1 // TR1 cmath -*- C++ -*- 2 3 // Copyright (C) 2006, 2007, 2008, 2009 Free Software Foundation, Inc. 4 // 5 // This file is part of the GNU ISO C++ Library. This library is free 6 // software; you can redistribute it and/or modify it under the 7 // terms of the GNU General Public License as published by the 8 // Free Software Foundation; either version 3, or (at your option) 9 // any later version. 10 11 // This library is distributed in the hope that it will be useful, 12 // but WITHOUT ANY WARRANTY; without even the implied warranty of 13 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 14 // GNU General Public License for more details. 15 16 // Under Section 7 of GPL version 3, you are granted additional 17 // permissions described in the GCC Runtime Library Exception, version 18 // 3.1, as published by the Free Software Foundation. 19 20 // You should have received a copy of the GNU General Public License and 21 // a copy of the GCC Runtime Library Exception along with this program; 22 // see the files COPYING3 and COPYING.RUNTIME respectively. If not, see 23 // <http://www.gnu.org/licenses/>. 24 25 /** @file tr1/cmath 26 * This is a TR1 C++ Library header. 27 */ 28 29 #ifndef _GLIBCXX_TR1_CMATH 30 #define _GLIBCXX_TR1_CMATH 1 31 32 #pragma GCC system_header 33 34 #if defined(_GLIBCXX_INCLUDE_AS_CXX0X) 35 # error TR1 header cannot be included from C++0x header 36 #endif 37 38 #include <cmath> 39 40 #if defined(_GLIBCXX_INCLUDE_AS_TR1) 41 # include <tr1_impl/cmath> 42 #else 43 # define _GLIBCXX_INCLUDE_AS_TR1 44 # define _GLIBCXX_BEGIN_NAMESPACE_TR1 namespace tr1 { 45 # define _GLIBCXX_END_NAMESPACE_TR1 } 46 # define _GLIBCXX_TR1 tr1:: 47 # include <tr1_impl/cmath> 48 # undef _GLIBCXX_TR1 49 # undef _GLIBCXX_END_NAMESPACE_TR1 50 # undef _GLIBCXX_BEGIN_NAMESPACE_TR1 51 # undef _GLIBCXX_INCLUDE_AS_TR1 52 #endif 53 54 namespace std 55 { 56 namespace tr1 57 { 58 // DR 550. What should the return type of pow(float,int) be? 59 // NB: C++0x and TR1 != C++03. 60 inline double 61 pow(double __x, double __y) 62 { return std::pow(__x, __y); } 63 64 inline float 65 pow(float __x, float __y) 66 { return std::pow(__x, __y); } 67 68 inline long double 69 pow(long double __x, long double __y) 70 { return std::pow(__x, __y); } 71 72 template<typename _Tp, typename _Up> 73 inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type 74 pow(_Tp __x, _Up __y) 75 { 76 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type; 77 return std::pow(__type(__x), __type(__y)); 78 } 79 } 80 } 81 82 #include <bits/stl_algobase.h> 83 #include <limits> 84 #include <tr1/type_traits> 85 86 #include <tr1/gamma.tcc> 87 #include <tr1/bessel_function.tcc> 88 #include <tr1/beta_function.tcc> 89 #include <tr1/ell_integral.tcc> 90 #include <tr1/exp_integral.tcc> 91 #include <tr1/hypergeometric.tcc> 92 #include <tr1/legendre_function.tcc> 93 #include <tr1/modified_bessel_func.tcc> 94 #include <tr1/poly_hermite.tcc> 95 #include <tr1/poly_laguerre.tcc> 96 #include <tr1/riemann_zeta.tcc> 97 98 namespace std 99 { 100 namespace tr1 101 { 102 /** 103 * @defgroup tr1_math_spec_func Mathematical Special Functions 104 * @ingroup numerics 105 * 106 * A collection of advanced mathematical special functions. 