Imported Upstream version 1.57.0upstream/1.57.0

1 files changed, 359 insertions, 0 deletions

diff --git a/boost/math/special_functions/bessel_prime.hpp b/boost/math/special_functions/bessel_prime.hpp
new file mode 100644
index 0000000000..c5f2d58c2b
--- /dev/null
+++ b/boost/math/special_functions/bessel_prime.hpp
@@ -0,0 +1,359 @@
+//  Copyright (c) 2013 Anton Bikineev
+//  Use, modification and distribution are subject to the
+//  Boost Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+//
+#ifndef BOOST_MATH_BESSEL_DERIVATIVES_HPP
+#define BOOST_MATH_BESSEL_DERIVATIVES_HPP
+
+#ifdef _MSC_VER
+#  pragma once
+#endif
+
+#include <boost/math/special_functions/math_fwd.hpp>
+#include <boost/math/special_functions/bessel.hpp>
+#include <boost/math/special_functions/detail/bessel_jy_derivatives_asym.hpp>
+#include <boost/math/special_functions/detail/bessel_jy_derivatives_series.hpp>
+#include <boost/math/special_functions/detail/bessel_derivatives_linear.hpp>
+
+namespace boost{ namespace math{
+
+namespace detail{
+
+template <class Tag, class T, class Policy>
+inline T cyl_bessel_j_prime_imp(T v, T x, const Policy& pol)
+{
+   static const char* const function = "boost::math::cyl_bessel_j_prime<%1%>(%1%,%1%)";
+   BOOST_MATH_STD_USING
+   //
+   // Prevent complex result:
+   //
+   if (x < 0 && floor(v) != v)
+      return boost::math::policies::raise_domain_error<T>(
+         function,
+         "Got x = %1%, but function requires x >= 0", x, pol);
+   //
+   // Special cases for x == 0:
+   //
+   if (x == 0)
+   {
+      if (v == 1)
+         return 0.5;
+      else if (v == -1)
+         return -0.5;
+      else if (floor(v) == v || v > 1)
+         return 0;
+      else return boost::math::policies::raise_domain_error<T>(
+         function,
+         "Got x = %1%, but function is indeterminate for this order", x, pol);
+   }
+   //
+   // Special case for large x: use asymptotic expansion:
+   //
+   if (boost::math::detail::asymptotic_bessel_derivative_large_x_limit(v, x))
+      return boost::math::detail::asymptotic_bessel_j_derivative_large_x_2(v, x);
+   //
+   // Special case for small x: use Taylor series:
+   //
+   if ((abs(x) < 5) || (abs(v) > x * x / 4))
+   {
+      bool inversed = false;
+      if (floor(v) == v && v < 0)
+      {
+         v = -v;
+         if (itrunc(v, pol) & 1)
+            inversed = true;
+      }
+      T r = boost::math::detail::bessel_j_derivative_small_z_series(v, x, pol);
+      return inversed ? T(-r) : r;
+   }
+   //
+   // Special case for v == 0:
+   //
+   if (v == 0)
+      return -boost::math::detail::cyl_bessel_j_imp<T>(1, x, Tag(), pol);
+   //
+   // Default case:
+   //
+   return boost::math::detail::bessel_j_derivative_linear(v, x, Tag(), pol);
+}
+
+template <class T, class Policy>
+inline T sph_bessel_j_prime_imp(unsigned v, T x, const Policy& pol)
+{
+   static const char* const function = "boost::math::sph_bessel_prime<%1%>(%1%,%1%)";
+   //
+   // Prevent complex result:
+   //
+   if (x < 0)
+      return boost::math::policies::raise_domain_error<T>(
+         function,
+         "Got x = %1%, but function requires x >= 0.", x, pol);
+   //
+   // Special case for v == 0:
+   //
+   if (v == 0)
+      return (x == 0) ? boost::math::policies::raise_overflow_error<T>(function, 0, pol)
+         : static_cast<T>(-boost::math::detail::sph_bessel_j_imp<T>(1, x, pol));
+   //
+   // Special case for x == 0 and v > 0:
