this branch will *not* be taken on the
-         // next iteration:
-         delta2 = delta * 3;
-         BOOST_MATH_INSTRUMENT_VARIABLE(delta);
-      }
-      guess = result;
-      result -= delta;
-      BOOST_MATH_INSTRUMENT_VARIABLE(result);
-
-      // check for out of bounds step:
-      if(result < min)
-      {
-         T diff = ((fabs(min) < 1) && (fabs(result) > 1) && (tools::max_value<T>() / fabs(result) < fabs(min))) ? T(1000)  : T(result / min);
-         if(fabs(diff) < 1)
-            diff = 1 / diff;
-         if(!out_of_bounds_sentry && (diff > 0) && (diff < 3))
+         T convergence = fabs(delta / delta2);
+         if((convergence > 0.8) && (convergence < 2))
          {
-            // Only a small out of bounds step, lets assume that the result
-            // is probably approximately at min:
-            delta = 0.99f * (guess  - min);
-            result = guess - delta;
-            out_of_bounds_sentry = true; // only take this branch once!
+            // last two steps haven't converged, try bisection:
+            delta = (delta > 0) ? (result - min) / 2 : (result - max) / 2;
+            if(fabs(delta) > result)
+               delta = sign(delta) * result; // protect against huge jumps!
+            // reset delta2 so that this branch will *not* be taken on the
+            // next iteration:
+            delta2 = delta * 3;
+            BOOST_MATH_INSTRUMENT_VARIABLE(delta);
          }
-         else
+         guess = result;
+         result -= delta;
+         BOOST_MATH_INSTRUMENT_VARIABLE(result);
+
+         // check for out of bounds step:
+         if(result < min)
          {
-            delta = (guess - min) / 2;
-            result = guess - delta;
-            if((result == min) || (result == max))
-               break;
+            T diff = ((fabs(min) < 1) && (fabs(result) > 1) && (tools::max_value<T>() / fabs(result) < fabs(min))) ? T(1000) : T(result / min);
+            if(fabs(diff) < 1)
+               diff = 1 / diff;
+            if(!out_of_bounds_sentry && (diff > 0) && (diff < 3))
+            {
+               // Only a small out of bounds step, lets assume that the result
+               // is probably approximately at min:
+               delta = 0.99f * (guess - min);
+               result = guess - delta;
+               out_of_bounds_sentry = true; // only take this branch once!
+            }
+            else
+            {
+               delta = (guess - min) / 2;
+               result = guess - delta;
+               if((result == min) || (result == max))
+                  break;
+            }
          }
-      }
-      else if(result > max)
-      {
-         T diff = ((fabs(max) < 1) && (fabs(result) > 1) && (tools::max_value<T>() / fabs(result) < fabs(max))) ? T(1000) : T(result / max);
-         if(fabs(diff) < 1)
-            diff = 1 / diff;
-         if(!out_of_bounds_sentry && (diff > 0) && (diff < 3))
+         else if(result > max)
          {
-            // Only a small out of bounds step, lets assume that the result
-            // is probably approximately at min:
-            delta = 0.99f * (guess  - max);
-            result = guess - delta;
-            out_of_bounds_sentry = true; // only take this branch once!
+            T diff = ((fabs(max) < 1) && (fabs(result) > 1) && (tools::max_value<T>() / fabs(result) < fabs(max))) ? T(1000) : T(result / max);
+            if(fabs(diff) < 1)
+               diff = 1 / diff;
+            if(!out_of_bounds_sentry && (diff > 0) && (diff < 3))
+            {
+               // Only a small out of bounds step, lets assume that the result
+               // is probably approximately at min:
+               delta = 0.99f * (guess - max);
+               result = guess - delta;
+               out_of_bounds_sentry = true; // only take this branch once!
+            }
+            else
+            {
+               delta = (guess - max) / 2;
+               result = guess - delta;
+               if((result == min) || (result == max))
+                  break;
+            }
          }
+         // update brackets:
+         if(delta > 0)
+            max = guess;
          else
-         {
-            delta = (guess - max) / 2;
-            result = guess - delta;
-            if((result == min) || (result == max))
-               break;
-         }
-      }
-      // update brackets:
-      if(delta > 0)
-         max = guess;
-      else
-         min = guess;
-   }while(--count && (fabs(result * factor) < fabs(delta)));
+            min = guess;
+      } while(count && (fabs(result * factor) < fabs(delta)));
 
