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1 | // math_fwd.hpp |
2 | ||
3 | // TODO revise completely for new distribution classes. | |
4 | ||
5 | // Copyright Paul A. Bristow 2006. | |
6 | // Copyright John Maddock 2006. | |
7 | ||
8 | // Use, modification and distribution are subject to the | |
9 | // Boost Software License, Version 1.0. | |
10 | // (See accompanying file LICENSE_1_0.txt | |
11 | // or copy at http://www.boost.org/LICENSE_1_0.txt) | |
12 | ||
13 | // Omnibus list of forward declarations of math special functions. | |
14 | ||
15 | // IT = Integer type. | |
16 | // RT = Real type (built-in floating-point types, float, double, long double) & User Defined Types | |
17 | // AT = Integer or Real type | |
18 | ||
19 | #ifndef BOOST_MATH_SPECIAL_MATH_FWD_HPP | |
20 | #define BOOST_MATH_SPECIAL_MATH_FWD_HPP | |
21 | ||
22 | #ifdef _MSC_VER | |
23 | #pragma once | |
24 | #endif | |
25 | ||
26 | #include <boost/math/special_functions/detail/round_fwd.hpp> | |
27 | #include <boost/math/tools/promotion.hpp> // for argument promotion. | |
28 | #include <boost/math/policies/policy.hpp> | |
29 | #include <boost/mpl/comparison.hpp> | |
30 | #include <boost/utility/enable_if.hpp> | |
31 | #include <boost/config/no_tr1/complex.hpp> | |
32 | ||
33 | #define BOOST_NO_MACRO_EXPAND /**/ | |
34 | ||
35 | namespace boost | |
36 | { | |
37 | namespace math | |
38 | { // Math functions (in roughly alphabetic order). | |
39 | ||
40 | // Beta functions. | |
41 | template <class RT1, class RT2> | |
42 | typename tools::promote_args<RT1, RT2>::type | |
43 | beta(RT1 a, RT2 b); // Beta function (2 arguments). | |
44 | ||
45 | template <class RT1, class RT2, class A> | |
46 | typename tools::promote_args<RT1, RT2, A>::type | |
47 | beta(RT1 a, RT2 b, A x); // Beta function (3 arguments). | |
48 | ||
49 | template <class RT1, class RT2, class RT3, class Policy> | |
50 | typename tools::promote_args<RT1, RT2, RT3>::type | |
51 | beta(RT1 a, RT2 b, RT3 x, const Policy& pol); // Beta function (3 arguments). | |
52 | ||
53 | template <class RT1, class RT2, class RT3> | |
54 | typename tools::promote_args<RT1, RT2, RT3>::type | |
55 | betac(RT1 a, RT2 b, RT3 x); | |
56 | ||
57 | template <class RT1, class RT2, class RT3, class Policy> | |
58 | typename tools::promote_args<RT1, RT2, RT3>::type | |
59 | betac(RT1 a, RT2 b, RT3 x, const Policy& pol); | |
60 | ||
61 | template <class RT1, class RT2, class RT3> | |
62 | typename tools::promote_args<RT1, RT2, RT3>::type | |
63 | ibeta(RT1 a, RT2 b, RT3 x); // Incomplete beta function. | |
64 | ||
65 | template <class RT1, class RT2, class RT3, class Policy> | |
66 | typename tools::promote_args<RT1, RT2, RT3>::type | |
67 | ibeta(RT1 a, RT2 b, RT3 x, const Policy& pol); // Incomplete beta function. | |
68 | ||
69 | template <class RT1, class RT2, class RT3> | |
70 | typename tools::promote_args<RT1, RT2, RT3>::type | |
71 | ibetac(RT1 a, RT2 b, RT3 x); // Incomplete beta complement function. | |
72 | ||
73 | template <class RT1, class RT2, class RT3, class Policy> | |
74 | typename tools::promote_args<RT1, RT2, RT3>::type | |
75 | ibetac(RT1 a, RT2 b, RT3 x, const Policy& pol); // Incomplete beta complement function. | |
76 | ||
77 | template <class T1, class T2, class T3, class T4> | |
78 | typename tools::promote_args<T1, T2, T3, T4>::type | |
79 | ibeta_inv(T1 a, T2 b, T3 p, T4* py); | |
80 | ||
81 | template <class T1, class T2, class T3, class T4, class Policy> | |
82 | typename tools::promote_args<T1, T2, T3, T4>::type | |
83 | ibeta_inv(T1 a, T2 b, T3 p, T4* py, const Policy& pol); | |
84 | ||
85 | template <class RT1, class RT2, class RT3> | |
86 | typename tools::promote_args<RT1, RT2, RT3>::type | |
87 | ibeta_inv(RT1 a, RT2 b, RT3 p); // Incomplete beta inverse function. | |
88 | ||
89 | template <class RT1, class RT2, class RT3, class Policy> | |
90 | typename tools::promote_args<RT1, RT2, RT3>::type | |
91 | ibeta_inv(RT1 a, RT2 b, RT3 p, const Policy&); // Incomplete beta inverse function. | |
92 | ||
93 | template <class RT1, class RT2, class RT3> | |
94 | typename tools::promote_args<RT1, RT2, RT3>::type | |
95 | ibeta_inva(RT1 a, RT2 b, RT3 p); // Incomplete beta inverse function. | |
96 | ||
97 | template <class RT1, class RT2, class RT3, class Policy> | |
98 | typename tools::promote_args<RT1, RT2, RT3>::type | |
99 | ibeta_inva(RT1 a, RT2 b, RT3 p, const Policy&); // Incomplete beta inverse function. | |
100 | ||
101 | template <class RT1, class RT2, class RT3> | |
102 | typename tools::promote_args<RT1, RT2, RT3>::type | |
103 | ibeta_invb(RT1 a, RT2 b, RT3 p); // Incomplete beta inverse function. | |
104 | ||
105 | template <class RT1, class RT2, class RT3, class Policy> | |
106 | typename tools::promote_args<RT1, RT2, RT3>::type | |
107 | ibeta_invb(RT1 a, RT2 b, RT3 p, const Policy&); // Incomplete beta inverse function. | |
108 | ||
109 | template <class T1, class T2, class T3, class T4> | |
110 | typename tools::promote_args<T1, T2, T3, T4>::type | |
111 | ibetac_inv(T1 a, T2 b, T3 q, T4* py); | |
112 | ||
113 | template <class T1, class T2, class T3, class T4, class Policy> | |
114 | typename tools::promote_args<T1, T2, T3, T4>::type | |
115 | ibetac_inv(T1 a, T2 b, T3 q, T4* py, const Policy& pol); | |
116 | ||
117 | template <class RT1, class RT2, class RT3> | |
118 | typename tools::promote_args<RT1, RT2, RT3>::type | |
119 | ibetac_inv(RT1 a, RT2 b, RT3 q); // Incomplete beta complement inverse function. | |
120 | ||
121 | template <class RT1, class RT2, class RT3, class Policy> | |
122 | typename tools::promote_args<RT1, RT2, RT3>::type | |
123 | ibetac_inv(RT1 a, RT2 b, RT3 q, const Policy&); // Incomplete beta complement inverse function. | |
124 | ||
125 | template <class RT1, class RT2, class RT3> | |
126 | typename tools::promote_args<RT1, RT2, RT3>::type | |
127 | ibetac_inva(RT1 a, RT2 b, RT3 q); // Incomplete beta complement inverse function. | |
128 | ||
129 | template <class RT1, class RT2, class RT3, class Policy> | |
130 | typename tools::promote_args<RT1, RT2, RT3>::type | |
131 | ibetac_inva(RT1 a, RT2 b, RT3 q, const Policy&); // Incomplete beta complement inverse function. | |
132 | ||
133 | template <class RT1, class RT2, class RT3> | |
134 | typename tools::promote_args<RT1, RT2, RT3>::type | |
135 | ibetac_invb(RT1 a, RT2 b, RT3 q); // Incomplete beta complement inverse function. | |
136 | ||
137 | template <class RT1, class RT2, class RT3, class Policy> | |
138 | typename tools::promote_args<RT1, RT2, RT3>::type | |
139 | ibetac_invb(RT1 a, RT2 b, RT3 q, const Policy&); // Incomplete beta complement inverse function. | |
140 | ||
141 | template <class RT1, class RT2, class RT3> | |
142 | typename tools::promote_args<RT1, RT2, RT3>::type | |
143 | ibeta_derivative(RT1 a, RT2 b, RT3 x); // derivative of incomplete beta | |
144 | ||
145 | template <class RT1, class RT2, class RT3, class Policy> | |
146 | typename tools::promote_args<RT1, RT2, RT3>::type | |
147 | ibeta_derivative(RT1 a, RT2 b, RT3 x, const Policy& pol); // derivative of incomplete beta | |
148 | ||
149 | // Binomial: | |
150 | template <class T, class Policy> | |
151 | T binomial_coefficient(unsigned n, unsigned k, const Policy& pol); | |
152 | template <class T> | |
153 | T binomial_coefficient(unsigned n, unsigned k); | |
154 | ||
155 | // erf & erfc error functions. | |
156 | template <class RT> // Error function. | |
157 | typename tools::promote_args<RT>::type erf(RT z); | |
158 | template <class RT, class Policy> // Error function. | |
159 | typename tools::promote_args<RT>::type erf(RT z, const Policy&); | |
160 | ||
161 | template <class RT>// Error function complement. | |
162 | typename tools::promote_args<RT>::type erfc(RT z); | |
163 | template <class RT, class Policy>// Error function complement. | |
164 | typename tools::promote_args<RT>::type erfc(RT z, const Policy&); | |
165 | ||
166 | template <class RT>// Error function inverse. | |
167 | typename tools::promote_args<RT>::type erf_inv(RT z); | |
168 | template <class RT, class Policy>// Error function inverse. | |
169 | typename tools::promote_args<RT>::type erf_inv(RT z, const Policy& pol); | |
170 | ||
171 | template <class RT>// Error function complement inverse. | |
172 | typename tools::promote_args<RT>::type erfc_inv(RT z); | |
173 | template <class RT, class Policy>// Error function complement inverse. | |
174 | typename tools::promote_args<RT>::type erfc_inv(RT z, const Policy& pol); | |
175 | ||
176 | // Polynomials: | |
177 | template <class T1, class T2, class T3> | |
178 | typename tools::promote_args<T1, T2, T3>::type | |
179 | legendre_next(unsigned l, T1 x, T2 Pl, T3 Plm1); | |
180 | ||
181 | template <class T> | |
182 | typename tools::promote_args<T>::type | |
183 | legendre_p(int l, T x); | |
184 | #if !BOOST_WORKAROUND(BOOST_MSVC, <= 1310) | |
185 | template <class T, class Policy> | |
186 | typename boost::enable_if_c<policies::is_policy<Policy>::value, typename tools::promote_args<T>::type>::type | |
187 | legendre_p(int l, T x, const Policy& pol); | |
188 | #endif | |
189 | template <class T> | |
190 | typename tools::promote_args<T>::type | |
191 | legendre_q(unsigned l, T x); | |
192 | #if !BOOST_WORKAROUND(BOOST_MSVC, <= 1310) | |
193 | template <class T, class Policy> | |
194 | typename boost::enable_if_c<policies::is_policy<Policy>::value, typename tools::promote_args<T>::type>::type | |
195 | legendre_q(unsigned l, T x, const Policy& pol); | |
196 | #endif | |
197 | template <class T1, class T2, class T3> | |
198 | typename tools::promote_args<T1, T2, T3>::type | |
199 | legendre_next(unsigned l, unsigned m, T1 x, T2 Pl, T3 Plm1); | |
200 | ||
201 | template <class T> | |
