cmath revision 1.1.1.4
1 // TR1 cmath -*- C++ -*- 2 3 // Copyright (C) 2006-2015 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 // types 155 using ::double_t; 156 using ::float_t; 157 158 // functions 159 using ::acosh; 160 using ::acoshf; 161 using ::acoshl; 162 163 using ::asinh; 164 using ::asinhf; 165 using ::asinhl; 166 167 using ::atanh; 168 using ::atanhf; 169 using ::atanhl; 170 171 using ::cbrt; 172 using ::cbrtf; 173 using ::cbrtl; 174 175 using ::copysign; 176 using ::copysignf; 177 using ::copysignl; 178 179 using ::erf; 180 using ::erff; 181 using ::erfl; 182 183 using ::erfc; 184 using ::erfcf; 185 using ::erfcl; 186 187 using ::exp2; 188 using ::exp2f; 189 using ::exp2l; 190 191 using ::expm1; 192 using ::expm1f; 193 using ::expm1l; 194 195 using ::fdim; 196 using ::fdimf; 197 using ::fdiml; 198 199 using ::fma; 200 using ::fmaf; 201 using ::fmal; 202 203 using ::fmax; 204 using ::fmaxf; 205 using ::fmaxl; 206 207 using ::fmin; 208 using ::fminf; 209 using ::fminl; 210 211 using ::hypot; 212 using ::hypotf; 213 using ::hypotl; 214 215 using ::ilogb; 216 using ::ilogbf; 217 using ::ilogbl; 218 219 using ::lgamma; 220 using ::lgammaf; 221 using ::lgammal; 222 223 using ::llrint; 224 using ::llrintf; 225 using ::llrintl; 226 227 using ::llround; 228 using ::llroundf; 229 using ::llroundl; 230 231 using ::log1p; 232 using ::log1pf; 233 using ::log1pl; 234 235 using ::log2; 236 using ::log2f; 237 using ::log2l; 238 239 using ::logb; 240 using ::logbf; 241 using ::logbl; 242 243 using ::lrint; 244 using ::lrintf; 245 using ::lrintl; 246 247 using ::lround; 248 using ::lroundf; 249 using ::lroundl; 250 251 using ::nan; 252 using ::nanf; 253 using ::nanl; 254 255 using ::nearbyint; 256 using ::nearbyintf; 257 using ::nearbyintl; 258 259 using ::nextafter; 260 using ::nextafterf; 261 using ::nextafterl; 262 263 using ::nexttoward; 264 using ::nexttowardf; 265 using ::nexttowardl; 266 267 using ::remainder; 268 using ::remainderf; 269 using ::remainderl; 270 271 using ::remquo; 272 using ::remquof; 273 using ::remquol; 274 275 using ::rint; 276 using ::rintf; 277 using ::rintl; 278 279 using ::round; 280 using ::roundf; 281 using ::roundl; 282 283 using ::scalbln; 284 using ::scalblnf; 285 using ::scalblnl; 286 287 using ::scalbn; 288 using ::scalbnf; 289 using ::scalbnl; 290 291 using ::tgamma; 292 using ::tgammaf; 293 using ::tgammal; 294 295 using ::trunc; 296 using ::truncf; 297 using ::truncl; 298 299 #endif 300 301 #if _GLIBCXX_USE_C99_MATH 302 #if !_GLIBCXX_USE_C99_FP_MACROS_DYNAMIC 303 304 /// Function template definitions [8.16.3]. 305 template<typename _Tp> 306 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value, 307 int>::__type 308 fpclassify(_Tp __f) 309 { 310 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 311 return __builtin_fpclassify(FP_NAN, FP_INFINITE, FP_NORMAL, 312 FP_SUBNORMAL, FP_ZERO, __type(__f)); 313 } 314 315 template<typename _Tp> 316 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value, 317 int>::__type 318 isfinite(_Tp __f) 319 { 320 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 321 return __builtin_isfinite(__type(__f)); 322 } 323 324 template<typename _Tp> 325 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value, 326 int>::__type 327 isinf(_Tp __f) 328 { 329 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 330 return __builtin_isinf(__type(__f)); 331 } 332 333 template<typename _Tp> 334 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value, 335 int>::__type 336 isnan(_Tp __f) 337 { 338 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 339 return __builtin_isnan(__type(__f)); 340 } 341 342 template<typename _Tp> 343 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value, 344 int>::__type 345 isnormal(_Tp __f) 346 { 347 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 348 return __builtin_isnormal(__type(__f)); 349 } 350 351 template<typename _Tp> 352 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value, 353 int>::__type 354 signbit(_Tp __f) 355 { 356 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 357 return __builtin_signbit(__type(__f)); 358 } 359 360 template<typename _Tp> 361 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value, 362 int>::__type 363 isgreater(_Tp __f1, _Tp __f2) 364 { 365 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 366 return __builtin_isgreater(__type(__f1), __type(__f2)); 367 } 368 369 template<typename _Tp> 370 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value, 371 int>::__type 372 isgreaterequal(_Tp __f1, _Tp __f2) 373 { 374 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 375 return __builtin_isgreaterequal(__type(__f1), __type(__f2)); 376 } 377 378 template<typename _Tp> 379 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value, 380 int>::__type 381 isless(_Tp __f1, _Tp __f2) 382 { 383 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 384 return __builtin_isless(__type(__f1), __type(__f2)); 385 } 386 387 template<typename _Tp> 388 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value, 389 int>::__type 390 islessequal(_Tp __f1, _Tp __f2) 391 { 392 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 393 return __builtin_islessequal(__type(__f1), __type(__f2)); 394 } 395 396 template<typename _Tp> 397 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value, 398 int>::__type 399 islessgreater(_Tp __f1, _Tp __f2) 400 { 401 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 402 return __builtin_islessgreater(__type(__f1), __type(__f2)); 403 } 404 405 template<typename _Tp> 406 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value, 407 int>::__type 408 isunordered(_Tp __f1, _Tp __f2) 409 { 410 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 411 return __builtin_isunordered(__type(__f1), __type(__f2)); 412 } 413 414 #endif 415 #endif 416 417 #if _GLIBCXX_USE_C99_MATH_TR1 418 419 /// Additional overloads [8.16.4]. 420 using std::acos; 421 422 #ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO 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 #endif 431 432 template<typename _Tp> 433 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 434 double>::__type 435 acosh(_Tp __x) 436 { return __builtin_acosh(__x); } 437 438 using std::asin; 439 440 #ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO 441 inline float 442 asinh(float __x) 443 { return __builtin_asinhf(__x); } 444 445 inline long double 446 asinh(long double __x) 447 { return __builtin_asinhl(__x); } 448 #endif 449 450 template<typename _Tp> 451 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 452 double>::__type 453 asinh(_Tp __x) 454 { return __builtin_asinh(__x); } 455 456 using std::atan; 457 using std::atan2; 458 459 #ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO 460 inline float 461 atanh(float __x) 462 { return __builtin_atanhf(__x); } 463 464 inline long double 465 atanh(long double __x) 466 { return __builtin_atanhl(__x); } 467 #endif 468 469 template<typename _Tp> 470 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 471 double>::__type 472 atanh(_Tp __x) 473 { return __builtin_atanh(__x); } 474 475 #ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO 476 inline float 477 cbrt(float __x) 478 { return __builtin_cbrtf(__x); } 479 480 inline long double 481 cbrt(long double __x) 482 { return __builtin_cbrtl(__x); } 483 #endif 484 485 template<typename _Tp> 486 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 487 double>::__type 488 cbrt(_Tp __x) 489 { return __builtin_cbrt(__x); } 490 491 using std::ceil; 492 493 #ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP 494 inline float 495 copysign(float __x, float __y) 496 { return __builtin_copysignf(__x, __y); } 497 498 inline long double 499 copysign(long double __x, long double __y) 500 { return __builtin_copysignl(__x, __y); } 501 #endif 502 503 template<typename _Tp, typename _Up> 504 inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type 505 copysign(_Tp __x, _Up __y) 506 { 507 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type; 508 return copysign(__type(__x), __type(__y)); 509 } 510 511 using std::cos; 512 using std::cosh; 513 514 #ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP 515 inline float 516 erf(float __x) 517 { return __builtin_erff(__x); } 518 519 inline long double 520 erf(long double __x) 521 { return __builtin_erfl(__x); } 522 #endif 523 524 template<typename _Tp> 525 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 526 double>::__type 527 erf(_Tp __x) 528 { return __builtin_erf(__x); } 529 530 #ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP 531 inline float 532 erfc(float __x) 533 { return __builtin_erfcf(__x); } 534 535 inline long double 536 erfc(long double __x) 537 { return __builtin_erfcl(__x); } 538 #endif 539 540 template<typename _Tp> 541 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 542 double>::__type 543 erfc(_Tp __x) 544 { return __builtin_erfc(__x); } 545 546 using std::exp; 547 548 #ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP 549 inline float 550 exp2(float __x) 551 { return __builtin_exp2f(__x); } 552 553 inline long double 554 exp2(long double __x) 555 { return __builtin_exp2l(__x); } 556 #endif 557 558 template<typename _Tp> 559 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 560 double>::__type 561 exp2(_Tp __x) 562 { return __builtin_exp2(__x); } 563 564 #ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP 565 inline float 566 expm1(float __x) 567 { return __builtin_expm1f(__x); } 568 569 inline long double 570 expm1(long double __x) 571 { return __builtin_expm1l(__x); } 572 #endif 573 574 template<typename _Tp> 575 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 576 double>::__type 577 expm1(_Tp __x) 578 { return __builtin_expm1(__x); } 579 580 // Note: we deal with fabs in a special way, because an using std::fabs 581 // would bring in also the overloads for complex types, which in C++0x 582 // mode have a different return type. 583 // With __CORRECT_ISO_CPP_MATH_H_PROTO, math.h imports std::fabs in the 584 // global namespace after the declarations of the float / double / long 585 // double overloads but before the std::complex overloads. 