cmath revision 1.1.1.5.2.1
1 // TR1 cmath -*- C++ -*- 2 3 // Copyright (C) 2006-2017 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 #include <cmath> 35 36 #ifdef _GLIBCXX_USE_C99_MATH_TR1 37 38 #undef acosh 39 #undef acoshf 40 #undef acoshl 41 #undef asinh 42 #undef asinhf 43 #undef asinhl 44 #undef atanh 45 #undef atanhf 46 #undef atanhl 47 #undef cbrt 48 #undef cbrtf 49 #undef cbrtl 50 #undef copysign 51 #undef copysignf 52 #undef copysignl 53 #undef erf 54 #undef erff 55 #undef erfl 56 #undef erfc 57 #undef erfcf 58 #undef erfcl 59 #undef exp2 60 #undef exp2f 61 #undef exp2l 62 #undef expm1 63 #undef expm1f 64 #undef expm1l 65 #undef fdim 66 #undef fdimf 67 #undef fdiml 68 #undef fma 69 #undef fmaf 70 #undef fmal 71 #undef fmax 72 #undef fmaxf 73 #undef fmaxl 74 #undef fmin 75 #undef fminf 76 #undef fminl 77 #undef hypot 78 #undef hypotf 79 #undef hypotl 80 #undef ilogb 81 #undef ilogbf 82 #undef ilogbl 83 #undef lgamma 84 #undef lgammaf 85 #undef lgammal 86 #undef llrint 87 #undef llrintf 88 #undef llrintl 89 #undef llround 90 #undef llroundf 91 #undef llroundl 92 #undef log1p 93 #undef log1pf 94 #undef log1pl 95 #undef log2 96 #undef log2f 97 #undef log2l 98 #undef logb 99 #undef logbf 100 #undef logbl 101 #undef lrint 102 #undef lrintf 103 #undef lrintl 104 #undef lround 105 #undef lroundf 106 #undef lroundl 107 #undef nan 108 #undef nanf 109 #undef nanl 110 #undef nearbyint 111 #undef nearbyintf 112 #undef nearbyintl 113 #undef nextafter 114 #undef nextafterf 115 #undef nextafterl 116 #undef nexttoward 117 #undef nexttowardf 118 #undef nexttowardl 119 #undef remainder 120 #undef remainderf 121 #undef remainderl 122 #undef remquo 123 #undef remquof 124 #undef remquol 125 #undef rint 126 #undef rintf 127 #undef rintl 128 #undef round 129 #undef roundf 130 #undef roundl 131 #undef scalbln 132 #undef scalblnf 133 #undef scalblnl 134 #undef scalbn 135 #undef scalbnf 136 #undef scalbnl 137 #undef tgamma 138 #undef tgammaf 139 #undef tgammal 140 #undef trunc 141 #undef truncf 142 #undef truncl 143 144 #endif 145 146 namespace std _GLIBCXX_VISIBILITY(default) 147 { 148 namespace tr1 149 { 150 _GLIBCXX_BEGIN_NAMESPACE_VERSION 151 152 #if _GLIBCXX_USE_C99_MATH_TR1 153 154 // Using declarations to bring names from libc's <math.h> into std::tr1. 155 156 // types 157 using ::double_t; 158 using ::float_t; 159 160 // functions 161 using ::acosh; 162 using ::acoshf; 163 using ::acoshl; 164 165 using ::asinh; 166 using ::asinhf; 167 using ::asinhl; 168 169 using ::atanh; 170 using ::atanhf; 171 using ::atanhl; 172 173 using ::cbrt; 174 using ::cbrtf; 175 using ::cbrtl; 176 177 using ::copysign; 178 using ::copysignf; 179 using ::copysignl; 180 181 using ::erf; 182 using ::erff; 183 using ::erfl; 184 185 using ::erfc; 186 using ::erfcf; 187 using ::erfcl; 188 189 using ::exp2; 190 using ::exp2f; 191 using ::exp2l; 192 193 using ::expm1; 194 using ::expm1f; 195 using ::expm1l; 196 197 using ::fdim; 198 using ::fdimf; 199 using ::fdiml; 200 201 using ::fma; 202 using ::fmaf; 203 using ::fmal; 204 205 using ::fmax; 206 using ::fmaxf; 207 using ::fmaxl; 208 209 using ::fmin; 210 using ::fminf; 211 using ::fminl; 212 213 using ::hypot; 214 using ::hypotf; 215 using ::hypotl; 216 217 using ::ilogb; 218 using ::ilogbf; 219 using ::ilogbl; 220 221 using ::lgamma; 222 using ::lgammaf; 223 using ::lgammal; 224 225 using ::llrint; 226 using ::llrintf; 227 using ::llrintl; 228 229 using ::llround; 230 using ::llroundf; 231 using ::llroundl; 232 233 using ::log1p; 234 using ::log1pf; 235 using ::log1pl; 236 237 using ::log2; 238 using ::log2f; 239 using ::log2l; 240 241 using ::logb; 242 using ::logbf; 243 using ::logbl; 244 245 using ::lrint; 246 using ::lrintf; 247 using ::lrintl; 248 249 using ::lround; 250 using ::lroundf; 251 using ::lroundl; 252 253 using ::nan; 254 using ::nanf; 255 using ::nanl; 256 257 using ::nearbyint; 258 using ::nearbyintf; 259 using ::nearbyintl; 260 261 using ::nextafter; 262 using ::nextafterf; 263 using ::nextafterl; 264 265 using ::nexttoward; 266 using ::nexttowardf; 267 using ::nexttowardl; 268 269 using ::remainder; 270 using ::remainderf; 271 using ::remainderl; 272 273 using ::remquo; 274 using ::remquof; 275 using ::remquol; 276 277 using ::rint; 278 using ::rintf; 279 using ::rintl; 280 281 using ::round; 282 using ::roundf; 283 using ::roundl; 284 285 using ::scalbln; 286 using ::scalblnf; 287 using ::scalblnl; 288 289 using ::scalbn; 290 using ::scalbnf; 291 using ::scalbnl; 292 293 using ::tgamma; 294 using ::tgammaf; 295 using ::tgammal; 296 297 using ::trunc; 298 using ::truncf; 299 using ::truncl; 300 301 #endif 302 303 #if _GLIBCXX_USE_C99_MATH 304 #if !_GLIBCXX_USE_C99_FP_MACROS_DYNAMIC 305 306 /// Function template definitions [8.16.3]. 307 template<typename _Tp> 308 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value, 309 int>::__type 310 fpclassify(_Tp __f) 311 { 312 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 313 return __builtin_fpclassify(FP_NAN, FP_INFINITE, FP_NORMAL, 314 FP_SUBNORMAL, FP_ZERO, __type(__f)); 315 } 316 317 template<typename _Tp> 318 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value, 319 int>::__type 320 isfinite(_Tp __f) 321 { 322 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 323 return __builtin_isfinite(__type(__f)); 324 } 325 326 template<typename _Tp> 327 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value, 328 int>::__type 329 isinf(_Tp __f) 330 { 331 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 332 return __builtin_isinf(__type(__f)); 333 } 334 335 template<typename _Tp> 336 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value, 337 int>::__type 338 isnan(_Tp __f) 339 { 340 