202 | typename tools::promote_args<T>::type | |
203 | legendre_p(int l, int m, T x); | |
204 | ||
205 | template <class T, class Policy> | |
206 | typename tools::promote_args<T>::type | |
207 | legendre_p(int l, int m, T x, const Policy& pol); | |
208 | ||
209 | template <class T1, class T2, class T3> | |
210 | typename tools::promote_args<T1, T2, T3>::type | |
211 | laguerre_next(unsigned n, T1 x, T2 Ln, T3 Lnm1); | |
212 | ||
213 | template <class T1, class T2, class T3> | |
214 | typename tools::promote_args<T1, T2, T3>::type | |
215 | laguerre_next(unsigned n, unsigned l, T1 x, T2 Pl, T3 Plm1); | |
216 | ||
217 | template <class T> | |
218 | typename tools::promote_args<T>::type | |
219 | laguerre(unsigned n, T x); | |
220 | ||
221 | template <class T, class Policy> | |
222 | typename tools::promote_args<T>::type | |
223 | laguerre(unsigned n, unsigned m, T x, const Policy& pol); | |
224 | ||
225 | template <class T1, class T2> | |
226 | struct laguerre_result | |
227 | { | |
228 | typedef typename mpl::if_< | |
229 | policies::is_policy<T2>, | |
230 | typename tools::promote_args<T1>::type, | |
231 | typename tools::promote_args<T2>::type | |
232 | >::type type; | |
233 | }; | |
234 | ||
235 | template <class T1, class T2> | |
236 | typename laguerre_result<T1, T2>::type | |
237 | laguerre(unsigned n, T1 m, T2 x); | |
238 | ||
239 | template <class T> | |
240 | typename tools::promote_args<T>::type | |
241 | hermite(unsigned n, T x); | |
242 | ||
243 | template <class T, class Policy> | |
244 | typename tools::promote_args<T>::type | |
245 | hermite(unsigned n, T x, const Policy& pol); | |
246 | ||
247 | template <class T1, class T2, class T3> | |
248 | typename tools::promote_args<T1, T2, T3>::type | |
249 | hermite_next(unsigned n, T1 x, T2 Hn, T3 Hnm1); | |
250 | ||
251 | template <class T1, class T2> | |
252 | std::complex<typename tools::promote_args<T1, T2>::type> | |
253 | spherical_harmonic(unsigned n, int m, T1 theta, T2 phi); | |
254 | ||
255 | template <class T1, class T2, class Policy> | |
256 | std::complex<typename tools::promote_args<T1, T2>::type> | |
257 | spherical_harmonic(unsigned n, int m, T1 theta, T2 phi, const Policy& pol); | |
258 | ||
259 | template <class T1, class T2> | |
260 | typename tools::promote_args<T1, T2>::type | |
261 | spherical_harmonic_r(unsigned n, int m, T1 theta, T2 phi); | |
262 | ||
263 | template <class T1, class T2, class Policy> | |
264 | typename tools::promote_args<T1, T2>::type | |
265 | spherical_harmonic_r(unsigned n, int m, T1 theta, T2 phi, const Policy& pol); | |
266 | ||
267 | template <class T1, class T2> | |
268 | typename tools::promote_args<T1, T2>::type | |
269 | spherical_harmonic_i(unsigned n, int m, T1 theta, T2 phi); | |
270 | ||
271 | template <class T1, class T2, class Policy> | |
272 | typename tools::promote_args<T1, T2>::type | |
273 | spherical_harmonic_i(unsigned n, int m, T1 theta, T2 phi, const Policy& pol); | |
274 | ||
275 | // Elliptic integrals: | |
276 | template <class T1, class T2, class T3> | |
277 | typename tools::promote_args<T1, T2, T3>::type | |
278 | ellint_rf(T1 x, T2 y, T3 z); | |
279 | ||
280 | template <class T1, class T2, class T3, class Policy> | |
281 | typename tools::promote_args<T1, T2, T3>::type | |
282 | ellint_rf(T1 x, T2 y, T3 z, const Policy& pol); | |
283 | ||
284 | template <class T1, class T2, class T3> | |
285 | typename tools::promote_args<T1, T2, T3>::type | |
286 | ellint_rd(T1 x, T2 y, T3 z); | |
287 | ||
288 | template <class T1, class T2, class T3, class Policy> | |
289 | typename tools::promote_args<T1, T2, T3>::type | |
290 | ellint_rd(T1 x, T2 y, T3 z, const Policy& pol); | |
291 | ||
292 | template <class T1, class T2> | |
293 | typename tools::promote_args<T1, T2>::type | |
294 | ellint_rc(T1 x, T2 y); | |
295 | ||
296 | template <class T1, class T2, class Policy> | |
297 | typename tools::promote_args<T1, T2>::type | |
298 | ellint_rc(T1 x, T2 y, const Policy& pol); | |
299 | ||
300 | template <class T1, class T2, class T3, class T4> | |
301 | typename tools::promote_args<T1, T2, T3, T4>::type | |
302 | ellint_rj(T1 x, T2 y, T3 z, T4 p); | |
303 | ||
304 | template <class T1, class T2, class T3, class T4, class Policy> | |
305 | typename tools::promote_args<T1, T2, T3, T4>::type | |
306 | ellint_rj(T1 x, T2 y, T3 z, T4 p, const Policy& pol); | |
307 | ||
308 | template <class T1, class T2, class T3> | |
309 | typename tools::promote_args<T1, T2, T3>::type | |
310 | ellint_rg(T1 x, T2 y, T3 z); | |
311 | ||
312 | template <class T1, class T2, class T3, class Policy> | |
313 | typename tools::promote_args<T1, T2, T3>::type | |
314 | ellint_rg(T1 x, T2 y, T3 z, const Policy& pol); | |
315 | ||
316 | template <typename T> | |
317 | typename tools::promote_args<T>::type ellint_2(T k); | |
318 | ||
319 | template <class T1, class T2> | |
320 | typename tools::promote_args<T1, T2>::type ellint_2(T1 k, T2 phi); | |
321 | ||
322 | template <class T1, class T2, class Policy> | |
323 | typename tools::promote_args<T1, T2>::type ellint_2(T1 k, T2 phi, const Policy& pol); | |
324 | ||
325 | template <typename T> | |
326 | typename tools::promote_args<T>::type ellint_1(T k); | |
327 | ||
328 | template <class T1, class T2> | |
329 | typename tools::promote_args<T1, T2>::type ellint_1(T1 k, T2 phi); | |
330 | ||
331 | template <class T1, class T2, class Policy> | |
332 | typename tools::promote_args<T1, T2>::type ellint_1(T1 k, T2 phi, const Policy& pol); | |
333 | ||
334 | template <typename T> | |
335 | typename tools::promote_args<T>::type ellint_d(T k); | |
336 | ||
337 | template <class T1, class T2> | |
338 | typename tools::promote_args<T1, T2>::type ellint_d(T1 k, T2 phi); | |
339 | ||
340 | template <class T1, class T2, class Policy> | |
341 | typename tools::promote_args<T1, T2>::type ellint_d(T1 k, T2 phi, const Policy& pol); | |
342 | ||
343 | template <class T1, class T2> | |
344 | typename tools::promote_args<T1, T2>::type jacobi_zeta(T1 k, T2 phi); | |
345 | ||
346 | template <class T1, class T2, class Policy> | |
347 | typename tools::promote_args<T1, T2>::type jacobi_zeta(T1 k, T2 phi, const Policy& pol); | |
348 | ||
349 | template <class T1, class T2> | |
350 | typename tools::promote_args<T1, T2>::type heuman_lambda(T1 k, T2 phi); | |
351 | ||
352 | template <class T1, class T2, class Policy> | |
353 | typename tools::promote_args<T1, T2>::type heuman_lambda(T1 k, T2 phi, const Policy& pol); | |
354 | ||
355 | namespace detail{ | |
356 | ||
357 | template <class T, class U, class V> | |
358 | struct ellint_3_result | |
359 | { | |
360 | typedef typename mpl::if_< | |
361 | policies::is_policy<V>, | |
362 | typename tools::promote_args<T, U>::type, | |
363 | typename tools::promote_args<T, U, V>::type | |
364 | >::type type; | |
365 | }; | |
366 | ||
367 | } // namespace detail | |
368 | ||
369 | ||
370 | template <class T1, class T2, class T3> | |
371 | typename detail::ellint_3_result<T1, T2, T3>::type ellint_3(T1 k, T2 v, T3 phi); | |
372 | ||
373 | template <class T1, class T2, class T3, class Policy> | |
374 | typename tools::promote_args<T1, T2, T3>::type ellint_3(T1 k, T2 v, T3 phi, const Policy& pol); | |
375 | ||
376 | template <class T1, class T2> | |
377 | typename tools::promote_args<T1, T2>::type ellint_3(T1 k, T2 v); | |
378 | ||
379 | // Factorial functions. | |
380 | // Note: not for integral types, at present. | |
381 | template <class RT> | |
382 | struct max_factorial; | |
383 | template <class RT> | |
384 | RT factorial(unsigned int); | |
385 | template <class RT, class Policy> | |
386 | RT factorial(unsigned int, const Policy& pol); | |
387 | template <class RT> | |
388 | RT unchecked_factorial(unsigned int BOOST_MATH_APPEND_EXPLICIT_TEMPLATE_TYPE(RT)); | |
389 | template <class RT> | |
390 | RT double_factorial(unsigned i); | |
391 | template <class RT, class Policy> | |
392 | RT double_factorial(unsigned i, const Policy& pol); | |
393 | ||
394 | template <class RT> | |
395 | typename tools::promote_args<RT>::type falling_factorial(RT x, unsigned n); | |
396 | ||
397 | template <class RT, class Policy> | |
398 | typename tools::promote_args<RT>::type falling_factorial(RT x, unsigned n, const Policy& pol); | |
399 | ||
400 | template <class RT> | |
401 | typename tools::promote_args<RT>::type rising_factorial(RT x, int n); | |
402 | ||
403 | template <class RT, class Policy> | |
404 | typename tools::promote_args<RT>::type rising_factorial(RT x, int n, const Policy& pol); | |
405 | ||
406 | // Gamma functions. | |
407 | template <class RT> | |
408 | typename tools::promote_args<RT>::type tgamma(RT z); | |
409 | ||
410 | template <class RT> | |
411 | typename tools::promote_args<RT>::type tgamma1pm1(RT z); | |
412 | ||
413 | template <class RT, class Policy> | |
414 | typename tools::promote_args<RT>::type tgamma1pm1(RT z, const Policy& pol); | |
415 | ||
416 | template <class RT1, class RT2> | |
417 | typename tools::promote_args<RT1, RT2>::type tgamma(RT1 a, RT2 z); | |
418 | ||
419 | template <class RT1, class RT2, class Policy> | |
420 | typename tools::promote_args<RT1, RT2>::type tgamma(RT1 a, RT2 z, const Policy& pol); | |
421 | ||
422 | template <class RT> | |
423 | typename tools::promote_args<RT>::type lgamma(RT z, int* sign); | |
424 | ||
425 | template <class RT, class Policy> | |
426 | typename tools::promote_args<RT>::type lgamma(RT z, int* sign, const Policy& pol); | |
427 | ||
428 | template <class RT> | |
429 | typename tools::promote_args<RT>::type lgamma(RT x); | |
430 | ||
431 | template <class RT, class Policy> | |
432 | typename tools::promote_args<RT>::type lgamma(RT x, const Policy& pol); | |
433 | ||