-   max_iter -= count;
+      max_iter -= count;
 
 #ifdef BOOST_MATH_INSTRUMENT
-   std::cout << "Halley iteration, final count = " << max_iter << std::endl;
+      std::cout << "Second order root iteration, final count = " << max_iter << std::endl;
 #endif
 
-   return result;
+      return result;
+   }
+
 }
 
 template <class F, class T>
-inline T halley_iterate(F f, T guess, T min, T max, int digits)
+T halley_iterate(F f, T guess, T min, T max, int digits, boost::uintmax_t& max_iter) BOOST_NOEXCEPT_IF(BOOST_MATH_IS_FLOAT(T) && noexcept(std::declval<F>()(std::declval<T>())))
 {
-   boost::uintmax_t m = (std::numeric_limits<boost::uintmax_t>::max)();
-   return halley_iterate(f, guess, min, max, digits, m);
+   return detail::second_order_root_finder<detail::halley_step>(f, guess, min, max, digits, max_iter);
 }
 
 template <class F, class T>
-T schroeder_iterate(F f, T guess, T min, T max, int digits, boost::uintmax_t& max_iter)
+inline T halley_iterate(F f, T guess, T min, T max, int digits) BOOST_NOEXCEPT_IF(BOOST_MATH_IS_FLOAT(T) && noexcept(std::declval<F>()(std::declval<T>())))
 {
-   BOOST_MATH_STD_USING
-
-   T f0(0), f1, f2, last_f0(0);
-   T result = guess;
-
-   T factor = static_cast<T>(ldexp(1.0, 1 - digits));
-   T delta = 0;
-   T delta1 = tools::max_value<T>();
-   T delta2 = tools::max_value<T>();
-
-#ifdef BOOST_MATH_INSTRUMENT
-   std::cout << "Schroeder iteration, limit = " << factor << std::endl;
-#endif
+   boost::uintmax_t m = (std::numeric_limits<boost::uintmax_t>::max)();
+   return halley_iterate(f, guess, min, max, digits, m);
+}
 
-   boost::uintmax_t count(max_iter);
+namespace detail{
 
-   do{
-      last_f0 = f0;
-      delta2 = delta1;
-      delta1 = delta;
-      boost::math::tie(f0, f1, f2) = f(result);
-      if(0 == f0)
-         break;
-      if((f1 == 0) && (f2 == 0))
-      {
-         // Oops zero derivative!!!
-#ifdef BOOST_MATH_INSTRUMENT
-         std::cout << "Halley iteration, zero derivative found" << std::endl;
-#endif
-         detail::handle_zero_derivative(f, last_f0, f0, delta, result, guess, min, max);
-      }
-      else
+   struct schroder_stepper
+   {
+      template <class T>
+      static T step(const T& x, const T& f0, const T& f1, const T& f2) BOOST_NOEXCEPT_IF(BOOST_MATH_IS_FLOAT(T))
       {
          T ratio = f0 / f1;
-         if(ratio / result < 0.1)
+         T delta;
+         if(ratio / x < 0.1)
          {
             delta = ratio + (f2 / (2 * f1)) * ratio * ratio;
             // check second derivative doesn't over compensate:
@@ -477,66 +520,44 @@ T schroeder_iterate(F f, T guess, T min, T max, int digits, boost::uintmax_t& ma
          }
          else
             delta = ratio;  // fall back to Newton iteration.
+         return delta;
       }
-      if(fabs(delta * 2) > fabs(delta2))
-      {
-         // last two steps haven't converged, try bisection:
-         delta = (delta > 0) ? (result - min) / 2 : (result - max) / 2;
-      }
-      guess = result;
-      result -= delta;
-#ifdef BOOST_MATH_INSTRUMENT
-      std::cout << "Halley iteration, delta = " << delta << std::endl;
-#endif
-      if(result <= min)
-      {
-         delta = 0.5F * (guess - min);
-         result = guess - delta;
-         if((result == min) || (result == max))
-            break;
-      }
-      else if(result >= max)
-      {
-         delta = 0.5F * (guess - max);
-         result = guess - delta;
-         if((result == min) || (result == max))
-            break;
-      }
-      // update brackets:
-      if(delta > 0)
-         max = guess;
-      else
-         min = guess;
-   }while(--count && (fabs(result * factor) < fabs(delta)));
-
-   max_iter -= count;
+   };
 