586 using ::fabs; 587 588 #ifndef __CORRECT_ISO_CPP_MATH_H_PROTO 589 #ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO 590 inline float 591 fabs(float __x) 592 { return __builtin_fabsf(__x); } 593 594 inline long double 595 fabs(long double __x) 596 { return __builtin_fabsl(__x); } 597 #endif 598 599 template<typename _Tp> 600 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 601 double>::__type 602 fabs(_Tp __x) 603 { return __builtin_fabs(__x); } 604 #endif 605 606 #ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP 607 inline float 608 fdim(float __x, float __y) 609 { return __builtin_fdimf(__x, __y); } 610 611 inline long double 612 fdim(long double __x, long double __y) 613 { return __builtin_fdiml(__x, __y); } 614 #endif 615 616 template<typename _Tp, typename _Up> 617 inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type 618 fdim(_Tp __x, _Up __y) 619 { 620 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type; 621 return fdim(__type(__x), __type(__y)); 622 } 623 624 using std::floor; 625 626 #ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP 627 inline float 628 fma(float __x, float __y, float __z) 629 { return __builtin_fmaf(__x, __y, __z); } 630 631 inline long double 632 fma(long double __x, long double __y, long double __z) 633 { return __builtin_fmal(__x, __y, __z); } 634 #endif 635 636 template<typename _Tp, typename _Up, typename _Vp> 637 inline typename __gnu_cxx::__promote_3<_Tp, _Up, _Vp>::__type 638 fma(_Tp __x, _Up __y, _Vp __z) 639 { 640 typedef typename __gnu_cxx::__promote_3<_Tp, _Up, _Vp>::__type __type; 641 return fma(__type(__x), __type(__y), __type(__z)); 642 } 643 644 #ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP 645 inline float 646 fmax(float __x, float __y) 647 { return __builtin_fmaxf(__x, __y); } 648 649 inline long double 650 fmax(long double __x, long double __y) 651 { return __builtin_fmaxl(__x, __y); } 652 #endif 653 654 template<typename _Tp, typename _Up> 655 inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type 656 fmax(_Tp __x, _Up __y) 657 { 658 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type; 659 return fmax(__type(__x), __type(__y)); 660 } 661 662 #ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP 663 inline float 664 fmin(float __x, float __y) 665 { return __builtin_fminf(__x, __y); } 666 667 inline long double 668 fmin(long double __x, long double __y) 669 { return __builtin_fminl(__x, __y); } 670 #endif 671 672 template<typename _Tp, typename _Up> 673 inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type 674 fmin(_Tp __x, _Up __y) 675 { 676 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type; 677 return fmin(__type(__x), __type(__y)); 678 } 679 680 using std::fmod; 681 using std::frexp; 682 683 #ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP 684 inline float 685 hypot(float __x, float __y) 686 { return __builtin_hypotf(__x, __y); } 687 688 inline long double 689 hypot(long double __x, long double __y) 690 { return __builtin_hypotl(__x, __y); } 691 #endif 692 693 template<typename _Tp, typename _Up> 694 inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type 695 hypot(_Tp __y, _Up __x) 696 { 697 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type; 698 return hypot(__type(__y), __type(__x)); 699 } 700 701 #ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO 702 inline int 703 ilogb(float __x) 704 { return __builtin_ilogbf(__x); } 705 706 inline int 707 ilogb(long double __x) 708 { return __builtin_ilogbl(__x); } 709 #endif 710 711 template<typename _Tp> 712 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 713 int>::__type 714 ilogb(_Tp __x) 715 { return __builtin_ilogb(__x); } 716 717 using std::ldexp; 718 719 #ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP 720 inline float 721 lgamma(float __x) 722 { return __builtin_lgammaf(__x); } 723 724 inline long double 725 lgamma(long double __x) 726 { return __builtin_lgammal(__x); } 727 #endif 728 729 template<typename _Tp> 730 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 731 double>::__type 732 lgamma(_Tp __x) 733 { return __builtin_lgamma(__x); } 734 735 #ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP 736 inline long long 737 llrint(float __x) 738 { return __builtin_llrintf(__x); } 739 740 inline long long 741 llrint(long double __x) 742 { return __builtin_llrintl(__x); } 743 #endif 744 745 template<typename _Tp> 746 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 747 long long>::__type 748 llrint(_Tp __x) 749 { return __builtin_llrint(__x); } 750 751 #ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP 