--- /dev/null
+// Copyright (c) 2007, 2013 John Maddock
+// Copyright Christopher Kormanyos 2013.
+// Use, modification and distribution are subject to the
+// Boost Software License, Version 1.0. (See accompanying file
+// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+//
+// This header just defines the function entry points, and adds dispatch
+// to the right implementation method. Most of the implementation details
+// are in separate headers and copyright Xiaogang Zhang.
+//
+#ifndef BOOST_MATH_BESSEL_HPP
+#define BOOST_MATH_BESSEL_HPP
+
+#ifdef _MSC_VER
+# pragma once
+#endif
+
+#include <boost/math/special_functions/detail/bessel_jy.hpp>
+#include <boost/math/special_functions/detail/bessel_jn.hpp>
+#include <boost/math/special_functions/detail/bessel_yn.hpp>
+#include <boost/math/special_functions/detail/bessel_jy_zero.hpp>
+#include <boost/math/special_functions/detail/bessel_ik.hpp>
+#include <boost/math/special_functions/detail/bessel_i0.hpp>
+#include <boost/math/special_functions/detail/bessel_i1.hpp>
+#include <boost/math/special_functions/detail/bessel_kn.hpp>
+#include <boost/math/special_functions/detail/iconv.hpp>
+#include <boost/math/special_functions/sin_pi.hpp>
+#include <boost/math/special_functions/cos_pi.hpp>
+#include <boost/math/special_functions/sinc.hpp>
+#include <boost/math/special_functions/trunc.hpp>
+#include <boost/math/special_functions/round.hpp>
+#include <boost/math/tools/rational.hpp>
+#include <boost/math/tools/promotion.hpp>
+#include <boost/math/tools/series.hpp>
+#include <boost/math/tools/roots.hpp>
+
+namespace boost{ namespace math{
+
+namespace detail{
+
+template <class T, class Policy>
+struct sph_bessel_j_small_z_series_term
+{
+ typedef T result_type;
+
+ sph_bessel_j_small_z_series_term(unsigned v_, T x)
+ : N(0), v(v_)
+ {
+ BOOST_MATH_STD_USING
+ mult = x / 2;
+ if(v + 3 > max_factorial<T>::value)
+ {
+ term = v * log(mult) - boost::math::lgamma(v+1+T(0.5f), Policy());
+ term = exp(term);
+ }
+ else
+ term = pow(mult, T(v)) / boost::math::tgamma(v+1+T(0.5f), Policy());
+ mult *= -mult;
+ }
+ T operator()()
+ {
+ T r = term;
+ ++N;
+ term *= mult / (N * T(N + v + 0.5f));
+ return r;
+ }
+private:
+ unsigned N;
+ unsigned v;
+ T mult;
+ T term;
+};
+
+template <class T, class Policy>
+inline T sph_bessel_j_small_z_series(unsigned v, T x, const Policy& pol)
+{
+ BOOST_MATH_STD_USING // ADL of std names
+ sph_bessel_j_small_z_series_term<T, Policy> s(v, x);
+ boost::uintmax_t max_iter = policies::get_max_series_iterations<Policy>();
+#if BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x582))
+ T zero = 0;
+ T result = boost::math::tools::sum_series(s, boost::math::policies::get_epsilon<T, Policy>(), max_iter, zero);
+#else
+ T result = boost::math::tools::sum_series(s, boost::math::policies::get_epsilon<T, Policy>(), max_iter);
+#endif
+ policies::check_series_iterations<T>("boost::math::sph_bessel_j_small_z_series<%1%>(%1%,%1%)", max_iter, pol);
+ return result * sqrt(constants::pi<T>() / 4);
+}
+
+template <class T, class Policy>
+T cyl_bessel_j_imp(T v, T x, const bessel_no_int_tag& t, const Policy& pol)
+{
+ BOOST_MATH_STD_USING
+ static const char* function = "boost::math::bessel_j<%1%>(%1%,%1%)";
+ if(x < 0)
+ {
+ // better have integer v:
+ if(floor(v) == v)
+ {
+ T r = cyl_bessel_j_imp(v, T(-x), t, pol);
+ if(iround(v, pol) & 1)
+ r = -r;
+ return r;
+ }
+ else
+ return policies::raise_domain_error<T>(
+ function,
+ "Got x = %1%, but we need x >= 0", x, pol);
+ }
+
+ T j, y;
+ bessel_jy(v, x, &j, &y, need_j, pol);
+ return j;
+}
+
+template <class T, class Policy>
+inline T cyl_bessel_j_imp(T v, T x, const bessel_maybe_int_tag&, const Policy& pol)
+{
+ BOOST_MATH_STD_USING // ADL of std names.