+   //
+   if (x == 0)
+      return boost::math::policies::raise_domain_error<T>(
+         function,
+         "Got x = %1%, but function is indeterminate for this order", x, pol);
+   //
+   // Default case:
+   //
+   return boost::math::detail::sph_bessel_j_derivative_linear(v, x, pol);
+}
+
+template <class T, class Policy>
+inline T cyl_bessel_i_prime_imp(T v, T x, const Policy& pol)
+{
+   static const char* const function = "boost::math::cyl_bessel_i_prime<%1%>(%1%,%1%)";
+   BOOST_MATH_STD_USING
+   //
+   // Prevent complex result:
+   //
+   if (x < 0 && floor(v) != v)
+      return boost::math::policies::raise_domain_error<T>(
+         function,
+         "Got x = %1%, but function requires x >= 0", x, pol);
+   //
+   // Special cases for x == 0:
+   //
+   if (x == 0)
+   {
+      if (v == 1 || v == -1)
+         return 0.5;
+      else if (floor(v) == v || v > 1)
+         return 0;
+      else return boost::math::policies::raise_domain_error<T>(
+         function,
+         "Got x = %1%, but function is indeterminate for this order", x, pol);
+   }
+   //
+   // Special case for v == 0:
+   //
+   if (v == 0)
+      return boost::math::detail::cyl_bessel_i_imp<T>(1, x, pol);
+   //
+   // Default case:
+   //
+   return boost::math::detail::bessel_i_derivative_linear(v, x, pol);
+}
+
+template <class Tag, class T, class Policy>
+inline T cyl_bessel_k_prime_imp(T v, T x, const Policy& pol)
+{
+   //
+   // Prevent complex and indeterminate results:
+   //
+   if (x <= 0)
+      return boost::math::policies::raise_domain_error<T>(
+         "boost::math::cyl_bessel_k_prime<%1%>(%1%,%1%)",
+         "Got x = %1%, but function requires x > 0", x, pol);
+   //
+   // Special case for v == 0:
+   //
+   if (v == 0)
+      return -boost::math::detail::cyl_bessel_k_imp<T>(1, x, Tag(), pol);
+   //
+   // Default case:
+   //
+   return boost::math::detail::bessel_k_derivative_linear(v, x, Tag(), pol);
+}
+
+template <class Tag, class T, class Policy>
+inline T cyl_neumann_prime_imp(T v, T x, const Policy& pol)
+{
+   BOOST_MATH_STD_USING
+   //
+   // Prevent complex and indeterminate results:
+   //
+   if (x <= 0)
+      return boost::math::policies::raise_domain_error<T>(
+         "boost::math::cyl_neumann_prime<%1%>(%1%,%1%)",
+         "Got x = %1%, but function requires x > 0", x, pol);
+   //
+   // Special case for large x: use asymptotic expansion:
+   //
+   if (boost::math::detail::asymptotic_bessel_derivative_large_x_limit(v, x))
+      return boost::math::detail::asymptotic_bessel_y_derivative_large_x_2(v, x);
+   //
+   // Special case for small x: use Taylor series:
+   //
+   if (v > 0 && floor(v) != v)
+   {
+      const T eps = boost::math::policies::get_epsilon<T, Policy>();
+      if (log(eps / 2) > v * log((x * x) / (v * 4)))
+         return boost::math::detail::bessel_y_derivative_small_z_series(v, x, pol);
+   }
+   //
+   // Special case for v == 0:
+   //
+   if (v == 0)
+      return -boost::math::detail::cyl_neumann_imp<T>(1, x, Tag(), pol);
+   //
+   // Default case:
+   //
+   return boost::math::detail::bessel_y_derivative_linear(v, x, Tag(), pol);
+}
+
+template <class T, class Policy>
+inline T sph_neumann_prime_imp(unsigned v, T x, const Policy& pol)
+{
+   //
+   // Prevent complex and indeterminate result:
+   //
+   if (x <= 0)
+      return boost::math::policies::raise_domain_error<T>(
