1// -*- C++ -*- 2//===----------------------------------------------------------------------===// 3// 4// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions. 5// See https://llvm.org/LICENSE.txt for license information. 6// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception 7// 8//===----------------------------------------------------------------------===// 9 10#ifndef _LIBCPP_CMATH 11#define _LIBCPP_CMATH 12 13/* 14 cmath synopsis 15 16Macros: 17 18 HUGE_VAL 19 HUGE_VALF // C99 20 HUGE_VALL // C99 21 INFINITY // C99 22 NAN // C99 23 FP_INFINITE // C99 24 FP_NAN // C99 25 FP_NORMAL // C99 26 FP_SUBNORMAL // C99 27 FP_ZERO // C99 28 FP_FAST_FMA // C99 29 FP_FAST_FMAF // C99 30 FP_FAST_FMAL // C99 31 FP_ILOGB0 // C99 32 FP_ILOGBNAN // C99 33 MATH_ERRNO // C99 34 MATH_ERREXCEPT // C99 35 math_errhandling // C99 36 37namespace std 38{ 39 40Types: 41 42 float_t // C99 43 double_t // C99 44 45// C90 46 47floating_point abs(floating_point x); 48 49floating_point acos (arithmetic x); 50float acosf(float x); 51long double acosl(long double x); 52 53floating_point asin (arithmetic x); 54float asinf(float x); 55long double asinl(long double x); 56 57floating_point atan (arithmetic x); 58float atanf(float x); 59long double atanl(long double x); 60 61floating_point atan2 (arithmetic y, arithmetic x); 62float atan2f(float y, float x); 63long double atan2l(long double y, long double x); 64 65floating_point ceil (arithmetic x); 66float ceilf(float x); 67long double ceill(long double x); 68 69floating_point cos (arithmetic x); 70float cosf(float x); 71long double cosl(long double x); 72 73floating_point cosh (arithmetic x); 74float coshf(float x); 75long double coshl(long double x); 76 77floating_point exp (arithmetic x); 78float expf(float x); 79long double expl(long double x); 80 81floating_point fabs (arithmetic x); 82float fabsf(float x); 83long double fabsl(long double x); 84 85floating_point floor (arithmetic x); 86float floorf(float x); 87long double floorl(long double x); 88 89floating_point fmod (arithmetic x, arithmetic y); 90float fmodf(float x, float y); 91long double fmodl(long double x, long double y); 92 93floating_point frexp (arithmetic value, int* exp); 94float frexpf(float value, int* exp); 95long double frexpl(long double value, int* exp); 96 97floating_point ldexp (arithmetic value, int exp); 98float ldexpf(float value, int exp); 99long double ldexpl(long double value, int exp); 100 101floating_point log (arithmetic x); 102float logf(float x); 103long double logl(long double x); 104 105floating_point log10 (arithmetic x); 106float log10f(float x); 107long double log10l(long double x); 108 109floating_point modf (floating_point value, floating_point* iptr); 110float modff(float value, float* iptr); 111long double modfl(long double value, long double* iptr); 112 113floating_point pow (arithmetic x, arithmetic y); 114float powf(float x, float y); 115long double powl(long double x, long double y); 116 117floating_point sin (arithmetic x); 118float sinf(float x); 119long double sinl(long double x); 120 121floating_point sinh (arithmetic x); 122float sinhf(float x); 123long double sinhl(long double x); 124 125floating_point sqrt (arithmetic x); 126float sqrtf(float x); 127long double sqrtl(long double x); 128 129floating_point tan (arithmetic x); 130float tanf(float x); 131long double tanl(long double x); 132 133floating_point tanh (arithmetic x); 134float tanhf(float x); 135long double tanhl(long double x); 136 137// C99 138 139bool signbit(arithmetic x); 140 141int fpclassify(arithmetic x); 142 143bool isfinite(arithmetic x); 144bool isinf(arithmetic x); 145bool isnan(arithmetic x); 146bool isnormal(arithmetic x); 147 148bool isgreater(arithmetic x, arithmetic y); 149bool isgreaterequal(arithmetic x, arithmetic y); 150bool