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 341 return __builtin_isnan(__type(__f)); 342 } 343 344 template<typename _Tp> 345 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value, 346 int>::__type 347 isnormal(_Tp __f) 348 { 349 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 350 return __builtin_isnormal(__type(__f)); 351 } 352 353 template<typename _Tp> 354 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value, 355 int>::__type 356 signbit(_Tp __f) 357 { 358 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 359 return __builtin_signbit(__type(__f)); 360 } 361 362 template<typename _Tp> 363 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value, 364 int>::__type 365 isgreater(_Tp __f1, _Tp __f2) 366 { 367 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 368 return __builtin_isgreater(__type(__f1), __type(__f2)); 369 } 370 371 template<typename _Tp> 372 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value, 373 int>::__type 374 isgreaterequal(_Tp __f1, _Tp __f2) 375 { 376 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 377 return __builtin_isgreaterequal(__type(__f1), __type(__f2)); 378 } 379 380 template<typename _Tp> 381 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value, 382 int>::__type 383 isless(_Tp __f1, _Tp __f2) 384 { 385 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 386 return __builtin_isless(__type(__f1), __type(__f2)); 387 } 388 389 template<typename _Tp> 390 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value, 391 int>::__type 392 islessequal(_Tp __f1, _Tp __f2) 393 { 394 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 395 return __builtin_islessequal(__type(__f1), __type(__f2)); 396 } 397 398 template<typename _Tp> 399 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value, 400 int>::__type 401 islessgreater(_Tp __f1, _Tp __f2) 402 { 403 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 404 return __builtin_islessgreater(__type(__f1), __type(__f2)); 405 } 406 407 template<typename _Tp> 408 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value, 409 int>::__type 410 isunordered(_Tp __f1, _Tp __f2) 411 { 412 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 413 return __builtin_isunordered(__type(__f1), __type(__f2)); 414 } 415 416 #endif 417 #endif 418 419 #if _GLIBCXX_USE_C99_MATH_TR1 420 421 /** Additional overloads [8.16.4]. 422 * @{ 423 */ 424 425 // For functions defined in C++03 the additional overloads are already 426 // declared in <cmath> so we can just re-declare them in std::tr1. 427 428 using std::acos; 429 using std::asin; 430 using std::atan; 431 using std::atan2; 432 using std::ceil; 433 using std::cos; 434 using std::cosh; 435 using std::exp; 436 using std::floor; 437 using std::fmod; 438 using std::frexp; 439 using std::ldexp; 440 using std::log; 441 using std::log10; 442 using std::sin; 443 using std::sinh; 444 using std::sqrt; 445 using std::tan; 446 using std::tanh; 447 448 #if __cplusplus >= 201103L 449 450 // Since C++11, <cmath> defines additional overloads for these functions 451 // in namespace std. 452 453 using std::acosh; 454 using std::asinh; 455 using std::atanh; 456 using std::cbrt; 457 using std::copysign; 458 using std::erf; 459 using std::erfc; 460 using std::exp2; 461 using std::expm1; 462 using std::fdim; 463 using std::fma; 464 using std::fmax; 465 using std::fmin; 466 using std::hypot; 467 using std::ilogb; 468 using std::lgamma; 469 using std::llrint; 470 using std::llround; 471 using std::log1p; 472 using std::log2; 473 using std::logb; 474 using std::lrint; 475 using std::lround; 476 using std::nan; 477 using std::nearbyint; 478 using std::nextafter; 479 using std::nexttoward; 480 using std::remainder; 481 using std::remquo; 482 using std::rint; 483 using std::round; 484 using std::scalbln; 485 using std::scalbn; 486 using std::tgamma; 487 using std::trunc; 488 489 #else // __cplusplus < 201103L 490 491 // In C++03 we need to provide the additional overloads. 492 493 #ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP 494 inline float 495 acosh(float __x) 496 { return __builtin_acoshf(__x); } 497 498 inline long double 499 acosh(long double __x) 500 { return __builtin_acoshl(__x); } 501 #endif 502 503 template<typename _Tp> 504 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 505 double>::__type 506 acosh(_Tp __x) 507 { return __builtin_acosh(__x); } 508 509 #ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP 510 inline float 511 asinh(float __x) 512 { return __builtin_asinhf(__x); } 513 514 inline long double 515 asinh(long double __x) 516 { return __builtin_asinhl(__x); } 517 #endif 518 519 template<typename _Tp> 520 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 521 double>::__type 522 asinh(_Tp __x) 523 { return __builtin_asinh(__x); } 524 525 #ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP 526 inline float 527 atanh(float __x) 528 { return __builtin_atanhf(__x); } 529 530 inline long double 531 atanh(long double __x) 532 { return __builtin_atanhl(__x); } 533 #endif 534 535 template<typename _Tp> 536 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 537 double>::__type 538 atanh(_Tp __x) 539 { return __builtin_atanh(__x); } 540 541 #ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP 542 inline float 543 cbrt(float __x) 544 { return __builtin_cbrtf(__x); } 545 546 inline long double 547 cbrt(long double __x) 548 { return __builtin_cbrtl(__x); } 549 #endif 550 551 template<typename _Tp> 552 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 553 double>::__type 554 cbrt(_Tp __x) 555 { return __builtin_cbrt(__x); } 556 557 #ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP 558 inline float 559 copysign(float __x, float __y) 560 { return __builtin_copysignf(__x, __y); } 561 562 inline long double 563 copysign(long double __x, long double __y) 564 { return __builtin_copysignl(__x, __y); } 565 #endif 566 567 template<typename _Tp, typename _Up> 568 inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type 569 copysign(_Tp __x, _Up __y) 570 { 571 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type; 572 return copysign(__type(__x), __type(__y)); 573 } 574 575 #ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP 576 inline float 577 erf(float __x) 578 { return __builtin_erff(__x); } 579 580 inline long double 581 erf(long double __x) 582 { return __builtin_erfl(__x); } 583 #endif 584 585 template<typename _Tp> 586 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 587 double>::__type 588 erf(_Tp __x) 589 { return __builtin_erf(__x); } 590 591 #ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP 592 inline float 593 erfc(float __x) 594 { return __builtin_erfcf(__x); } 595 596 inline long double 597 erfc(long double __x) 598 { return __builtin_erfcl(__x); } 599 #endif 600 601 template<typename _Tp> 602 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 603 double>::__type 604 erfc(_Tp __x) 605 { return __builtin_erfc(__x); } 606 607 #ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP 608 inline float 609 exp2(float __x) 610 { return __builtin_exp2f(__x); } 611 612 inline long double 613 exp2(long double __x) 614 { return __builtin_exp2l(__x); } 615 #endif 616 617 template<typename _Tp> 618 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 619 double>::__type 620 exp2(_Tp __x) 621 { return __builtin_exp2(__x); } 622 623 #ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP 624 inline float 625 expm1(float __x) 626 { return __builtin_expm1f(__x); } 627 628 inline long double 629 expm1(long double __x) 630 { return __builtin_expm1l(__x); } 631 #endif 632 633 template<typename _Tp> 634 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 635 double>::__type 636 expm1(_Tp __x) 637 { return __builtin_expm1(__x); } 638 639 #ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP 640 inline float 641 fdim(float __x, float __y) 642 { return __builtin_fdimf(__x, __y); } 643 644 inline long double 645 fdim(long double __x, long double __y) 646 { return __builtin_fdiml(__x, __y); } 647 #endif 648 649 template<typename _Tp, typename _Up> 650 inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type 651 fdim(_Tp __x, _Up __y) 652 { 653 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type; 654 return fdim(__type(__x), __type(__y)); 655 } 656 657 #ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP 658 inline float 659 fma(float __x, float __y, float __z) 660 { return __builtin_fmaf(__x, __y, __z); } 661 662 inline long double 663 fma(long double __x, long double __y, long double __z) 664 { return __builtin_fmal(__x, __y, __z); } 665 #endif 666 667 template<typename _Tp, typename _Up, typename _Vp> 668 inline typename __gnu_cxx::__promote_3<_Tp, _Up, _Vp>::__type 669 fma(_Tp __x, _Up __y, _Vp __z) 670 { 671 typedef typename __gnu_cxx::__promote_3<_Tp, _Up, _Vp>::__type __type; 672 return fma(__type(__x), __type(__y), __type(__z)); 673 } 674 675 #ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP 676 inline float 677 fmax(float __x, float __y) 678 { return __builtin_fmaxf(__x, __y); } 679 680 inline long double 681 fmax(long double __x, long double __y) 682 { return __builtin_fmaxl(__x, __y); } 683 #endif 684 685 template<typename _Tp, typename _Up> 686 inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type 687 fmax(_Tp __x, _Up __y) 688 { 689 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type; 690 return fmax(__type(__x), __type(__y)); 691 } 692 693 #ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP 694 inline float 695 fmin(float __x, float __y) 696 { return __builtin_fminf(__x, __y); } 697 698 inline long double 699 fmin(long double __x, long double __y) 700 { return __builtin_fminl(__x, __y); } 701 #endif 702 703 template<typename _Tp, typename _Up> 704 inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type 705 fmin(_Tp __x, _Up __y) 706 { 707 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type; 708 return fmin(__type(__x), __type(__y)); 709 } 710 711 #ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP 712 inline float 713 hypot(float __x, float __y) 714 { return __builtin_hypotf(__x, __y); } 715 716 inline long double 717 hypot(long double __x, long double __y) 718 { return __builtin_hypotl(__x, __y); } 719 #endif 720 721 template<typename _Tp, typename _Up> 722 inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type 723 hypot(_Tp __y, _Up __x) 724 { 725 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type; 726 return hypot(__type(__y), __type(__x)); 727 } 728 729 #ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP 730 inline int 731 ilogb(float __x) 732 { return __builtin_ilogbf(__x); } 733 734 inline int 735 ilogb(long double __x) 736 { return __builtin_ilogbl(__x); } 737 #endif 738 739 template<typename _Tp> 740 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 741 int>::__type 742 ilogb(_Tp __x) 743 { return __builtin_ilogb(__x); } 744 745 #ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP 746 inline float 747 lgamma(float __x) 748 { return __builtin_lgammaf(__x); } 749 750 inline long double 751 lgamma(long double __x) 752 { return __builtin_lgammal(__x); } 753 #endif 754 755 template<typename _Tp> 756 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 757 double>::__type 758 lgamma(_Tp __x) 759 { return __builtin_lgamma(__x); } 760 761 #ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP 762 inline long long 763 llrint(float __x) 764 { return __builtin_llrintf(__x); } 