1 // TR1 cmath -*- C++ -*- 2 3 // Copyright (C) 2006, 2007, 2008, 2009, 2010, 2011 4 // Free Software Foundation, Inc. 5 // 6 // This file is part of the GNU ISO C++ Library. This library is free 7 // software; you can redistribute it and/or modify it under the 8 // terms of the GNU General Public License as published by the 9 // Free Software Foundation; either version 3, or (at your option) 10 // any later version. 11 12 // This library is distributed in the hope that it will be useful, 13 // but WITHOUT ANY WARRANTY; without even the implied warranty of 14 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 15 // GNU General Public License for more details. 16 17 // Under Section 7 of GPL version 3, you are granted additional 18 // permissions described in the GCC Runtime Library Exception, version 19 // 3.1, as published by the Free Software Foundation. 20 21 // You should have received a copy of the GNU General Public License and 22 // a copy of the GCC Runtime Library Exception along with this program; 23 // see the files COPYING3 and COPYING.RUNTIME respectively. If not, see 24 // <http://www.gnu.org/licenses/>. 25 26 /** @file tr1/cmath 27 * This is a TR1 C++ Library header. 28 */ 29 30 #ifndef _GLIBCXX_TR1_CMATH 31 #define _GLIBCXX_TR1_CMATH 1 32 33 #pragma GCC system_header 34 35 #include <cmath> 36 37 #ifdef _GLIBCXX_USE_C99_MATH_TR1 38 39 #undef acosh 40 #undef acoshf 41 #undef acoshl 42 #undef asinh 43 #undef asinhf 44 #undef asinhl 45 #undef atanh 46 #undef atanhf 47 #undef atanhl 48 #undef cbrt 49 #undef cbrtf 50 #undef cbrtl 51 #undef copysign 52 #undef copysignf 53 #undef copysignl 54 #undef erf 55 #undef erff 56 #undef erfl 57 #undef erfc 58 #undef erfcf 59 #undef erfcl 60 #undef exp2 61 #undef exp2f 62 #undef exp2l 63 #undef expm1 64 #undef expm1f 65 #undef expm1l 66 #undef fdim 67 #undef fdimf 68 #undef fdiml 69 #undef fma 70 #undef fmaf 71 #undef fmal 72 #undef fmax 73 #undef fmaxf 74 #undef fmaxl 75 #undef fmin 76 #undef fminf 77 #undef fminl 78 #undef hypot 79 #undef hypotf 80 #undef hypotl 81 #undef ilogb 82 #undef ilogbf 83 #undef ilogbl 84 #undef lgamma 85 #undef lgammaf 86 #undef lgammal 87 #undef llrint 88 #undef llrintf 89 #undef llrintl 90 #undef llround 91 #undef llroundf 92 #undef llroundl 93 #undef log1p 94 #undef log1pf 95 #undef log1pl 96 #undef log2 97 #undef log2f 98 #undef log2l 99 #undef logb 100 #undef logbf 101 #undef logbl 102 #undef lrint 103 #undef lrintf 104 #undef lrintl 105 #undef lround 106 #undef lroundf 107 #undef lroundl 108 #undef nan 109 #undef nanf 110 #undef nanl 111 #undef nearbyint 112 #undef nearbyintf 113 #undef nearbyintl 114 #undef nextafter 115 #undef nextafterf 116 #undef nextafterl 117 #undef nexttoward 118 #undef nexttowardf 119 #undef nexttowardl 120 #undef remainder 121 #undef remainderf 122 #undef remainderl 123 #undef remquo 124 #undef remquof 125 #undef remquol 126 #undef rint 127 #undef rintf 128 #undef rintl 129 #undef round 130 #undef roundf 131 #undef roundl 132 #undef scalbln 133 #undef scalblnf 134 #undef scalblnl 135 #undef scalbn 136 #undef scalbnf 137 #undef scalbnl 138 #undef tgamma 139 #undef tgammaf 140 #undef tgammal 141 #undef trunc 142 #undef truncf 143 #undef truncl 144 145 #endif 146 147 namespace std _GLIBCXX_VISIBILITY(default) 148 { 149 namespace tr1 150 { 151 _GLIBCXX_BEGIN_NAMESPACE_VERSION 152 153 #if _GLIBCXX_USE_C99_MATH_TR1 154 155 // types 156 using ::double_t; 157 using ::float_t; 158 159 // functions 160 using ::acosh; 161 using ::acoshf; 162 using ::acoshl; 163 164 using ::asinh; 165 using ::asinhf; 166 using ::asinhl; 167 168 using ::atanh; 169 using ::atanhf; 170 using ::atanhl; 171 172 using ::cbrt; 173 using ::cbrtf; 174 using ::cbrtl; 175 176 using ::copysign; 177 using ::copysignf; 178 using ::copysignl; 179 180 using ::erf; 181 using ::erff; 182 using ::erfl; 183 184 using ::erfc; 185 using ::erfcf; 186 using ::erfcl; 187 188 using ::exp2; 189 using ::exp2f; 190 using ::exp2l; 191 192 using ::expm1; 193 using ::expm1f; 194 using ::expm1l; 195 196 using ::fdim; 197 using ::fdimf; 198 using ::fdiml; 199 200 using ::fma; 201 using ::fmaf; 202 using ::fmal; 203 204 using ::fmax; 205 using ::fmaxf; 206 using ::fmaxl; 207 208 using ::fmin; 209 using ::fminf; 210 using ::fminl; 211 212 using ::hypot; 213 using ::hypotf; 214 using ::hypotl; 215 216 using ::ilogb; 217 using ::ilogbf; 218 using ::ilogbl; 219 220 using ::lgamma; 221 using ::lgammaf; 222 using ::lgammal; 223 224 using ::llrint; 225 using ::llrintf; 226 using ::llrintl; 227 228 using ::llround; 229 using ::llroundf; 230 using ::llroundl; 231 232 using ::log1p; 233 using ::log1pf; 234 using ::log1pl; 235 236 using ::log2; 237 using ::log2f; 238 using ::log2l; 239 240 using ::logb; 241 using ::logbf; 242 using ::logbl; 243 244 using ::lrint; 245 using ::lrintf; 246 using ::lrintl; 247 248 using ::lround; 249 using ::lroundf; 250 using ::lroundl; 251 252 using ::nan; 253 using ::nanf; 254 using ::nanl; 255 256 using ::nearbyint; 257 using ::nearbyintf; 258 using ::nearbyintl; 259 260 using ::nextafter; 261 using ::nextafterf; 262 using ::nextafterl; 263 264 using ::nexttoward; 265 using ::nexttowardf; 266 using ::nexttowardl; 267 268 using ::remainder; 269 using ::remainderf; 270 using ::remainderl; 271 272 using ::remquo; 273 using ::remquof; 274 using ::remquol; 275 276 using ::rint; 277 using ::rintf; 278 using ::rintl; 279 280 using ::round; 281 using ::roundf; 282 using ::roundl; 283 284 using ::scalbln; 285 using ::scalblnf; 286 using ::scalblnl; 287 288 using ::scalbn; 289 using ::scalbnf; 290 using ::scalbnl; 291 292 using ::tgamma; 293 using ::tgammaf; 294 using ::tgammal; 295 296 using ::trunc; 297 using ::truncf; 298 using ::truncl; 299 300 #endif 301 302 #if _GLIBCXX_USE_C99_MATH 303 #if !_GLIBCXX_USE_C99_FP_MACROS_DYNAMIC 304 305 /// Function template definitions [8.16.3]. 306 template<typename _Tp> 307 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value, 308 int>::__type 309 fpclassify(_Tp __f) 310 { 311 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 312 return __builtin_fpclassify(FP_NAN, FP_INFINITE, FP_NORMAL, 313 FP_SUBNORMAL, FP_ZERO, __type(__f)); 314 } 315 316 template<typename _Tp> 317 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value, 318 int>::__type 319 isfinite(_Tp __f) 320 { 321 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 322 return __builtin_isfinite(__type(__f)); 323 } 324 325 template<typename _Tp> 326 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value, 327 int>::__type 328 isinf(_Tp __f) 329 { 330 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 331 return __builtin_isinf(__type(__f)); 332 } 333 334 template<typename _Tp> 335 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value, 336 int>::__type 337 isnan(_Tp __f) 338 { 339 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 340 return __builtin_isnan(__type(__f)); 341 } 342 343 template<typename _Tp> 344 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value, 345 int>::__type 346 isnormal(_Tp __f) 347 { 348 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 349 return __builtin_isnormal(__type(__f)); 350 } 351 352 template<typename _Tp> 353 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value, 354 int>::__type 355 signbit(_Tp __f) 356 { 357 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 358 return __builtin_signbit(__type(__f)); 359 } 360 361 template<typename _Tp> 362 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value, 363 int>::__type 364 isgreater(_Tp __f1, _Tp __f2) 365 { 366 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 367 return __builtin_isgreater(__type(__f1), __type(__f2)); 368 } 369 370 template<typename _Tp> 371 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value, 372 int>::__type 373 isgreaterequal(_Tp __f1, _Tp __f2) 374 { 375 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 376 return __builtin_isgreaterequal(__type(__f1), __type(__f2)); 377 } 378 379 template<typename _Tp> 380 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value, 381 int>::__type 382 isless(_Tp __f1, _Tp __f2) 383 { 384 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 385 return __builtin_isless(__type(__f1), __type(__f2)); 386 } 387 388 template<typename _Tp> 389 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value, 390 int>::__type 391 islessequal(_Tp __f1, _Tp __f2) 392 { 393 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 394 return __builtin_islessequal(__type(__f1), __type(__f2)); 395 } 396 397 template<typename _Tp> 398 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value, 399 int>::__type 400 islessgreater(_Tp __f1, _Tp __f2) 401 { 402 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 403 return __builtin_islessgreater(__type(__f1), __type(__f2)); 404 } 405 406 template<typename _Tp> 407 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value, 408 int>::__type 409 isunordered(_Tp __f1, _Tp __f2) 410 { 411 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 412 return __builtin_isunordered(__type(__f1), __type(__f2)); 413 } 414 415 #endif 416 #endif 417 418 #if _GLIBCXX_USE_C99_MATH_TR1 419 420 /// Additional overloads [8.16.4]. 