+ int ival = detail::iconv(v, pol);
+ // If v is an integer, use the integer recursion
+ // method, both that and Steeds method are O(v):
+ if((0 == v - ival))
+ {
+ return bessel_jn(ival, x, pol);
+ }
+ return cyl_bessel_j_imp(v, x, bessel_no_int_tag(), pol);
+}
+
+template <class T, class Policy>
+inline T cyl_bessel_j_imp(int v, T x, const bessel_int_tag&, const Policy& pol)
+{
+ BOOST_MATH_STD_USING
+ return bessel_jn(v, x, pol);
+}
+
+template <class T, class Policy>
+inline T sph_bessel_j_imp(unsigned n, T x, const Policy& pol)
+{
+ BOOST_MATH_STD_USING // ADL of std names
+ if(x < 0)
+ return policies::raise_domain_error<T>(
+ "boost::math::sph_bessel_j<%1%>(%1%,%1%)",
+ "Got x = %1%, but function requires x > 0.", x, pol);
+ //
+ // Special case, n == 0 resolves down to the sinus cardinal of x:
+ //
+ if(n == 0)
+ return boost::math::sinc_pi(x, pol);
+ //
+ // Special case for x == 0:
+ //
+ if(x == 0)
+ return 0;
+ //
+ // When x is small we may end up with 0/0, use series evaluation
+ // instead, especially as it converges rapidly:
+ //
+ if(x < 1)
+ return sph_bessel_j_small_z_series(n, x, pol);
+ //
+ // Default case is just a naive evaluation of the definition:
+ //
+ return sqrt(constants::pi<T>() / (2 * x))
+ * cyl_bessel_j_imp(T(T(n)+T(0.5f)), x, bessel_no_int_tag(), pol);
+}
+
+template <class T, class Policy>
+T cyl_bessel_i_imp(T v, T x, const Policy& pol)
+{
+ //
+ // This handles all the bessel I functions, note that we don't optimise
+ // for integer v, other than the v = 0 or 1 special cases, as Millers
+ // algorithm is at least as inefficient as the general case (the general
+ // case has better error handling too).
+ //
+ BOOST_MATH_STD_USING
+ if(x < 0)
+ {
+ // better have integer v:
+ if(floor(v) == v)
+ {
+ T r = cyl_bessel_i_imp(v, T(-x), pol);
+ if(iround(v, pol) & 1)
+ r = -r;
+ return r;
+ }
+ else
+ return policies::raise_domain_error<T>(
+ "boost::math::cyl_bessel_i<%1%>(%1%,%1%)",
+ "Got x = %1%, but we need x >= 0", x, pol);
+ }
+ if(x == 0)
+ {
+ return (v == 0) ? 1 : 0;
+ }
+ if(v == 0.5f)
+ {
+ // common special case, note try and avoid overflow in exp(x):
+ if(x >= tools::log_max_value<T>())
+ {
+ T e = exp(x / 2);
+ return e * (e / sqrt(2 * x * constants::pi<T>()));
+ }
+ return sqrt(2 / (x * constants::pi<T>())) * sinh(x);
+ }
+ if(policies::digits<T, Policy>() <= 64)
+ {
+ if(v == 0)
+ {
+ return bessel_i0(x);
+ }
+ if(v == 1)
+ {
+ return bessel_i1(x);
+ }
+ }
+ if((v > 0) && (x / v < 0.25))
+ return bessel_i_small_z_series(v, x, pol);
+ T I, K;
+ bessel_ik(v, x, &I, &K, need_i, pol);
+ return I;
+}
+
+template <class T, class Policy>
+inline T cyl_bessel_k_imp(T v, T x, const bessel_no_int_tag& /* t */, const Policy& pol)
+{
+ static const char* function = "boost::math::cyl_bessel_k<%1%>(%1%,%1%)";