765 766 inline long long 767 llrint(long double __x) 768 { return __builtin_llrintl(__x); } 769 #endif 770 771 template<typename _Tp> 772 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 773 long long>::__type 774 llrint(_Tp __x) 775 { return __builtin_llrint(__x); } 776 777 #ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP 778 inline long long 779 llround(float __x) 780 { return __builtin_llroundf(__x); } 781 782 inline long long 783 llround(long double __x) 784 { return __builtin_llroundl(__x); } 785 #endif 786 787 template<typename _Tp> 788 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 789 long long>::__type 790 llround(_Tp __x) 791 { return __builtin_llround(__x); } 792 793 #ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP 794 inline float 795 log1p(float __x) 796 { return __builtin_log1pf(__x); } 797 798 inline long double 799 log1p(long double __x) 800 { return __builtin_log1pl(__x); } 801 #endif 802 803 template<typename _Tp> 804 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 805 double>::__type 806 log1p(_Tp __x) 807 { return __builtin_log1p(__x); } 808 809 // DR 568. 810 #ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP 811 inline float 812 log2(float __x) 813 { return __builtin_log2f(__x); } 814 815 inline long double 816 log2(long double __x) 817 { return __builtin_log2l(__x); } 818 #endif 819 820 template<typename _Tp> 821 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 822 double>::__type 823 log2(_Tp __x) 824 { return __builtin_log2(__x); } 825 826 #ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP 827 inline float 828 logb(float __x) 829 { return __builtin_logbf(__x); } 830 831 inline long double 832 logb(long double __x) 833 { return __builtin_logbl(__x); } 834 #endif 835 836 template<typename _Tp> 837 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 838 double>::__type 839 logb(_Tp __x) 840 { 841 return __builtin_logb(__x); 842 } 843 844 #ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP 845 inline long 846 lrint(float __x) 847 { return __builtin_lrintf(__x); } 848 849 inline long 850 lrint(long double __x) 851 { return __builtin_lrintl(__x); } 852 #endif 853 854 template<typename _Tp> 855 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 856 long>::__type 857 lrint(_Tp __x) 858 { return __builtin_lrint(__x); } 859 860 #ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP 861 inline long 862 lround(float __x) 863 { return __builtin_lroundf(__x); } 864 865 inline long 866 lround(long double __x) 867 { return __builtin_lroundl(__x); } 868 #endif 869 870 template<typename _Tp> 871 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 872 long>::__type 873 lround(_Tp __x) 874 { return __builtin_lround(__x); } 875 876 #ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP 877 inline float 878 nearbyint(float __x) 879 { return __builtin_nearbyintf(__x); } 880 881 inline long double 882 nearbyint(long double __x) 883 { return __builtin_nearbyintl(__x); } 884 #endif 885 886 template<typename _Tp> 887 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 888 double>::__type 889 nearbyint(_Tp __x) 890 { return __builtin_nearbyint(__x); } 891 892 #ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP 893 inline float 894 nextafter(float __x, float __y) 895 { return __builtin_nextafterf(__x, __y); } 896 897 inline long double 898 nextafter(long double __x, long double __y) 899 { return __builtin_nextafterl(__x, __y); } 900 #endif 901 902 template<typename _Tp, typename _Up> 903 inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type 904 nextafter(_Tp __x, _Up __y) 905 { 906 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type; 907 return nextafter(__type(__x), __type(__y)); 908 } 909 910 #ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP 911 inline float 912 nexttoward(float __x, long double __y) 913 { return __builtin_nexttowardf(__x, __y); } 914 915 inline long double 916 nexttoward(long double __x, long double __y) 917 { return __builtin_nexttowardl(__x, __y); } 918 #endif 919 920 template<typename _Tp> 921 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 922 double>::__type 923 nexttoward(_Tp __x, long double __y) 924 { return __builtin_nexttoward(__x, __y); } 925 926 #ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP 927 inline float 928 remainder(float __x, float __y) 929 { return __builtin_remainderf(__x, __y); } 930 931 inline long double 932 remainder(long double __x, long double __y) 933 { return __builtin_remainderl(__x, __y); } 934 #endif 935 936 template<typename _Tp, typename _Up> 937 inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type 938 remainder(_Tp __x, _Up __y) 939 { 940 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type; 941 return remainder(__type(__x), __type(__y)); 942 } 943 944 #ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP 945 inline float 946 remquo(float __x, float __y, int* __pquo) 947 { return __builtin_remquof(__x, __y, __pquo); } 948 949 inline long double 950 remquo(long double __x, long double __y, int* __pquo) 951 { return __builtin_remquol(__x, __y, __pquo); } 952 #endif 953 954 template<typename _Tp, typename _Up> 955 inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type 956 remquo(_Tp __x, _Up __y, int* __pquo) 957 { 958 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type; 959 return remquo(__type(__x), __type(__y), __pquo); 960 } 961 962 #ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP 963 inline float 964 rint(float __x) 965 { return __builtin_rintf(__x); } 966 967 inline long double 968 rint(long double __x) 969 { return __builtin_rintl(__x); } 970 #endif 971 972 template<typename _Tp> 973 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 