421 using std::acos; 422 423 inline float 424 acosh(float __x) 425 { return __builtin_acoshf(__x); } 426 427 inline long double 428 acosh(long double __x) 429 { return __builtin_acoshl(__x); } 430 431 template<typename _Tp> 432 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 433 double>::__type 434 acosh(_Tp __x) 435 { return __builtin_acosh(__x); } 436 437 using std::asin; 438 439 inline float 440 asinh(float __x) 441 { return __builtin_asinhf(__x); } 442 443 inline long double 444 asinh(long double __x) 445 { return __builtin_asinhl(__x); } 446 447 template<typename _Tp> 448 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 449 double>::__type 450 asinh(_Tp __x) 451 { return __builtin_asinh(__x); } 452 453 using std::atan; 454 using std::atan2; 455 456 inline float 457 atanh(float __x) 458 { return __builtin_atanhf(__x); } 459 460 inline long double 461 atanh(long double __x) 462 { return __builtin_atanhl(__x); } 463 464 template<typename _Tp> 465 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 466 double>::__type 467 atanh(_Tp __x) 468 { return __builtin_atanh(__x); } 469 470 inline float 471 cbrt(float __x) 472 { return __builtin_cbrtf(__x); } 473 474 inline long double 475 cbrt(long double __x) 476 { return __builtin_cbrtl(__x); } 477 478 template<typename _Tp> 479 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 480 double>::__type 481 cbrt(_Tp __x) 482 { return __builtin_cbrt(__x); } 483 484 using std::ceil; 485 486 inline float 487 copysign(float __x, float __y) 488 { return __builtin_copysignf(__x, __y); } 489 490 inline long double 491 copysign(long double __x, long double __y) 492 { return __builtin_copysignl(__x, __y); } 493 494 template<typename _Tp, typename _Up> 495 inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type 496 copysign(_Tp __x, _Up __y) 497 { 498 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type; 499 return copysign(__type(__x), __type(__y)); 500 } 501 502 using std::cos; 503 using std::cosh; 504 505 inline float 506 erf(float __x) 507 { return __builtin_erff(__x); } 508 509 inline long double 510 erf(long double __x) 511 { return __builtin_erfl(__x); } 512 513 template<typename _Tp> 514 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 515 double>::__type 516 erf(_Tp __x) 517 { return __builtin_erf(__x); } 518 519 inline float 520 erfc(float __x) 521 { return __builtin_erfcf(__x); } 522 523 inline long double 524 erfc(long double __x) 525 { return __builtin_erfcl(__x); } 526 527 template<typename _Tp> 528 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 529 double>::__type 530 erfc(_Tp __x) 531 { return __builtin_erfc(__x); } 532 533 using std::exp; 534 535 inline float 536 exp2(float __x) 537 { return __builtin_exp2f(__x); } 538 539 inline long double 540 exp2(long double __x) 541 { return __builtin_exp2l(__x); } 542 543 template<typename _Tp> 544 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 545 double>::__type 546 exp2(_Tp __x) 547 { return __builtin_exp2(__x); } 548 549 inline float 550 expm1(float __x) 551 { return __builtin_expm1f(__x); } 552 553 inline long double 554 expm1(long double __x) 555 { return __builtin_expm1l(__x); } 556 557 template<typename _Tp> 558 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 559 double>::__type 560 expm1(_Tp __x) 561 { return __builtin_expm1(__x); } 562 563 // Note: we deal with fabs in a special way, because an using std::fabs 564 // would bring in also the overloads for complex types, which in C++0x 565 // mode have a different return type. 566 // With __CORRECT_ISO_CPP_MATH_H_PROTO1, math.h imports std::fabs in the 567 // global namespace after the declarations of the float / double / long 568 // double overloads but before the std::complex overloads. 569 using ::fabs; 570 571 #ifndef __CORRECT_ISO_CPP_MATH_H_PROTO1 572 inline float 573 fabs(float __x) 574 { return __builtin_fabsf(__x); } 575 576 inline long double 577 fabs(long double __x) 578 { return __builtin_fabsl(__x); } 579 580 template<typename _Tp> 581 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 582 double>::__type 583 fabs(_Tp __x) 584 { return __builtin_fabs(__x); } 585 #endif 586 587 inline float 588 fdim(float __x, float __y) 589 { return __builtin_fdimf(__x, __y); } 590 591 inline long double 592 fdim(long double __x, long double __y) 593 { return __builtin_fdiml(__x, __y); } 594 595 template<typename _Tp, typename _Up> 596 inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type 597 fdim(_Tp __x, _Up __y) 598 { 599 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type; 600 return fdim(__type(__x), __type(__y)); 601 } 602 603 using std::floor; 604 605 inline float 606 fma(float __x, float __y, float __z) 607 { return __builtin_fmaf(__x, __y, __z); } 608 609 inline long double 610 fma(long double __x, long double __y, long double __z) 611 { return __builtin_fmal(__x, __y, __z); } 612 613 template<typename _Tp, typename _Up, typename _Vp> 614 inline typename __gnu_cxx::__promote_3<_Tp, _Up, _Vp>::__type 615 fma(_Tp __x, _Up __y, _Vp __z) 616 { 617 typedef typename __gnu_cxx::__promote_3<_Tp, _Up, _Vp>::__type __type; 618 return fma(__type(__x), __type(__y), __type(__z)); 619 } 620 621 inline float 622 fmax(float __x, float __y) 623 { return __builtin_fmaxf(__x, __y); } 624 625 inline long double 626 fmax(long double __x, long double __y) 627 { return __builtin_fmaxl(__x, __y); } 628 629 template<typename _Tp, typename _Up> 630 inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type 631 fmax(_Tp __x, _Up __y) 632 { 633 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type; 634 return fmax(__type(__x), __type(__y)); 635 } 636 637 inline