+ BOOST_MATH_STD_USING
+ if(x < 0)
+ {
+ return policies::raise_domain_error<T>(
+ function,
+ "Got x = %1%, but we need x > 0", x, pol);
+ }
+ if(x == 0)
+ {
+ return (v == 0) ? policies::raise_overflow_error<T>(function, 0, pol)
+ : policies::raise_domain_error<T>(
+ function,
+ "Got x = %1%, but we need x > 0", x, pol);
+ }
+ T I, K;
+ bessel_ik(v, x, &I, &K, need_k, pol);
+ return K;
+}
+
+template <class T, class Policy>
+inline T cyl_bessel_k_imp(T v, T x, const bessel_maybe_int_tag&, const Policy& pol)
+{
+ BOOST_MATH_STD_USING
+ if((floor(v) == v))
+ {
+ return bessel_kn(itrunc(v), x, pol);
+ }
+ return cyl_bessel_k_imp(v, x, bessel_no_int_tag(), pol);
+}
+
+template <class T, class Policy>
+inline T cyl_bessel_k_imp(int v, T x, const bessel_int_tag&, const Policy& pol)
+{
+ return bessel_kn(v, x, pol);
+}
+
+template <class T, class Policy>
+inline T cyl_neumann_imp(T v, T x, const bessel_no_int_tag&, const Policy& pol)
+{
+ static const char* function = "boost::math::cyl_neumann<%1%>(%1%,%1%)";
+
+ BOOST_MATH_INSTRUMENT_VARIABLE(v);
+ BOOST_MATH_INSTRUMENT_VARIABLE(x);
+
+ if(x <= 0)
+ {
+ return (v == 0) && (x == 0) ?
+ policies::raise_overflow_error<T>(function, 0, pol)
+ : policies::raise_domain_error<T>(
+ function,
+ "Got x = %1%, but result is complex for x <= 0", x, pol);
+ }
+ T j, y;
+ bessel_jy(v, x, &j, &y, need_y, pol);
+ //
+ // Post evaluation check for internal overflow during evaluation,
+ // can occur when x is small and v is large, in which case the result
+ // is -INF:
+ //
+ if(!(boost::math::isfinite)(y))
+ return -policies::raise_overflow_error<T>(function, 0, pol);
+ return y;
+}
+
+template <class T, class Policy>
+inline T cyl_neumann_imp(T v, T x, const bessel_maybe_int_tag&, const Policy& pol)
+{
+ BOOST_MATH_STD_USING
+
+ BOOST_MATH_INSTRUMENT_VARIABLE(v);
+ BOOST_MATH_INSTRUMENT_VARIABLE(x);
+
+ if(floor(v) == v)
+ {
+ if(asymptotic_bessel_large_x_limit(v, x))
+ {
+ T r = asymptotic_bessel_y_large_x_2(static_cast<T>(abs(v)), x);
+ if((v < 0) && (itrunc(v, pol) & 1))
+ r = -r;
+ BOOST_MATH_INSTRUMENT_VARIABLE(r);
+ return r;
+ }
+ else
+ {
+ T r = bessel_yn(itrunc(v, pol), x, pol);
+ BOOST_MATH_INSTRUMENT_VARIABLE(r);
+ return r;
+ }
+ }
+ T r = cyl_neumann_imp<T>(v, x, bessel_no_int_tag(), pol);
+ BOOST_MATH_INSTRUMENT_VARIABLE(r);
+ return r;
+}
+
+template <class T, class Policy>
+inline T cyl_neumann_imp(int v, T x, const bessel_int_tag&, const Policy& pol)
+{
+ BOOST_MATH_STD_USING
+
+ BOOST_MATH_INSTRUMENT_VARIABLE(v);
+ BOOST_MATH_INSTRUMENT_VARIABLE(x);
+
+ if(asymptotic_bessel_large_x_limit(T(v), x))
+ {
+ T r = asymptotic_bessel_y_large_x_2(static_cast<T>(abs(v)), x);
+ if((v < 0) && (v & 1))
+ r = -r;
+ return r;
+ }
+ else
+ return bessel_yn(v, x, pol);
+}
+
+template <class T, class Policy>