isless(arithmetic x, arithmetic y); 151bool islessequal(arithmetic x, arithmetic y); 152bool islessgreater(arithmetic x, arithmetic y); 153bool isunordered(arithmetic x, arithmetic y); 154 155floating_point acosh (arithmetic x); 156float acoshf(float x); 157long double acoshl(long double x); 158 159floating_point asinh (arithmetic x); 160float asinhf(float x); 161long double asinhl(long double x); 162 163floating_point atanh (arithmetic x); 164float atanhf(float x); 165long double atanhl(long double x); 166 167floating_point cbrt (arithmetic x); 168float cbrtf(float x); 169long double cbrtl(long double x); 170 171floating_point copysign (arithmetic x, arithmetic y); 172float copysignf(float x, float y); 173long double copysignl(long double x, long double y); 174 175floating_point erf (arithmetic x); 176float erff(float x); 177long double erfl(long double x); 178 179floating_point erfc (arithmetic x); 180float erfcf(float x); 181long double erfcl(long double x); 182 183floating_point exp2 (arithmetic x); 184float exp2f(float x); 185long double exp2l(long double x); 186 187floating_point expm1 (arithmetic x); 188float expm1f(float x); 189long double expm1l(long double x); 190 191floating_point fdim (arithmetic x, arithmetic y); 192float fdimf(float x, float y); 193long double fdiml(long double x, long double y); 194 195floating_point fma (arithmetic x, arithmetic y, arithmetic z); 196float fmaf(float x, float y, float z); 197long double fmal(long double x, long double y, long double z); 198 199floating_point fmax (arithmetic x, arithmetic y); 200float fmaxf(float x, float y); 201long double fmaxl(long double x, long double y); 202 203floating_point fmin (arithmetic x, arithmetic y); 204float fminf(float x, float y); 205long double fminl(long double x, long double y); 206 207floating_point hypot (arithmetic x, arithmetic y); 208float hypotf(float x, float y); 209long double hypotl(long double x, long double y); 210 211double hypot(double x, double y, double z); // C++17 212float hypot(float x, float y, float z); // C++17 213long double hypot(long double x, long double y, long double z); // C++17 214 215int ilogb (arithmetic x); 216int ilogbf(float x); 217int ilogbl(long double x); 218 219floating_point lgamma (arithmetic x); 220float lgammaf(float x); 221long double lgammal(long double x); 222 223long long llrint (arithmetic x); 224long long llrintf(float x); 225long long llrintl(long double x); 226 227long long llround (arithmetic x); 228long long llroundf(float x); 229long long llroundl(long double x); 230 231floating_point log1p (arithmetic x); 232float log1pf(float x); 233long double log1pl(long double x); 234 235floating_point log2 (arithmetic x); 236float log2f(float x); 237long double log2l(long double x); 238 239floating_point logb (arithmetic x); 240float logbf(float x); 241long double logbl(long double x); 242 243long lrint (arithmetic x); 244long lrintf(float x); 245long lrintl(long double x); 246 247long lround (arithmetic x); 248long lroundf(float x); 249long lroundl(long double x); 250 251double nan (const char* str); 252float nanf(const char* str); 253long double nanl(const char* str); 254 255floating_point nearbyint (arithmetic x); 256float nearbyintf(float x); 257long double nearbyintl(long double x); 258 259floating_point nextafter (arithmetic x, arithmetic y); 260float nextafterf(float x, float y); 261long double nextafterl(long double x, long double y); 262 263floating_point nexttoward (arithmetic x, long double y); 264float nexttowardf(float x, long double y); 265long double nexttowardl(long double x, long double y); 266 267floating_point remainder (arithmetic x, arithmetic y); 268float remainderf(float x, float y); 269long double remainderl(long double x, long double y); 270 271floating_point remquo (arithmetic