float 638 fmin(float __x, float __y) 639 { return __builtin_fminf(__x, __y); } 640 641 inline long double 642 fmin(long double __x, long double __y) 643 { return __builtin_fminl(__x, __y); } 644 645 template<typename _Tp, typename _Up> 646 inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type 647 fmin(_Tp __x, _Up __y) 648 { 649 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type; 650 return fmin(__type(__x), __type(__y)); 651 } 652 653 using std::fmod; 654 using std::frexp; 655 656 inline float 657 hypot(float __x, float __y) 658 { return __builtin_hypotf(__x, __y); } 659 660 inline long double 661 hypot(long double __x, long double __y) 662 { return __builtin_hypotl(__x, __y); } 663 664 template<typename _Tp, typename _Up> 665 inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type 666 hypot(_Tp __y, _Up __x) 667 { 668 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type; 669 return hypot(__type(__y), __type(__x)); 670 } 671 672 inline int 673 ilogb(float __x) 674 { return __builtin_ilogbf(__x); } 675 676 inline int 677 ilogb(long double __x) 678 { return __builtin_ilogbl(__x); } 679 680 template<typename _Tp> 681 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 682 int>::__type 683 ilogb(_Tp __x) 684 { return __builtin_ilogb(__x); } 685 686 using std::ldexp; 687 688 inline float 689 lgamma(float __x) 690 { return __builtin_lgammaf(__x); } 691 692 inline long double 693 lgamma(long double __x) 694 { return __builtin_lgammal(__x); } 695 696 template<typename _Tp> 697 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 698 double>::__type 699 lgamma(_Tp __x) 700 { return __builtin_lgamma(__x); } 701 702 inline long long 703 llrint(float __x) 704 { return __builtin_llrintf(__x); } 705 706 inline long long 707 llrint(long double __x) 708 { return __builtin_llrintl(__x); } 709 710 template<typename _Tp> 711 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 712 long long>::__type 713 llrint(_Tp __x) 714 { return __builtin_llrint(__x); } 715 716 inline long long 717 llround(float __x) 718 { return __builtin_llroundf(__x); } 719 720 inline long long 721 llround(long double __x) 722 { return __builtin_llroundl(__x); } 723 724 template<typename _Tp> 725 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 726 long long>::__type 727 llround(_Tp __x) 728 { return __builtin_llround(__x); } 729 730 using std::log; 731 using std::log10; 732 733 inline float 734 log1p(float __x) 735 { return __builtin_log1pf(__x); } 736 737 inline long double 738 log1p(long double __x) 739 { return __builtin_log1pl(__x); } 740 741 template<typename _Tp> 742 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 743 double>::__type 744 log1p(_Tp __x) 745 { return __builtin_log1p(__x); } 746 747 // DR 568. 748 inline float 749 log2(float __x) 750 { return __builtin_log2f(__x); } 751 752 inline long double 753 log2(long double __x) 754 { return __builtin_log2l(__x); } 755 756 template<typename _Tp> 757 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 758 double>::__type 759 log2(_Tp __x) 760 { return __builtin_log2(__x); } 761 762 inline float 763 logb(float __x) 764 { return __builtin_logbf(__x); } 765 766 inline long double 767 logb(long double __x) 768 { return __builtin_logbl(__x); } 769 770 template<typename _Tp> 771 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 772 double>::__type 773 logb(_Tp __x) 774 { 775 return __builtin_logb(__x); 776 } 777 778 inline long 779 lrint(float __x) 780 { return __builtin_lrintf(__x); } 781 782 inline long 783 lrint(long double __x) 784 { return __builtin_lrintl(__x); } 785 786 template<typename _Tp> 787 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 788 long>::__type 789 lrint(_Tp __x) 790 { return __builtin_lrint(__x); } 791 792 inline long 793 lround(float __x) 794 { return __builtin_lroundf(__x); } 795 796 inline long 797 lround(long double __x) 798 { return __builtin_lroundl(__x); } 799 800 template<typename _Tp> 801 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 802 long>::__type 803 lround(_Tp __x) 804 { return __builtin_lround(__x); } 805 806 inline float 807 nearbyint(float __x) 808 { return __builtin_nearbyintf(__x); } 809 810 inline long double 811 nearbyint(long double __x) 812 { return __builtin_nearbyintl(__x); } 813 814 template<typename _Tp> 815 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 816 double>::__type 817 nearbyint(_Tp __x) 818 { return __builtin_nearbyint(__x); } 819 820 inline float 821 nextafter(float __x, float __y) 822 { return __builtin_nextafterf(__x, __y); } 823 824 inline long double 825 nextafter(long double __x, long double __y) 826 { return __builtin_nextafterl(__x, __y); } 827 828 template<typename _Tp, typename _Up> 829 inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type 830 nextafter(_Tp __x, _Up __y) 831 { 832 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type; 833 return nextafter(__type(__x), __type(__y)); 834 } 835 836 inline float 837 nexttoward(float __x, long double __y) 838 { return __builtin_nexttowardf(__x, __y); } 839 840 inline long double 841 nexttoward(long double __x, long double __y) 842 { return __builtin_nexttowardl(__x, __y); } 843 844 template<typename _Tp> 845 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 846 double>::__type 847 nexttoward(_Tp __x, long double __y) 848 { return __builtin_nexttoward(__x, __y); } 849 850 // DR 550. What should the return type of pow(float,int) be? 851 // NB: C++0x and TR1 != C++03. 