+inline T sph_neumann_imp(unsigned v, T x, const Policy& pol)
+{
+ BOOST_MATH_STD_USING // ADL of std names
+ static const char* function = "boost::math::sph_neumann<%1%>(%1%,%1%)";
+ //
+ // Nothing much to do here but check for errors, and
+ // evaluate the function's definition directly:
+ //
+ if(x < 0)
+ return policies::raise_domain_error<T>(
+ function,
+ "Got x = %1%, but function requires x > 0.", x, pol);
+
+ if(x < 2 * tools::min_value<T>())
+ return -policies::raise_overflow_error<T>(function, 0, pol);
+
+ T result = cyl_neumann_imp(T(T(v)+0.5f), x, bessel_no_int_tag(), pol);
+ T tx = sqrt(constants::pi<T>() / (2 * x));
+
+ if((tx > 1) && (tools::max_value<T>() / tx < result))
+ return -policies::raise_overflow_error<T>(function, 0, pol);
+
+ return result * tx;
+}
+
+template <class T, class Policy>
+inline T cyl_bessel_j_zero_imp(T v, int m, const Policy& pol)
+{
+ BOOST_MATH_STD_USING // ADL of std names, needed for floor.
+
+ static const char* function = "boost::math::cyl_bessel_j_zero<%1%>(%1%, int)";
+
+ const T half_epsilon(boost::math::tools::epsilon<T>() / 2U);
+
+ // Handle non-finite order.
+ if (!(boost::math::isfinite)(v) )
+ {
+ return policies::raise_domain_error<T>(function, "Order argument is %1%, but must be finite >= 0 !", v, pol);
+ }
+
+ // Handle negative rank.
+ if(m < 0)
+ {
+ // Zeros of Jv(x) with negative rank are not defined and requesting one raises a domain error.
+ return policies::raise_domain_error<T>(function, "Requested the %1%'th zero, but the rank must be positive !", m, pol);
+ }
+
+ // Get the absolute value of the order.
+ const bool order_is_negative = (v < 0);
+ const T vv((!order_is_negative) ? v : T(-v));
+
+ // Check if the order is very close to zero or very close to an integer.
+ const bool order_is_zero = (vv < half_epsilon);
+ const bool order_is_integer = ((vv - floor(vv)) < half_epsilon);
+
+ if(m == 0)
+ {
+ if(order_is_zero)
+ {
+ // The zero'th zero of J0(x) is not defined and requesting it raises a domain error.
+ return policies::raise_domain_error<T>(function, "Requested the %1%'th zero of J0, but the rank must be > 0 !", m, pol);
+ }
+
+ // The zero'th zero of Jv(x) for v < 0 is not defined
+ // unless the order is a negative integer.
+ if(order_is_negative && (!order_is_integer))
+ {
+ // For non-integer, negative order, requesting the zero'th zero raises a domain error.
+ return policies::raise_domain_error<T>(function, "Requested the %1%'th zero of Jv for negative, non-integer order, but the rank must be > 0 !", m, pol);
+ }
+
+ // The zero'th zero does exist and its value is zero.
+ return T(0);
+ }
+
+ // Set up the initial guess for the upcoming root-finding.
+ // If the order is a negative integer, then use the corresponding
+ // positive integer for the order.
