[ceph.git] / ceph / src / boost / boost / math / special_functions / detail / bessel_j1.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_J1_HPP
#define BOOST_MATH_BESSEL_J1_HPP

#ifdef _MSC_VER
#pragma once
#endif

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

#if defined(__GNUC__) && defined(BOOST_MATH_USE_FLOAT128)
//
// This is the only way we can avoid
// warning: non-standard suffix on floating constant [-Wpedantic]
// when building with -Wall -pedantic.  Neither __extension__
// nor #pragma dianostic ignored work :(
//
#pragma GCC system_header
#endif

// Bessel function of the first kind of order one
// x <= 8, minimax rational approximations on root-bracketing intervals
// x > 8, Hankel asymptotic expansion in Hart, Computer Approximations, 1968

namespace boost { namespace math{  namespace detail{

template <typename T>
T bessel_j1(T x);

template <class T>
struct bessel_j1_initializer
{
   struct init
   {
      init()
      {
         do_init();
      }
      static void do_init()
      {
         bessel_j1(T(1));
      }
      void force_instantiate()const{}
   };
   static const init initializer;
   static void force_instantiate()
   {
      initializer.force_instantiate();
   }
};

template <class T>
const typename bessel_j1_initializer<T>::init bessel_j1_initializer<T>::initializer;

template <typename T>
T bessel_j1(T x)
{
    bessel_j1_initializer<T>::force_instantiate();

    static const T P1[] = {
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.4258509801366645672e+11)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 6.6781041261492395835e+09)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.1548696764841276794e+08)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 9.8062904098958257677e+05)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -4.4615792982775076130e+03)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0650724020080236441e+01)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.0767857011487300348e-02))
    };
    static const T Q1[] = {
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 4.1868604460820175290e+12)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 4.2091902282580133541e+10)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.0228375140097033958e+08)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 5.9117614494174794095e+05)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0742272239517380498e+03)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 0.0))
    };
    static const T P2[] = {
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.7527881995806511112e+16)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.6608531731299018674e+15)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -3.6658018905416665164e+13)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.5580665670910619166e+11)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.8113931269860667829e+09)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 5.0793266148011179143e+06)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -7.5023342220781607561e+03)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 4.6179191852758252278e+00))
    };
    static const T Q2[] = {
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.7253905888447681194e+18)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.7128800897135812012e+16)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 8.4899346165481429307e+13)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.7622777286244082666e+11)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 6.4872502899596389593e+08)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.1267125065029138050e+06)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.3886978985861357615e+03)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0))
    };
    static const T PC[] = {
        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -4.4357578167941278571e+06)),
        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -9.9422465050776411957e+06)),
        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -6.6033732483649391093e+06)),
        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.5235293511811373833e+06)),
        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.0982405543459346727e+05)),
        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.6116166443246101165e+03)),
        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 0.0))
    };
    static const T QC[] = {
        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -4.4357578167941278568e+06)),
        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -9.9341243899345856590e+06)),
        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -6.5853394797230870728e+06)),
        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.5118095066341608816e+06)),
        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.0726385991103820119e+05)),
        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.4550094401904961825e+03)),
        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0))
    };
    static const T PS[] = {
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.3220913409857223519e+04)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 8.5145160675335701966e+04)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 6.6178836581270835179e+04)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.8494262873223866797e+04)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.7063754290207680021e+03)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.5265133846636032186e+01)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 0.0))
    };
    static const T QS[] = {
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 7.0871281941028743574e+05)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.8194580422439972989e+06)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.4194606696037208929e+06)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 4.0029443582266975117e+05)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.7890229745772202641e+04)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 8.6383677696049909675e+02)),
         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0))
    };
    static const T x1  =  static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.8317059702075123156e+00)),
                   x2  =  static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 7.0155866698156187535e+00)),
                   x11 =  static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 9.810e+02)),
                   x12 =  static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -3.2527979248768438556e-04)),
                   x21 =  static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.7960e+03)),
                   x22 =  static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -3.8330184381246462950e-05));

    T value, factor, r, rc, rs, w;