x, arithmetic y, int* pquo); 272float remquof(float x, float y, int* pquo); 273long double remquol(long double x, long double y, int* pquo); 274 275floating_point rint (arithmetic x); 276float rintf(float x); 277long double rintl(long double x); 278 279floating_point round (arithmetic x); 280float roundf(float x); 281long double roundl(long double x); 282 283floating_point scalbln (arithmetic x, long ex); 284float scalblnf(float x, long ex); 285long double scalblnl(long double x, long ex); 286 287floating_point scalbn (arithmetic x, int ex); 288float scalbnf(float x, int ex); 289long double scalbnl(long double x, int ex); 290 291floating_point tgamma (arithmetic x); 292float tgammaf(float x); 293long double tgammal(long double x); 294 295floating_point trunc (arithmetic x); 296float truncf(float x); 297long double truncl(long double x); 298 299constexpr float lerp(float a, float b, float t) noexcept; // C++20 300constexpr double lerp(double a, double b, double t) noexcept; // C++20 301constexpr long double lerp(long double a, long double b, long double t) noexcept; // C++20 302 303} // std 304 305*/ 306 307#include <__assert> // all public C++ headers provide the assertion handler 308#include <__config> 309#include <__type_traits/enable_if.h> 310#include <__type_traits/is_arithmetic.h> 311#include <__type_traits/is_constant_evaluated.h> 312#include <__type_traits/is_floating_point.h> 313#include <__type_traits/is_same.h> 314#include <__type_traits/promote.h> 315#include <__type_traits/remove_cv.h> 316#include <limits> 317#include <version> 318 319#include <math.h> 320 321#ifndef _LIBCPP_MATH_H 322# error <cmath> tried including <math.h> but didn't find libc++'s <math.h> header. \ 323 This usually means that your header search paths are not configured properly. \ 324 The header search paths should contain the C++ Standard Library headers before \ 325 any C Standard Library, and you are probably using compiler flags that make that \ 326 not be the case. 327#endif 328 329#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER) 330# pragma GCC system_header 331#endif 332 333_LIBCPP_PUSH_MACROS 334#include <__undef_macros> 335 336_LIBCPP_BEGIN_NAMESPACE_STD 337 338using ::signbit _LIBCPP_USING_IF_EXISTS; 339using ::fpclassify _LIBCPP_USING_IF_EXISTS; 340using ::isfinite _LIBCPP_USING_IF_EXISTS; 341using ::isinf _LIBCPP_USING_IF_EXISTS; 342using ::isnan _LIBCPP_USING_IF_EXISTS; 343using ::isnormal _LIBCPP_USING_IF_EXISTS; 344using ::isgreater _LIBCPP_USING_IF_EXISTS; 345using ::isgreaterequal _LIBCPP_USING_IF_EXISTS; 346using ::isless _LIBCPP_USING_IF_EXISTS; 347using ::islessequal _LIBCPP_USING_IF_EXISTS; 348using ::islessgreater _LIBCPP_USING_IF_EXISTS; 349using ::isunordered _LIBCPP_USING_IF_EXISTS; 350using ::isunordered _LIBCPP_USING_IF_EXISTS; 351 352using ::float_t _LIBCPP_USING_IF_EXISTS; 353using ::double_t _LIBCPP_USING_IF_EXISTS; 354 355using ::abs _LIBCPP_USING_IF_EXISTS; 356 357using ::acos _LIBCPP_USING_IF_EXISTS; 358using ::acosf _LIBCPP_USING_IF_EXISTS; 359using ::asin _LIBCPP_USING_IF_EXISTS; 360using ::asinf _LIBCPP_USING_IF_EXISTS; 361using ::atan _LIBCPP_USING_IF_EXISTS; 362using ::atanf _LIBCPP_USING_IF_EXISTS; 363using ::atan2 _LIBCPP_USING_IF_EXISTS; 364using ::atan2f _LIBCPP_USING_IF_EXISTS; 365using ::ceil _LIBCPP_USING_IF_EXISTS; 366using ::ceilf _LIBCPP_USING_IF_EXISTS; 367using ::cos _LIBCPP_USING_IF_EXISTS; 368using ::cosf _LIBCPP_USING_IF_EXISTS; 369using ::cosh _LIBCPP_USING_IF_EXISTS; 370using ::coshf _LIBCPP_USING_IF_EXISTS; 371 372using ::exp _LIBCPP_USING_IF_EXISTS; 373using ::expf _LIBCPP_USING_IF_EXISTS; 374 375using ::fabs _LIBCPP_USING_IF_EXISTS; 376using ::fabsf _LIBCPP_USING_IF_EXISTS; 377using ::floor _LIBCPP_USING_IF_EXISTS; 378using ::floorf _LIBCPP_USING_IF_EXISTS; 379 380using ::fmod _LIBCPP_USING_IF_EXISTS; 