752 inline long long 753 llround(float __x) 754 { return __builtin_llroundf(__x); } 755 756 inline long long 757 llround(long double __x) 758 { return __builtin_llroundl(__x); } 759 #endif 760 761 template<typename _Tp> 762 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 763 long long>::__type 764 llround(_Tp __x) 765 { return __builtin_llround(__x); } 766 767 using std::log; 768 using std::log10; 769 770 #ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP 771 inline float 772 log1p(float __x) 773 { return __builtin_log1pf(__x); } 774 775 inline long double 776 log1p(long double __x) 777 { return __builtin_log1pl(__x); } 778 #endif 779 780 template<typename _Tp> 781 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 782 double>::__type 783 log1p(_Tp __x) 784 { return __builtin_log1p(__x); } 785 786 // DR 568. 787 #ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP 788 inline float 789 log2(float __x) 790 { return __builtin_log2f(__x); } 791 792 inline long double 793 log2(long double __x) 794 { return __builtin_log2l(__x); } 795 #endif 796 797 template<typename _Tp> 798 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 799 double>::__type 800 log2(_Tp __x) 801 { return __builtin_log2(__x); } 802 803 #ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP 804 inline float 805 logb(float __x) 806 { return __builtin_logbf(__x); } 807 808 inline long double 809 logb(long double __x) 810 { return __builtin_logbl(__x); } 811 #endif 812 813 template<typename _Tp> 814 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 815 double>::__type 816 logb(_Tp __x) 817 { 818 return __builtin_logb(__x); 819 } 820 821 #ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP 822 inline long 823 lrint(float __x) 824 { return __builtin_lrintf(__x); } 825 826 inline long 827 lrint(long double __x) 828 { return __builtin_lrintl(__x); } 829 #endif 830 831 template<typename _Tp> 832 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 833 long>::__type 834 lrint(_Tp __x) 835 { return __builtin_lrint(__x); } 836 837 #ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP 838 inline long 839 lround(float __x) 840 { return __builtin_lroundf(__x); } 841 842 inline long 843 lround(long double __x) 844 { return __builtin_lroundl(__x); } 845 #endif 846 847 template<typename _Tp> 848 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 849 long>::__type 850 lround(_Tp __x) 851 { return __builtin_lround(__x); } 852 853 #ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP_FP 854 inline float 855 nearbyint(float __x) 856 { return __builtin_nearbyintf(__x); } 857 858 inline long double 859 nearbyint(long double __x) 860 { return __builtin_nearbyintl(__x); } 861 #endif 862 863 template<typename _Tp> 864 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 865 double>::__type 866 nearbyint(_Tp __x) 867 { return __builtin_nearbyint(__x); } 868 869 #ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP 870 inline float 871 nextafter(float __x, float __y) 872 { return __builtin_nextafterf(__x, __y); } 873 874 inline long double 875 nextafter(long double __x, long double __y) 876 { return __builtin_nextafterl(__x, __y); } 877 #endif 878 879 template<typename _Tp, typename _Up> 880 inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type 881 nextafter(_Tp __x, _Up __y) 882 { 883 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type; 884 return nextafter(__type(__x), __type(__y)); 885 } 886 887 #ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP_FP 888 inline float 889 nexttoward(float __x, long double __y) 890 { return __builtin_nexttowardf(__x, __y); } 891 892 inline long double 893 nexttoward(long double __x, long double __y) 894 { return __builtin_nexttowardl(__x, __y); } 895 #endif 896 897 template<typename _Tp> 898 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 899 double>::__type 900 nexttoward(_Tp __x, long double __y) 901 { return __builtin_nexttoward(__x, __y); } 902 903 #ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP 904 inline float 905 remainder(float __x, float __y) 906 { return __builtin_remainderf(__x, __y); } 907 908 inline long double 909 remainder(long double __x, long double __y) 910 { return __builtin_remainderl(__x, __y); } 911 #endif 912 913 template<typename _Tp, typename _Up> 914 inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type 915 remainder(_Tp __x, _Up __y) 916 { 917 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type; 918 return remainder(__type(__x), __type(__y)); 919 } 920 921 #ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP 922 inline float 923 remquo(float __x, float __y, int* __pquo) 924 { return __builtin_remquof(__x, __y, __pquo); } 925 926 inline long double 927 remquo(long double __x, long double __y, int* __pquo) 928 { return __builtin_remquol(__x, __y, __pquo); } 929 #endif 930 931 template<typename _Tp, typename _Up> 932 inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type 933 remquo(_Tp __x, _Up __y, int* __pquo) 934 { 935 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type; 936 return remquo(__type(__x), __type(__y), __pquo); 937 } 938 939 #ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP 940 inline float 941 rint(float __x) 942 { return __builtin_rintf(__x); } 943 944 inline long double 945 rint(long double __x) 946 { return __builtin_rintl(__x); } 947 #endif 948 949 template<typename _Tp> 950 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 951 double>::__type 952 rint(_Tp __x) 953 { return __builtin_rint(__x); } 954 955 #ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP 956 inline float 957 round(float __x) 958 { return __builtin_roundf(__x); } 959 960 inline long double 961 round(long double __x) 962 { return __builtin_roundl(__x); } 963 #endif 964 965 template<typename _Tp> 966 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 967 double>::__type 968 round(_Tp __x) 969 { return __builtin_round(__x); } 970 971 #ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP 972 inline float 973 scalbln(float __x, long __ex) 974 { return __builtin_scalblnf(__x, __ex); } 975 976 inline long double 977 scalbln(long double __x, long __ex) 978 { return __builtin_scalblnl(__x, __ex); } 979 #endif 980 981 template<typename _Tp> 982 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 983 double>::__type 984 scalbln(_Tp __x, long __ex) 985 { return __builtin_scalbln(__x, __ex); } 986 987 #ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP 988 inline float 989 scalbn(float __x, int __ex) 990 { return __builtin_scalbnf(__x, __ex); } 991 992 inline long double 993 scalbn(long double __x, int __ex) 994 { return __builtin_scalbnl(__x, __ex); } 995 #endif 996 997 template<typename _Tp> 998 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 999 double>::__type 1000 scalbn(_Tp __x, int __ex) 1001 { return __builtin_scalbn(__x, __ex); } 1002 1003 using std::sin; 1004 using std::sinh; 1005 using std::sqrt; 1006 using std::tan; 1007 using std::tanh; 1008 1009 #ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP 1010 inline float 1011 tgamma(float __x) 1012 { return __builtin_tgammaf(__x); } 1013 1014 inline long double 1015 tgamma(long double __x) 1016 { return __builtin_tgammal(__x); } 1017 #endif 1018 1019 template<typename _Tp> 1020 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 1021 double>::__type 1022 tgamma(_Tp __x) 1023 { return __builtin_tgamma(__x); } 1024 1025 #ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP 1026 inline float 1027 trunc(float __x) 1028 { return __builtin_truncf(__x); } 1029 1030 inline long double 1031 trunc(long double __x) 1032 { return __builtin_truncl(__x); } 1033 #endif 1034 1035 template<typename _Tp> 1036 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 1037 double>::__type 1038 trunc(_Tp __x) 1039 { return __builtin_trunc(__x); } 1040 1041 #endif 1042 _GLIBCXX_END_NAMESPACE_VERSION 1043 } 1044 } 1045 1046 namespace std _GLIBCXX_VISIBILITY(default) 1047 { 1048 namespace tr1 1049 { 1050 _GLIBCXX_BEGIN_NAMESPACE_VERSION 1051 1052 // DR 550. What should the return type of pow(float,int) be? 1053 // NB: C++0x and TR1 != C++03. 1054 1055 // The std::tr1::pow(double, double) overload cannot be provided 1056 // here, because it would clash with ::pow(double,double) declared 1057 // in <math.h>, if <tr1/math.h> is included at the same time (raised 1058 // by the fix of PR c++/54537). It is not possible either to use the 1059 // using-declaration 'using ::pow;' here, because if the user code 1060 // has a 'using std::pow;', it would bring the pow(*,int) averloads 1061 // in the tr1 namespace, which is undesirable. Consequently, the 1062 // solution is to forward std::tr1::pow(double,double) to 1063 // std::pow(double,double) via the templatized version below. See 1064 // the discussion about this issue here: 1065 // http://gcc.gnu.org/ml/gcc-patches/2012-09/msg01278.html 1066 1067 #ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP 1068 inline float 1069 pow(float __x, float __y) 1070 { return std::pow(__x, __y); } 1071 1072 inline long double 1073 pow(long double __x, long double __y) 1074 { return std::pow(__x, __y); } 1075 #endif 1076 1077 template<typename _Tp, typename _Up> 1078 inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type 1079 pow(_Tp __x, _Up __y) 1080 { 1081 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type; 1082 return std::pow(__type(__x), __type(__y)); 1083 } 1084 1085 _GLIBCXX_END_NAMESPACE_VERSION 1086 } 1087 } 1088 1089 #include <bits/stl_algobase.h> 1090 #include <limits> 1091 #include <tr1/type_traits> 1092 1093 #include <tr1/gamma.tcc> 1094 #include <tr1/bessel_function.tcc> 1095 #include <tr1/beta_function.tcc> 1096 #include <tr1/ell_integral.tcc> 1097 #include <tr1/exp_integral.tcc> 1098 #include <tr1/hypergeometric.tcc> 1099 #include <tr1/legendre_function.tcc> 1100 #include <tr1/modified_bessel_func.tcc> 1101 #include <tr1/poly_hermite.tcc> 1102 #include <tr1/poly_laguerre.tcc> 1103 #include <tr1/riemann_zeta.tcc> 1104 1105 namespace std _GLIBCXX_VISIBILITY(default) 1106 { 1107 namespace tr1 1108 { 1109 _GLIBCXX_BEGIN_NAMESPACE_VERSION 1110 1111 /** 1112 * @defgroup tr1_math_spec_func Mathematical Special Functions 1113 * @ingroup numerics 1114 * 1115 * A collection of advanced mathematical special functions. 