+         "boost::math::sph_neumann_prime<%1%>(%1%,%1%)",
+         "Got x = %1%, but function requires x > 0.", x, pol);
+   //
+   // Special case for v == 0:
+   //
+   if (v == 0)
+      return -boost::math::detail::sph_neumann_imp<T>(1, x, pol);
+   //
+   // Default case:
+   //
+   return boost::math::detail::sph_neumann_derivative_linear(v, x, pol);
+}
+
+} // namespace detail
+
+template <class T1, class T2, class Policy>
+inline typename detail::bessel_traits<T1, T2, Policy>::result_type cyl_bessel_j_prime(T1 v, T2 x, const Policy& /* pol */)
+{
+   BOOST_FPU_EXCEPTION_GUARD
+   typedef typename detail::bessel_traits<T1, T2, Policy>::result_type result_type;
+   typedef typename detail::bessel_traits<T1, T2, Policy>::optimisation_tag tag_type;
+   typedef typename policies::evaluation<result_type, Policy>::type value_type;
+   typedef typename policies::normalise<
+      Policy,
+      policies::promote_float<false>,
+      policies::promote_double<false>,
+      policies::discrete_quantile<>,
+      policies::assert_undefined<> >::type forwarding_policy;
+   return policies::checked_narrowing_cast<result_type, Policy>(detail::cyl_bessel_j_prime_imp<tag_type, value_type>(v, static_cast<value_type>(x), forwarding_policy()), "boost::math::cyl_bessel_j_prime<%1%,%1%>(%1%,%1%)");
+}
+
+template <class T1, class T2>
+inline typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type cyl_bessel_j_prime(T1 v, T2 x)
+{
+   return cyl_bessel_j_prime(v, x, policies::policy<>());
+}
+
+template <class T, class Policy>
+inline typename detail::bessel_traits<T, T, Policy>::result_type sph_bessel_prime(unsigned v, T x, const Policy& /* pol */)
+{
+   BOOST_FPU_EXCEPTION_GUARD
+   typedef typename detail::bessel_traits<T, T, Policy>::result_type result_type;
+   typedef typename policies::evaluation<result_type, Policy>::type value_type;
+   typedef typename policies::normalise<
+      Policy,
+      policies::promote_float<false>,
+      policies::promote_double<false>,
+      policies::discrete_quantile<>,
+      policies::assert_undefined<> >::type forwarding_policy;
+   return policies::checked_narrowing_cast<result_type, Policy>(detail::sph_bessel_j_prime_imp<value_type>(v, static_cast<value_type>(x), forwarding_policy()), "boost::math::sph_bessel_j_prime<%1%>(%1%,%1%)");
+}
+
+template <class T>
+inline typename detail::bessel_traits<T, T, policies::policy<> >::result_type sph_bessel_prime(unsigned v, T x)
+{
+   return sph_bessel_prime(v, x, policies::policy<>());
+}
+
+template <class T1, class T2, class Policy>
+inline typename detail::bessel_traits<T1, T2, Policy>::result_type cyl_bessel_i_prime(T1 v, T2 x, const Policy& /* pol */)
+{
+   BOOST_FPU_EXCEPTION_GUARD
+   typedef typename detail::bessel_traits<T1, T2, Policy>::result_type result_type;
+   typedef typename policies::evaluation<result_type, Policy>::type value_type;
+   typedef typename policies::normalise<
+      Policy,
+      policies::promote_float<false>,
+      policies::promote_double<false>,
+      policies::discrete_quantile<>,
+      policies::assert_undefined<> >::type forwarding_policy;
+   return policies::checked_narrowing_cast<result_type, Policy>(detail::cyl_bessel_i_prime_imp<value_type>(v, static_cast<value_type>(x), forwarding_policy()), "boost::math::cyl_bessel_i_prime<%1%>(%1%,%1%)");
+}
+
+template <class T1, class T2>
+inline typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type cyl_bessel_i_prime(T1 v, T2 x)