852 // using std::pow; 853 854 inline float 855 remainder(float __x, float __y) 856 { return __builtin_remainderf(__x, __y); } 857 858 inline long double 859 remainder(long double __x, long double __y) 860 { return __builtin_remainderl(__x, __y); } 861 862 template<typename _Tp, typename _Up> 863 inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type 864 remainder(_Tp __x, _Up __y) 865 { 866 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type; 867 return remainder(__type(__x), __type(__y)); 868 } 869 870 inline float 871 remquo(float __x, float __y, int* __pquo) 872 { return __builtin_remquof(__x, __y, __pquo); } 873 874 inline long double 875 remquo(long double __x, long double __y, int* __pquo) 876 { return __builtin_remquol(__x, __y, __pquo); } 877 878 template<typename _Tp, typename _Up> 879 inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type 880 remquo(_Tp __x, _Up __y, int* __pquo) 881 { 882 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type; 883 return remquo(__type(__x), __type(__y), __pquo); 884 } 885 886 inline float 887 rint(float __x) 888 { return __builtin_rintf(__x); } 889 890 inline long double 891 rint(long double __x) 892 { return __builtin_rintl(__x); } 893 894 template<typename _Tp> 895 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 896 double>::__type 897 rint(_Tp __x) 898 { return __builtin_rint(__x); } 899 900 inline float 901 round(float __x) 902 { return __builtin_roundf(__x); } 903 904 inline long double 905 round(long double __x) 906 { return __builtin_roundl(__x); } 907 908 template<typename _Tp> 909 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 910 double>::__type 911 round(_Tp __x) 912 { return __builtin_round(__x); } 913 914 inline float 915 scalbln(float __x, long __ex) 916 { return __builtin_scalblnf(__x, __ex); } 917 918 inline long double 919 scalbln(long double __x, long __ex) 920 { return __builtin_scalblnl(__x, __ex); } 921 922 template<typename _Tp> 923 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 924 double>::__type 925 scalbln(_Tp __x, long __ex) 926 { return __builtin_scalbln(__x, __ex); } 927 928 inline float 929 scalbn(float __x, int __ex) 930 { return __builtin_scalbnf(__x, __ex); } 931 932 inline long double 933 scalbn(long double __x, int __ex) 934 { return __builtin_scalbnl(__x, __ex); } 935 936 template<typename _Tp> 937 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 938 double>::__type 939 scalbn(_Tp __x, int __ex) 940 { return __builtin_scalbn(__x, __ex); } 941 942 using std::sin; 943 using std::sinh; 944 using std::sqrt; 945 using std::tan; 946 using std::tanh; 947 948 inline float 949 tgamma(float __x) 950 { return __builtin_tgammaf(__x); } 951 952 inline long double 953 tgamma(long double __x) 954 { return __builtin_tgammal(__x); } 955 956 template<typename _Tp> 957 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 958 double>::__type 959 tgamma(_Tp __x) 960 { return __builtin_tgamma(__x); } 961 962 inline float 963 trunc(float __x) 964 { return __builtin_truncf(__x); } 965 966 inline long double 967 trunc(long double __x) 968 { return __builtin_truncl(__x); } 969 970 template<typename _Tp> 971 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 972 double>::__type 973 trunc(_Tp __x) 974 { return __builtin_trunc(__x); } 975 976 #endif 977 _GLIBCXX_END_NAMESPACE_VERSION 978 } 979 } 980 981 namespace std _GLIBCXX_VISIBILITY(default) 982 { 983 namespace tr1 984 { 985 _GLIBCXX_BEGIN_NAMESPACE_VERSION 986 987 // DR 550. What should the return type of pow(float,int) be? 988 // NB: C++0x and TR1 != C++03. 989 inline double 990 pow(double __x, double __y) 991 { return std::pow(__x, __y); } 992 993 inline float 994 pow(float __x, float __y) 995 { return std::pow(__x, __y); } 996 997 inline long double 998 pow(long double __x, long double __y) 999 { return std::pow(__x, __y); } 1000 1001 template<typename _Tp, typename _Up> 1002 inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type 1003 pow(_Tp __x, _Up __y) 1004 { 1005 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type; 1006 return std::pow(__type(__x), __type(__y)); 1007 } 1008 1009 _GLIBCXX_END_NAMESPACE_VERSION 1010 } 1011 } 1012 1013 #include <bits/stl_algobase.h> 1014 #include <limits> 1015 #include <tr1/type_traits> 1016 1017 #include <tr1/gamma.tcc> 1018 #include <tr1/bessel_function.tcc> 1019 #include <tr1/beta_function.tcc> 1020 #include <tr1/ell_integral.tcc> 1021 #include <tr1/exp_integral.tcc> 1022 #include <tr1/hypergeometric.tcc> 1023 #include <tr1/legendre_function.tcc> 1024 #include <tr1/modified_bessel_func.tcc> 1025 #include <tr1/poly_hermite.tcc> 1026 #include <tr1/poly_laguerre.tcc> 1027 #include <tr1/riemann_zeta.tcc> 1028 1029 namespace std _GLIBCXX_VISIBILITY(default) 1030 { 1031 namespace tr1 1032 { 1033 _GLIBCXX_BEGIN_NAMESPACE_VERSION 1034 1035 /** 1036 * @defgroup tr1_math_spec_func Mathematical Special Functions 1037 * @ingroup numerics 1038 * 1039 * A collection of advanced mathematical special functions. 