[ceph.git] / ceph / src / boost / libs / math / include / boost / math / special_functions / detail / bessel_k0.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_K0_HPP
#define BOOST_MATH_BESSEL_K0_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 zero
// 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_k0(T x, const Policy&);

template <class T, class Policy>
struct bessel_k0_initializer
{
   struct init
   {
      init()
      {
         do_init();
      }
      static void do_init()
      {
         bessel_k0(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_k0_initializer<T, Policy>::init bessel_k0_initializer<T, Policy>::initializer;

template <typename T, typename Policy>
T bessel_k0(T x, const Policy& pol)
{
    BOOST_MATH_INSTRUMENT_CODE(x);

    bessel_k0_initializer<T, Policy>::force_instantiate();

    static const T P1[] = {
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.4708152720399552679e+03)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 5.9169059852270512312e+03)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 4.6850901201934832188e+02)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.1999463724910714109e+01)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.3166052564989571850e-01)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 5.8599221412826100000e-04))
    };
    static const T Q1[] = {
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.1312714303849120380e+04)),
        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.4994418972832303646e+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, -1.6128136304458193998e+06)),
        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -3.7333769444840079748e+05)),
        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.7984434409411765813e+04)),
        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.9501657892958843865e+02)),
        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.6414452837299064100e+00))
    };
    static const T Q2[] = {
        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.6128136304458193998e+06)),
        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.9865713163054025489e+04)),
        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.5064972445877992730e+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, 1.1600249425076035558e+02)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.3444738764199315021e+03)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.8321525870183537725e+04)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 7.1557062783764037541e+04)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.5097646353289914539e+05)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.7398867902565686251e+05)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0577068948034021957e+05)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.1075408980684392399e+04)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.6832589957340267940e+03)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.1394980557384778174e+02))
    };
    static const T Q3[] = {
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 9.2556599177304839811e+01)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.8821890840982713696e+03)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.4847228371802360957e+04)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 5.8824616785857027752e+04)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.2689839587977598727e+05)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.5144644673520157801e+05)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 9.7418829762268075784e+04)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.1474655750295278825e+04)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 4.4329628889746408858e+03)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.0013443064949242491e+02)),
         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_k0<%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;
    }
    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;
        BOOST_MATH_INSTRUMENT_CODE("y = " << y);
        BOOST_MATH_INSTRUMENT_CODE("r = " << r);
        BOOST_MATH_INSTRUMENT_CODE("factor = " << factor);
        BOOST_MATH_INSTRUMENT_CODE("value = " << value);
    }

    return value;
}

}}} // namespaces

#ifdef _MSC_VER
#pragma warning(pop)
#endif

#endif // BOOST_MATH_BESSEL_K0_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_K0_HPP
	7	#define BOOST_MATH_BESSEL_K0_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 zero
	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_k0(T x, const Policy&);
	28
	29	template <class T, class Policy>
	30	struct bessel_k0_initializer
	31	{
	32	struct init
	33	{
	34	init()
	35	{
	36	do_init();
	37	}
	38	static void do_init()
	39	{
	40	bessel_k0(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_k0_initializer<T, Policy>::init bessel_k0_initializer<T, Policy>::initializer;
	53
	54	template <typename T, typename Policy>
	55	T bessel_k0(T x, const Policy& pol)
	56	{
	57	BOOST_MATH_INSTRUMENT_CODE(x);
	58
	59	bessel_k0_initializer<T, Policy>::force_instantiate();
	60
	61	static const T P1[] = {
	62	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.4708152720399552679e+03)),
	63	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 5.9169059852270512312e+03)),
	64	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 4.6850901201934832188e+02)),
65	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.1999463724910714109e+01)),
66	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.3166052564989571850e-01)),
67	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 5.8599221412826100000e-04))
68	};
69	static const T Q1[] = {
70	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.1312714303849120380e+04)),
71	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.4994418972832303646e+02)),
72	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0))
73	};
74	static const T P2[] = {
75	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.6128136304458193998e+06)),
76	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -3.7333769444840079748e+05)),
77	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.7984434409411765813e+04)),
78	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.9501657892958843865e+02)),
79	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.6414452837299064100e+00))
80	};
81	static const T Q2[] = {
82	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.6128136304458193998e+06)),
83	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.9865713163054025489e+04)),
84	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.5064972445877992730e+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, 1.1600249425076035558e+02)),
89	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.3444738764199315021e+03)),
90	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.8321525870183537725e+04)),
91	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 7.1557062783764037541e+04)),
92	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.5097646353289914539e+05)),
93	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.7398867902565686251e+05)),
94	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0577068948034021957e+05)),
95	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.1075408980684392399e+04)),
96	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.6832589957340267940e+03)),
97	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.1394980557384778174e+02))
98	};
99	static const T Q3[] = {
100	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 9.2556599177304839811e+01)),
101	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.8821890840982713696e+03)),
102	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.4847228371802360957e+04)),
103	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 5.8824616785857027752e+04)),
104	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.2689839587977598727e+05)),
105	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.5144644673520157801e+05)),
106	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 9.7418829762268075784e+04)),
107	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.1474655750295278825e+04)),
108	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 4.4329628889746408858e+03)),
109	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.0013443064949242491e+02)),
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_k0<%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;
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	BOOST_MATH_INSTRUMENT_CODE("y = " << y);
143	BOOST_MATH_INSTRUMENT_CODE("r = " << r);
144	BOOST_MATH_INSTRUMENT_CODE("factor = " << factor);
145	BOOST_MATH_INSTRUMENT_CODE("value = " << value);
146	}
147
148	return value;
149	}
150
151	}}} // namespaces
152
153	#ifdef _MSC_VER
154	#pragma warning(pop)
155	#endif
156
157	#endif // BOOST_MATH_BESSEL_K0_HPP
158