+ const T guess_root = boost::math::detail::bessel_zero::cyl_bessel_j_zero_detail::initial_guess<T, Policy>((order_is_integer ? vv : v), m, pol);
+
+ // Select the maximum allowed iterations from the policy.
+ boost::uintmax_t number_of_iterations = policies::get_max_root_iterations<Policy>();
+
+ // Select the desired number of binary digits of precision.
+ // Account for the radix of number representations having non-two radix!
+ const int my_digits2 = policies::digits<T, Policy>();
+
+ const T delta_lo = ((guess_root > 0.2F) ? T(0.2) : T(guess_root / 2U));
+
+ // Perform the root-finding using Newton-Raphson iteration from Boost.Math.
+ const T jvm =
+ boost::math::tools::newton_raphson_iterate(
+ boost::math::detail::bessel_zero::cyl_bessel_j_zero_detail::function_object_jv_and_jv_prime<T, Policy>((order_is_integer ? vv : v), order_is_zero, pol),
+ guess_root,
+ T(guess_root - delta_lo),
+ T(guess_root + 0.2F),
+ my_digits2,
+ number_of_iterations);
+
+ if(number_of_iterations >= policies::get_max_root_iterations<Policy>())
+ {
+ policies::raise_evaluation_error<T>(function, "Unable to locate root in a reasonable time:"
+ " Current best guess is %1%", jvm, Policy());
+ }
+
+ return jvm;
+}
+
+template <class T, class Policy>
+inline T cyl_neumann_zero_imp(T v, int m, const Policy& pol)
+{
+ BOOST_MATH_STD_USING // ADL of std names, needed for floor.
+
+ static const char* function = "boost::math::cyl_neumann_zero<%1%>(%1%, int)";
+
+ // Handle non-finite order.
+ if (!(boost::math::isfinite)(v) )
+ {
+ return policies::raise_domain_error<T>(function, "Order argument is %1%, but must be finite >= 0 !", v, pol);
+ }
+
+ // Handle negative rank.
+ if(m < 0)
+ {
+ return policies::raise_domain_error<T>(function, "Requested the %1%'th zero, but the rank must be positive !", m, pol);
+ }
+
+ const T half_epsilon(boost::math::tools::epsilon<T>() / 2U);
+
+ // Get the absolute value of the order.
+ const bool order_is_negative = (v < 0);
+ const T vv((!order_is_negative) ? v : T(-v));
+
+ const bool order_is_integer = ((vv - floor(vv)) < half_epsilon);
+
+ // For negative integers, use reflection to positive integer order.
+ if(order_is_negative && order_is_integer)
+ return boost::math::detail::cyl_neumann_zero_imp(vv, m, pol);
+
+ // Check if the order is very close to a negative half-integer.
+ const T delta_half_integer(vv - (floor(vv) + 0.5F));
+
+ const bool order_is_negative_half_integer =
+ (order_is_negative && ((delta_half_integer > -half_epsilon) && (delta_half_integer < +half_epsilon)));
+
+ // The zero'th zero of Yv(x) for v < 0 is not defined
+ // unless the order is a negative integer.
+ if((m == 0) && (!order_is_negative_half_integer))
+ {
+ // For non-integer, negative order, requesting the zero'th zero raises a domain error.
+ return policies::raise_domain_error<T>(function, "Requested the %1%'th zero of Yv for negative, non-half-integer order, but the rank must be > 0 !", m, pol);
+ }
+
+ // For negative half-integers, use the corresponding
+ // spherical Bessel function of positive half-integer order.
+ if(order_is_negative_half_integer)
+ return boost::math::detail::cyl_bessel_j_zero_imp(vv, m, pol);
+
+ // Set up the initial guess for the upcoming root-finding.
+ // If the order is a negative integer, then use the corresponding
+ // positive integer for the order.
+ const T guess_root = boost::math::detail::bessel_zero::cyl_neumann_zero_detail::initial_guess<T, Policy>(v, m, pol);
+
+ // Select the maximum allowed iterations from the policy.
+ boost::uintmax_t number_of_iterations = policies::get_max_root_iterations<Policy>();
+
+ // Select the desired number of binary digits of precision.