434 | template <class RT1, class RT2> | |
435 | typename tools::promote_args<RT1, RT2>::type tgamma_lower(RT1 a, RT2 z); | |
436 | ||
437 | template <class RT1, class RT2, class Policy> | |
438 | typename tools::promote_args<RT1, RT2>::type tgamma_lower(RT1 a, RT2 z, const Policy&); | |
439 | ||
440 | template <class RT1, class RT2> | |
441 | typename tools::promote_args<RT1, RT2>::type gamma_q(RT1 a, RT2 z); | |
442 | ||
443 | template <class RT1, class RT2, class Policy> | |
444 | typename tools::promote_args<RT1, RT2>::type gamma_q(RT1 a, RT2 z, const Policy&); | |
445 | ||
446 | template <class RT1, class RT2> | |
447 | typename tools::promote_args<RT1, RT2>::type gamma_p(RT1 a, RT2 z); | |
448 | ||
449 | template <class RT1, class RT2, class Policy> | |
450 | typename tools::promote_args<RT1, RT2>::type gamma_p(RT1 a, RT2 z, const Policy&); | |
451 | ||
452 | template <class T1, class T2> | |
453 | typename tools::promote_args<T1, T2>::type tgamma_delta_ratio(T1 z, T2 delta); | |
454 | ||
455 | template <class T1, class T2, class Policy> | |
456 | typename tools::promote_args<T1, T2>::type tgamma_delta_ratio(T1 z, T2 delta, const Policy&); | |
457 | ||
458 | template <class T1, class T2> | |
459 | typename tools::promote_args<T1, T2>::type tgamma_ratio(T1 a, T2 b); | |
460 | ||
461 | template <class T1, class T2, class Policy> | |
462 | typename tools::promote_args<T1, T2>::type tgamma_ratio(T1 a, T2 b, const Policy&); | |
463 | ||
464 | template <class T1, class T2> | |
465 | typename tools::promote_args<T1, T2>::type gamma_p_derivative(T1 a, T2 x); | |
466 | ||
467 | template <class T1, class T2, class Policy> | |
468 | typename tools::promote_args<T1, T2>::type gamma_p_derivative(T1 a, T2 x, const Policy&); | |
469 | ||
470 | // gamma inverse. | |
471 | template <class T1, class T2> | |
472 | typename tools::promote_args<T1, T2>::type gamma_p_inv(T1 a, T2 p); | |
473 | ||
474 | template <class T1, class T2, class Policy> | |
475 | typename tools::promote_args<T1, T2>::type gamma_p_inva(T1 a, T2 p, const Policy&); | |
476 | ||
477 | template <class T1, class T2> | |
478 | typename tools::promote_args<T1, T2>::type gamma_p_inva(T1 a, T2 p); | |
479 | ||
480 | template <class T1, class T2, class Policy> | |
481 | typename tools::promote_args<T1, T2>::type gamma_p_inv(T1 a, T2 p, const Policy&); | |
482 | ||
483 | template <class T1, class T2> | |
484 | typename tools::promote_args<T1, T2>::type gamma_q_inv(T1 a, T2 q); | |
485 | ||
486 | template <class T1, class T2, class Policy> | |
487 | typename tools::promote_args<T1, T2>::type gamma_q_inv(T1 a, T2 q, const Policy&); | |
488 | ||
489 | template <class T1, class T2> | |
490 | typename tools::promote_args<T1, T2>::type gamma_q_inva(T1 a, T2 q); | |
491 | ||
492 | template <class T1, class T2, class Policy> | |
493 | typename tools::promote_args<T1, T2>::type gamma_q_inva(T1 a, T2 q, const Policy&); | |
494 | ||
495 | // digamma: | |
496 | template <class T> | |
497 | typename tools::promote_args<T>::type digamma(T x); | |
498 | ||
499 | template <class T, class Policy> | |
500 | typename tools::promote_args<T>::type digamma(T x, const Policy&); | |
501 | ||
502 | // trigamma: | |
503 | template <class T> | |
504 | typename tools::promote_args<T>::type trigamma(T x); | |
505 | ||
506 | template <class T, class Policy> | |
507 | typename tools::promote_args<T>::type trigamma(T x, const Policy&); | |
508 | ||
509 | // polygamma: | |
510 | template <class T> | |
511 | typename tools::promote_args<T>::type polygamma(int n, T x); | |
512 | ||
513 | template <class T, class Policy> | |
514 | typename tools::promote_args<T>::type polygamma(int n, T x, const Policy&); | |
515 | ||
516 | // Hypotenuse function sqrt(x ^ 2 + y ^ 2). | |
517 | template <class T1, class T2> | |
518 | typename tools::promote_args<T1, T2>::type | |
519 | hypot(T1 x, T2 y); | |
520 | ||
521 | template <class T1, class T2, class Policy> | |
522 | typename tools::promote_args<T1, T2>::type | |
523 | hypot(T1 x, T2 y, const Policy&); | |
524 | ||
525 | // cbrt - cube root. | |
526 | template <class RT> | |
527 | typename tools::promote_args<RT>::type cbrt(RT z); | |
528 | ||
529 | template <class RT, class Policy> | |
530 | typename tools::promote_args<RT>::type cbrt(RT z, const Policy&); | |
531 | ||
532 | // log1p is log(x + 1) | |
533 | template <class T> | |
534 | typename tools::promote_args<T>::type log1p(T); | |
535 | ||
536 | template <class T, class Policy> | |
537 | typename tools::promote_args<T>::type log1p(T, const Policy&); | |
538 | ||
539 | // log1pmx is log(x + 1) - x | |
540 | template <class T> | |
541 | typename tools::promote_args<T>::type log1pmx(T); | |
542 | ||
543 | template <class T, class Policy> | |
544 | typename tools::promote_args<T>::type log1pmx(T, const Policy&); | |
545 | ||
546 | // Exp (x) minus 1 functions. | |
547 | template <class T> | |
548 | typename tools::promote_args<T>::type expm1(T); | |
549 | ||
550 | template <class T, class Policy> | |
551 | typename tools::promote_args<T>::type expm1(T, const Policy&); | |
552 | ||
553 | // Power - 1 | |
554 | template <class T1, class T2> | |
555 | typename tools::promote_args<T1, T2>::type | |
556 | powm1(const T1 a, const T2 z); | |
557 | ||
558 | template <class T1, class T2, class Policy> | |
559 | typename tools::promote_args<T1, T2>::type | |
560 | powm1(const T1 a, const T2 z, const Policy&); | |
561 | ||
562 | // sqrt(1+x) - 1 | |
563 | template <class T> | |
564 | typename tools::promote_args<T>::type sqrt1pm1(const T& val); | |
565 | ||
566 | template <class T, class Policy> | |
567 | typename tools::promote_args<T>::type sqrt1pm1(const T& val, const Policy&); | |
568 | ||
569 | // sinus cardinals: | |
570 | template <class T> | |
571 | typename tools::promote_args<T>::type sinc_pi(T x); | |
572 | ||
573 | template <class T, class Policy> | |
574 | typename tools::promote_args<T>::type sinc_pi(T x, const Policy&); | |
575 | ||
576 | template <class T> | |
577 | typename tools::promote_args<T>::type sinhc_pi(T x); | |
578 | ||
579 | template <class T, class Policy> | |
580 | typename tools::promote_args<T>::type sinhc_pi(T x, const Policy&); | |
581 | ||
582 | // inverse hyperbolics: | |
583 | template<typename T> | |
584 | typename tools::promote_args<T>::type asinh(T x); | |
585 | ||
586 | template<typename T, class Policy> | |
587 | typename tools::promote_args<T>::type asinh(T x, const Policy&); | |
588 | ||
589 | template<typename T> | |
590 | typename tools::promote_args<T>::type acosh(T x); | |
591 | ||
592 | template<typename T, class Policy> | |
593 | typename tools::promote_args<T>::type acosh(T x, const Policy&); | |
594 | ||
595 | template<typename T> | |
596 | typename tools::promote_args<T>::type atanh(T x); | |
597 | ||
598 | template<typename T, class Policy> | |
599 | typename tools::promote_args<T>::type atanh(T x, const Policy&); | |
600 | ||
601 | namespace detail{ | |
602 | ||
603 | typedef mpl::int_<0> bessel_no_int_tag; // No integer optimisation possible. | |
604 | typedef mpl::int_<1> bessel_maybe_int_tag; // Maybe integer optimisation. | |
605 | typedef mpl::int_<2> bessel_int_tag; // Definite integer optimistaion. | |
606 | ||
607 | template <class T1, class T2, class Policy> | |
608 | struct bessel_traits | |
609 | { | |
610 | typedef typename mpl::if_< | |
611 | is_integral<T1>, | |
612 | typename tools::promote_args<T2>::type, | |
613 | typename tools::promote_args<T1, T2>::type | |
614 | >::type result_type; | |
615 | ||
616 | typedef typename policies::precision<result_type, Policy>::type precision_type; | |
617 | ||
618 | typedef typename mpl::if_< | |
619 | mpl::or_< | |
620 | mpl::less_equal<precision_type, mpl::int_<0> >, | |
621 | mpl::greater<precision_type, mpl::int_<64> > >, | |
622 | bessel_no_int_tag, | |
623 | typename mpl::if_< | |
624 | is_integral<T1>, | |
625 | bessel_int_tag, | |
626 | bessel_maybe_int_tag | |
627 | >::type | |
628 | >::type optimisation_tag; | |
629 | }; | |
630 | } // detail | |
631 | ||
632 | // Bessel functions: | |
633 | template <class T1, class T2, class Policy> | |
634 | typename detail::bessel_traits<T1, T2, Policy>::result_type cyl_bessel_j(T1 v, T2 x, const Policy& pol); | |
635 | template <class T1, class T2, class Policy> | |
636 | typename detail::bessel_traits<T1, T2, Policy>::result_type cyl_bessel_j_prime(T1 v, T2 x, const Policy& pol); | |
637 | ||
638 | template <class T1, class T2> | |
639 | typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type cyl_bessel_j(T1 v, T2 x); | |
640 | template <class T1, class T2> | |
641 | typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type cyl_bessel_j_prime(T1 v, T2 x); | |
642 | ||
643 | template <class T, class Policy> | |
644 | typename detail::bessel_traits<T, T, Policy>::result_type sph_bessel(unsigned v, T x, const Policy& pol); | |
645 | template <class T, class Policy> | |
646 | typename detail::bessel_traits<T, T, Policy>::result_type sph_bessel_prime(unsigned v, T x, const Policy& pol); | |
647 | ||
648 | template <class T> | |
649 | typename detail::bessel_traits<T, T, policies::policy<> >::result_type sph_bessel(unsigned v, T x); | |
650 | template <class T> | |
651 | typename detail::bessel_traits<T, T, policies::policy<> >::result_type sph_bessel_prime(unsigned v, T x); | |
652 | ||
653 | template <class T1, class T2, class Policy> | |
654 | typename detail::bessel_traits<T1, T2, Policy>::result_type cyl_bessel_i(T1 v, T2 x, const Policy& pol); | |
655 | template <class T1, class T2, class Policy> | |
656 | typename detail::bessel_traits<T1, T2, Policy>::result_type cyl_bessel_i_prime(T1 v, T2 x, const Policy& pol); | |
657 | ||
658 | template <class T1, class T2> | |