-#ifdef BOOST_MATH_INSTRUMENT
-   std::cout << "Schroeder iteration, final count = " << max_iter << std::endl;
+}
 
-   static boost::uintmax_t max_count = 0;
-   if(max_iter > max_count)
-   {
-      max_count = max_iter;
-      std::cout << "Maximum iterations: " << max_iter << std::endl;
-   }
-#endif
+template <class F, class T>
+T schroder_iterate(F f, T guess, T min, T max, int digits, boost::uintmax_t& max_iter) BOOST_NOEXCEPT_IF(BOOST_MATH_IS_FLOAT(T) && noexcept(std::declval<F>()(std::declval<T>())))
+{
+   return detail::second_order_root_finder<detail::schroder_stepper>(f, guess, min, max, digits, max_iter);
+}
 
-   return result;
+template <class F, class T>
+inline T schroder_iterate(F f, T guess, T min, T max, int digits) BOOST_NOEXCEPT_IF(BOOST_MATH_IS_FLOAT(T) && noexcept(std::declval<F>()(std::declval<T>())))
+{
+   boost::uintmax_t m = (std::numeric_limits<boost::uintmax_t>::max)();
+   return schroder_iterate(f, guess, min, max, digits, m);
+}
+//
+// These two are the old spelling of this function, retained for backwards compatibity just in case:
+//
+template <class F, class T>
+T schroeder_iterate(F f, T guess, T min, T max, int digits, boost::uintmax_t& max_iter) BOOST_NOEXCEPT_IF(BOOST_MATH_IS_FLOAT(T) && noexcept(std::declval<F>()(std::declval<T>())))
+{
+   return detail::second_order_root_finder<detail::schroder_stepper>(f, guess, min, max, digits, max_iter);
 }
 
 template <class F, class T>
-inline T schroeder_iterate(F f, T guess, T min, T max, int digits)
+inline T schroeder_iterate(F f, T guess, T min, T max, int digits) BOOST_NOEXCEPT_IF(BOOST_MATH_IS_FLOAT(T) && noexcept(std::declval<F>()(std::declval<T>())))
 {
    boost::uintmax_t m = (std::numeric_limits<boost::uintmax_t>::max)();
-   return schroeder_iterate(f, guess, min, max, digits, m);
+   return schroder_iterate(f, guess, min, max, digits, m);
 }
 
+
 } // namespace tools
 } // namespace math
 } // namespace boost
 
 #endif // BOOST_MATH_TOOLS_NEWTON_SOLVER_HPP
 
-
-
diff --git a/boost/math/tools/series.hpp b/boost/math/tools/series.hpp
index a32a33fba1..ab01549a2d 100644
--- a/boost/math/tools/series.hpp
+++ b/boost/math/tools/series.hpp
@@ -21,7 +21,7 @@ namespace boost{ namespace math{ namespace tools{
 // Simple series summation come first:
 //
 template <class Functor, class U, class V>
-inline typename Functor::result_type sum_series(Functor& func, const U& factor, boost::uintmax_t& max_terms, const V& init_value)
+inline typename Functor::result_type sum_series(Functor& func, const U& factor, boost::uintmax_t& max_terms, const V& init_value) BOOST_NOEXCEPT_IF(BOOST_MATH_IS_FLOAT(typename Functor::result_type) && noexcept(std::declval<Functor>()()))
 {
    BOOST_MATH_STD_USING
 