107 * @{ 108 */ 109 110 inline float 111 assoc_laguerref(unsigned int __n, unsigned int __m, float __x) 112 { return __detail::__assoc_laguerre<float>(__n, __m, __x); } 113 114 inline long double 115 assoc_laguerrel(unsigned int __n, unsigned int __m, long double __x) 116 { 117 return __detail::__assoc_laguerre<long double>(__n, __m, __x); 118 } 119 120 /// 5.2.1.1 Associated Laguerre polynomials. 121 template<typename _Tp> 122 inline typename __gnu_cxx::__promote<_Tp>::__type 123 assoc_laguerre(unsigned int __n, unsigned int __m, _Tp __x) 124 { 125 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 126 return __detail::__assoc_laguerre<__type>(__n, __m, __x); 127 } 128 129 inline float 130 assoc_legendref(unsigned int __l, unsigned int __m, float __x) 131 { return __detail::__assoc_legendre_p<float>(__l, __m, __x); } 132 133 inline long double 134 assoc_legendrel(unsigned int __l, unsigned int __m, long double __x) 135 { return __detail::__assoc_legendre_p<long double>(__l, __m, __x); } 136 137 /// 5.2.1.2 Associated Legendre functions. 138 template<typename _Tp> 139 inline typename __gnu_cxx::__promote<_Tp>::__type 140 assoc_legendre(unsigned int __l, unsigned int __m, _Tp __x) 141 { 142 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 143 return __detail::__assoc_legendre_p<__type>(__l, __m, __x); 144 } 145 146 inline float 147 betaf(float __x, float __y) 148 { return __detail::__beta<float>(__x, __y); } 149 150 inline long double 151 betal(long double __x, long double __y) 152 { return __detail::__beta<long double>(__x, __y); } 153 154 /// 5.2.1.3 Beta functions. 155 template<typename _Tpx, typename _Tpy> 156 inline typename __gnu_cxx::__promote_2<_Tpx, _Tpy>::__type 157 beta(_Tpx __x, _Tpy __y) 158 { 159 typedef typename __gnu_cxx::__promote_2<_Tpx, _Tpy>::__type __type; 160 return __detail::__beta<__type>(__x, __y); 161 } 162 163 inline float 164 comp_ellint_1f(float __k) 165 { return __detail::__comp_ellint_1<float>(__k); } 166 167 inline long double 168 comp_ellint_1l(long double __k) 169 { return __detail::__comp_ellint_1<long double>(__k); } 170 171 /// 5.2.1.4 Complete elliptic integrals of the first kind. 172 template<typename _Tp> 173 inline typename __gnu_cxx::__promote<_Tp>::__type 174 comp_ellint_1(_Tp __k) 175 { 176 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 177 return __detail::__comp_ellint_1<__type>(__k); 178 } 179 180 inline float 181 comp_ellint_2f(float __k) 182 { return __detail::__comp_ellint_2<float>(__k); } 183 184 inline long double 185 comp_ellint_2l(long double __k) 186 { return __detail::__comp_ellint_2<long double>(__k); } 187 188 /// 5.2.1.5 Complete elliptic integrals of the second kind. 189 template<typename _Tp> 190 inline typename __gnu_cxx::__promote<_Tp>::__type 191 comp_ellint_2(_Tp __k) 192 { 193 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 194 return __detail::__comp_ellint_2<__type>(__k); 195 } 196 197 inline float 198 comp_ellint_3f(float __k, float __nu) 199 { return __detail::__comp_ellint_3<float>(__k, __nu); } 200 201 inline long double 202 comp_ellint_3l(long double __k, long double __nu) 203 { return __detail::__comp_ellint_3<long double>(__k, __nu); } 204 205 /// 5.2.1.6 Complete elliptic integrals of the third kind. 206 template<typename _Tp, typename _Tpn> 207 inline typename __gnu_cxx::__promote_2<_Tp, _Tpn>::__type 208 comp_ellint_3(_Tp __k, _Tpn __nu) 209 { 210 typedef typename __gnu_cxx::__promote_2<_Tp, _Tpn>::__type __type; 211 return __detail::__comp_ellint_3<__type>(__k, __nu); 212 } 213 214 inline float 215 conf_hypergf(float __a, float __c, float __x) 216 { return __detail::__conf_hyperg<float>(__a, __c, __x); } 217 218 inline long double 219 conf_hypergl(long double __a, long double __c, long double __x) 220 { return __detail::__conf_hyperg<long double>(__a, __c, __x); } 221 222 /// 5.2.1.7 Confluent hypergeometric functions. 