1040 * @{ 1041 */ 1042 1043 inline float 1044 assoc_laguerref(unsigned int __n, unsigned int __m, float __x) 1045 { return __detail::__assoc_laguerre<float>(__n, __m, __x); } 1046 1047 inline long double 1048 assoc_laguerrel(unsigned int __n, unsigned int __m, long double __x) 1049 { 1050 return __detail::__assoc_laguerre<long double>(__n, __m, __x); 1051 } 1052 1053 /// 5.2.1.1 Associated Laguerre polynomials. 1054 template<typename _Tp> 1055 inline typename __gnu_cxx::__promote<_Tp>::__type 1056 assoc_laguerre(unsigned int __n, unsigned int __m, _Tp __x) 1057 { 1058 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 1059 return __detail::__assoc_laguerre<__type>(__n, __m, __x); 1060 } 1061 1062 inline float 1063 assoc_legendref(unsigned int __l, unsigned int __m, float __x) 1064 { return __detail::__assoc_legendre_p<float>(__l, __m, __x); } 1065 1066 inline long double 1067 assoc_legendrel(unsigned int __l, unsigned int __m, long double __x) 1068 { return __detail::__assoc_legendre_p<long double>(__l, __m, __x); } 1069 1070 /// 5.2.1.2 Associated Legendre functions. 1071 template<typename _Tp> 1072 inline typename __gnu_cxx::__promote<_Tp>::__type 1073 assoc_legendre(unsigned int __l, unsigned int __m, _Tp __x) 1074 { 1075 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 1076 return __detail::__assoc_legendre_p<__type>(__l, __m, __x); 1077 } 1078 1079 inline float 1080 betaf(float __x, float __y) 1081 { return __detail::__beta<float>(__x, __y); } 1082 1083 inline long double 1084 betal(long double __x, long double __y) 1085 { return __detail::__beta<long double>(__x, __y); } 1086 1087 /// 5.2.1.3 Beta functions. 1088 template<typename _Tpx, typename _Tpy> 1089 inline typename __gnu_cxx::__promote_2<_Tpx, _Tpy>::__type 1090 beta(_Tpx __x, _Tpy __y) 1091 { 1092 typedef typename __gnu_cxx::__promote_2<_Tpx, _Tpy>::__type __type; 1093 return __detail::__beta<__type>(__x, __y); 1094 } 1095 1096 inline float 1097 comp_ellint_1f(float __k) 1098 { return __detail::__comp_ellint_1<float>(__k); } 1099 1100 inline long double 1101 comp_ellint_1l(long double __k) 1102 { return __detail::__comp_ellint_1<long double>(__k); } 1103 1104 /// 5.2.1.4 Complete elliptic integrals of the first kind. 1105 template<typename _Tp> 1106 inline typename __gnu_cxx::__promote<_Tp>::__type 1107 comp_ellint_1(_Tp __k) 1108 { 1109 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 1110 return __detail::__comp_ellint_1<__type>(__k); 1111 } 1112 1113 inline float 1114 comp_ellint_2f(float __k) 1115 { return __detail::__comp_ellint_2<float>(__k); } 1116 1117 inline long double 1118 comp_ellint_2l(long double __k) 1119 { return __detail::__comp_ellint_2<long double>(__k); } 1120 1121 /// 5.2.1.5 Complete elliptic integrals of the second kind. 1122 template<typename _Tp> 1123 inline typename __gnu_cxx::__promote<_Tp>::__type 1124 comp_ellint_2(_Tp __k) 1125 { 1126 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 1127 return __detail::__comp_ellint_2<__type>(__k); 1128 } 1129 1130 inline float 1131 comp_ellint_3f(float __k, float __nu) 1132 { return __detail::__comp_ellint_3<float>(__k, __nu); } 1133 1134 inline long double 1135 comp_ellint_3l(long double __k, long double __nu) 1136 { return __detail::__comp_ellint_3<long double>(__k, __nu); } 1137 1138 /// 5.2.1.6 Complete elliptic integrals of the third kind. 1139 template<typename _Tp, typename _Tpn> 1140 inline typename __gnu_cxx::__promote_2<_Tp, _Tpn>::__type 1141 comp_ellint_3(_Tp __k, _Tpn __nu) 1142 { 1143 typedef typename __gnu_cxx::__promote_2<_Tp, _Tpn>::__type __type; 1144 return __detail::__comp_ellint_3<__type>(__k, __nu); 1145 } 1146 1147 inline float 1148 conf_hypergf(float __a, float __c, float __x) 1149 { return __detail::__conf_hyperg<float>(__a, __c, __x); } 1150 1151 inline long double 1152 conf_hypergl(long double __a, long double __c, long double __x) 1153 { return __detail::__conf_hyperg<long double>(__a, __c, __x); } 1154 1155 /// 5.2.1.7 Confluent hypergeometric functions. 1156 template<typename _Tpa, typename _Tpc, typename _Tp> 1157 inline typename __gnu_cxx::__promote_3<_Tpa, _Tpc, _Tp>::__type 1158 conf_hyperg(_Tpa __a, _Tpc __c, _Tp __x) 1159 { 1160 typedef typename __gnu_cxx::__promote_3<_Tpa, _Tpc, _Tp>::__type __type; 1161 return __detail::__conf_hyperg<__type>(__a, __c, __x); 1162 } 1163 1164 inline float 1165 cyl_bessel_if(float __nu, float __x) 1166 { return __detail::__cyl_bessel_i<float>(__nu, __x); } 1167 1168 inline long double 1169 cyl_bessel_il(long double __nu, long double __x) 1170 { return __detail::__cyl_bessel_i<long double>(__nu, __x); } 1171 1172 /// 5.2.1.8 Regular modified cylindrical Bessel functions. 