974 double>::__type 975 rint(_Tp __x) 976 { return __builtin_rint(__x); } 977 978 #ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP 979 inline float 980 round(float __x) 981 { return __builtin_roundf(__x); } 982 983 inline long double 984 round(long double __x) 985 { return __builtin_roundl(__x); } 986 #endif 987 988 template<typename _Tp> 989 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 990 double>::__type 991 round(_Tp __x) 992 { return __builtin_round(__x); } 993 994 #ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP 995 inline float 996 scalbln(float __x, long __ex) 997 { return __builtin_scalblnf(__x, __ex); } 998 999 inline long double 1000 scalbln(long double __x, long __ex) 1001 { return __builtin_scalblnl(__x, __ex); } 1002 #endif 1003 1004 template<typename _Tp> 1005 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 1006 double>::__type 1007 scalbln(_Tp __x, long __ex) 1008 { return __builtin_scalbln(__x, __ex); } 1009 1010 #ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP 1011 inline float 1012 scalbn(float __x, int __ex) 1013 { return __builtin_scalbnf(__x, __ex); } 1014 1015 inline long double 1016 scalbn(long double __x, int __ex) 1017 { return __builtin_scalbnl(__x, __ex); } 1018 #endif 1019 1020 template<typename _Tp> 1021 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 1022 double>::__type 1023 scalbn(_Tp __x, int __ex) 1024 { return __builtin_scalbn(__x, __ex); } 1025 1026 #ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP 1027 inline float 1028 tgamma(float __x) 1029 { return __builtin_tgammaf(__x); } 1030 1031 inline long double 1032 tgamma(long double __x) 1033 { return __builtin_tgammal(__x); } 1034 #endif 1035 1036 template<typename _Tp> 1037 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 1038 double>::__type 1039 tgamma(_Tp __x) 1040 { return __builtin_tgamma(__x); } 1041 1042 #ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP 1043 inline float 1044 trunc(float __x) 1045 { return __builtin_truncf(__x); } 1046 1047 inline long double 1048 trunc(long double __x) 1049 { return __builtin_truncl(__x); } 1050 #endif 1051 1052 template<typename _Tp> 1053 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 1054 double>::__type 1055 trunc(_Tp __x) 1056 { return __builtin_trunc(__x); } 1057 1058 #endif // __cplusplus < 201103L 1059 1060 // @} 1061 1062 #endif 1063 _GLIBCXX_END_NAMESPACE_VERSION 1064 } 1065 } 1066 1067 namespace std _GLIBCXX_VISIBILITY(default) 1068 { 1069 namespace tr1 1070 { 1071 _GLIBCXX_BEGIN_NAMESPACE_VERSION 1072 1073 // DR 550. What should the return type of pow(float,int) be? 1074 // NB: C++11 and TR1 != C++03. 1075 1076 // We cannot do "using std::pow;" because that would bring in unwanted 1077 // pow(*, int) overloads in C++03, with the wrong return type. Instead we 1078 // define all the necessary overloads, but the std::tr1::pow(double, double) 1079 // overload cannot be provided here, because <tr1/math.h> would add it to 1080 // the global namespace where it would clash with ::pow(double,double) from 1081 // libc (revealed by the fix of PR c++/54537). 1082 // The solution is to forward std::tr1::pow(double,double) to 1083 // std::pow(double,double) via the function template below. See 1084 // the discussion about this issue here: 1085 // http://gcc.gnu.org/ml/gcc-patches/2012-09/msg01278.html 1086 1087 #ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP 1088 inline float 1089 pow(float __x, float __y) 1090 { return std::pow(__x, __y); } 1091 1092 inline long double 1093 pow(long double __x, long double __y) 1094 { return std::pow(__x, __y); } 1095 #endif 1096 1097 template<typename _Tp, typename _Up> 1098 inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type 1099 pow(_Tp __x, _Up __y) 1100 { 1101 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type; 1102 return std::pow(__type(__x), __type(__y)); 1103 } 1104 1105 #if __cplusplus >= 201103L 1106 // We also deal with fabs in a special way, because "using std::fabs;" 1107 // could bring in C++11's std::fabs<T>(const std::complex<T>&) with a 1108 // different return type from std::tr1::fabs<T>(const std::complex<T>&). 1109 // We define the necessary overloads, except std::tr1::fabs(double) which 1110 // could clash with ::fabs(double) from libc. 1111 // The function template handles double as well as integers, forwarding 1112 // to std::fabs. 1113 1114 #ifndef __CORRECT_ISO_CPP_MATH_H_PROTO 1115 #ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP 1116 inline float 1117 fabs(float __x) 1118 { return __builtin_fabsf(__x); } 1119 1120 inline long double 1121 fabs(long double __x) 1122 { return __builtin_fabsl(__x); } 1123 #endif 1124 #endif 1125 1126 template<typename _Tp> 1127 inline typename __gnu_cxx::__promote<_Tp>::__type 1128 fabs(_Tp __x) 1129 { return std::fabs(__x); } 1130 1131 #else // ! C++11 1132 1133 // For C++03 just use std::fabs as there is no overload for std::complex<>. 1134 using std::fabs; 1135 1136 #endif // C++11 1137 1138 1139 1140 _GLIBCXX_END_NAMESPACE_VERSION 1141 } 1142 } 1143 1144 #if _GLIBCXX_USE_STD_SPEC_FUNCS 1145 1146 namespace std _GLIBCXX_VISIBILITY(default) 1147 { 1148 namespace tr1 1149 { 1150 _GLIBCXX_BEGIN_NAMESPACE_VERSION 1151 1152 /** 1153 * @defgroup tr1_math_spec_func Mathematical Special Functions 1154 * @ingroup numerics 1155 * 1156 * A collection of advanced mathematical special functions. 