@@ -44,14 +44,14 @@ inline typename Functor::result_type sum_series(Functor& func, const U& factor,
 }
 
 template <class Functor, class U>
-inline typename Functor::result_type sum_series(Functor& func, const U& factor, boost::uintmax_t& max_terms)
+inline typename Functor::result_type sum_series(Functor& func, const U& factor, boost::uintmax_t& max_terms) BOOST_NOEXCEPT_IF(BOOST_MATH_IS_FLOAT(typename Functor::result_type) && noexcept(std::declval<Functor>()()))
 {
    typename Functor::result_type init_value = 0;
    return sum_series(func, factor, max_terms, init_value);
 }
 
 template <class Functor, class U>
-inline typename Functor::result_type sum_series(Functor& func, int bits, boost::uintmax_t& max_terms, const U& init_value)
+inline typename Functor::result_type sum_series(Functor& func, int bits, boost::uintmax_t& max_terms, const U& init_value) BOOST_NOEXCEPT_IF(BOOST_MATH_IS_FLOAT(typename Functor::result_type) && noexcept(std::declval<Functor>()()))
 {
    BOOST_MATH_STD_USING
    typedef typename Functor::result_type result_type;
@@ -60,7 +60,7 @@ inline typename Functor::result_type sum_series(Functor& func, int bits, boost::
 }
 
 template <class Functor>
-inline typename Functor::result_type sum_series(Functor& func, int bits)
+inline typename Functor::result_type sum_series(Functor& func, int bits) BOOST_NOEXCEPT_IF(BOOST_MATH_IS_FLOAT(typename Functor::result_type) && noexcept(std::declval<Functor>()()))
 {
    BOOST_MATH_STD_USING
    typedef typename Functor::result_type result_type;
@@ -70,7 +70,7 @@ inline typename Functor::result_type sum_series(Functor& func, int bits)
 }
 
 template <class Functor>
-inline typename Functor::result_type sum_series(Functor& func, int bits, boost::uintmax_t& max_terms)
+inline typename Functor::result_type sum_series(Functor& func, int bits, boost::uintmax_t& max_terms) BOOST_NOEXCEPT_IF(BOOST_MATH_IS_FLOAT(typename Functor::result_type) && noexcept(std::declval<Functor>()()))
 {
    BOOST_MATH_STD_USING
    typedef typename Functor::result_type result_type;
@@ -79,7 +79,7 @@ inline typename Functor::result_type sum_series(Functor& func, int bits, boost::
 }
 
 template <class Functor, class U>
-inline typename Functor::result_type sum_series(Functor& func, int bits, const U& init_value)
+inline typename Functor::result_type sum_series(Functor& func, int bits, const U& init_value) BOOST_NOEXCEPT_IF(BOOST_MATH_IS_FLOAT(typename Functor::result_type) && noexcept(std::declval<Functor>()()))
 {
    BOOST_MATH_STD_USING
    boost::uintmax_t iters = (std::numeric_limits<boost::uintmax_t>::max)();
@@ -99,7 +99,7 @@ inline typename Functor::result_type sum_series(Functor& func, int bits, const U
 // in any case the result is still much better than a naive summation.
 //
 template <class Functor>
-inline typename Functor::result_type kahan_sum_series(Functor& func, int bits)
+inline typename Functor::result_type kahan_sum_series(Functor& func, int bits) BOOST_NOEXCEPT_IF(BOOST_MATH_IS_FLOAT(typename Functor::result_type) && noexcept(std::declval<Functor>()()))
 {
    BOOST_MATH_STD_USING
 