659 | typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type cyl_bessel_i(T1 v, T2 x); | |
660 | template <class T1, class T2> | |
661 | typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type cyl_bessel_i_prime(T1 v, T2 x); | |
662 | ||
663 | template <class T1, class T2, class Policy> | |
664 | typename detail::bessel_traits<T1, T2, Policy>::result_type cyl_bessel_k(T1 v, T2 x, const Policy& pol); | |
665 | template <class T1, class T2, class Policy> | |
666 | typename detail::bessel_traits<T1, T2, Policy>::result_type cyl_bessel_k_prime(T1 v, T2 x, const Policy& pol); | |
667 | ||
668 | template <class T1, class T2> | |
669 | typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type cyl_bessel_k(T1 v, T2 x); | |
670 | template <class T1, class T2> | |
671 | typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type cyl_bessel_k_prime(T1 v, T2 x); | |
672 | ||
673 | template <class T1, class T2, class Policy> | |
674 | typename detail::bessel_traits<T1, T2, Policy>::result_type cyl_neumann(T1 v, T2 x, const Policy& pol); | |
675 | template <class T1, class T2, class Policy> | |
676 | typename detail::bessel_traits<T1, T2, Policy>::result_type cyl_neumann_prime(T1 v, T2 x, const Policy& pol); | |
677 | ||
678 | template <class T1, class T2> | |
679 | typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type cyl_neumann(T1 v, T2 x); | |
680 | template <class T1, class T2> | |
681 | typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type cyl_neumann_prime(T1 v, T2 x); | |
682 | ||
683 | template <class T, class Policy> | |
684 | typename detail::bessel_traits<T, T, Policy>::result_type sph_neumann(unsigned v, T x, const Policy& pol); | |
685 | template <class T, class Policy> | |
686 | typename detail::bessel_traits<T, T, Policy>::result_type sph_neumann_prime(unsigned v, T x, const Policy& pol); | |
687 | ||
688 | template <class T> | |
689 | typename detail::bessel_traits<T, T, policies::policy<> >::result_type sph_neumann(unsigned v, T x); | |
690 | template <class T> | |
691 | typename detail::bessel_traits<T, T, policies::policy<> >::result_type sph_neumann_prime(unsigned v, T x); | |
692 | ||
693 | template <class T, class Policy> | |
694 | typename detail::bessel_traits<T, T, Policy>::result_type cyl_bessel_j_zero(T v, int m, const Policy& pol); | |
695 | ||
696 | template <class T> | |
697 | typename detail::bessel_traits<T, T, policies::policy<> >::result_type cyl_bessel_j_zero(T v, int m); | |
698 | ||
699 | template <class T, class OutputIterator> | |
700 | OutputIterator cyl_bessel_j_zero(T v, | |
701 | int start_index, | |
702 | unsigned number_of_zeros, | |
703 | OutputIterator out_it); | |
704 | ||
705 | template <class T, class OutputIterator, class Policy> | |
706 | OutputIterator cyl_bessel_j_zero(T v, | |
707 | int start_index, | |
708 | unsigned number_of_zeros, | |
709 | OutputIterator out_it, | |
710 | const Policy&); | |
711 | ||
712 | template <class T, class Policy> | |
713 | typename detail::bessel_traits<T, T, Policy>::result_type cyl_neumann_zero(T v, int m, const Policy& pol); | |
714 | ||
715 | template <class T> | |
716 | typename detail::bessel_traits<T, T, policies::policy<> >::result_type cyl_neumann_zero(T v, int m); | |
717 | ||
718 | template <class T, class OutputIterator> | |
719 | OutputIterator cyl_neumann_zero(T v, | |
720 | int start_index, | |
721 | unsigned number_of_zeros, | |
722 | OutputIterator out_it); | |
723 | ||
724 | template <class T, class OutputIterator, class Policy> | |
725 | OutputIterator cyl_neumann_zero(T v, | |
726 | int start_index, | |
727 | unsigned number_of_zeros, | |
728 | OutputIterator out_it, | |
729 | const Policy&); | |
730 | ||
731 | template <class T1, class T2> | |
732 | std::complex<typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type> cyl_hankel_1(T1 v, T2 x); | |
733 | ||
734 | template <class T1, class T2, class Policy> | |
735 | std::complex<typename detail::bessel_traits<T1, T2, Policy>::result_type> cyl_hankel_1(T1 v, T2 x, const Policy& pol); | |
736 | ||
737 | template <class T1, class T2, class Policy> | |
738 | std::complex<typename detail::bessel_traits<T1, T2, Policy>::result_type> cyl_hankel_2(T1 v, T2 x, const Policy& pol); | |
739 | ||
740 | template <class T1, class T2> | |
741 | std::complex<typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type> cyl_hankel_2(T1 v, T2 x); | |
742 | ||
743 | template <class T1, class T2, class Policy> | |
744 | std::complex<typename detail::bessel_traits<T1, T2, Policy>::result_type> sph_hankel_1(T1 v, T2 x, const Policy& pol); | |
745 | ||
746 | template <class T1, class T2> | |
747 | std::complex<typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type> sph_hankel_1(T1 v, T2 x); | |
748 | ||
749 | template <class T1, class T2, class Policy> | |
750 | std::complex<typename detail::bessel_traits<T1, T2, Policy>::result_type> sph_hankel_2(T1 v, T2 x, const Policy& pol); | |
751 | ||
752 | template <class T1, class T2> | |
753 | std::complex<typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type> sph_hankel_2(T1 v, T2 x); | |
754 | ||
755 | template <class T, class Policy> | |
756 | typename tools::promote_args<T>::type airy_ai(T x, const Policy&); | |
757 | ||
758 | template <class T> | |
759 | typename tools::promote_args<T>::type airy_ai(T x); | |
760 | ||
761 | template <class T, class Policy> | |
762 | typename tools::promote_args<T>::type airy_bi(T x, const Policy&); | |
763 | ||
764 | template <class T> | |
765 | typename tools::promote_args<T>::type airy_bi(T x); | |
766 | ||
767 | template <class T, class Policy> | |
768 | typename tools::promote_args<T>::type airy_ai_prime(T x, const Policy&); | |
769 | ||
770 | template <class T> | |
771 | typename tools::promote_args<T>::type airy_ai_prime(T x); | |
772 | ||
773 | template <class T, class Policy> | |
774 | typename tools::promote_args<T>::type airy_bi_prime(T x, const Policy&); | |
775 | ||
776 | template <class T> | |
777 | typename tools::promote_args<T>::type airy_bi_prime(T x); | |
778 | ||
779 | template <class T> | |
780 | T airy_ai_zero(int m); | |
781 | template <class T, class Policy> | |
782 | T airy_ai_zero(int m, const Policy&); | |
783 | ||
784 | template <class OutputIterator> | |
785 | OutputIterator airy_ai_zero( | |
786 | int start_index, | |
787 | unsigned number_of_zeros, | |
788 | OutputIterator out_it); | |
789 | template <class OutputIterator, class Policy> | |
790 | OutputIterator airy_ai_zero( | |
791 | int start_index, | |
792 | unsigned number_of_zeros, | |
793 | OutputIterator out_it, | |
794 | const Policy&); | |
795 | ||
796 | template <class T> | |
797 | T airy_bi_zero(int m); | |
798 | template <class T, class Policy> | |
799 | T airy_bi_zero(int m, const Policy&); | |
800 | ||
801 | template <class OutputIterator> | |
802 | OutputIterator airy_bi_zero( | |
803 | int start_index, | |
804 | unsigned number_of_zeros, | |
805 | OutputIterator out_it); | |
806 | template <class OutputIterator, class Policy> | |
807 | OutputIterator airy_bi_zero( | |
808 | int start_index, | |
809 | unsigned number_of_zeros, | |
810 | OutputIterator out_it, | |
811 | const Policy&); | |
812 | ||
813 | template <class T, class Policy> | |
814 | typename tools::promote_args<T>::type sin_pi(T x, const Policy&); | |
815 | ||
816 | template <class T> | |
817 | typename tools::promote_args<T>::type sin_pi(T x); | |
818 | ||
819 | template <class T, class Policy> | |
820 | typename tools::promote_args<T>::type cos_pi(T x, const Policy&); | |
821 | ||
822 | template <class T> | |
823 | typename tools::promote_args<T>::type cos_pi(T x); | |
824 | ||
825 | template <class T> | |
826 | int fpclassify BOOST_NO_MACRO_EXPAND(T t); | |
827 | ||
828 | template <class T> | |
829 | bool isfinite BOOST_NO_MACRO_EXPAND(T z); | |
830 | ||
831 | template <class T> | |
832 | bool isinf BOOST_NO_MACRO_EXPAND(T t); | |
833 | ||
834 | template <class T> | |
835 | bool isnan BOOST_NO_MACRO_EXPAND(T t); | |
836 | ||
837 | template <class T> | |
838 | bool isnormal BOOST_NO_MACRO_EXPAND(T t); | |
839 | ||
840 | template<class T> | |
841 | int signbit BOOST_NO_MACRO_EXPAND(T x); | |
842 | ||
843 | template <class T> | |
844 | int sign BOOST_NO_MACRO_EXPAND(const T& z); | |
845 | ||
846 | template <class T, class U> | |
847 | typename tools::promote_args_permissive<T, U>::type copysign BOOST_NO_MACRO_EXPAND(const T& x, const U& y); | |
848 | ||
849 | template <class T> | |
850 | typename tools::promote_args_permissive<T>::type changesign BOOST_NO_MACRO_EXPAND(const T& z); | |
851 | ||
852 | // Exponential integrals: | |
853 | namespace detail{ | |
854 | ||
855 | template <class T, class U> | |
856 | struct expint_result | |
857 | { | |
858 | typedef typename mpl::if_< | |
859 | policies::is_policy<U>, | |
860 | typename tools::promote_args<T>::type, | |
861 | typename tools::promote_args<U>::type | |
862 | >::type type; | |
863 | }; | |
864 | ||
865 | } // namespace detail | |
866 | ||
867 | template <class T, class Policy> | |
868 | typename tools::promote_args<T>::type expint(unsigned n, T z, const Policy&); | |
869 | ||
870 | template <class T, class U> | |
871 | typename detail::expint_result<T, U>::type expint(T const z, U const u); | |
872 | ||
873 | template <class T> | |
874 | typename tools::promote_args<T>::type expint(T z); | |
875 | ||
876 | // Zeta: | |
877 | template <class T, class Policy> | |
878 | typename tools::promote_args<T>::type zeta(T s, const Policy&); | |
879 | ||
880 | // Owen's T function: | |
881 | template <class T1, class T2, class Policy> | |
882 | typename tools::promote_args<T1, T2>::type owens_t(T1 h, T2 a, const Policy& pol); | |
883 | ||