    BOOST_MATH_STD_USING
    using namespace boost::math::tools;
    using namespace boost::math::constants;

    w = abs(x);
    if (x == 0)
    {
        return static_cast<T>(0);
    }
    if (w <= 4)                       // w in (0, 4]
    {
        T y = x * x;
        BOOST_ASSERT(sizeof(P1) == sizeof(Q1));
        r = evaluate_rational(P1, Q1, y);
        factor = w * (w + x1) * ((w - x11/256) - x12);
        value = factor * r;
    }
    else if (w <= 8)                  // w in (4, 8]
    {
        T y = x * x;
        BOOST_ASSERT(sizeof(P2) == sizeof(Q2));
        r = evaluate_rational(P2, Q2, y);
        factor = w * (w + x2) * ((w - x21/256) - x22);
        value = factor * r;
    }
    else                                // w in (8, \infty)
    {
        T y = 8 / w;
        T y2 = y * y;
        BOOST_ASSERT(sizeof(PC) == sizeof(QC));
        BOOST_ASSERT(sizeof(PS) == sizeof(QS));
        rc = evaluate_rational(PC, QC, y2);
        rs = evaluate_rational(PS, QS, y2);
        factor = 1 / (sqrt(w) * constants::root_pi<T>());
        //
        // What follows is really just:
        //
        // T z = w - 0.75f * pi<T>();
        // value = factor * (rc * cos(z) - y * rs * sin(z));
        //
        // but using the sin/cos addition rules plus constants
        // for the values of sin/cos of 3PI/4 which then cancel
        // out with corresponding terms in "factor".
        //
        T sx = sin(x);
        T cx = cos(x);
        value = factor * (rc * (sx - cx) + y * rs * (sx + cx));
    }

    if (x < 0)
    {
        value *= -1;                 // odd function
    }
    return value;
}