@@ -122,7 +122,7 @@ inline typename Functor::result_type kahan_sum_series(Functor& func, int bits)
 }
 
 template <class Functor>
-inline typename Functor::result_type kahan_sum_series(Functor& func, int bits, boost::uintmax_t& max_terms)
+inline typename Functor::result_type kahan_sum_series(Functor& func, int bits, boost::uintmax_t& max_terms) BOOST_NOEXCEPT_IF(BOOST_MATH_IS_FLOAT(typename Functor::result_type) && noexcept(std::declval<Functor>()()))
 {
    BOOST_MATH_STD_USING
 
diff --git a/boost/math/tools/toms748_solve.hpp b/boost/math/tools/toms748_solve.hpp
index 48737a821a..dca6bf0218 100644
--- a/boost/math/tools/toms748_solve.hpp
+++ b/boost/math/tools/toms748_solve.hpp
@@ -31,6 +31,10 @@ template <class T>
 class eps_tolerance
 {
 public:
+   eps_tolerance()
+   {
+      eps = 4 * tools::epsilon<T>();
+   }
    eps_tolerance(unsigned bits)
    {
       BOOST_MATH_STD_USING
@@ -108,7 +112,7 @@ void bracket(F f, T& a, T& b, T c, T& fa, T& fb, T& d, T& fd)
    }
    else if(c >= b - fabs(b) * tol)
    {
-      c = b - fabs(a) * tol;
+      c = b - fabs(b) * tol;
    }
    //
    // OK, lets invoke f(c):
diff --git a/boost/math/tools/traits.hpp b/boost/math/tools/traits.hpp
index c49bf19b86..385388a5e3 100644
--- a/boost/math/tools/traits.hpp
+++ b/boost/math/tools/traits.hpp
@@ -26,8 +26,7 @@ as defined above, and has member functions "scale" and "location".
 #endif
 
 #include <boost/mpl/has_xxx.hpp>
-// should be the last #include
-#include <boost/type_traits/detail/bool_trait_def.hpp>
+#include <boost/type_traits/integral_constant.hpp>
 
 namespace boost{ namespace math{ namespace tools{
 
@@ -101,8 +100,8 @@ struct is_scaled_distribution_imp
 
 } // namespace detail
 
-BOOST_TT_AUX_BOOL_TRAIT_DEF1(is_distribution,T,::boost::math::tools::detail::is_distribution_imp<T>::value)
-BOOST_TT_AUX_BOOL_TRAIT_DEF1(is_scaled_distribution,T,::boost::math::tools::detail::is_scaled_distribution_imp<T>::value)
+template <class T> struct is_distribution : public boost::integral_constant<bool, ::boost::math::tools::detail::is_distribution_imp<T>::value> {};
+template <class T> struct is_scaled_distribution : public boost::integral_constant<bool, ::boost::math::tools::detail::is_scaled_distribution_imp<T>::value> {};
 
 }}}
 
diff --git a/boost/math/tools/workaround.hpp b/boost/math/tools/workaround.hpp
index 20106814c7..29ce8b1c04 100644
--- a/boost/math/tools/workaround.hpp
+++ b/boost/math/tools/workaround.hpp
@@ -19,14 +19,14 @@ namespace boost{ namespace math{ namespace tools{
 // std::fmod(1185.0L, 1.5L);
 //
 template <class T>
-inline T fmod_workaround(T a, T b)
+inline T fmod_workaround(T a, T b) BOOST_MATH_NOEXCEPT(T)
 {
    BOOST_MATH_STD_USING
    return fmod(a, b);
 }
 #if (defined(macintosh) || defined(__APPLE__) || defined(__APPLE_CC__)) && ((LDBL_MANT_DIG == 106) || (__LDBL_MANT_DIG__ == 106))
 template <>
-inline long double fmod_workaround(long double a, long double b)
+inline long double fmod_workaround(long double a, long double b) BOOST_NOEXCEPT
 {
    return ::fmodl(a, b);
 }