+ // Account for the radix of number representations having non-two radix!
+ const int my_digits2 = policies::digits<T, Policy>();
+
+ const T delta_lo = ((guess_root > 0.2F) ? T(0.2) : T(guess_root / 2U));
+
+ // Perform the root-finding using Newton-Raphson iteration from Boost.Math.
+ const T yvm =
+ boost::math::tools::newton_raphson_iterate(
+ boost::math::detail::bessel_zero::cyl_neumann_zero_detail::function_object_yv_and_yv_prime<T, Policy>(v, pol),
+ guess_root,
+ T(guess_root - delta_lo),
+ T(guess_root + 0.2F),
+ my_digits2,
+ number_of_iterations);
+
+ if(number_of_iterations >= policies::get_max_root_iterations<Policy>())
+ {
+ policies::raise_evaluation_error<T>(function, "Unable to locate root in a reasonable time:"
+ " Current best guess is %1%", yvm, Policy());
+ }
+
+ return yvm;
+}
+
+} // namespace detail
+
+template <class T1, class T2, class Policy>
+inline typename detail::bessel_traits<T1, T2, Policy>::result_type cyl_bessel_j(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_imp<value_type>(v, static_cast<value_type>(x), tag_type(), forwarding_policy()), "boost::math::cyl_bessel_j<%1%>(%1%,%1%)");
+}
+
+template <class T1, class T2>
+inline typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type cyl_bessel_j(T1 v, T2 x)
+{
+ return cyl_bessel_j(v, x, policies::policy<>());
+}
+
+template <class T, class Policy>
+inline typename detail::bessel_traits<T, T, Policy>::result_type sph_bessel(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_imp<value_type>(v, static_cast<value_type>(x), forwarding_policy()), "boost::math::sph_bessel<%1%>(%1%,%1%)");
+}
+
+template <class T>
+inline typename detail::bessel_traits<T, T, policies::policy<> >::result_type sph_bessel(unsigned v, T x)
+{
+ return sph_bessel(v, x, policies::policy<>());
+}
+
+template <class T1, class T2, class Policy>
+inline typename detail::bessel_traits<T1, T2, Policy>::result_type cyl_bessel_i(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_imp<value_type>(v, static_cast<value_type>(x), forwarding_policy()), "boost::math::cyl_bessel_i<%1%>(%1%,%1%)");
+}
+
+template <class T1, class T2>
+inline typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type cyl_bessel_i(T1 v, T2 x)
+{
+ return cyl_bessel_i(v, x, policies::policy<>());
+}
+
+template <class T1, class T2, class Policy>
+inline typename detail::bessel_traits<T1, T2, Policy>::result_type cyl_bessel_k(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_imp<value_type>(v, static_cast<value_type>(x), tag_type(), forwarding_policy()), "boost::math::cyl_bessel_k<%1%>(%1%,%1%)");
+}
+
+template <class T1, class T2>
+inline typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type cyl_bessel_k(T1 v, T2 x)
+{
+ return cyl_bessel_k(v, x, policies::policy<>());
+}
+
+template <class T1, class T2, class Policy>
+inline typename detail::bessel_traits<T1, T2, Policy>::result_type cyl_neumann(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_imp<value_type>(v, static_cast<value_type>(x), tag_type(), forwarding_policy()), "boost::math::cyl_neumann<%1%>(%1%,%1%)");
+}
+
+template <class T1, class T2>
+inline typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type cyl_neumann(T1 v, T2 x)
+{
+ return cyl_neumann(v, x, policies::policy<>());
+}
+
+template <class T, class Policy>
+inline typename detail::bessel_traits<T, T, Policy>::result_type sph_neumann(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_imp<value_type>(v, static_cast<value_type>(x), forwarding_policy()), "boost::math::sph_neumann<%1%>(%1%,%1%)");