}}} // namespaces

#endif // BOOST_MATH_BESSEL_J1_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_J1_HPP
	7	#define BOOST_MATH_BESSEL_J1_HPP
	8
	9	#ifdef _MSC_VER
	10	#pragma once
	11	#endif
	12
	13	#include <boost/math/constants/constants.hpp>
	14	#include <boost/math/tools/rational.hpp>
	15	#include <boost/math/tools/big_constant.hpp>
	16	#include <boost/assert.hpp>
	17
92f5a8d4 TL	18	#if defined(__GNUC__) && defined(BOOST_MATH_USE_FLOAT128)
	19	//
	20	// This is the only way we can avoid
	21	// warning: non-standard suffix on floating constant [-Wpedantic]
	22	// when building with -Wall -pedantic. Neither __extension__
	23	// nor #pragma dianostic ignored work :(
	24	//
	25	#pragma GCC system_header
	26	#endif
	27
7c673cae FG	28	// Bessel function of the first kind of order one
	29	// x <= 8, minimax rational approximations on root-bracketing intervals
	30	// x > 8, Hankel asymptotic expansion in Hart, Computer Approximations, 1968
	31
	32	namespace boost { namespace math{ namespace detail{
	33
	34	template <typename T>
	35	T bessel_j1(T x);
	36
	37	template <class T>
	38	struct bessel_j1_initializer
	39	{
	40	struct init
	41	{
	42	init()
	43	{
	44	do_init();
	45	}
	46	static void do_init()
	47	{
	48	bessel_j1(T(1));
	49	}
	50	void force_instantiate()const{}
	51	};
	52	static const init initializer;
	53	static void force_instantiate()
	54	{
	55	initializer.force_instantiate();
	56	}
	57	};
	58
	59	template <class T>
	60	const typename bessel_j1_initializer<T>::init bessel_j1_initializer<T>::initializer;
	61
	62	template <typename T>
	63	T bessel_j1(T x)
	64	{
	65	bessel_j1_initializer<T>::force_instantiate();
	66
	67	static const T P1[] = {
	68	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.4258509801366645672e+11)),
	69	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 6.6781041261492395835e+09)),
	70	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.1548696764841276794e+08)),
	71	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 9.8062904098958257677e+05)),
	72	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -4.4615792982775076130e+03)),
	73	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0650724020080236441e+01)),
	74	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.0767857011487300348e-02))
	75	};
	76	static const T Q1[] = {
	77	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 4.1868604460820175290e+12)),
	78	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 4.2091902282580133541e+10)),
	79	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.0228375140097033958e+08)),
	80	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 5.9117614494174794095e+05)),
	81	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0742272239517380498e+03)),
	82	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0)),
	83	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 0.0))
	84	};
	85	static const T P2[] = {
	86	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.7527881995806511112e+16)),
	87	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.6608531731299018674e+15)),
	88	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -3.6658018905416665164e+13)),
	89	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.5580665670910619166e+11)),
	90	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.8113931269860667829e+09)),
	91	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 5.0793266148011179143e+06)),
92	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -7.5023342220781607561e+03)),
93	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 4.6179191852758252278e+00))
94	};
95	static const T Q2[] = {
96	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.7253905888447681194e+18)),
97	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.7128800897135812012e+16)),
98	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 8.4899346165481429307e+13)),
99	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.7622777286244082666e+11)),
100	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 6.4872502899596389593e+08)),
101	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.1267125065029138050e+06)),
102	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.3886978985861357615e+03)),
103	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0))
104	};
105	static const T PC[] = {
106	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -4.4357578167941278571e+06)),
107	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -9.9422465050776411957e+06)),
108	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -6.6033732483649391093e+06)),
109	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.5235293511811373833e+06)),
110	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.0982405543459346727e+05)),
111	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.6116166443246101165e+03)),
112	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 0.0))
113	};
114	static const T QC[] = {
115	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -4.4357578167941278568e+06)),
116	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -9.9341243899345856590e+06)),
117	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -6.5853394797230870728e+06)),
118	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.5118095066341608816e+06)),
119	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.0726385991103820119e+05)),
120	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.4550094401904961825e+03)),
121	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0))
122	};
123	static const T PS[] = {
124	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.3220913409857223519e+04)),
125	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 8.5145160675335701966e+04)),
126	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 6.6178836581270835179e+04)),
127	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.8494262873223866797e+04)),
128	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.7063754290207680021e+03)),
129	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.5265133846636032186e+01)),
130	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 0.0))
131	};
132	static const T QS[] = {
133	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 7.0871281941028743574e+05)),
134	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.8194580422439972989e+06)),
135	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.4194606696037208929e+06)),
136	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 4.0029443582266975117e+05)),
137	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.7890229745772202641e+04)),
138	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 8.6383677696049909675e+02)),
139	static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0))
140	};
141	static const T x1 = static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.8317059702075123156e+00)),
142	x2 = static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 7.0155866698156187535e+00)),
143	x11 = static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 9.810e+02)),
144	x12 = static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -3.2527979248768438556e-04)),
145	x21 = static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.7960e+03)),
146	x22 = static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -3.8330184381246462950e-05));
147
148	T value, factor, r, rc, rs, w;
149
150	BOOST_MATH_STD_USING
151	using namespace boost::math::tools;
152	using namespace boost::math::constants;
153
154	w = abs(x);
155	if (x == 0)
156	{
157	return static_cast<T>(0);
158	}
159	if (w <= 4) // w in (0, 4]
160	{
161	T y = x * x;
162	BOOST_ASSERT(sizeof(P1) == sizeof(Q1));
163	r = evaluate_rational(P1, Q1, y);
164	factor = w * (w + x1) * ((w - x11/256) - x12);
165	value = factor * r;
166	}
167	else if (w <= 8) // w in (4, 8]
168	{
169	T y = x * x;
170	BOOST_ASSERT(sizeof(P2) == sizeof(Q2));
171	r = evaluate_rational(P2, Q2, y);
172	factor = w * (w + x2) * ((w - x21/256) - x22);
173	value = factor * r;
174	}
175	else // w in (8, \infty)
176	{
177	T y = 8 / w;
178	T y2 = y * y;
179	BOOST_ASSERT(sizeof(PC) == sizeof(QC));
180	BOOST_ASSERT(sizeof(PS) == sizeof(QS));
181	rc = evaluate_rational(PC, QC, y2);
182	rs = evaluate_rational(PS, QS, y2);
183	factor = 1 / (sqrt(w) * constants::root_pi<T>());
184	//
185	// What follows is really just:
186	//
187	// T z = w - 0.75f * pi<T>();
188	// value = factor * (rc * cos(z) - y * rs * sin(z));
189	//
190	// but using the sin/cos addition rules plus constants
191	// for the values of sin/cos of 3PI/4 which then cancel
192	// out with corresponding terms in "factor".
193	//
194	T sx = sin(x);
195	T cx = cos(x);
196	value = factor * (rc * (sx - cx) + y * rs * (sx + cx));
197	}
198
199	if (x < 0)
200	{
201	value *= -1; // odd function
202	}
203	return value;
204	}
205
206	}}} // namespaces
207
208	#endif // BOOST_MATH_BESSEL_J1_HPP
209