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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_J0_HPP | |
7 | #define BOOST_MATH_BESSEL_J0_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> | |
1e59de90 | 16 | #include <boost/math/tools/assert.hpp> |
7c673cae | 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__ | |
f67539c2 | 23 | // nor #pragma diagnostic ignored work :( |
92f5a8d4 TL |
24 | // |
25 | #pragma GCC system_header | |
26 | #endif | |
27 | ||
7c673cae FG |
28 | // Bessel function of the first kind of order zero |
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_j0(T x); | |
36 | ||
37 | template <class T> | |
38 | struct bessel_j0_initializer | |
39 | { | |
40 | struct init | |
41 | { | |
42 | init() | |
43 | { | |
44 | do_init(); | |
45 | } | |
46 | static void do_init() | |
47 | { | |
48 | bessel_j0(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_j0_initializer<T>::init bessel_j0_initializer<T>::initializer; | |
61 | ||
62 | template <typename T> | |
63 | T bessel_j0(T x) | |
64 | { | |
65 | bessel_j0_initializer<T>::force_instantiate(); | |
66 | ||
1e59de90 TL |
67 | #ifdef BOOST_MATH_INSTRUMENT |
68 | static bool b = false; | |
69 | if (!b) | |
70 | { | |
71 | std::cout << "bessel_j0 called with " << typeid(x).name() << std::endl; | |
72 | std::cout << "double = " << typeid(double).name() << std::endl; | |
73 | std::cout << "long double = " << typeid(long double).name() << std::endl; | |
74 | b = true; | |
75 | } | |
76 | #endif | |
77 | ||
7c673cae FG |
78 | static const T P1[] = { |
79 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -4.1298668500990866786e+11)), | |
80 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.7282507878605942706e+10)), | |
81 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -6.2140700423540120665e+08)), | |
82 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 6.6302997904833794242e+06)), | |
83 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -3.6629814655107086448e+04)), | |
84 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0344222815443188943e+02)), | |
85 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.2117036164593528341e-01)) | |
86 | }; | |
87 | static const T Q1[] = { | |
88 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.3883787996332290397e+12)), | |
89 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.6328198300859648632e+10)), | |
90 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.3985097372263433271e+08)), | |
91 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 4.5612696224219938200e+05)), | |
92 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 9.3614022392337710626e+02)), | |
93 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0)), | |
94 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 0.0)) | |
95 | }; | |
96 | static const T P2[] = { | |
97 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.8319397969392084011e+03)), | |
98 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.2254078161378989535e+04)), | |
99 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -7.2879702464464618998e+03)), | |
100 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0341910641583726701e+04)), | |
101 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.1725046279757103576e+04)), | |
102 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 4.4176707025325087628e+03)), | |
103 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 7.4321196680624245801e+02)), | |
104 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 4.8591703355916499363e+01)) | |
105 | }; | |
106 | static const T Q2[] = { | |
107 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -3.5783478026152301072e+05)), | |
108 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.4599102262586308984e+05)), | |
109 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -8.4055062591169562211e+04)), | |
110 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.8680990008359188352e+04)), | |
111 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.9458766545509337327e+03)), | |
112 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.3307310774649071172e+02)), | |
113 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.5258076240801555057e+01)), | |
114 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0)) | |
115 | }; | |
116 | static const T PC[] = { | |
117 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.2779090197304684302e+04)), | |
118 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 4.1345386639580765797e+04)), | |
119 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.1170523380864944322e+04)), | |
120 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.4806486443249270347e+03)), | |