1157 * @{ 1158 */ 1159 1160 using std::assoc_laguerref; 1161 using std::assoc_laguerrel; 1162 using std::assoc_laguerre; 1163 1164 using std::assoc_legendref; 1165 using std::assoc_legendrel; 1166 using std::assoc_legendre; 1167 1168 using std::betaf; 1169 using std::betal; 1170 using std::beta; 1171 1172 using std::comp_ellint_1f; 1173 using std::comp_ellint_1l; 1174 using std::comp_ellint_1; 1175 1176 using std::comp_ellint_2f; 1177 using std::comp_ellint_2l; 1178 using std::comp_ellint_2; 1179 1180 using std::comp_ellint_3f; 1181 using std::comp_ellint_3l; 1182 using std::comp_ellint_3; 1183 1184 using __gnu_cxx::conf_hypergf; 1185 using __gnu_cxx::conf_hypergl; 1186 using __gnu_cxx::conf_hyperg; 1187 1188 using std::cyl_bessel_if; 1189 using std::cyl_bessel_il; 1190 using std::cyl_bessel_i; 1191 1192 using std::cyl_bessel_jf; 1193 using std::cyl_bessel_jl; 1194 using std::cyl_bessel_j; 1195 1196 using std::cyl_bessel_kf; 1197 using std::cyl_bessel_kl; 1198 using std::cyl_bessel_k; 1199 1200 using std::cyl_neumannf; 1201 using std::cyl_neumannl; 1202 using std::cyl_neumann; 1203 1204 using std::ellint_1f; 1205 using std::ellint_1l; 1206 using std::ellint_1; 1207 1208 using std::ellint_2f; 1209 using std::ellint_2l; 1210 using std::ellint_2; 1211 1212 using std::ellint_3f; 1213 using std::ellint_3l; 1214 using std::ellint_3; 1215 1216 using std::expintf; 1217 using std::expintl; 1218 using std::expint; 1219 1220 using std::hermitef; 1221 using std::hermitel; 1222 using std::hermite; 1223 1224 using __gnu_cxx::hypergf; 1225 using __gnu_cxx::hypergl; 1226 using __gnu_cxx::hyperg; 1227 1228 using std::laguerref; 1229 using std::laguerrel; 1230 using std::laguerre; 1231 1232 using std::legendref; 1233 using std::legendrel; 1234 using std::legendre; 1235 1236 using std::riemann_zetaf; 1237 using std::riemann_zetal; 1238 using std::riemann_zeta; 1239 1240 using std::sph_besself; 1241 using std::sph_bessell; 1242 using std::sph_bessel; 1243 1244 using std::sph_legendref; 1245 using std::sph_legendrel; 1246 using std::sph_legendre; 1247 1248 using std::sph_neumannf; 1249 using std::sph_neumannl; 1250 using std::sph_neumann; 1251 1252 /* @} */ // tr1_math_spec_func 1253 _GLIBCXX_END_NAMESPACE_VERSION 1254 } 1255 } 1256 1257 #else // ! _GLIBCXX_USE_STD_SPEC_FUNCS 1258 1259 #include <bits/stl_algobase.h> 1260 #include <limits> 1261 #include <tr1/type_traits> 1262 1263 #include <tr1/gamma.tcc> 1264 #include <tr1/bessel_function.tcc> 1265 #include <tr1/beta_function.tcc> 1266 #include <tr1/ell_integral.tcc> 1267 #include <tr1/exp_integral.tcc> 1268 #include <tr1/hypergeometric.tcc> 1269 #include <tr1/legendre_function.tcc> 1270 #include <tr1/modified_bessel_func.tcc> 1271 #include <tr1/poly_hermite.tcc> 1272 #include <tr1/poly_laguerre.tcc> 1273 #include <tr1/riemann_zeta.tcc> 1274 1275 namespace std _GLIBCXX_VISIBILITY(default) 1276 { 1277 namespace tr1 1278 { 1279 _GLIBCXX_BEGIN_NAMESPACE_VERSION 1280 1281 /** 1282 * @defgroup tr1_math_spec_func Mathematical Special Functions 1283 * @ingroup numerics 1284 * 1285 * A collection of advanced mathematical special functions. 1286 * @{ 1287 */ 1288 1289 inline float 1290 assoc_laguerref(unsigned int __n, unsigned int __m, float __x) 1291 { return __detail::__assoc_laguerre<float>(__n, __m, __x); } 1292 1293 inline long double 1294 assoc_laguerrel(unsigned int __n, unsigned int __m, long double __x) 1295 { 1296 return __detail::__assoc_laguerre<long double>(__n, __m, __x); 1297 } 1298 1299 /// 5.2.1.1 Associated Laguerre polynomials. 1300 template<typename _Tp> 1301 inline typename __gnu_cxx::__promote<_Tp>::__type 1302 assoc_laguerre(unsigned int __n, unsigned int __m, _Tp __x) 1303 { 1304 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 1305 return __detail::__assoc_laguerre<__type>(__n, __m, __x); 1306 } 1307 1308 inline float 1309 assoc_legendref(unsigned int __l, unsigned int __m, float __x) 1310 { return __detail::__assoc_legendre_p<float>(__l, __m, __x); } 1311 1312 inline long double 1313 assoc_legendrel(unsigned int __l, unsigned int __m, long double __x) 1314 { return __detail::__assoc_legendre_p<long double>(__l, __m, __x); } 1315 1316 /// 5.2.1.2 Associated Legendre functions. 1317 template<typename _Tp> 1318 inline typename __gnu_cxx::__promote<_Tp>::__type 1319 assoc_legendre(unsigned int __l, unsigned int __m, _Tp __x) 1320 { 1321 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 1322 return __detail::__assoc_legendre_p<__type>(__l, __m, __x); 1323 } 1324 1325 inline float 1326 betaf(float __x, float __y) 1327 { return __detail::__beta<float>(__x, __y); } 1328 1329 inline long double 1330 betal(long double __x, long double __y) 1331 { return __detail::__beta<long double>(__x, __y); } 1332 1333 /// 5.2.1.3 Beta functions. 1334 template<typename _Tpx, typename _Tpy> 1335 inline typename __gnu_cxx::__promote_2<_Tpx, _Tpy>::__type 1336 beta(_Tpx __x, _Tpy __y) 1337 { 1338 typedef typename __gnu_cxx::__promote_2<_Tpx, _Tpy>::__type __type; 1339 return __detail::__beta<__type>(__x, __y); 1340 } 1341 1342 inline float 1343 comp_ellint_1f(float __k) 1344 { return __detail::__comp_ellint_1<float>(__k); } 1345 1346 inline long double 1347 comp_ellint_1l(long double __k) 1348 { return __detail::__comp_ellint_1<long double>(__k); } 1349 1350 /// 5.2.1.4 Complete elliptic integrals of the first kind. 1351 template<typename _Tp> 1352 inline typename __gnu_cxx::__promote<_Tp>::__type 1353 comp_ellint_1(_Tp __k) 1354 { 1355 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 1356 return __detail::__comp_ellint_1<__type>(__k); 1357 } 1358 1359 inline float 1360 comp_ellint_2f(float __k) 1361 { return __detail::__comp_ellint_2<float>(__k); } 1362 1363 inline long double 1364 comp_ellint_2l(long double __k) 1365 { return __detail::__comp_ellint_2<long double>(__k); } 1366 1367 /// 5.2.1.5 Complete elliptic integrals of the second kind. 1368 template<typename _Tp> 1369 inline typename __gnu_cxx::__promote<_Tp>::__type 1370 comp_ellint_2(_Tp __k) 1371 { 1372 