884 | template <class T1, class T2> | |
885 | typename tools::promote_args<T1, T2>::type owens_t(T1 h, T2 a); | |
886 | ||
887 | // Jacobi Functions: | |
888 | template <class T, class U, class V, class Policy> | |
889 | typename tools::promote_args<T, U, V>::type jacobi_elliptic(T k, U theta, V* pcn, V* pdn, const Policy&); | |
890 | ||
891 | template <class T, class U, class V> | |
892 | typename tools::promote_args<T, U, V>::type jacobi_elliptic(T k, U theta, V* pcn = 0, V* pdn = 0); | |
893 | ||
894 | template <class U, class T, class Policy> | |
895 | typename tools::promote_args<T, U>::type jacobi_sn(U k, T theta, const Policy& pol); | |
896 | ||
897 | template <class U, class T> | |
898 | typename tools::promote_args<T, U>::type jacobi_sn(U k, T theta); | |
899 | ||
900 | template <class T, class U, class Policy> | |
901 | typename tools::promote_args<T, U>::type jacobi_cn(T k, U theta, const Policy& pol); | |
902 | ||
903 | template <class T, class U> | |
904 | typename tools::promote_args<T, U>::type jacobi_cn(T k, U theta); | |
905 | ||
906 | template <class T, class U, class Policy> | |
907 | typename tools::promote_args<T, U>::type jacobi_dn(T k, U theta, const Policy& pol); | |
908 | ||
909 | template <class T, class U> | |
910 | typename tools::promote_args<T, U>::type jacobi_dn(T k, U theta); | |
911 | ||
912 | template <class T, class U, class Policy> | |
913 | typename tools::promote_args<T, U>::type jacobi_cd(T k, U theta, const Policy& pol); | |
914 | ||
915 | template <class T, class U> | |
916 | typename tools::promote_args<T, U>::type jacobi_cd(T k, U theta); | |
917 | ||
918 | template <class T, class U, class Policy> | |
919 | typename tools::promote_args<T, U>::type jacobi_dc(T k, U theta, const Policy& pol); | |
920 | ||
921 | template <class T, class U> | |
922 | typename tools::promote_args<T, U>::type jacobi_dc(T k, U theta); | |
923 | ||
924 | template <class T, class U, class Policy> | |
925 | typename tools::promote_args<T, U>::type jacobi_ns(T k, U theta, const Policy& pol); | |
926 | ||
927 | template <class T, class U> | |
928 | typename tools::promote_args<T, U>::type jacobi_ns(T k, U theta); | |
929 | ||
930 | template <class T, class U, class Policy> | |
931 | typename tools::promote_args<T, U>::type jacobi_sd(T k, U theta, const Policy& pol); | |
932 | ||
933 | template <class T, class U> | |
934 | typename tools::promote_args<T, U>::type jacobi_sd(T k, U theta); | |
935 | ||
936 | template <class T, class U, class Policy> | |
937 | typename tools::promote_args<T, U>::type jacobi_ds(T k, U theta, const Policy& pol); | |
938 | ||
939 | template <class T, class U> | |
940 | typename tools::promote_args<T, U>::type jacobi_ds(T k, U theta); | |
941 | ||
942 | template <class T, class U, class Policy> | |
943 | typename tools::promote_args<T, U>::type jacobi_nc(T k, U theta, const Policy& pol); | |
944 | ||
945 | template <class T, class U> | |
946 | typename tools::promote_args<T, U>::type jacobi_nc(T k, U theta); | |
947 | ||
948 | template <class T, class U, class Policy> | |
949 | typename tools::promote_args<T, U>::type jacobi_nd(T k, U theta, const Policy& pol); | |
950 | ||
951 | template <class T, class U> | |
952 | typename tools::promote_args<T, U>::type jacobi_nd(T k, U theta); | |
953 | ||
954 | template <class T, class U, class Policy> | |
955 | typename tools::promote_args<T, U>::type jacobi_sc(T k, U theta, const Policy& pol); | |
956 | ||
957 | template <class T, class U> | |
958 | typename tools::promote_args<T, U>::type jacobi_sc(T k, U theta); | |
959 | ||
960 | template <class T, class U, class Policy> | |
961 | typename tools::promote_args<T, U>::type jacobi_cs(T k, U theta, const Policy& pol); | |
962 | ||
963 | template <class T, class U> | |
964 | typename tools::promote_args<T, U>::type jacobi_cs(T k, U theta); | |
965 | ||
966 | ||
967 | template <class T> | |
968 | typename tools::promote_args<T>::type zeta(T s); | |
969 | ||
970 | // pow: | |
971 | template <int N, typename T, class Policy> | |
972 | typename tools::promote_args<T>::type pow(T base, const Policy& policy); | |
973 | ||
974 | template <int N, typename T> | |
975 | typename tools::promote_args<T>::type pow(T base); | |
976 | ||
977 | // next: | |
978 | template <class T, class U, class Policy> | |
979 | typename tools::promote_args<T, U>::type nextafter(const T&, const U&, const Policy&); | |
980 | template <class T, class U> | |
981 | typename tools::promote_args<T, U>::type nextafter(const T&, const U&); | |
982 | template <class T, class Policy> | |
983 | typename tools::promote_args<T>::type float_next(const T&, const Policy&); | |
984 | template <class T> | |
985 | typename tools::promote_args<T>::type float_next(const T&); | |
986 | template <class T, class Policy> | |
987 | typename tools::promote_args<T>::type float_prior(const T&, const Policy&); | |
988 | template <class T> | |
989 | typename tools::promote_args<T>::type float_prior(const T&); | |
990 | template <class T, class U, class Policy> | |
991 | typename tools::promote_args<T, U>::type float_distance(const T&, const U&, const Policy&); | |
992 | template <class T, class U> | |
993 | typename tools::promote_args<T, U>::type float_distance(const T&, const U&); | |
994 | template <class T, class Policy> | |
995 | typename tools::promote_args<T>::type float_advance(T val, int distance, const Policy& pol); | |
996 | template <class T> | |
997 | typename tools::promote_args<T>::type float_advance(const T& val, int distance); | |
998 | ||
999 | template <class T, class Policy> | |
1000 | typename tools::promote_args<T>::type ulp(const T& val, const Policy& pol); | |
1001 | template <class T> | |
1002 | typename tools::promote_args<T>::type ulp(const T& val); | |
1003 | ||
1004 | template <class T, class U> | |
1005 | typename tools::promote_args<T, U>::type relative_difference(const T&, const U&); | |
1006 | template <class T, class U> | |
1007 | typename tools::promote_args<T, U>::type epsilon_difference(const T&, const U&); | |
1008 | ||
1009 | template<class T> | |
1010 | T unchecked_bernoulli_b2n(const std::size_t n); | |
1011 | template <class T, class Policy> | |
1012 | T bernoulli_b2n(const int i, const Policy &pol); | |
1013 | template <class T> | |
1014 | T bernoulli_b2n(const int i); | |
1015 | template <class T, class OutputIterator, class Policy> | |
1016 | OutputIterator bernoulli_b2n(const int start_index, | |
1017 | const unsigned number_of_bernoullis_b2n, | |
1018 | OutputIterator out_it, | |
1019 | const Policy& pol); | |
1020 | template <class T, class OutputIterator> | |
1021 | OutputIterator bernoulli_b2n(const int start_index, | |
1022 | const unsigned number_of_bernoullis_b2n, | |
1023 | OutputIterator out_it); | |
1024 | template <class T, class Policy> | |
1025 | T tangent_t2n(const int i, const Policy &pol); | |
1026 | template <class T> | |
1027 | T tangent_t2n(const int i); | |
1028 | template <class T, class OutputIterator, class Policy> | |
1029 | OutputIterator tangent_t2n(const int start_index, | |
1030 | const unsigned number_of_bernoullis_b2n, | |
1031 | OutputIterator out_it, | |
1032 | const Policy& pol); | |
1033 | template <class T, class OutputIterator> | |
1034 | OutputIterator tangent_t2n(const int start_index, | |
1035 | const unsigned number_of_bernoullis_b2n, | |
1036 | OutputIterator out_it); | |
1037 | ||
1038 | } // namespace math | |
1039 | } // namespace boost | |
1040 | ||
1041 | #ifdef BOOST_HAS_LONG_LONG | |
1042 | #define BOOST_MATH_DETAIL_LL_FUNC(Policy)\ | |
1043 | \ | |
1044 | template <class T>\ | |
1045 | inline T modf(const T& v, boost::long_long_type* ipart){ using boost::math::modf; return modf(v, ipart, Policy()); }\ | |
1046 | \ | |
1047 | template <class T>\ | |
1048 | inline boost::long_long_type lltrunc(const T& v){ using boost::math::lltrunc; return lltrunc(v, Policy()); }\ | |
1049 | \ | |
1050 | template <class T>\ | |
1051 | inline boost::long_long_type llround(const T& v){ using boost::math::llround; return llround(v, Policy()); }\ | |
1052 | ||
1053 | #else | |
1054 | #define BOOST_MATH_DETAIL_LL_FUNC(Policy) | |
1055 | #endif | |
1056 | ||
1057 | #define BOOST_MATH_DECLARE_SPECIAL_FUNCTIONS(Policy)\ | |
1058 | \ | |
1059 | BOOST_MATH_DETAIL_LL_FUNC(Policy)\ | |
1060 | \ | |
1061 | template <class RT1, class RT2>\ | |
1062 | inline typename boost::math::tools::promote_args<RT1, RT2>::type \ | |
1063 | beta(RT1 a, RT2 b) { return ::boost::math::beta(a, b, Policy()); }\ | |
1064 | \ | |
1065 | template <class RT1, class RT2, class A>\ | |
1066 | inline typename boost::math::tools::promote_args<RT1, RT2, A>::type \ | |
1067 | beta(RT1 a, RT2 b, A x){ return ::boost::math::beta(a, b, x, Policy()); }\ | |
1068 | \ | |
1069 | template <class RT1, class RT2, class RT3>\ | |
1070 | inline typename boost::math::tools::promote_args<RT1, RT2, RT3>::type \ | |
1071 | betac(RT1 a, RT2 b, RT3 x) { return ::boost::math::betac(a, b, x, Policy()); }\ | |
1072 | \ | |
1073 | template <class RT1, class RT2, class RT3>\ | |
1074 | inline typename boost::math::tools::promote_args<RT1, RT2, RT3>::type \ | |
1075 | ibeta(RT1 a, RT2 b, RT3 x){ return ::boost::math::ibeta(a, b, x, Policy()); }\ | |
1076 | \ | |
1077 | template <class RT1, class RT2, class RT3>\ | |
1078 | inline typename boost::math::tools::promote_args<RT1, RT2, RT3>::type \ | |
1079 | ibetac(RT1 a, RT2 b, RT3 x){ return ::boost::math::ibetac(a, b, x, Policy()); }\ | |
1080 | \ | |
1081 | template <class T1, class T2, class T3, class T4>\ | |
1082 | inline typename boost::math::tools::promote_args<T1, T2, T3, T4>::type \ | |
1083 | ibeta_inv(T1 a, T2 b, T3 p, T4* py){ return ::boost::math::ibeta_inv(a, b, p, py, Policy()); }\ | |