223 template<typename _Tpa, typename _Tpc, typename _Tp> 224 inline typename __gnu_cxx::__promote_3<_Tpa, _Tpc, _Tp>::__type 225 conf_hyperg(_Tpa __a, _Tpc __c, _Tp __x) 226 { 227 typedef typename __gnu_cxx::__promote_3<_Tpa, _Tpc, _Tp>::__type __type; 228 return __detail::__conf_hyperg<__type>(__a, __c, __x); 229 } 230 231 inline float 232 cyl_bessel_if(float __nu, float __x) 233 { return __detail::__cyl_bessel_i<float>(__nu, __x); } 234 235 inline long double 236 cyl_bessel_il(long double __nu, long double __x) 237 { return __detail::__cyl_bessel_i<long double>(__nu, __x); } 238 239 /// 5.2.1.8 Regular modified cylindrical Bessel functions. 240 template<typename _Tpnu, typename _Tp> 241 inline typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type 242 cyl_bessel_i(_Tpnu __nu, _Tp __x) 243 { 244 typedef typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type __type; 245 return __detail::__cyl_bessel_i<__type>(__nu, __x); 246 } 247 248 inline float 249 cyl_bessel_jf(float __nu, float __x) 250 { return __detail::__cyl_bessel_j<float>(__nu, __x); } 251 252 inline long double 253 cyl_bessel_jl(long double __nu, long double __x) 254 { return __detail::__cyl_bessel_j<long double>(__nu, __x); } 255 256 /// 5.2.1.9 Cylindrical Bessel functions (of the first kind). 257 template<typename _Tpnu, typename _Tp> 258 inline typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type 259 cyl_bessel_j(_Tpnu __nu, _Tp __x) 260 { 261 typedef typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type __type; 262 return __detail::__cyl_bessel_j<__type>(__nu, __x); 263 } 264 265 inline float 266 cyl_bessel_kf(float __nu, float __x) 267 { return __detail::__cyl_bessel_k<float>(__nu, __x); } 268 269 inline long double 270 cyl_bessel_kl(long double __nu, long double __x) 271 { return __detail::__cyl_bessel_k<long double>(__nu, __x); } 272 273 /// 5.2.1.10 Irregular modified cylindrical Bessel functions. 274 template<typename _Tpnu, typename _Tp> 275 inline typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type 276 cyl_bessel_k(_Tpnu __nu, _Tp __x) 277 { 278 typedef typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type __type; 279 return __detail::__cyl_bessel_k<__type>(__nu, __x); 280 } 281 282 inline float 283 cyl_neumannf(float __nu, float __x) 284 { return __detail::__cyl_neumann_n<float>(__nu, __x); } 285 286 inline long double 287 cyl_neumannl(long double __nu, long double __x) 288 { return __detail::__cyl_neumann_n<long double>(__nu, __x); } 289 290 /// 5.2.1.11 Cylindrical Neumann functions. 291 template<typename _Tpnu, typename _Tp> 292 inline typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type 293 cyl_neumann(_Tpnu __nu, _Tp __x) 294 { 295 typedef typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type __type; 296 return __detail::__cyl_neumann_n<__type>(__nu, __x); 297 } 298 299 inline float 300 ellint_1f(float __k, float __phi) 301 { return __detail::__ellint_1<float>(__k, __phi); } 302 303 inline long double 304 ellint_1l(long double __k, long double __phi) 305 { return __detail::__ellint_1<long double>(__k, __phi); } 306 307 /// 5.2.1.12 Incomplete elliptic integrals of the first kind. 308 template<typename _Tp, typename _Tpp> 309 inline typename __gnu_cxx::__promote_2<_Tp, _Tpp>::__type 310 ellint_1(_Tp __k, _Tpp __phi) 311 { 312 typedef typename __gnu_cxx::__promote_2<_Tp, _Tpp>::__type __type; 313 return __detail::__ellint_1<__type>(__k, __phi); 314 } 315 316 inline float 317 ellint_2f(float __k, float __phi) 318 { return __detail::__ellint_2<float>(__k, __phi); } 319 320 inline long double 321 ellint_2l(long double __k, long double __phi) 322 { return __detail::__ellint_2<long double>(__k, __phi); } 323 324 /// 5.2.1.13 Incomplete elliptic integrals of the second kind. 325 template<typename _Tp, typename _Tpp> 326 inline typename __gnu_cxx::__promote_2<_Tp, _Tpp>::__type 327 ellint_2(_Tp __k, _Tpp __phi) 328 { 329 typedef typename __gnu_cxx::__promote_2<_Tp, _Tpp>::__type __type; 330 return __detail::__ellint_2<__type>(__k, __phi); 331 } 332 333 inline float 334 ellint_3f(float __k, float __nu, float __phi) 335 { return __detail::__ellint_3<float>(__k, __nu, __phi); } 336 337 inline long double 338 ellint_3l(long double __k, long double __nu, long double __phi) 339 { return __detail::__ellint_3<long double>(__k, __nu, __phi); } 340 341 /// 5.2.1.14 Incomplete elliptic integrals of the third kind. 342 template<typename _Tp, typename _Tpn, typename _Tpp> 343 inline typename __gnu_cxx::__promote_3<_Tp, _Tpn, _Tpp>::__type 344 ellint_3(_Tp __k, _Tpn __nu, _Tpp __phi) 345 { 346 typedef typename __gnu_cxx::__promote_3<_Tp, _Tpn, _Tpp>::__type __type; 347 return __detail::__ellint_3<__type>(__k, __nu, __phi); 348 } 349 350 inline float 351 expintf(float __x) 352 { return __detail::__expint<float>(__x); } 353 354 inline long double 355 expintl(long double __x) 356 { return __detail::__expint<long double>(__x); } 357 358 /// 5.2.1.15 Exponential integrals. 359 template<typename _Tp> 360 inline typename __gnu_cxx::__promote<_Tp>::__type 361 expint(_Tp __x) 362 { 363 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 364 return __detail::__expint<__type>(__x); 365 } 366 367 inline float 368 hermitef(unsigned int __n, float __x) 369 { return __detail::__poly_hermite<float>(__n, __x); } 370 371 inline long double 372 hermitel(unsigned int __n, long double __x) 373 { return __detail::__poly_hermite<long double>(__n, __x); } 374 375 /// 5.2.1.16 Hermite polynomials. 376 template<typename _Tp> 377 inline typename __gnu_cxx::__promote<_Tp>::__type 378 hermite(unsigned int __n, _Tp __x) 379 { 380 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 381 return __detail::__poly_hermite<__type>(__n, __x); 382 } 383 384 inline float 385 hypergf(float __a, float __b, float __c, float __x) 386 { return __detail::__hyperg<float>(__a, __b, __c, __x); } 387 388 inline long double 389 hypergl(long double __a, long double __b, long double __c, long double __x) 390 { return __detail::__hyperg<long double>(__a, __b, __c, __x); } 391 392 /// 5.2.1.17 Hypergeometric functions. 393 template<typename _Tpa, typename _Tpb, typename _Tpc, typename _Tp> 394 inline typename __gnu_cxx::__promote_4<_Tpa, _Tpb, _Tpc, _Tp>::__type 395 hyperg(_Tpa __a, _Tpb __b, _Tpc __c, _Tp __x) 396 { 397 typedef typename __gnu_cxx::__promote_4<_Tpa, _Tpb, _Tpc, _Tp>::__type __type; 398 return __detail::__hyperg<__type>(__a, __b, __c, __x); 399 } 400 401 inline float 402 laguerref(unsigned int __n, float __x) 403 { return __detail::__laguerre<float>(__n, __x); } 404 405 inline long double 406 laguerrel(unsigned int __n, long double __x) 407 { return __detail::__laguerre<long double>(__n, __x); } 408 409 /// 5.2.1.18 Laguerre polynomials. 