[ceph.git] / ceph / src / boost / libs / math / include / boost / math / special_functions / detail / bessel_k1.hpp

//  Copyright (c) 2006 Xiaogang Zhang
//  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_K1_HPP
#define BOOST_MATH_BESSEL_K1_HPP

#ifdef _MSC_VER
#pragma once
#pragma warning(push)
#pragma warning(disable:4702) // Unreachable code (release mode only warning)
#endif

#include <boost/math/tools/rational.hpp>
#include <boost/math/tools/big_constant.hpp>
#include <boost/math/policies/error_handling.hpp>
#include <boost/assert.hpp>

// Modified Bessel function of the second kind of order one
// minimax rational approximations on intervals, see
// Russon and Blair, Chalk River Report AECL-3461, 1969

namespace boost { namespace math { namespace detail{

template <typename T, typename Policy>
T bessel_k1(T x, const Policy&);

template <class T, class Policy>
struct bessel_k1_initializer
{
   struct init
   {
      init()
      {
         do_init();
      }
      static void do_init()
      {
         bessel_k1(T(1), Policy());
      }
      void force_instantiate()const{}
   };
   static const init initializer;
   static void force_instantiate()
   {
      initializer.force_instantiate();
   }
};

template <class T, class Policy>
const typename bessel_k1_initializer<T, Policy>::init bessel_k1_initializer<T, Policy>::initializer;

template <typename T, typename Policy>
T bessel_k1(T x, const Policy& pol)
{
    bessel_k1_initializer<T, Policy>::force_instantiate();

    static const T P1[] = {
        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.2149374878243304548e+06)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 7.1938920065420586101e+05)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.7733324035147015630e+05)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 7.1885382604084798576e+03)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 9.9991373567429309922e+01)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 4.8127070456878442310e-01))
    };
    static const T Q1[] = {
        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.2149374878243304548e+06)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.7264298672067697862e+04)),
        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.8143915754538725829e+02)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0))
    };
    static const T P2[] = {
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 0.0)),
        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.3531161492785421328e+06)),
        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.4758069205414222471e+05)),
        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -4.5051623763436087023e+03)),
        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -5.3103913335180275253e+01)),
        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.2795590826955002390e-01))
    };
    static const T Q2[] = {
        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.7062322985570842656e+06)),
        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 4.3117653211351080007e+04)),
        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -3.0507151578787595807e+02)),
        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0))
    };
    static const T P3[] = {
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.2196792496874548962e+00)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 4.4137176114230414036e+01)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.4122953486801312910e+02)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.3319486433183221990e+03)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.8590657697910288226e+03)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.4540675585544584407e+03)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.3123742209168871550e+03)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 8.1094256146537402173e+02)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.3182609918569941308e+02)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 7.5584584631176030810e+00)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 6.4257745859173138767e-02))
    };
    static const T Q3[] = {
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.7710478032601086579e+00)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.4552228452758912848e+01)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.5951223655579051357e+02)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 9.6929165726802648634e+02)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.9448440788918006154e+03)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.1181000487171943810e+03)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.2082692316002348638e+03)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.3031020088765390854e+02)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.6001069306861518855e+01)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0))
    };
    T value, factor, r, r1, r2;

    BOOST_MATH_STD_USING
    using namespace boost::math::tools;

    static const char* function = "boost::math::bessel_k1<%1%>(%1%,%1%)";

    if (x < 0)
    {
       return policies::raise_domain_error<T>(function,
            "Got x = %1%, but argument x must be non-negative, complex number result not supported.", x, pol);
    }
    if (x == 0)
    {
       return policies::raise_overflow_error<T>(function, 0, pol);
    }
    if (x <= 1)                         // x in (0, 1]
    {
        T y = x * x;
        r1 = evaluate_polynomial(P1, y) /  evaluate_polynomial(Q1, y);
        r2 = evaluate_polynomial(P2, y) /  evaluate_polynomial(Q2, y);
        factor = log(x);
        value = (r1 + factor * r2) / x;
    }
    else                                // x in (1, \infty)
    {
        T y = 1 / x;
        r = evaluate_polynomial(P3, y) /  evaluate_polynomial(Q3, y);
        factor = exp(-x) / sqrt(x);
        value = factor * r;
    }