+}
+
+template <class T>
+inline typename detail::bessel_traits<T, T, policies::policy<> >::result_type sph_neumann(unsigned v, T x)
+{
+ return sph_neumann(v, x, policies::policy<>());
+}
+
+template <class T, class Policy>
+inline typename detail::bessel_traits<T, T, Policy>::result_type cyl_bessel_j_zero(T v, int m, 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;
+ BOOST_STATIC_ASSERT_MSG(false == std::numeric_limits<value_type>::is_integer, "Order must be a floating-point type.");
+ return policies::checked_narrowing_cast<result_type, Policy>(detail::cyl_bessel_j_zero_imp<value_type>(v, m, forwarding_policy()), "boost::math::cyl_bessel_j_zero<%1%>(%1%,%1%)");
+}
+
+template <class T>
+inline typename detail::bessel_traits<T, T, policies::policy<> >::result_type cyl_bessel_j_zero(T v, int m)
+{
+ BOOST_STATIC_ASSERT_MSG(false == std::numeric_limits<T>::is_integer, "Order must be a floating-point type.");
+ return cyl_bessel_j_zero<T, policies::policy<> >(v, m, policies::policy<>());
+}
+
+template <class T, class OutputIterator, class Policy>
+inline OutputIterator cyl_bessel_j_zero(T v,
+ int start_index,
+ unsigned number_of_zeros,
+ OutputIterator out_it,
+ const Policy& pol)
+{
+ BOOST_STATIC_ASSERT_MSG(false == std::numeric_limits<T>::is_integer, "Order must be a floating-point type.");
+ for(unsigned i = 0; i < number_of_zeros; ++i)
+ {
+ *out_it = boost::math::cyl_bessel_j_zero(v, start_index + i, pol);
+ ++out_it;
+ }
+ return out_it;
+}
+
+template <class T, class OutputIterator>
+inline OutputIterator cyl_bessel_j_zero(T v,
+ int start_index,
+ unsigned number_of_zeros,
+ OutputIterator out_it)
+{
+ return cyl_bessel_j_zero(v, start_index, number_of_zeros, out_it, policies::policy<>());
+}
+
+template <class T, class Policy>
+inline typename detail::bessel_traits<T, T, Policy>::result_type cyl_neumann_zero(T v, int m, 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;
+ BOOST_STATIC_ASSERT_MSG(false == std::numeric_limits<value_type>::is_integer, "Order must be a floating-point type.");
+ return policies::checked_narrowing_cast<result_type, Policy>(detail::cyl_neumann_zero_imp<value_type>(v, m, forwarding_policy()), "boost::math::cyl_neumann_zero<%1%>(%1%,%1%)");
+}
+
+template <class T>
+inline typename detail::bessel_traits<T, T, policies::policy<> >::result_type cyl_neumann_zero(T v, int m)
+{
+ BOOST_STATIC_ASSERT_MSG(false == std::numeric_limits<T>::is_integer, "Order must be a floating-point type.");
+ return cyl_neumann_zero<T, policies::policy<> >(v, m, policies::policy<>());
+}
+
+template <class T, class OutputIterator, class Policy>
+inline OutputIterator cyl_neumann_zero(T v,
+ int start_index,
+ unsigned number_of_zeros,
+ OutputIterator out_it,
+ const Policy& pol)
+{
+ BOOST_STATIC_ASSERT_MSG(false == std::numeric_limits<T>::is_integer, "Order must be a floating-point type.");
+ for(unsigned i = 0; i < number_of_zeros; ++i)
+ {
+ *out_it = boost::math::cyl_neumann_zero(v, start_index + i, pol);
+ ++out_it;
+ }
+ return out_it;
+}
+
+template <class T, class OutputIterator>
+inline OutputIterator cyl_neumann_zero(T v,
+ int start_index,
+ unsigned number_of_zeros,
+ OutputIterator out_it)
+{
+ return cyl_neumann_zero(v, start_index, number_of_zeros, out_it, policies::policy<>());
+}
+
+} // namespace math
+} // namespace boost
+
+#endif // BOOST_MATH_BESSEL_HPP
+
+
projects / rsem.git / blobdiff