1116 * @{ 1117 */ 1118 1119 inline float 1120 assoc_laguerref(unsigned int __n, unsigned int __m, float __x) 1121 { return __detail::__assoc_laguerre<float>(__n, __m, __x); } 1122 1123 inline long double 1124 assoc_laguerrel(unsigned int __n, unsigned int __m, long double __x) 1125 { 1126 return __detail::__assoc_laguerre<long double>(__n, __m, __x); 1127 } 1128 1129 /// 5.2.1.1 Associated Laguerre polynomials. 1130 template<typename _Tp> 1131 inline typename __gnu_cxx::__promote<_Tp>::__type 1132 assoc_laguerre(unsigned int __n, unsigned int __m, _Tp __x) 1133 { 1134 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 1135 return __detail::__assoc_laguerre<__type>(__n, __m, __x); 1136 } 1137 1138 inline float 1139 assoc_legendref(unsigned int __l, unsigned int __m, float __x) 1140 { return __detail::__assoc_legendre_p<float>(__l, __m, __x); } 1141 1142 inline long double 1143 assoc_legendrel(unsigned int __l, unsigned int __m, long double __x) 1144 { return __detail::__assoc_legendre_p<long double>(__l, __m, __x); } 1145 1146 /// 5.2.1.2 Associated Legendre functions. 1147 template<typename _Tp> 1148 inline typename __gnu_cxx::__promote<_Tp>::__type 1149 assoc_legendre(unsigned int __l, unsigned int __m, _Tp __x) 1150 { 1151 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 1152 return __detail::__assoc_legendre_p<__type>(__l, __m, __x); 1153 } 1154 1155 inline float 1156 betaf(float __x, float __y) 1157 { return __detail::__beta<float>(__x, __y); } 1158 1159 inline long double 1160 betal(long double __x, long double __y) 1161 { return __detail::__beta<long double>(__x, __y); } 1162 1163 /// 5.2.1.3 Beta functions. 1164 template<typename _Tpx, typename _Tpy> 1165 inline typename __gnu_cxx::__promote_2<_Tpx, _Tpy>::__type 1166 beta(_Tpx __x, _Tpy __y) 1167 { 1168 typedef typename __gnu_cxx::__promote_2<_Tpx, _Tpy>::__type __type; 1169 return __detail::__beta<__type>(__x, __y); 1170 } 1171 1172 inline float 1173 comp_ellint_1f(float __k) 1174 { return __detail::__comp_ellint_1<float>(__k); } 1175 1176 inline long double 1177 comp_ellint_1l(long double __k) 1178 { return __detail::__comp_ellint_1<long double>(__k); } 1179 1180 /// 5.2.1.4 Complete elliptic integrals of the first kind. 1181 template<typename _Tp> 1182 inline typename __gnu_cxx::__promote<_Tp>::__type 1183 comp_ellint_1(_Tp __k) 1184 { 1185 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 1186 return __detail::__comp_ellint_1<__type>(__k); 1187 } 1188 1189 inline float 1190 comp_ellint_2f(float __k) 1191 { return __detail::__comp_ellint_2<float>(__k); } 1192 1193 inline long double 1194 comp_ellint_2l(long double __k) 1195 { return __detail::__comp_ellint_2<long double>(__k); } 1196 1197 /// 5.2.1.5 Complete elliptic integrals of the second kind. 1198 template<typename _Tp> 1199 inline typename __gnu_cxx::__promote<_Tp>::__type 1200 comp_ellint_2(_Tp __k) 1201 { 1202 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 1203 return __detail::__comp_ellint_2<__type>(__k); 1204 } 1205 1206 inline float 1207 comp_ellint_3f(float __k, float __nu) 1208 { return __detail::__comp_ellint_3<float>(__k, __nu); } 1209 1210 inline long double 1211 comp_ellint_3l(long double __k, long double __nu) 1212 { return __detail::__comp_ellint_3<long double>(__k, __nu); } 1213 1214 /// 5.2.1.6 Complete elliptic integrals of the third kind. 1215 template<typename _Tp, typename _Tpn> 1216 inline typename __gnu_cxx::__promote_2<_Tp, _Tpn>::__type 1217 comp_ellint_3(_Tp __k, _Tpn __nu) 1218 { 1219 typedef typename __gnu_cxx::__promote_2<_Tp, _Tpn>::__type __type; 1220 return __detail::__comp_ellint_3<__type>(__k, __nu); 1221 } 1222 1223 inline float 1224 conf_hypergf(float __a, float __c, float __x) 1225 { return __detail::__conf_hyperg<float>(__a, __c, __x); } 1226 1227 inline long double 1228 conf_hypergl(long double __a, long double __c, long double __x) 1229 { return __detail::__conf_hyperg<long double>(__a, __c, __x); } 1230 1231 /// 5.2.1.7 Confluent hypergeometric functions. 1232 template<typename _Tpa, typename _Tpc, typename _Tp> 1233 inline typename __gnu_cxx::__promote_3<_Tpa, _Tpc, _Tp>::__type 1234 conf_hyperg(_Tpa __a, _Tpc __c, _Tp __x) 1235 { 1236 typedef typename __gnu_cxx::__promote_3<_Tpa, _Tpc, _Tp>::__type __type; 1237 return __detail::__conf_hyperg<__type>(__a, __c, __x); 1238 } 1239 1240 inline float 1241 cyl_bessel_if(float __nu, float __x) 1242 { return __detail::__cyl_bessel_i<float>(__nu, __x); } 1243 1244 inline long double 1245 cyl_bessel_il(long double __nu, long double __x) 1246 { return __detail::__cyl_bessel_i<long double>(__nu, __x); } 1247 1248 /// 5.2.1.8 Regular modified cylindrical Bessel functions. 