1173 template<typename _Tpnu, typename _Tp> 1174 inline typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type 1175 cyl_bessel_i(_Tpnu __nu, _Tp __x) 1176 { 1177 typedef typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type __type; 1178 return __detail::__cyl_bessel_i<__type>(__nu, __x); 1179 } 1180 1181 inline float 1182 cyl_bessel_jf(float __nu, float __x) 1183 { return __detail::__cyl_bessel_j<float>(__nu, __x); } 1184 1185 inline long double 1186 cyl_bessel_jl(long double __nu, long double __x) 1187 { return __detail::__cyl_bessel_j<long double>(__nu, __x); } 1188 1189 /// 5.2.1.9 Cylindrical Bessel functions (of the first kind). 1190 template<typename _Tpnu, typename _Tp> 1191 inline typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type 1192 cyl_bessel_j(_Tpnu __nu, _Tp __x) 1193 { 1194 typedef typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type __type; 1195 return __detail::__cyl_bessel_j<__type>(__nu, __x); 1196 } 1197 1198 inline float 1199 cyl_bessel_kf(float __nu, float __x) 1200 { return __detail::__cyl_bessel_k<float>(__nu, __x); } 1201 1202 inline long double 1203 cyl_bessel_kl(long double __nu, long double __x) 1204 { return __detail::__cyl_bessel_k<long double>(__nu, __x); } 1205 1206 /// 5.2.1.10 Irregular modified cylindrical Bessel functions. 1207 template<typename _Tpnu, typename _Tp> 1208 inline typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type 1209 cyl_bessel_k(_Tpnu __nu, _Tp __x) 1210 { 1211 typedef typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type __type; 1212 return __detail::__cyl_bessel_k<__type>(__nu, __x); 1213 } 1214 1215 inline float 1216 cyl_neumannf(float __nu, float __x) 1217 { return __detail::__cyl_neumann_n<float>(__nu, __x); } 1218 1219 inline long double 1220 cyl_neumannl(long double __nu, long double __x) 1221 { return __detail::__cyl_neumann_n<long double>(__nu, __x); } 1222 1223 /// 5.2.1.11 Cylindrical Neumann functions. 1224 template<typename _Tpnu, typename _Tp> 1225 inline typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type 1226 cyl_neumann(_Tpnu __nu, _Tp __x) 1227 { 1228 typedef typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type __type; 1229 return __detail::__cyl_neumann_n<__type>(__nu, __x); 1230 } 1231 1232 inline float 1233 ellint_1f(float __k, float __phi) 1234 { return __detail::__ellint_1<float>(__k, __phi); } 1235 1236 inline long double 1237 ellint_1l(long double __k, long double __phi) 1238 { return __detail::__ellint_1<long double>(__k, __phi); } 1239 1240 /// 5.2.1.12 Incomplete elliptic integrals of the first kind. 1241 template<typename _Tp, typename _Tpp> 1242 inline typename __gnu_cxx::__promote_2<_Tp, _Tpp>::__type 1243 ellint_1(_Tp __k, _Tpp __phi) 1244 { 1245 typedef typename __gnu_cxx::__promote_2<_Tp, _Tpp>::__type __type; 1246 return __detail::__ellint_1<__type>(__k, __phi); 1247 } 1248 1249 inline float 1250 ellint_2f(float __k, float __phi) 1251 { return __detail::__ellint_2<float>(__k, __phi); } 1252 1253 inline long double 1254 ellint_2l(long double __k, long double __phi) 1255 { return __detail::__ellint_2<long double>(__k, __phi); } 1256 1257 /// 5.2.1.13 Incomplete elliptic integrals of the second kind. 1258 template<typename _Tp, typename _Tpp> 1259 inline typename __gnu_cxx::__promote_2<_Tp, _Tpp>::__type 1260 ellint_2(_Tp __k, _Tpp __phi) 1261 { 1262 typedef typename __gnu_cxx::__promote_2<_Tp, _Tpp>::__type __type; 1263 return __detail::__ellint_2<__type>(__k, __phi); 1264 } 1265 1266 inline float 1267 ellint_3f(float __k, float __nu, float __phi) 1268 { return __detail::__ellint_3<float>(__k, __nu, __phi); } 1269 1270 inline long double 1271 ellint_3l(long double __k, long double __nu, long double __phi) 1272 { return __detail::__ellint_3<long double>(__k, __nu, __phi); } 1273 1274 /// 5.2.1.14 Incomplete elliptic integrals of the third kind. 1275 template<typename _Tp, typename _Tpn, typename _Tpp> 1276 inline typename __gnu_cxx::__promote_3<_Tp, _Tpn, _Tpp>::__type 1277 ellint_3(_Tp __k, _Tpn __nu, _Tpp __phi) 1278 { 1279 typedef typename __gnu_cxx::__promote_3<_Tp, _Tpn, _Tpp>::__type __type; 1280 return __detail::__ellint_3<__type>(__k, __nu, __phi); 1281 } 1282 1283 inline float 1284 expintf(float __x) 1285 { return __detail::__expint<float>(__x); } 1286 1287 inline long double 1288 expintl(long double __x) 1289 { return __detail::__expint<long double>(__x); } 1290 1291 /// 5.2.1.15 Exponential integrals. 