1084 | \ | |
1085 | template <class RT1, class RT2, class RT3>\ | |
1086 | inline typename boost::math::tools::promote_args<RT1, RT2, RT3>::type \ | |
1087 | ibeta_inv(RT1 a, RT2 b, RT3 p){ return ::boost::math::ibeta_inv(a, b, p, Policy()); }\ | |
1088 | \ | |
1089 | template <class T1, class T2, class T3, class T4>\ | |
1090 | inline typename boost::math::tools::promote_args<T1, T2, T3, T4>::type \ | |
1091 | ibetac_inv(T1 a, T2 b, T3 q, T4* py){ return ::boost::math::ibetac_inv(a, b, q, py, Policy()); }\ | |
1092 | \ | |
1093 | template <class RT1, class RT2, class RT3>\ | |
1094 | inline typename boost::math::tools::promote_args<RT1, RT2, RT3>::type \ | |
1095 | ibeta_inva(RT1 a, RT2 b, RT3 p){ return ::boost::math::ibeta_inva(a, b, p, Policy()); }\ | |
1096 | \ | |
1097 | template <class T1, class T2, class T3>\ | |
1098 | inline typename boost::math::tools::promote_args<T1, T2, T3>::type \ | |
1099 | ibetac_inva(T1 a, T2 b, T3 q){ return ::boost::math::ibetac_inva(a, b, q, Policy()); }\ | |
1100 | \ | |
1101 | template <class RT1, class RT2, class RT3>\ | |
1102 | inline typename boost::math::tools::promote_args<RT1, RT2, RT3>::type \ | |
1103 | ibeta_invb(RT1 a, RT2 b, RT3 p){ return ::boost::math::ibeta_invb(a, b, p, Policy()); }\ | |
1104 | \ | |
1105 | template <class T1, class T2, class T3>\ | |
1106 | inline typename boost::math::tools::promote_args<T1, T2, T3>::type \ | |
1107 | ibetac_invb(T1 a, T2 b, T3 q){ return ::boost::math::ibetac_invb(a, b, q, Policy()); }\ | |
1108 | \ | |
1109 | template <class RT1, class RT2, class RT3>\ | |
1110 | inline typename boost::math::tools::promote_args<RT1, RT2, RT3>::type \ | |
1111 | ibetac_inv(RT1 a, RT2 b, RT3 q){ return ::boost::math::ibetac_inv(a, b, q, Policy()); }\ | |
1112 | \ | |
1113 | template <class RT1, class RT2, class RT3>\ | |
1114 | inline typename boost::math::tools::promote_args<RT1, RT2, RT3>::type \ | |
1115 | ibeta_derivative(RT1 a, RT2 b, RT3 x){ return ::boost::math::ibeta_derivative(a, b, x, Policy()); }\ | |
1116 | \ | |
1117 | template <class T> T binomial_coefficient(unsigned n, unsigned k){ return ::boost::math::binomial_coefficient<T, Policy>(n, k, Policy()); }\ | |
1118 | \ | |
1119 | template <class RT>\ | |
1120 | inline typename boost::math::tools::promote_args<RT>::type erf(RT z) { return ::boost::math::erf(z, Policy()); }\ | |
1121 | \ | |
1122 | template <class RT>\ | |
1123 | inline typename boost::math::tools::promote_args<RT>::type erfc(RT z){ return ::boost::math::erfc(z, Policy()); }\ | |
1124 | \ | |
1125 | template <class RT>\ | |
1126 | inline typename boost::math::tools::promote_args<RT>::type erf_inv(RT z) { return ::boost::math::erf_inv(z, Policy()); }\ | |
1127 | \ | |
1128 | template <class RT>\ | |
1129 | inline typename boost::math::tools::promote_args<RT>::type erfc_inv(RT z){ return ::boost::math::erfc_inv(z, Policy()); }\ | |
1130 | \ | |
1131 | using boost::math::legendre_next;\ | |
1132 | \ | |
1133 | template <class T>\ | |
1134 | inline typename boost::math::tools::promote_args<T>::type \ | |
1135 | legendre_p(int l, T x){ return ::boost::math::legendre_p(l, x, Policy()); }\ | |
1136 | \ | |
1137 | template <class T>\ | |
1138 | inline typename boost::math::tools::promote_args<T>::type \ | |
1139 | legendre_q(unsigned l, T x){ return ::boost::math::legendre_q(l, x, Policy()); }\ | |
1140 | \ | |
1141 | using ::boost::math::legendre_next;\ | |
1142 | \ | |
1143 | template <class T>\ | |
1144 | inline typename boost::math::tools::promote_args<T>::type \ | |
1145 | legendre_p(int l, int m, T x){ return ::boost::math::legendre_p(l, m, x, Policy()); }\ | |
1146 | \ | |
1147 | using ::boost::math::laguerre_next;\ | |
1148 | \ | |
1149 | template <class T>\ | |
1150 | inline typename boost::math::tools::promote_args<T>::type \ | |
1151 | laguerre(unsigned n, T x){ return ::boost::math::laguerre(n, x, Policy()); }\ | |
1152 | \ | |
1153 | template <class T1, class T2>\ | |
1154 | inline typename boost::math::laguerre_result<T1, T2>::type \ | |
1155 | laguerre(unsigned n, T1 m, T2 x) { return ::boost::math::laguerre(n, m, x, Policy()); }\ | |
1156 | \ | |
1157 | template <class T>\ | |
1158 | inline typename boost::math::tools::promote_args<T>::type \ | |
1159 | hermite(unsigned n, T x){ return ::boost::math::hermite(n, x, Policy()); }\ | |
1160 | \ | |
1161 | using boost::math::hermite_next;\ | |
1162 | \ | |
1163 | template <class T1, class T2>\ | |
1164 | inline std::complex<typename boost::math::tools::promote_args<T1, T2>::type> \ | |
1165 | spherical_harmonic(unsigned n, int m, T1 theta, T2 phi){ return boost::math::spherical_harmonic(n, m, theta, phi, Policy()); }\ | |
1166 | \ | |
1167 | template <class T1, class T2>\ | |
1168 | inline typename boost::math::tools::promote_args<T1, T2>::type \ | |
1169 | spherical_harmonic_r(unsigned n, int m, T1 theta, T2 phi){ return ::boost::math::spherical_harmonic_r(n, m, theta, phi, Policy()); }\ | |
1170 | \ | |
1171 | template <class T1, class T2>\ | |
1172 | inline typename boost::math::tools::promote_args<T1, T2>::type \ | |
1173 | spherical_harmonic_i(unsigned n, int m, T1 theta, T2 phi){ return boost::math::spherical_harmonic_i(n, m, theta, phi, Policy()); }\ | |
1174 | \ | |
1175 | template <class T1, class T2, class Policy>\ | |
1176 | inline typename boost::math::tools::promote_args<T1, T2>::type \ | |
1177 | spherical_harmonic_i(unsigned n, int m, T1 theta, T2 phi, const Policy& pol);\ | |
1178 | \ | |
1179 | template <class T1, class T2, class T3>\ | |
1180 | inline typename boost::math::tools::promote_args<T1, T2, T3>::type \ | |
1181 | ellint_rf(T1 x, T2 y, T3 z){ return ::boost::math::ellint_rf(x, y, z, Policy()); }\ | |
1182 | \ | |
1183 | template <class T1, class T2, class T3>\ | |
1184 | inline typename boost::math::tools::promote_args<T1, T2, T3>::type \ | |
1185 | ellint_rd(T1 x, T2 y, T3 z){ return ::boost::math::ellint_rd(x, y, z, Policy()); }\ | |
1186 | \ | |
1187 | template <class T1, class T2>\ | |
1188 | inline typename boost::math::tools::promote_args<T1, T2>::type \ | |
1189 | ellint_rc(T1 x, T2 y){ return ::boost::math::ellint_rc(x, y, Policy()); }\ | |
1190 | \ | |
1191 | template <class T1, class T2, class T3, class T4>\ | |
1192 | inline typename boost::math::tools::promote_args<T1, T2, T3, T4>::type \ | |
1193 | ellint_rj(T1 x, T2 y, T3 z, T4 p){ return boost::math::ellint_rj(x, y, z, p, Policy()); }\ | |
1194 | \ | |
1195 | template <class T1, class T2, class T3>\ | |
1196 | inline typename boost::math::tools::promote_args<T1, T2, T3>::type \ | |
1197 | ellint_rg(T1 x, T2 y, T3 z){ return ::boost::math::ellint_rg(x, y, z, Policy()); }\ | |
1198 | \ | |
1199 | template <typename T>\ | |
1200 | inline typename boost::math::tools::promote_args<T>::type ellint_2(T k){ return boost::math::ellint_2(k, Policy()); }\ | |
1201 | \ | |
1202 | template <class T1, class T2>\ | |
1203 | inline typename boost::math::tools::promote_args<T1, T2>::type ellint_2(T1 k, T2 phi){ return boost::math::ellint_2(k, phi, Policy()); }\ | |
1204 | \ | |
1205 | template <typename T>\ | |
1206 | inline typename boost::math::tools::promote_args<T>::type ellint_d(T k){ return boost::math::ellint_d(k, Policy()); }\ | |
1207 | \ | |
1208 | template <class T1, class T2>\ | |
1209 | inline typename boost::math::tools::promote_args<T1, T2>::type ellint_d(T1 k, T2 phi){ return boost::math::ellint_d(k, phi, Policy()); }\ | |
1210 | \ | |
1211 | template <class T1, class T2>\ | |
1212 | inline typename boost::math::tools::promote_args<T1, T2>::type jacobi_zeta(T1 k, T2 phi){ return boost::math::jacobi_zeta(k, phi, Policy()); }\ | |
1213 | \ | |
1214 | template <class T1, class T2>\ | |
1215 | inline typename boost::math::tools::promote_args<T1, T2>::type heuman_lambda(T1 k, T2 phi){ return boost::math::heuman_lambda(k, phi, Policy()); }\ | |
1216 | \ | |
1217 | template <typename T>\ | |
1218 | inline typename boost::math::tools::promote_args<T>::type ellint_1(T k){ return boost::math::ellint_1(k, Policy()); }\ | |
1219 | \ | |
1220 | template <class T1, class T2>\ | |
1221 | inline typename boost::math::tools::promote_args<T1, T2>::type ellint_1(T1 k, T2 phi){ return boost::math::ellint_1(k, phi, Policy()); }\ | |
1222 | \ | |
1223 | template <class T1, class T2, class T3>\ | |
1224 | inline typename boost::math::tools::promote_args<T1, T2, T3>::type ellint_3(T1 k, T2 v, T3 phi){ return boost::math::ellint_3(k, v, phi, Policy()); }\ | |
1225 | \ | |
1226 | template <class T1, class T2>\ | |
1227 | inline typename boost::math::tools::promote_args<T1, T2>::type ellint_3(T1 k, T2 v){ return boost::math::ellint_3(k, v, Policy()); }\ | |
1228 | \ | |
1229 | using boost::math::max_factorial;\ | |
1230 | template <class RT>\ | |
1231 | inline RT factorial(unsigned int i) { return boost::math::factorial<RT>(i, Policy()); }\ | |
1232 | using boost::math::unchecked_factorial;\ | |
1233 | template <class RT>\ | |
1234 | inline RT double_factorial(unsigned i){ return boost::math::double_factorial<RT>(i, Policy()); }\ | |
1235 | template <class RT>\ | |
1236 | inline typename boost::math::tools::promote_args<RT>::type falling_factorial(RT x, unsigned n){ return boost::math::falling_factorial(x, n, Policy()); }\ | |
1237 | template <class RT>\ | |
1238 | inline typename boost::math::tools::promote_args<RT>::type rising_factorial(RT x, unsigned n){ return boost::math::rising_factorial(x, n, Policy()); }\ | |
1239 | \ | |
1240 | template <class RT>\ | |
1241 | inline typename boost::math::tools::promote_args<RT>::type tgamma(RT z){ return boost::math::tgamma(z, Policy()); }\ | |
1242 | \ | |
1243 | template <class RT>\ | |