1249 template<typename _Tpnu, typename _Tp> 1250 inline typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type 1251 cyl_bessel_i(_Tpnu __nu, _Tp __x) 1252 { 1253 typedef typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type __type; 1254 return __detail::__cyl_bessel_i<__type>(__nu, __x); 1255 } 1256 1257 inline float 1258 cyl_bessel_jf(float __nu, float __x) 1259 { return __detail::__cyl_bessel_j<float>(__nu, __x); } 1260 1261 inline long double 1262 cyl_bessel_jl(long double __nu, long double __x) 1263 { return __detail::__cyl_bessel_j<long double>(__nu, __x); } 1264 1265 /// 5.2.1.9 Cylindrical Bessel functions (of the first kind). 1266 template<typename _Tpnu, typename _Tp> 1267 inline typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type 1268 cyl_bessel_j(_Tpnu __nu, _Tp __x) 1269 { 1270 typedef typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type __type; 1271 return __detail::__cyl_bessel_j<__type>(__nu, __x); 1272 } 1273 1274 inline float 1275 cyl_bessel_kf(float __nu, float __x) 1276 { return __detail::__cyl_bessel_k<float>(__nu, __x); } 1277 1278 inline long double 1279 cyl_bessel_kl(long double __nu, long double __x) 1280 { return __detail::__cyl_bessel_k<long double>(__nu, __x); } 1281 1282 /// 5.2.1.10 Irregular modified cylindrical Bessel functions. 1283 template<typename _Tpnu, typename _Tp> 1284 inline typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type 1285 cyl_bessel_k(_Tpnu __nu, _Tp __x) 1286 { 1287 typedef typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type __type; 1288 return __detail::__cyl_bessel_k<__type>(__nu, __x); 1289 } 1290 1291 inline float 1292 cyl_neumannf(float __nu, float __x) 1293 { return __detail::__cyl_neumann_n<float>(__nu, __x); } 1294 1295 inline long double 1296 cyl_neumannl(long double __nu, long double __x) 1297 { return __detail::__cyl_neumann_n<long double>(__nu, __x); } 1298 1299 /// 5.2.1.11 Cylindrical Neumann functions. 1300 template<typename _Tpnu, typename _Tp> 1301 inline typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type 1302 cyl_neumann(_Tpnu __nu, _Tp __x) 1303 { 1304 typedef typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type __type; 1305 return __detail::__cyl_neumann_n<__type>(__nu, __x); 1306 } 1307 1308 inline float 1309 ellint_1f(float __k, float __phi) 1310 { return __detail::__ellint_1<float>(__k, __phi); } 1311 1312 inline long double 1313 ellint_1l(long double __k, long double __phi) 1314 { return __detail::__ellint_1<long double>(__k, __phi); } 1315 1316 /// 5.2.1.12 Incomplete elliptic integrals of the first kind. 1317 template<typename _Tp, typename _Tpp> 1318 inline typename __gnu_cxx::__promote_2<_Tp, _Tpp>::__type 1319 ellint_1(_Tp __k, _Tpp __phi) 1320 { 1321 typedef typename __gnu_cxx::__promote_2<_Tp, _Tpp>::__type __type; 1322 return __detail::__ellint_1<__type>(__k, __phi); 1323 } 1324 1325 inline float 1326 ellint_2f(float __k, float __phi) 1327 { return __detail::__ellint_2<float>(__k, __phi); } 1328 1329 inline long double 1330 ellint_2l(long double __k, long double __phi) 1331 { return __detail::__ellint_2<long double>(__k, __phi); } 1332 1333 /// 5.2.1.13 Incomplete elliptic integrals of the second kind. 1334 template<typename _Tp, typename _Tpp> 1335 inline typename __gnu_cxx::__promote_2<_Tp, _Tpp>::__type 1336 ellint_2(_Tp __k, _Tpp __phi) 1337 { 1338 typedef typename __gnu_cxx::__promote_2<_Tp, _Tpp>::__type __type; 1339 return __detail::__ellint_2<__type>(__k, __phi); 1340 } 1341 1342 inline float 1343 ellint_3f(float __k, float __nu, float __phi) 1344 { return __detail::__ellint_3<float>(__k, __nu, __phi); } 1345 1346 inline long double 1347 ellint_3l(long double __k, long double __nu, long double __phi) 1348 { return __detail::__ellint_3<long double>(__k, __nu, __phi); } 1349 1350 /// 5.2.1.14 Incomplete elliptic integrals of the third kind. 1351 template<typename _Tp, typename _Tpn, typename _Tpp> 1352 inline typename __gnu_cxx::__promote_3<_Tp, _Tpn, _Tpp>::__type 1353 ellint_3(_Tp __k, _Tpn __nu, _Tpp __phi) 1354 { 1355 typedef typename __gnu_cxx::__promote_3<_Tp, _Tpn, _Tpp>::__type __type; 1356 return __detail::__ellint_3<__type>(__k, __nu, __phi); 1357 } 1358 1359 inline float 1360 expintf(float __x) 1361 { return __detail::__expint<float>(__x); } 1362 1363 inline long double 1364 expintl(long double __x) 1365 { return __detail::__expint<long double>(__x); } 1366 1367 /// 5.2.1.15 Exponential integrals. 