1292 template<typename _Tp> 1293 inline typename __gnu_cxx::__promote<_Tp>::__type 1294 expint(_Tp __x) 1295 { 1296 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 1297 return __detail::__expint<__type>(__x); 1298 } 1299 1300 inline float 1301 hermitef(unsigned int __n, float __x) 1302 { return __detail::__poly_hermite<float>(__n, __x); } 1303 1304 inline long double 1305 hermitel(unsigned int __n, long double __x) 1306 { return __detail::__poly_hermite<long double>(__n, __x); } 1307 1308 /// 5.2.1.16 Hermite polynomials. 1309 template<typename _Tp> 1310 inline typename __gnu_cxx::__promote<_Tp>::__type 1311 hermite(unsigned int __n, _Tp __x) 1312 { 1313 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 1314 return __detail::__poly_hermite<__type>(__n, __x); 1315 } 1316 1317 inline float 1318 hypergf(float __a, float __b, float __c, float __x) 1319 { return __detail::__hyperg<float>(__a, __b, __c, __x); } 1320 1321 inline long double 1322 hypergl(long double __a, long double __b, long double __c, long double __x) 1323 { return __detail::__hyperg<long double>(__a, __b, __c, __x); } 1324 1325 /// 5.2.1.17 Hypergeometric functions. 1326 template<typename _Tpa, typename _Tpb, typename _Tpc, typename _Tp> 1327 inline typename __gnu_cxx::__promote_4<_Tpa, _Tpb, _Tpc, _Tp>::__type 1328 hyperg(_Tpa __a, _Tpb __b, _Tpc __c, _Tp __x) 1329 { 1330 typedef typename __gnu_cxx::__promote_4<_Tpa, _Tpb, _Tpc, _Tp>::__type __type; 1331 return __detail::__hyperg<__type>(__a, __b, __c, __x); 1332 } 1333 1334 inline float 1335 laguerref(unsigned int __n, float __x) 1336 { return __detail::__laguerre<float>(__n, __x); } 1337 1338 inline long double 1339 laguerrel(unsigned int __n, long double __x) 1340 { return __detail::__laguerre<long double>(__n, __x); } 1341 1342 /// 5.2.1.18 Laguerre polynomials. 1343 template<typename _Tp> 1344 inline typename __gnu_cxx::__promote<_Tp>::__type 1345 laguerre(unsigned int __n, _Tp __x) 1346 { 1347 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 1348 return __detail::__laguerre<__type>(__n, __x); 1349 } 1350 1351 inline float 1352 legendref(unsigned int __n, float __x) 1353 { return __detail::__poly_legendre_p<float>(__n, __x); } 1354 1355 inline long double 1356 legendrel(unsigned int __n, long double __x) 1357 { return __detail::__poly_legendre_p<long double>(__n, __x); } 1358 1359 /// 5.2.1.19 Legendre polynomials. 1360 template<typename _Tp> 1361 inline typename __gnu_cxx::__promote<_Tp>::__type 1362 legendre(unsigned int __n, _Tp __x) 1363 { 1364 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 1365 return __detail::__poly_legendre_p<__type>(__n, __x); 1366 } 1367 1368 inline float 1369 riemann_zetaf(float __x) 1370 { return __detail::__riemann_zeta<float>(__x); } 1371 1372 inline long double 1373 riemann_zetal(long double __x) 1374 { return __detail::__riemann_zeta<long double>(__x); } 1375 1376 /// 5.2.1.20 Riemann zeta function. 1377 template<typename _Tp> 1378 inline typename __gnu_cxx::__promote<_Tp>::__type 1379 riemann_zeta(_Tp __x) 1380 { 1381 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 1382 return __detail::__riemann_zeta<__type>(__x); 1383 } 1384 1385 inline float 1386 sph_besself(unsigned int __n, float __x) 1387 { return __detail::__sph_bessel<float>(__n, __x); } 1388 1389 inline long double 1390 sph_bessell(unsigned int __n, long double __x) 1391 { return __detail::__sph_bessel<long double>(__n, __x); } 1392 1393 /// 5.2.1.21 Spherical Bessel functions. 1394 template<typename _Tp> 1395 inline typename __gnu_cxx::__promote<_Tp>::__type 1396 sph_bessel(unsigned int __n, _Tp __x) 1397 { 1398 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 1399 return __detail::__sph_bessel<__type>(__n, __x); 1400 } 1401 1402 inline float 1403 sph_legendref(unsigned int __l, unsigned int __m, float __theta) 1404 { return __detail::__sph_legendre<float>(__l, __m, __theta); } 1405 1406 inline long double 1407 sph_legendrel(unsigned int __l, unsigned int __m, long double __theta) 1408 { return __detail::__sph_legendre<long double>(__l, __m, __theta); } 1409 1410 /// 5.2.1.22 Spherical associated Legendre functions. 1411 template<typename _Tp> 1412 inline typename __gnu_cxx::__promote<_Tp>::__type 1413 sph_legendre(unsigned int __l, unsigned int __m, _Tp __theta) 1414 { 1415 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 1416 return __detail::__sph_legendre<__type>(__l, __m, __theta); 1417 } 1418 1419 inline float 1420 sph_neumannf(unsigned int __n, float __x) 1421 { return __detail::__sph_neumann<float>(__n, __x); } 1422 1423 inline long double 1424 sph_neumannl(unsigned int __n, long double __x) 1425 { return __detail::__sph_neumann<long double>(__n, __x); } 1426 1427 /// 5.2.1.23 Spherical Neumann functions. 1428 template<typename _Tp> 1429 inline typename __gnu_cxx::__promote<_Tp>::__type 1430 sph_neumann(unsigned int __n, _Tp __x) 1431 { 1432 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 1433 return __detail::__sph_neumann<__type>(__n, __x); 1434 } 1435 1436 /* @} */ // tr1_math_spec_func 1437 _GLIBCXX_END_NAMESPACE_VERSION 1438 } 1439 } 1440 1441 #endif // _GLIBCXX_TR1_CMATH 1442