410 template<typename _Tp> 411 inline typename __gnu_cxx::__promote<_Tp>::__type 412 laguerre(unsigned int __n, _Tp __x) 413 { 414 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 415 return __detail::__laguerre<__type>(__n, __x); 416 } 417 418 inline float 419 legendref(unsigned int __n, float __x) 420 { return __detail::__poly_legendre_p<float>(__n, __x); } 421 422 inline long double 423 legendrel(unsigned int __n, long double __x) 424 { return __detail::__poly_legendre_p<long double>(__n, __x); } 425 426 /// 5.2.1.19 Legendre polynomials. 427 template<typename _Tp> 428 inline typename __gnu_cxx::__promote<_Tp>::__type 429 legendre(unsigned int __n, _Tp __x) 430 { 431 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 432 return __detail::__poly_legendre_p<__type>(__n, __x); 433 } 434 435 inline float 436 riemann_zetaf(float __x) 437 { return __detail::__riemann_zeta<float>(__x); } 438 439 inline long double 440 riemann_zetal(long double __x) 441 { return __detail::__riemann_zeta<long double>(__x); } 442 443 /// 5.2.1.20 Riemann zeta function. 444 template<typename _Tp> 445 inline typename __gnu_cxx::__promote<_Tp>::__type 446 riemann_zeta(_Tp __x) 447 { 448 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 449 return __detail::__riemann_zeta<__type>(__x); 450 } 451 452 inline float 453 sph_besself(unsigned int __n, float __x) 454 { return __detail::__sph_bessel<float>(__n, __x); } 455 456 inline long double 457 sph_bessell(unsigned int __n, long double __x) 458 { return __detail::__sph_bessel<long double>(__n, __x); } 459 460 /// 5.2.1.21 Spherical Bessel functions. 461 template<typename _Tp> 462 inline typename __gnu_cxx::__promote<_Tp>::__type 463 sph_bessel(unsigned int __n, _Tp __x) 464 { 465 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 466 return __detail::__sph_bessel<__type>(__n, __x); 467 } 468 469 inline float 470 sph_legendref(unsigned int __l, unsigned int __m, float __theta) 471 { return __detail::__sph_legendre<float>(__l, __m, __theta); } 472 473 inline long double 474 sph_legendrel(unsigned int __l, unsigned int __m, long double __theta) 475 { return __detail::__sph_legendre<long double>(__l, __m, __theta); } 476 477 /// 5.2.1.22 Spherical associated Legendre functions. 478 template<typename _Tp> 479 inline typename __gnu_cxx::__promote<_Tp>::__type 480 sph_legendre(unsigned int __l, unsigned int __m, _Tp __theta) 481 { 482 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 483 return __detail::__sph_legendre<__type>(__l, __m, __theta); 484 } 485 486 inline float 487 sph_neumannf(unsigned int __n, float __x) 488 { return __detail::__sph_neumann<float>(__n, __x); } 489 490 inline long double 491 sph_neumannl(unsigned int __n, long double __x) 492 { return __detail::__sph_neumann<long double>(__n, __x); } 493 494 /// 5.2.1.23 Spherical Neumann functions. 495 template<typename _Tp> 496 inline typename __gnu_cxx::__promote<_Tp>::__type 497 sph_neumann(unsigned int __n, _Tp __x) 498 { 499 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 500 return __detail::__sph_neumann<__type>(__n, __x); 501 } 502 503 /* @} */ // tr1_math_spec_func 504 } 505 } 506 507 #endif // _GLIBCXX_TR1_CMATH 508