121 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.5376201909008354296e+02)), | |
122 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 8.8961548424210455236e-01)) | |
123 | }; | |
124 | static const T QC[] = { | |
125 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.2779090197304684318e+04)), | |
126 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 4.1370412495510416640e+04)), | |
127 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.1215350561880115730e+04)), | |
128 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.5028735138235608207e+03)), | |
129 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.5711159858080893649e+02)), | |
130 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0)) | |
131 | }; | |
132 | static const T PS[] = { | |
133 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -8.9226600200800094098e+01)), | |
134 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.8591953644342993800e+02)), | |
135 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.1183429920482737611e+02)), | |
136 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.2300261666214198472e+01)), | |
137 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.2441026745835638459e+00)), | |
138 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -8.8033303048680751817e-03)) | |
139 | }; | |
140 | static const T QS[] = { | |
141 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 5.7105024128512061905e+03)), | |
142 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.1951131543434613647e+04)), | |
143 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 7.2642780169211018836e+03)), | |
144 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.4887231232283756582e+03)), | |
145 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 9.0593769594993125859e+01)), | |
146 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0)) | |
147 | }; | |
148 | static const T x1 = static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.4048255576957727686e+00)), | |
149 | x2 = static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 5.5200781102863106496e+00)), | |
150 | x11 = static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 6.160e+02)), | |
151 | x12 = static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.42444230422723137837e-03)), | |
152 | x21 = static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.4130e+03)), | |
153 | x22 = static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 5.46860286310649596604e-04)); | |
154 | ||
155 | T value, factor, r, rc, rs; | |
156 | ||
157 | BOOST_MATH_STD_USING | |
158 | using namespace boost::math::tools; | |
159 | using namespace boost::math::constants; | |
160 | ||
161 | if (x < 0) | |
162 | { | |
163 | x = -x; // even function | |
164 | } | |
165 | if (x == 0) | |
166 | { | |
167 | return static_cast<T>(1); | |
168 | } | |
169 | if (x <= 4) // x in (0, 4] | |
170 | { | |
171 | T y = x * x; | |
1e59de90 | 172 | BOOST_MATH_ASSERT(sizeof(P1) == sizeof(Q1)); |
7c673cae FG |
173 | r = evaluate_rational(P1, Q1, y); |
174 | factor = (x + x1) * ((x - x11/256) - x12); | |
175 | value = factor * r; | |
176 | } | |
177 | else if (x <= 8.0) // x in (4, 8] | |
178 | { | |
179 | T y = 1 - (x * x)/64; | |
1e59de90 | 180 | BOOST_MATH_ASSERT(sizeof(P2) == sizeof(Q2)); |
7c673cae FG |
181 | r = evaluate_rational(P2, Q2, y); |
182 | factor = (x + x2) * ((x - x21/256) - x22); | |
183 | value = factor * r; | |
184 | } | |
185 | else // x in (8, \infty) | |
186 | { | |
187 | T y = 8 / x; | |
188 | T y2 = y * y; | |
1e59de90 TL |
189 | BOOST_MATH_ASSERT(sizeof(PC) == sizeof(QC)); |
190 | BOOST_MATH_ASSERT(sizeof(PS) == sizeof(QS)); | |
7c673cae FG |
191 | rc = evaluate_rational(PC, QC, y2); |
192 | rs = evaluate_rational(PS, QS, y2); | |
193 | factor = constants::one_div_root_pi<T>() / sqrt(x); | |
194 | // | |
195 | // What follows is really just: | |
196 | // | |
197 | // T z = x - pi/4; | |
198 | // value = factor * (rc * cos(z) - y * rs * sin(z)); | |
199 | // | |
200 | // But using the addition formulae for sin and cos, plus | |
201 | // the special values for sin/cos of pi/4. | |
202 | // | |
203 | T sx = sin(x); | |
204 | T cx = cos(x); | |
1e59de90 TL |
205 | BOOST_MATH_INSTRUMENT_VARIABLE(rc); |
206 | BOOST_MATH_INSTRUMENT_VARIABLE(rs); | |
207 | BOOST_MATH_INSTRUMENT_VARIABLE(factor); | |
208 | BOOST_MATH_INSTRUMENT_VARIABLE(sx); | |
209 | BOOST_MATH_INSTRUMENT_VARIABLE(cx); | |
7c673cae FG |
210 | value = factor * (rc * (cx + sx) - y * rs * (sx - cx)); |
211 | } | |
212 | ||
213 | return value; | |
214 | } | |
215 | ||
216 | }}} // namespaces | |
217 | ||
218 | #endif // BOOST_MATH_BESSEL_J0_HPP | |
219 |