+{
+   return cyl_bessel_i_prime(v, x, policies::policy<>());
+}
+
+template <class T1, class T2, class Policy>
+inline typename detail::bessel_traits<T1, T2, Policy>::result_type cyl_bessel_k_prime(T1 v, T2 x, const Policy& /* pol */)
+{
+   BOOST_FPU_EXCEPTION_GUARD
+   typedef typename detail::bessel_traits<T1, T2, Policy>::result_type result_type;
+   typedef typename detail::bessel_traits<T1, T2, Policy>::optimisation_tag tag_type;
+   typedef typename policies::evaluation<result_type, Policy>::type value_type;
+   typedef typename policies::normalise<
+      Policy,
+      policies::promote_float<false>,
+      policies::promote_double<false>,
+      policies::discrete_quantile<>,
+      policies::assert_undefined<> >::type forwarding_policy;
+   return policies::checked_narrowing_cast<result_type, Policy>(detail::cyl_bessel_k_prime_imp<tag_type, value_type>(v, static_cast<value_type>(x), forwarding_policy()), "boost::math::cyl_bessel_k_prime<%1%,%1%>(%1%,%1%)");
+}
+
+template <class T1, class T2>
+inline typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type cyl_bessel_k_prime(T1 v, T2 x)
+{
+   return cyl_bessel_k_prime(v, x, policies::policy<>());
+}
+
+template <class T1, class T2, class Policy>
+inline typename detail::bessel_traits<T1, T2, Policy>::result_type cyl_neumann_prime(T1 v, T2 x, const Policy& /* pol */)
+{
+   BOOST_FPU_EXCEPTION_GUARD
+   typedef typename detail::bessel_traits<T1, T2, Policy>::result_type result_type;
+   typedef typename detail::bessel_traits<T1, T2, Policy>::optimisation_tag tag_type;
+   typedef typename policies::evaluation<result_type, Policy>::type value_type;
+   typedef typename policies::normalise<
+      Policy,
+      policies::promote_float<false>,
+      policies::promote_double<false>,
+      policies::discrete_quantile<>,
+      policies::assert_undefined<> >::type forwarding_policy;
+   return policies::checked_narrowing_cast<result_type, Policy>(detail::cyl_neumann_prime_imp<tag_type, value_type>(v, static_cast<value_type>(x), forwarding_policy()), "boost::math::cyl_neumann_prime<%1%,%1%>(%1%,%1%)");
+}
+
+template <class T1, class T2>
+inline typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type cyl_neumann_prime(T1 v, T2 x)
+{
+   return cyl_neumann_prime(v, x, policies::policy<>());
+}
+
+template <class T, class Policy>
+inline typename detail::bessel_traits<T, T, Policy>::result_type sph_neumann_prime(unsigned v, T x, const Policy& /* pol */)
+{
+   BOOST_FPU_EXCEPTION_GUARD
+   typedef typename detail::bessel_traits<T, T, Policy>::result_type result_type;
+   typedef typename policies::evaluation<result_type, Policy>::type value_type;
+   typedef typename policies::normalise<
+      Policy,
+      policies::promote_float<false>,
+      policies::promote_double<false>,
+      policies::discrete_quantile<>,
+      policies::assert_undefined<> >::type forwarding_policy;
+   return policies::checked_narrowing_cast<result_type, Policy>(detail::sph_neumann_prime_imp<value_type>(v, static_cast<value_type>(x), forwarding_policy()), "boost::math::sph_neumann_prime<%1%>(%1%,%1%)");
+}
+
+template <class T>
+inline typename detail::bessel_traits<T, T, policies::policy<> >::result_type sph_neumann_prime(unsigned v, T x)
+{
+   return sph_neumann_prime(v, x, policies::policy<>());
+}
+
+} // namespace math
+} // namespace boost
+
+#endif // BOOST_MATH_BESSEL_DERIVATIVES_HPP