    return value;
}

}}} // namespaces

#ifdef _MSC_VER
#pragma warning(pop)
#endif

#endif // BOOST_MATH_BESSEL_K1_HPP
Commit	Line	Data
7c673cae FG	1	// Copyright (c) 2006 Xiaogang Zhang
	2	// Use, modification and distribution are subject to the
	3	// Boost Software License, Version 1.0. (See accompanying file
	4	// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
	5
	6	#ifndef BOOST_MATH_BESSEL_K1_HPP
	7	#define BOOST_MATH_BESSEL_K1_HPP
	8
	9	#ifdef _MSC_VER
	10	#pragma once
	11	#pragma warning(push)
	12	#pragma warning(disable:4702) // Unreachable code (release mode only warning)
	13	#endif
	14
	15	#include <boost/math/tools/rational.hpp>
	16	#include <boost/math/tools/big_constant.hpp>
	17	#include <boost/math/policies/error_handling.hpp>
	18	#include <boost/assert.hpp>
	19
	20	// Modified Bessel function of the second kind of order one
	21	// minimax rational approximations on intervals, see
	22	// Russon and Blair, Chalk River Report AECL-3461, 1969
	23
	24	namespace boost { namespace math { namespace detail{
	25
	26	template <typename T, typename Policy>
	27	T bessel_k1(T x, const Policy&);
	28
	29	template <class T, class Policy>
	30	struct bessel_k1_initializer
	31	{
	32	struct init
	33	{
	34	init()
	35	{
	36	do_init();
	37	}
	38	static void do_init()
	39	{
	40	bessel_k1(T(1), Policy());
	41	}
	42	void force_instantiate()const{}
	43	};
	44	static const init initializer;
	45	static void force_instantiate()
	46	{
	47	initializer.force_instantiate();
	48	}
	49	};
	50
	51	template <class T, class Policy>
	52	const typename bessel_k1_initializer<T, Policy>::init bessel_k1_initializer<T, Policy>::initializer;
	53
	54	template <typename T, typename Policy>
	55	T bessel_k1(T x, const Policy& pol)
	56	{
	57	bessel_k1_initializer<T, Policy>::force_instantiate();
	58
	59	static const T P1[] = {
	60	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.2149374878243304548e+06)),
	61	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 7.1938920065420586101e+05)),
	62	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.7733324035147015630e+05)),
	63	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 7.1885382604084798576e+03)),
	64	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 9.9991373567429309922e+01)),
65	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 4.8127070456878442310e-01))
66	};
67	static const T Q1[] = {
68	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.2149374878243304548e+06)),
69	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.7264298672067697862e+04)),
70	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.8143915754538725829e+02)),
71	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0))
72	};
73	static const T P2[] = {
74	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 0.0)),
75	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.3531161492785421328e+06)),
76	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.4758069205414222471e+05)),
77	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -4.5051623763436087023e+03)),
78	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -5.3103913335180275253e+01)),
79	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.2795590826955002390e-01))
80	};
81	static const T Q2[] = {
82	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.7062322985570842656e+06)),
83	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 4.3117653211351080007e+04)),
84	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -3.0507151578787595807e+02)),
85	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0))
86	};
87	static const T P3[] = {
88	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.2196792496874548962e+00)),
89	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 4.4137176114230414036e+01)),
90	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.4122953486801312910e+02)),
91	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.3319486433183221990e+03)),
92	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.8590657697910288226e+03)),
93	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.4540675585544584407e+03)),
94	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.3123742209168871550e+03)),
95	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 8.1094256146537402173e+02)),
96	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.3182609918569941308e+02)),
97	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 7.5584584631176030810e+00)),
98	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 6.4257745859173138767e-02))
99	};
100	static const T Q3[] = {
101	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.7710478032601086579e+00)),
102	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.4552228452758912848e+01)),
103	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.5951223655579051357e+02)),
104	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 9.6929165726802648634e+02)),
105	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.9448440788918006154e+03)),
106	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.1181000487171943810e+03)),
107	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.2082692316002348638e+03)),
108	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.3031020088765390854e+02)),
109	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.6001069306861518855e+01)),
110	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0))
111	};
112	T value, factor, r, r1, r2;
113
114	BOOST_MATH_STD_USING
115	using namespace boost::math::tools;
116
117	static const char* function = "boost::math::bessel_k1<%1%>(%1%,%1%)";
118
119	if (x < 0)
120	{
121	return policies::raise_domain_error<T>(function,
122	"Got x = %1%, but argument x must be non-negative, complex number result not supported.", x, pol);
123	}
124	if (x == 0)
125	{
126	return policies::raise_overflow_error<T>(function, 0, pol);
127	}
128	if (x <= 1) // x in (0, 1]
129	{
130	T y = x * x;
131	r1 = evaluate_polynomial(P1, y) / evaluate_polynomial(Q1, y);
132	r2 = evaluate_polynomial(P2, y) / evaluate_polynomial(Q2, y);
133	factor = log(x);
134	value = (r1 + factor * r2) / x;
135	}
136	else // x in (1, \infty)
137	{
138	T y = 1 / x;
139	r = evaluate_polynomial(P3, y) / evaluate_polynomial(Q3, y);
140	factor = exp(-x) / sqrt(x);
141	value = factor * r;
142	}
143
144	return value;
145	}
146
147	}}} // namespaces
148
149	#ifdef _MSC_VER
150	#pragma warning(pop)
151	#endif
152
153	#endif // BOOST_MATH_BESSEL_K1_HPP
154