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 1373 return __detail::__comp_ellint_2<__type>(__k); 1374 } 1375 1376 inline float 1377 comp_ellint_3f(float __k, float __nu) 1378 { return __detail::__comp_ellint_3<float>(__k, __nu); } 1379 1380 inline long double 1381 comp_ellint_3l(long double __k, long double __nu) 1382 { return __detail::__comp_ellint_3<long double>(__k, __nu); } 1383 1384 /// 5.2.1.6 Complete elliptic integrals of the third kind. 1385 template<typename _Tp, typename _Tpn> 1386 inline typename __gnu_cxx::__promote_2<_Tp, _Tpn>::__type 1387 comp_ellint_3(_Tp __k, _Tpn __nu) 1388 { 1389 typedef typename __gnu_cxx::__promote_2<_Tp, _Tpn>::__type __type; 1390 return __detail::__comp_ellint_3<__type>(__k, __nu); 1391 } 1392 1393 inline float 1394 conf_hypergf(float __a, float __c, float __x) 1395 { return __detail::__conf_hyperg<float>(__a, __c, __x); } 1396 1397 inline long double 1398 conf_hypergl(long double __a, long double __c, long double __x) 1399 { return __detail::__conf_hyperg<long double>(__a, __c, __x); } 1400 1401 /// 5.2.1.7 Confluent hypergeometric functions. 1402 template<typename _Tpa, typename _Tpc, typename _Tp> 1403 inline typename __gnu_cxx::__promote_3<_Tpa, _Tpc, _Tp>::__type 1404 conf_hyperg(_Tpa __a, _Tpc __c, _Tp __x) 1405 { 1406 typedef typename __gnu_cxx::__promote_3<_Tpa, _Tpc, _Tp>::__type __type; 1407 return __detail::__conf_hyperg<__type>(__a, __c, __x); 1408 } 1409 1410 inline float 1411 cyl_bessel_if(float __nu, float __x) 1412 { return __detail::__cyl_bessel_i<float>(__nu, __x); } 1413 1414 inline long double 1415 cyl_bessel_il(long double __nu, long double __x) 1416 { return __detail::__cyl_bessel_i<long double>(__nu, __x); } 1417 1418 /// 5.2.1.8 Regular modified cylindrical Bessel functions. 1419 template<typename _Tpnu, typename _Tp> 1420 inline typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type 1421 cyl_bessel_i(_Tpnu __nu, _Tp __x) 1422 { 1423 typedef typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type __type; 1424 return __detail::__cyl_bessel_i<__type>(__nu, __x); 1425 } 1426 1427 inline float 1428 cyl_bessel_jf(float __nu, float __x) 1429 { return __detail::__cyl_bessel_j<float>(__nu, __x); } 1430 1431 inline long double 1432 cyl_bessel_jl(long double __nu, long double __x) 1433 { return __detail::__cyl_bessel_j<long double>(__nu, __x); } 1434 1435 /// 5.2.1.9 Cylindrical Bessel functions (of the first kind). 1436 template<typename _Tpnu, typename _Tp> 1437 inline typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type 1438 cyl_bessel_j(_Tpnu __nu, _Tp __x) 1439 { 1440 typedef typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type __type; 1441 return __detail::__cyl_bessel_j<__type>(__nu, __x); 1442 } 1443 1444 inline float 1445 cyl_bessel_kf(float __nu, float __x) 1446 { return __detail::__cyl_bessel_k<float>(__nu, __x); } 1447 1448 inline long double 1449 cyl_bessel_kl(long double __nu, long double __x) 1450 { return __detail::__cyl_bessel_k<long double>(__nu, __x); } 1451 1452 /// 5.2.1.10 Irregular modified cylindrical Bessel functions. 1453 template<typename _Tpnu, typename _Tp> 1454 inline typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type 1455 cyl_bessel_k(_Tpnu __nu, _Tp __x) 1456 { 1457 typedef typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type __type; 1458 return __detail::__cyl_bessel_k<__type>(__nu, __x); 1459 } 1460 1461 inline float 1462 cyl_neumannf(float __nu, float __x) 1463 { return __detail::__cyl_neumann_n<float>(__nu, __x); } 1464 1465 inline long double 1466 cyl_neumannl(long double __nu, long double __x) 1467 { return __detail::__cyl_neumann_n<long double>(__nu, __x); } 1468 1469 /// 5.2.1.11 Cylindrical Neumann functions. 1470 template<typename _Tpnu, typename _Tp> 1471 inline typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type 1472 cyl_neumann(_Tpnu __nu, _Tp __x) 1473 { 1474 typedef typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type __type; 1475 return __detail::__cyl_neumann_n<__type>(__nu, __x); 1476 } 1477 1478 inline float 1479 ellint_1f(float __k, float __phi) 1480 { return __detail::__ellint_1<float>(__k, __phi); } 1481 1482 inline long double 1483 ellint_1l(long double __k, long double __phi) 1484 { return __detail::__ellint_1<long double>(__k, __phi); } 1485 1486 /// 5.2.1.12 Incomplete elliptic integrals of the first kind. 1487 template<typename _Tp, typename _Tpp> 1488 inline typename __gnu_cxx::__promote_2<_Tp, _Tpp>::__type 1489 ellint_1(_Tp __k, _Tpp __phi) 1490 { 1491 typedef typename __gnu_cxx::__promote_2<_Tp, _Tpp>::__type __type; 1492 return __detail::__ellint_1<__type>(__k, __phi); 1493 } 1494 1495 inline float 1496 ellint_2f(float __k, float __phi) 1497 { return __detail::__ellint_2<float>(__k, __phi); } 1498 1499 inline long double 1500 ellint_2l(long double __k, long double __phi) 1501 { return __detail::__ellint_2<long double>(__k, __phi); } 1502 1503 /// 5.2.1.13 Incomplete elliptic integrals of the second kind. 1504 template<typename _Tp, typename _Tpp> 1505 inline typename __gnu_cxx::__promote_2<_Tp, _Tpp>::__type 1506 ellint_2(_Tp __k, _Tpp __phi) 1507 { 1508 typedef typename __gnu_cxx::__promote_2<_Tp, _Tpp>::__type __type; 1509 return __detail::__ellint_2<__type>(__k, __phi); 1510 } 1511 1512 inline float 1513 ellint_3f(float __k, float __nu, float __phi) 1514 { return __detail::__ellint_3<float>(__k, __nu, __phi); } 1515 1516 inline long double 1517 ellint_3l(long double __k, long double __nu, long double __phi) 1518 { return __detail::__ellint_3<long double>(__k, __nu, __phi); } 1519 1520 /// 5.2.1.14 Incomplete elliptic integrals of the third kind. 1521 template<typename _Tp, typename _Tpn, typename _Tpp> 1522 inline typename __gnu_cxx::__promote_3<_Tp, _Tpn, _Tpp>::__type 1523 ellint_3(_Tp __k, _Tpn __nu, _Tpp __phi) 1524 { 1525 typedef typename __gnu_cxx::__promote_3<_Tp, _Tpn, _Tpp>::__type __type; 1526 return __detail::__ellint_3<__type>(__k, __nu, __phi); 1527 } 1528 1529 inline float 1530 expintf(float __x) 1531 { return __detail::__expint<float>(__x); } 1532 1533 inline long double 1534 expintl(long double __x) 1535 { return __detail::__expint<long double>(__x); } 1536 1537 /// 5.2.1.15 Exponential integrals. 