1244 | inline typename boost::math::tools::promote_args<RT>::type tgamma1pm1(RT z){ return boost::math::tgamma1pm1(z, Policy()); }\ | |
1245 | \ | |
1246 | template <class RT1, class RT2>\ | |
1247 | inline typename boost::math::tools::promote_args<RT1, RT2>::type tgamma(RT1 a, RT2 z){ return boost::math::tgamma(a, z, Policy()); }\ | |
1248 | \ | |
1249 | template <class RT>\ | |
1250 | inline typename boost::math::tools::promote_args<RT>::type lgamma(RT z, int* sign){ return boost::math::lgamma(z, sign, Policy()); }\ | |
1251 | \ | |
1252 | template <class RT>\ | |
1253 | inline typename boost::math::tools::promote_args<RT>::type lgamma(RT x){ return boost::math::lgamma(x, Policy()); }\ | |
1254 | \ | |
1255 | template <class RT1, class RT2>\ | |
1256 | inline typename boost::math::tools::promote_args<RT1, RT2>::type tgamma_lower(RT1 a, RT2 z){ return boost::math::tgamma_lower(a, z, Policy()); }\ | |
1257 | \ | |
1258 | template <class RT1, class RT2>\ | |
1259 | inline typename boost::math::tools::promote_args<RT1, RT2>::type gamma_q(RT1 a, RT2 z){ return boost::math::gamma_q(a, z, Policy()); }\ | |
1260 | \ | |
1261 | template <class RT1, class RT2>\ | |
1262 | inline typename boost::math::tools::promote_args<RT1, RT2>::type gamma_p(RT1 a, RT2 z){ return boost::math::gamma_p(a, z, Policy()); }\ | |
1263 | \ | |
1264 | template <class T1, class T2>\ | |
1265 | inline typename boost::math::tools::promote_args<T1, T2>::type tgamma_delta_ratio(T1 z, T2 delta){ return boost::math::tgamma_delta_ratio(z, delta, Policy()); }\ | |
1266 | \ | |
1267 | template <class T1, class T2>\ | |
1268 | inline typename boost::math::tools::promote_args<T1, T2>::type tgamma_ratio(T1 a, T2 b) { return boost::math::tgamma_ratio(a, b, Policy()); }\ | |
1269 | \ | |
1270 | template <class T1, class T2>\ | |
1271 | inline typename boost::math::tools::promote_args<T1, T2>::type gamma_p_derivative(T1 a, T2 x){ return boost::math::gamma_p_derivative(a, x, Policy()); }\ | |
1272 | \ | |
1273 | template <class T1, class T2>\ | |
1274 | inline typename boost::math::tools::promote_args<T1, T2>::type gamma_p_inv(T1 a, T2 p){ return boost::math::gamma_p_inv(a, p, Policy()); }\ | |
1275 | \ | |
1276 | template <class T1, class T2>\ | |
1277 | inline typename boost::math::tools::promote_args<T1, T2>::type gamma_p_inva(T1 a, T2 p){ return boost::math::gamma_p_inva(a, p, Policy()); }\ | |
1278 | \ | |
1279 | template <class T1, class T2>\ | |
1280 | inline typename boost::math::tools::promote_args<T1, T2>::type gamma_q_inv(T1 a, T2 q){ return boost::math::gamma_q_inv(a, q, Policy()); }\ | |
1281 | \ | |
1282 | template <class T1, class T2>\ | |
1283 | inline typename boost::math::tools::promote_args<T1, T2>::type gamma_q_inva(T1 a, T2 q){ return boost::math::gamma_q_inva(a, q, Policy()); }\ | |
1284 | \ | |
1285 | template <class T>\ | |
1286 | inline typename boost::math::tools::promote_args<T>::type digamma(T x){ return boost::math::digamma(x, Policy()); }\ | |
1287 | \ | |
1288 | template <class T>\ | |
1289 | inline typename boost::math::tools::promote_args<T>::type trigamma(T x){ return boost::math::trigamma(x, Policy()); }\ | |
1290 | \ | |
1291 | template <class T>\ | |
1292 | inline typename boost::math::tools::promote_args<T>::type polygamma(int n, T x){ return boost::math::polygamma(n, x, Policy()); }\ | |
1293 | \ | |
1294 | template <class T1, class T2>\ | |
1295 | inline typename boost::math::tools::promote_args<T1, T2>::type \ | |
1296 | hypot(T1 x, T2 y){ return boost::math::hypot(x, y, Policy()); }\ | |
1297 | \ | |
1298 | template <class RT>\ | |
1299 | inline typename boost::math::tools::promote_args<RT>::type cbrt(RT z){ return boost::math::cbrt(z, Policy()); }\ | |
1300 | \ | |
1301 | template <class T>\ | |
1302 | inline typename boost::math::tools::promote_args<T>::type log1p(T x){ return boost::math::log1p(x, Policy()); }\ | |
1303 | \ | |
1304 | template <class T>\ | |
1305 | inline typename boost::math::tools::promote_args<T>::type log1pmx(T x){ return boost::math::log1pmx(x, Policy()); }\ | |
1306 | \ | |
1307 | template <class T>\ | |
1308 | inline typename boost::math::tools::promote_args<T>::type expm1(T x){ return boost::math::expm1(x, Policy()); }\ | |
1309 | \ | |
1310 | template <class T1, class T2>\ | |
1311 | inline typename boost::math::tools::promote_args<T1, T2>::type \ | |
1312 | powm1(const T1 a, const T2 z){ return boost::math::powm1(a, z, Policy()); }\ | |
1313 | \ | |
1314 | template <class T>\ | |
1315 | inline typename boost::math::tools::promote_args<T>::type sqrt1pm1(const T& val){ return boost::math::sqrt1pm1(val, Policy()); }\ | |
1316 | \ | |
1317 | template <class T>\ | |
1318 | inline typename boost::math::tools::promote_args<T>::type sinc_pi(T x){ return boost::math::sinc_pi(x, Policy()); }\ | |
1319 | \ | |
1320 | template <class T>\ | |
1321 | inline typename boost::math::tools::promote_args<T>::type sinhc_pi(T x){ return boost::math::sinhc_pi(x, Policy()); }\ | |
1322 | \ | |
1323 | template<typename T>\ | |
1324 | inline typename boost::math::tools::promote_args<T>::type asinh(const T x){ return boost::math::asinh(x, Policy()); }\ | |
1325 | \ | |
1326 | template<typename T>\ | |
1327 | inline typename boost::math::tools::promote_args<T>::type acosh(const T x){ return boost::math::acosh(x, Policy()); }\ | |
1328 | \ | |
1329 | template<typename T>\ | |
1330 | inline typename boost::math::tools::promote_args<T>::type atanh(const T x){ return boost::math::atanh(x, Policy()); }\ | |
1331 | \ | |
1332 | template <class T1, class T2>\ | |
1333 | inline typename boost::math::detail::bessel_traits<T1, T2, Policy >::result_type cyl_bessel_j(T1 v, T2 x)\ | |
1334 | { return boost::math::cyl_bessel_j(v, x, Policy()); }\ | |
1335 | \ | |
1336 | template <class T1, class T2>\ | |
1337 | inline typename boost::math::detail::bessel_traits<T1, T2, Policy >::result_type cyl_bessel_j_prime(T1 v, T2 x)\ | |
1338 | { return boost::math::cyl_bessel_j_prime(v, x, Policy()); }\ | |
1339 | \ | |
1340 | template <class T>\ | |
1341 | inline typename boost::math::detail::bessel_traits<T, T, Policy >::result_type sph_bessel(unsigned v, T x)\ | |
1342 | { return boost::math::sph_bessel(v, x, Policy()); }\ | |
1343 | \ | |
1344 | template <class T>\ | |
1345 | inline typename boost::math::detail::bessel_traits<T, T, Policy >::result_type sph_bessel_prime(unsigned v, T x)\ | |
1346 | { return boost::math::sph_bessel_prime(v, x, Policy()); }\ | |
1347 | \ | |
1348 | template <class T1, class T2>\ | |
1349 | inline typename boost::math::detail::bessel_traits<T1, T2, Policy >::result_type \ | |
1350 | cyl_bessel_i(T1 v, T2 x) { return boost::math::cyl_bessel_i(v, x, Policy()); }\ | |
1351 | \ | |
1352 | template <class T1, class T2>\ | |
1353 | inline typename boost::math::detail::bessel_traits<T1, T2, Policy >::result_type \ | |
1354 | cyl_bessel_i_prime(T1 v, T2 x) { return boost::math::cyl_bessel_i_prime(v, x, Policy()); }\ | |
1355 | \ | |
1356 | template <class T1, class T2>\ | |
1357 | inline typename boost::math::detail::bessel_traits<T1, T2, Policy >::result_type \ | |
1358 | cyl_bessel_k(T1 v, T2 x) { return boost::math::cyl_bessel_k(v, x, Policy()); }\ | |
1359 | \ | |
1360 | template <class T1, class T2>\ | |
1361 | inline typename boost::math::detail::bessel_traits<T1, T2, Policy >::result_type \ | |
1362 | cyl_bessel_k_prime(T1 v, T2 x) { return boost::math::cyl_bessel_k_prime(v, x, Policy()); }\ | |
1363 | \ | |
1364 | template <class T1, class T2>\ | |
1365 | inline typename boost::math::detail::bessel_traits<T1, T2, Policy >::result_type \ | |
1366 | cyl_neumann(T1 v, T2 x){ return boost::math::cyl_neumann(v, x, Policy()); }\ | |
1367 | \ | |
1368 | template <class T1, class T2>\ | |
1369 | inline typename boost::math::detail::bessel_traits<T1, T2, Policy >::result_type \ | |
1370 | cyl_neumann_prime(T1 v, T2 x){ return boost::math::cyl_neumann_prime(v, x, Policy()); }\ | |
1371 | \ | |
1372 | template <class T>\ | |
1373 | inline typename boost::math::detail::bessel_traits<T, T, Policy >::result_type \ | |
1374 | sph_neumann(unsigned v, T x){ return boost::math::sph_neumann(v, x, Policy()); }\ | |
1375 | \ | |
1376 | template <class T>\ | |
1377 | inline typename boost::math::detail::bessel_traits<T, T, Policy >::result_type \ | |
1378 | sph_neumann_prime(unsigned v, T x){ return boost::math::sph_neumann_prime(v, x, Policy()); }\ | |
1379 | \ | |
1380 | template <class T>\ | |
1381 | inline typename boost::math::detail::bessel_traits<T, T, Policy >::result_type cyl_bessel_j_zero(T v, int m)\ | |
1382 | { return boost::math::cyl_bessel_j_zero(v, m, Policy()); }\ | |
1383 | \ | |
1384 | template <class OutputIterator, class T>\ | |
1385 | inline void cyl_bessel_j_zero(T v,\ | |
1386 | int start_index,\ | |
1387 | unsigned number_of_zeros,\ | |
1388 | OutputIterator out_it)\ | |
1389 | { boost::math::cyl_bessel_j_zero(v, start_index, number_of_zeros, out_it, Policy()); }\ | |
1390 | \ | |
1391 | template <class T>\ | |
1392 | inline typename boost::math::detail::bessel_traits<T, T, Policy >::result_type cyl_neumann_zero(T v, int m)\ | |
1393 | { return boost::math::cyl_neumann_zero(v, m, Policy()); }\ | |
1394 | \ | |
1395 | template <class OutputIterator, class T>\ | |
1396 | inline void cyl_neumann_zero(T v,\ | |
1397 | int start_index,\ | |
1398 | unsigned number_of_zeros,\ | |
1399 | OutputIterator out_it)\ | |
1400 | { boost::math::cyl_neumann_zero(v, start_index, number_of_zeros, out_it, Policy()); }\ | |
1401 | \ | |
1402 | template <class T>\ | |
1403 | inline typename boost::math::tools::promote_args<T>::type sin_pi(T x){ return boost::math::sin_pi(x); }\ | |
1404 | \ | |
1405 | template <class T>\ | |