1368 template<typename _Tp> 1369 inline typename __gnu_cxx::__promote<_Tp>::__type 1370 expint(_Tp __x) 1371 { 1372 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 1373 return __detail::__expint<__type>(__x); 1374 } 1375 1376 inline float 1377 hermitef(unsigned int __n, float __x) 1378 { return __detail::__poly_hermite<float>(__n, __x); } 1379 1380 inline long double 1381 hermitel(unsigned int __n, long double __x) 1382 { return __detail::__poly_hermite<long double>(__n, __x); } 1383 1384 /// 5.2.1.16 Hermite polynomials. 1385 template<typename _Tp> 1386 inline typename __gnu_cxx::__promote<_Tp>::__type 1387 hermite(unsigned int __n, _Tp __x) 1388 { 1389 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 1390 return __detail::__poly_hermite<__type>(__n, __x); 1391 } 1392 1393 inline float 1394 hypergf(float __a, float __b, float __c, float __x) 1395 { return __detail::__hyperg<float>(__a, __b, __c, __x); } 1396 1397 inline long double 1398 hypergl(long double __a, long double __b, long double __c, long double __x) 1399 { return __detail::__hyperg<long double>(__a, __b, __c, __x); } 1400 1401 /// 5.2.1.17 Hypergeometric functions. 1402 template<typename _Tpa, typename _Tpb, typename _Tpc, typename _Tp> 1403 inline typename __gnu_cxx::__promote_4<_Tpa, _Tpb, _Tpc, _Tp>::__type 1404 hyperg(_Tpa __a, _Tpb __b, _Tpc __c, _Tp __x) 1405 { 1406 typedef typename __gnu_cxx::__promote_4<_Tpa, _Tpb, _Tpc, _Tp>::__type __type; 1407 return __detail::__hyperg<__type>(__a, __b, __c, __x); 1408 } 1409 1410 inline float 1411 laguerref(unsigned int __n, float __x) 1412 { return __detail::__laguerre<float>(__n, __x); } 1413 1414 inline long double 1415 laguerrel(unsigned int __n, long double __x) 1416 { return __detail::__laguerre<long double>(__n, __x); } 1417 1418 /// 5.2.1.18 Laguerre polynomials. 1419 template<typename _Tp> 1420 inline typename __gnu_cxx::__promote<_Tp>::__type 1421 laguerre(unsigned int __n, _Tp __x) 1422 { 1423 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 1424 return __detail::__laguerre<__type>(__n, __x); 1425 } 1426 1427 inline float 1428 legendref(unsigned int __n, float __x) 1429 { return __detail::__poly_legendre_p<float>(__n, __x); } 1430 1431 inline long double 1432 legendrel(unsigned int __n, long double __x) 1433 { return __detail::__poly_legendre_p<long double>(__n, __x); } 1434 1435 /// 5.2.1.19 Legendre polynomials. 1436 template<typename _Tp> 1437 inline typename __gnu_cxx::__promote<_Tp>::__type 1438 legendre(unsigned int __n, _Tp __x) 1439 { 1440 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 1441 return __detail::__poly_legendre_p<__type>(__n, __x); 1442 } 1443 1444 inline float 1445 riemann_zetaf(float __x) 1446 { return __detail::__riemann_zeta<float>(__x); } 1447 1448 inline long double 1449 riemann_zetal(long double __x) 1450 { return __detail::__riemann_zeta<long double>(__x); } 1451 1452 /// 5.2.1.20 Riemann zeta function. 1453 template<typename _Tp> 1454 inline typename __gnu_cxx::__promote<_Tp>::__type 1455 riemann_zeta(_Tp __x) 1456 { 1457 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 1458 return __detail::__riemann_zeta<__type>(__x); 1459 } 1460 1461 inline float 1462 sph_besself(unsigned int __n, float __x) 1463 { return __detail::__sph_bessel<float>(__n, __x); } 1464 1465 inline long double 1466 sph_bessell(unsigned int __n, long double __x) 1467 { return __detail::__sph_bessel<long double>(__n, __x); } 1468 1469 /// 5.2.1.21 Spherical Bessel functions. 1470 template<typename _Tp> 1471 inline typename __gnu_cxx::__promote<_Tp>::__type 1472 sph_bessel(unsigned int __n, _Tp __x) 1473 { 1474 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 1475 return __detail::__sph_bessel<__type>(__n, __x); 1476 } 1477 1478 inline float 1479 sph_legendref(unsigned int __l, unsigned int __m, float __theta) 1480 { return __detail::__sph_legendre<float>(__l, __m, __theta); } 1481 1482 inline long double 1483 sph_legendrel(unsigned int __l, unsigned int __m, long double __theta) 1484 { return __detail::__sph_legendre<long double>(__l, __m, __theta); } 1485 1486 /// 5.2.1.22 Spherical associated Legendre functions. 1487 template<typename _Tp> 1488 inline typename __gnu_cxx::__promote<_Tp>::__type 1489 sph_legendre(unsigned int __l, unsigned int __m, _Tp __theta) 1490 { 1491 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 1492 return __detail::__sph_legendre<__type>(__l, __m, __theta); 1493 } 1494 1495 inline float 1496 sph_neumannf(unsigned int __n, float __x) 1497 { return __detail::__sph_neumann<float>(__n, __x); } 1498 1499 inline long double 1500 sph_neumannl(unsigned int __n, long double __x) 1501 { return __detail::__sph_neumann<long double>(__n, __x); } 1502 1503 /// 5.2.1.23 Spherical Neumann functions. 1504 template<typename _Tp> 1505 inline typename __gnu_cxx::__promote<_Tp>::__type 1506 sph_neumann(unsigned int __n, _Tp __x) 1507 { 1508 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 1509 return __detail::__sph_neumann<__type>(__n, __x); 1510 } 1511 1512 /* @} */ // tr1_math_spec_func 1513 _GLIBCXX_END_NAMESPACE_VERSION 1514 } 1515 } 1516 1517 #endif // _GLIBCXX_TR1_CMATH 1518
Indexes created Tue Sep 08 00:25:21 UTC 2026