1538 template<typename _Tp> 1539 inline typename __gnu_cxx::__promote<_Tp>::__type 1540 expint(_Tp __x) 1541 { 1542 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 1543 return __detail::__expint<__type>(__x); 1544 } 1545 1546 inline float 1547 hermitef(unsigned int __n, float __x) 1548 { return __detail::__poly_hermite<float>(__n, __x); } 1549 1550 inline long double 1551 hermitel(unsigned int __n, long double __x) 1552 { return __detail::__poly_hermite<long double>(__n, __x); } 1553 1554 /// 5.2.1.16 Hermite polynomials. 1555 template<typename _Tp> 1556 inline typename __gnu_cxx::__promote<_Tp>::__type 1557 hermite(unsigned int __n, _Tp __x) 1558 { 1559 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 1560 return __detail::__poly_hermite<__type>(__n, __x); 1561 } 1562 1563 inline float 1564 hypergf(float __a, float __b, float __c, float __x) 1565 { return __detail::__hyperg<float>(__a, __b, __c, __x); } 1566 1567 inline long double 1568 hypergl(long double __a, long double __b, long double __c, long double __x) 1569 { return __detail::__hyperg<long double>(__a, __b, __c, __x); } 1570 1571 /// 5.2.1.17 Hypergeometric functions. 1572 template<typename _Tpa, typename _Tpb, typename _Tpc, typename _Tp> 1573 inline typename __gnu_cxx::__promote_4<_Tpa, _Tpb, _Tpc, _Tp>::__type 1574 hyperg(_Tpa __a, _Tpb __b, _Tpc __c, _Tp __x) 1575 { 1576 typedef typename __gnu_cxx::__promote_4<_Tpa, _Tpb, _Tpc, _Tp>::__type __type; 1577 return __detail::__hyperg<__type>(__a, __b, __c, __x); 1578 } 1579 1580 inline float 1581 laguerref(unsigned int __n, float __x) 1582 { return __detail::__laguerre<float>(__n, __x); } 1583 1584 inline long double 1585 laguerrel(unsigned int __n, long double __x) 1586 { return __detail::__laguerre<long double>(__n, __x); } 1587 1588 /// 5.2.1.18 Laguerre polynomials. 1589 template<typename _Tp> 1590 inline typename __gnu_cxx::__promote<_Tp>::__type 1591 laguerre(unsigned int __n, _Tp __x) 1592 { 1593 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 1594 return __detail::__laguerre<__type>(__n, __x); 1595 } 1596 1597 inline float 1598 legendref(unsigned int __n, float __x) 1599 { return __detail::__poly_legendre_p<float>(__n, __x); } 1600 1601 inline long double 1602 legendrel(unsigned int __n, long double __x) 1603 { return __detail::__poly_legendre_p<long double>(__n, __x); } 1604 1605 /// 5.2.1.19 Legendre polynomials. 1606 template<typename _Tp> 1607 inline typename __gnu_cxx::__promote<_Tp>::__type 1608 legendre(unsigned int __n, _Tp __x) 1609 { 1610 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 1611 return __detail::__poly_legendre_p<__type>(__n, __x); 1612 } 1613 1614 inline float 1615 riemann_zetaf(float __x) 1616 { return __detail::__riemann_zeta<float>(__x); } 1617 1618 inline long double 1619 riemann_zetal(long double __x) 1620 { return __detail::__riemann_zeta<long double>(__x); } 1621 1622 /// 5.2.1.20 Riemann zeta function. 1623 template<typename _Tp> 1624 inline typename __gnu_cxx::__promote<_Tp>::__type 1625 riemann_zeta(_Tp __x) 1626 { 1627 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 1628 return __detail::__riemann_zeta<__type>(__x); 1629 } 1630 1631 inline float 1632 sph_besself(unsigned int __n, float __x) 1633 { return __detail::__sph_bessel<float>(__n, __x); } 1634 1635 inline long double 1636 sph_bessell(unsigned int __n, long double __x) 1637 { return __detail::__sph_bessel<long double>(__n, __x); } 1638 1639 /// 5.2.1.21 Spherical Bessel functions. 1640 template<typename _Tp> 1641 inline typename __gnu_cxx::__promote<_Tp>::__type 1642 sph_bessel(unsigned int __n, _Tp __x) 1643 { 1644 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 1645 return __detail::__sph_bessel<__type>(__n, __x); 1646 } 1647 1648 inline float 1649 sph_legendref(unsigned int __l, unsigned int __m, float __theta) 1650 { return __detail::__sph_legendre<float>(__l, __m, __theta); } 1651 1652 inline long double 1653 sph_legendrel(unsigned int __l, unsigned int __m, long double __theta) 1654 { return __detail::__sph_legendre<long double>(__l, __m, __theta); } 1655 1656 /// 5.2.1.22 Spherical associated Legendre functions. 1657 template<typename _Tp> 1658 inline typename __gnu_cxx::__promote<_Tp>::__type 1659 sph_legendre(unsigned int __l, unsigned int __m, _Tp __theta) 1660 { 1661 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 1662 return __detail::__sph_legendre<__type>(__l, __m, __theta); 1663 } 1664 1665 inline float 1666 sph_neumannf(unsigned int __n, float __x) 1667 { return __detail::__sph_neumann<float>(__n, __x); } 1668 1669 inline long double 1670 sph_neumannl(unsigned int __n, long double __x) 1671 { return __detail::__sph_neumann<long double>(__n, __x); } 1672 1673 /// 5.2.1.23 Spherical Neumann functions. 1674 template<typename _Tp> 1675 inline typename __gnu_cxx::__promote<_Tp>::__type 1676 sph_neumann(unsigned int __n, _Tp __x) 1677 { 1678 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 1679 return __detail::__sph_neumann<__type>(__n, __x); 1680 } 1681 1682 /* @} */ // tr1_math_spec_func 1683 _GLIBCXX_END_NAMESPACE_VERSION 1684 } 1685 } 1686 #endif // _GLIBCXX_USE_STD_SPEC_FUNCS 1687 1688 #endif // _GLIBCXX_TR1_CMATH 1689
Indexes created Wed Sep 09 00:24:13 UTC 2026