1406 | inline typename boost::math::tools::promote_args<T>::type cos_pi(T x){ return boost::math::cos_pi(x); }\ | |
1407 | \ | |
1408 | using boost::math::fpclassify;\ | |
1409 | using boost::math::isfinite;\ | |
1410 | using boost::math::isinf;\ | |
1411 | using boost::math::isnan;\ | |
1412 | using boost::math::isnormal;\ | |
1413 | using boost::math::signbit;\ | |
1414 | using boost::math::sign;\ | |
1415 | using boost::math::copysign;\ | |
1416 | using boost::math::changesign;\ | |
1417 | \ | |
1418 | template <class T, class U>\ | |
1419 | inline typename boost::math::tools::promote_args<T,U>::type expint(T const& z, U const& u)\ | |
1420 | { return boost::math::expint(z, u, Policy()); }\ | |
1421 | \ | |
1422 | template <class T>\ | |
1423 | inline typename boost::math::tools::promote_args<T>::type expint(T z){ return boost::math::expint(z, Policy()); }\ | |
1424 | \ | |
1425 | template <class T>\ | |
1426 | inline typename boost::math::tools::promote_args<T>::type zeta(T s){ return boost::math::zeta(s, Policy()); }\ | |
1427 | \ | |
1428 | template <class T>\ | |
1429 | inline T round(const T& v){ using boost::math::round; return round(v, Policy()); }\ | |
1430 | \ | |
1431 | template <class T>\ | |
1432 | inline int iround(const T& v){ using boost::math::iround; return iround(v, Policy()); }\ | |
1433 | \ | |
1434 | template <class T>\ | |
1435 | inline long lround(const T& v){ using boost::math::lround; return lround(v, Policy()); }\ | |
1436 | \ | |
1437 | template <class T>\ | |
1438 | inline T trunc(const T& v){ using boost::math::trunc; return trunc(v, Policy()); }\ | |
1439 | \ | |
1440 | template <class T>\ | |
1441 | inline int itrunc(const T& v){ using boost::math::itrunc; return itrunc(v, Policy()); }\ | |
1442 | \ | |
1443 | template <class T>\ | |
1444 | inline long ltrunc(const T& v){ using boost::math::ltrunc; return ltrunc(v, Policy()); }\ | |
1445 | \ | |
1446 | template <class T>\ | |
1447 | inline T modf(const T& v, T* ipart){ using boost::math::modf; return modf(v, ipart, Policy()); }\ | |
1448 | \ | |
1449 | template <class T>\ | |
1450 | inline T modf(const T& v, int* ipart){ using boost::math::modf; return modf(v, ipart, Policy()); }\ | |
1451 | \ | |
1452 | template <class T>\ | |
1453 | inline T modf(const T& v, long* ipart){ using boost::math::modf; return modf(v, ipart, Policy()); }\ | |
1454 | \ | |
1455 | template <int N, class T>\ | |
1456 | inline typename boost::math::tools::promote_args<T>::type pow(T v){ return boost::math::pow<N>(v, Policy()); }\ | |
1457 | \ | |
1458 | template <class T> T nextafter(const T& a, const T& b){ return boost::math::nextafter(a, b, Policy()); }\ | |
1459 | template <class T> T float_next(const T& a){ return boost::math::float_next(a, Policy()); }\ | |
1460 | template <class T> T float_prior(const T& a){ return boost::math::float_prior(a, Policy()); }\ | |
1461 | template <class T> T float_distance(const T& a, const T& b){ return boost::math::float_distance(a, b, Policy()); }\ | |
1462 | template <class T> T ulp(const T& a){ return boost::math::ulp(a, Policy()); }\ | |
1463 | \ | |
1464 | template <class RT1, class RT2>\ | |
1465 | inline typename boost::math::tools::promote_args<RT1, RT2>::type owens_t(RT1 a, RT2 z){ return boost::math::owens_t(a, z, Policy()); }\ | |
1466 | \ | |
1467 | template <class T1, class T2>\ | |
1468 | inline std::complex<typename boost::math::detail::bessel_traits<T1, T2, Policy >::result_type> cyl_hankel_1(T1 v, T2 x)\ | |
1469 | { return boost::math::cyl_hankel_1(v, x, Policy()); }\ | |
1470 | \ | |
1471 | template <class T1, class T2>\ | |
1472 | inline std::complex<typename boost::math::detail::bessel_traits<T1, T2, Policy >::result_type> cyl_hankel_2(T1 v, T2 x)\ | |
1473 | { return boost::math::cyl_hankel_2(v, x, Policy()); }\ | |
1474 | \ | |
1475 | template <class T1, class T2>\ | |
1476 | inline std::complex<typename boost::math::detail::bessel_traits<T1, T2, Policy >::result_type> sph_hankel_1(T1 v, T2 x)\ | |
1477 | { return boost::math::sph_hankel_1(v, x, Policy()); }\ | |
1478 | \ | |
1479 | template <class T1, class T2>\ | |
1480 | inline std::complex<typename boost::math::detail::bessel_traits<T1, T2, Policy >::result_type> sph_hankel_2(T1 v, T2 x)\ | |
1481 | { return boost::math::sph_hankel_2(v, x, Policy()); }\ | |
1482 | \ | |
1483 | template <class T>\ | |
1484 | inline typename boost::math::tools::promote_args<T>::type jacobi_elliptic(T k, T theta, T* pcn, T* pdn)\ | |
1485 | { return boost::math::jacobi_elliptic(k, theta, pcn, pdn, Policy()); }\ | |
1486 | \ | |
1487 | template <class U, class T>\ | |
1488 | inline typename boost::math::tools::promote_args<T, U>::type jacobi_sn(U k, T theta)\ | |
1489 | { return boost::math::jacobi_sn(k, theta, Policy()); }\ | |
1490 | \ | |
1491 | template <class T, class U>\ | |
1492 | inline typename boost::math::tools::promote_args<T, U>::type jacobi_cn(T k, U theta)\ | |
1493 | { return boost::math::jacobi_cn(k, theta, Policy()); }\ | |
1494 | \ | |
1495 | template <class T, class U>\ | |
1496 | inline typename boost::math::tools::promote_args<T, U>::type jacobi_dn(T k, U theta)\ | |
1497 | { return boost::math::jacobi_dn(k, theta, Policy()); }\ | |
1498 | \ | |
1499 | template <class T, class U>\ | |
1500 | inline typename boost::math::tools::promote_args<T, U>::type jacobi_cd(T k, U theta)\ | |
1501 | { return boost::math::jacobi_cd(k, theta, Policy()); }\ | |
1502 | \ | |
1503 | template <class T, class U>\ | |
1504 | inline typename boost::math::tools::promote_args<T, U>::type jacobi_dc(T k, U theta)\ | |
1505 | { return boost::math::jacobi_dc(k, theta, Policy()); }\ | |
1506 | \ | |
1507 | template <class T, class U>\ | |
1508 | inline typename boost::math::tools::promote_args<T, U>::type jacobi_ns(T k, U theta)\ | |
1509 | { return boost::math::jacobi_ns(k, theta, Policy()); }\ | |
1510 | \ | |
1511 | template <class T, class U>\ | |
1512 | inline typename boost::math::tools::promote_args<T, U>::type jacobi_sd(T k, U theta)\ | |
1513 | { return boost::math::jacobi_sd(k, theta, Policy()); }\ | |
1514 | \ | |
1515 | template <class T, class U>\ | |
1516 | inline typename boost::math::tools::promote_args<T, U>::type jacobi_ds(T k, U theta)\ | |
1517 | { return boost::math::jacobi_ds(k, theta, Policy()); }\ | |
1518 | \ | |
1519 | template <class T, class U>\ | |
1520 | inline typename boost::math::tools::promote_args<T, U>::type jacobi_nc(T k, U theta)\ | |
1521 | { return boost::math::jacobi_nc(k, theta, Policy()); }\ | |
1522 | \ | |
1523 | template <class T, class U>\ | |
1524 | inline typename boost::math::tools::promote_args<T, U>::type jacobi_nd(T k, U theta)\ | |
1525 | { return boost::math::jacobi_nd(k, theta, Policy()); }\ | |
1526 | \ | |
1527 | template <class T, class U>\ | |
1528 | inline typename boost::math::tools::promote_args<T, U>::type jacobi_sc(T k, U theta)\ | |
1529 | { return boost::math::jacobi_sc(k, theta, Policy()); }\ | |
1530 | \ | |
1531 | template <class T, class U>\ | |
1532 | inline typename boost::math::tools::promote_args<T, U>::type jacobi_cs(T k, U theta)\ | |
1533 | { return boost::math::jacobi_cs(k, theta, Policy()); }\ | |
1534 | \ | |
1535 | template <class T>\ | |
1536 | inline typename boost::math::tools::promote_args<T>::type airy_ai(T x)\ | |
1537 | { return boost::math::airy_ai(x, Policy()); }\ | |
1538 | \ | |
1539 | template <class T>\ | |
1540 | inline typename boost::math::tools::promote_args<T>::type airy_bi(T x)\ | |
1541 | { return boost::math::airy_bi(x, Policy()); }\ | |
1542 | \ | |
1543 | template <class T>\ | |
1544 | inline typename boost::math::tools::promote_args<T>::type airy_ai_prime(T x)\ | |
1545 | { return boost::math::airy_ai_prime(x, Policy()); }\ | |
1546 | \ | |
1547 | template <class T>\ | |
1548 | inline typename boost::math::tools::promote_args<T>::type airy_bi_prime(T x)\ | |
1549 | { return boost::math::airy_bi_prime(x, Policy()); }\ | |
1550 | \ | |
1551 | template <class T>\ | |
1552 | inline T airy_ai_zero(int m)\ | |
1553 | { return boost::math::airy_ai_zero<T>(m, Policy()); }\ | |
1554 | template <class T, class OutputIterator>\ | |
1555 | OutputIterator airy_ai_zero(int start_index, unsigned number_of_zeros, OutputIterator out_it)\ | |
1556 | { return boost::math::airy_ai_zero<T>(start_index, number_of_zeros, out_it, Policy()); }\ | |
1557 | \ | |
1558 | template <class T>\ | |
1559 | inline T airy_bi_zero(int m)\ | |
1560 | { return boost::math::airy_bi_zero<T>(m, Policy()); }\ | |
1561 | template <class T, class OutputIterator>\ | |
1562 | OutputIterator airy_bi_zero(int start_index, unsigned number_of_zeros, OutputIterator out_it)\ | |
1563 | { return boost::math::airy_bi_zero<T>(start_index, number_of_zeros, out_it, Policy()); }\ | |
1564 | \ | |
1565 | template <class T>\ | |
1566 | T bernoulli_b2n(const int i)\ | |
1567 | { return boost::math::bernoulli_b2n<T>(i, Policy()); }\ | |
1568 | template <class T, class OutputIterator>\ | |
1569 | OutputIterator bernoulli_b2n(int start_index, unsigned number_of_bernoullis_b2n, OutputIterator out_it)\ | |
1570 | { return boost::math::bernoulli_b2n<T>(start_index, number_of_bernoullis_b2n, out_it, Policy()); }\ | |
1571 | \ | |
1572 | template <class T>\ | |
1573 | T tangent_t2n(const int i)\ | |
1574 | { return boost::math::tangent_t2n<T>(i, Policy()); }\ | |
1575 | template <class T, class OutputIterator>\ | |
1576 | OutputIterator tangent_t2n(int start_index, unsigned number_of_bernoullis_b2n, OutputIterator out_it)\ | |
1577 | { return boost::math::tangent_t2n<T>(start_index, number_of_bernoullis_b2n, out_it, Policy()); }\ | |
1578 | \ | |
1579 | ||
1580 | ||
1581 | ||
1582 | ||
1583 | ||
1584 | #endif // BOOST_MATH_SPECIAL_MATH_FWD_HPP | |
1585 | ||
1586 |