381using ::fmodf _LIBCPP_USING_IF_EXISTS; 382 383using ::frexp _LIBCPP_USING_IF_EXISTS; 384using ::frexpf _LIBCPP_USING_IF_EXISTS; 385using ::ldexp _LIBCPP_USING_IF_EXISTS; 386using ::ldexpf _LIBCPP_USING_IF_EXISTS; 387 388using ::log _LIBCPP_USING_IF_EXISTS; 389using ::logf _LIBCPP_USING_IF_EXISTS; 390 391using ::log10 _LIBCPP_USING_IF_EXISTS; 392using ::log10f _LIBCPP_USING_IF_EXISTS; 393using ::modf _LIBCPP_USING_IF_EXISTS; 394using ::modff _LIBCPP_USING_IF_EXISTS; 395 396using ::pow _LIBCPP_USING_IF_EXISTS; 397using ::powf _LIBCPP_USING_IF_EXISTS; 398 399using ::sin _LIBCPP_USING_IF_EXISTS; 400using ::sinf _LIBCPP_USING_IF_EXISTS; 401using ::sinh _LIBCPP_USING_IF_EXISTS; 402using ::sinhf _LIBCPP_USING_IF_EXISTS; 403 404using ::sqrt _LIBCPP_USING_IF_EXISTS; 405using ::sqrtf _LIBCPP_USING_IF_EXISTS; 406using ::tan _LIBCPP_USING_IF_EXISTS; 407using ::tanf _LIBCPP_USING_IF_EXISTS; 408 409using ::tanh _LIBCPP_USING_IF_EXISTS; 410using ::tanhf _LIBCPP_USING_IF_EXISTS; 411 412using ::acosh _LIBCPP_USING_IF_EXISTS; 413using ::acoshf _LIBCPP_USING_IF_EXISTS; 414using ::asinh _LIBCPP_USING_IF_EXISTS; 415using ::asinhf _LIBCPP_USING_IF_EXISTS; 416using ::atanh _LIBCPP_USING_IF_EXISTS; 417using ::atanhf _LIBCPP_USING_IF_EXISTS; 418using ::cbrt _LIBCPP_USING_IF_EXISTS; 419using ::cbrtf _LIBCPP_USING_IF_EXISTS; 420 421using ::copysign _LIBCPP_USING_IF_EXISTS; 422using ::copysignf _LIBCPP_USING_IF_EXISTS; 423 424using ::erf _LIBCPP_USING_IF_EXISTS; 425using ::erff _LIBCPP_USING_IF_EXISTS; 426using ::erfc _LIBCPP_USING_IF_EXISTS; 427using ::erfcf _LIBCPP_USING_IF_EXISTS; 428using ::exp2 _LIBCPP_USING_IF_EXISTS; 429using ::exp2f _LIBCPP_USING_IF_EXISTS; 430using ::expm1 _LIBCPP_USING_IF_EXISTS; 431using ::expm1f _LIBCPP_USING_IF_EXISTS; 432using ::fdim _LIBCPP_USING_IF_EXISTS; 433using ::fdimf _LIBCPP_USING_IF_EXISTS; 434using ::fmaf _LIBCPP_USING_IF_EXISTS; 435using ::fma _LIBCPP_USING_IF_EXISTS; 436using ::fmax _LIBCPP_USING_IF_EXISTS; 437using ::fmaxf _LIBCPP_USING_IF_EXISTS; 438using ::fmin _LIBCPP_USING_IF_EXISTS; 439using ::fminf _LIBCPP_USING_IF_EXISTS; 440using ::hypot _LIBCPP_USING_IF_EXISTS; 441using ::hypotf _LIBCPP_USING_IF_EXISTS; 442using ::ilogb _LIBCPP_USING_IF_EXISTS; 443using ::ilogbf _LIBCPP_USING_IF_EXISTS; 444using ::lgamma _LIBCPP_USING_IF_EXISTS; 445using ::lgammaf _LIBCPP_USING_IF_EXISTS; 446using ::llrint _LIBCPP_USING_IF_EXISTS; 447using ::llrintf _LIBCPP_USING_IF_EXISTS; 448using ::llround _LIBCPP_USING_IF_EXISTS; 449using ::llroundf _LIBCPP_USING_IF_EXISTS; 450using ::log1p _LIBCPP_USING_IF_EXISTS; 451using ::log1pf _LIBCPP_USING_IF_EXISTS; 452using ::log2 _LIBCPP_USING_IF_EXISTS; 453using ::log2f _LIBCPP_USING_IF_EXISTS; 454using ::logb _LIBCPP_USING_IF_EXISTS; 455using ::logbf _LIBCPP_USING_IF_EXISTS; 456using ::lrint _LIBCPP_USING_IF_EXISTS; 457using ::lrintf _LIBCPP_USING_IF_EXISTS; 458using ::lround _LIBCPP_USING_IF_EXISTS; 459using ::lroundf _LIBCPP_USING_IF_EXISTS; 460 461using ::nan _LIBCPP_USING_IF_EXISTS; 462using ::nanf _LIBCPP_USING_IF_EXISTS; 463 464using ::nearbyint _LIBCPP_USING_IF_EXISTS; 465using ::nearbyintf _LIBCPP_USING_IF_EXISTS; 466using ::nextafter _LIBCPP_USING_IF_EXISTS; 467using ::nextafterf _LIBCPP_USING_IF_EXISTS; 468using ::nexttoward _LIBCPP_USING_IF_EXISTS; 469using ::nexttowardf _LIBCPP_USING_IF_EXISTS; 470using ::remainder _LIBCPP_USING_IF_EXISTS; 471using ::remainderf _LIBCPP_USING_IF_EXISTS; 472using ::remquo _LIBCPP_USING_IF_EXISTS; 473using ::remquof _LIBCPP_USING_IF_EXISTS; 474using ::rint _LIBCPP_USING_IF_EXISTS; 475using ::rintf _LIBCPP_USING_IF_EXISTS; 476using ::round _LIBCPP_USING_IF_EXISTS; 477using ::roundf _LIBCPP_USING_IF_EXISTS; 478using ::scalbln _LIBCPP_USING_IF_EXISTS; 479using ::scalblnf _LIBCPP_USING_IF_EXISTS; 480using ::scalbn _LIBCPP_USING_IF_EXISTS; 481using ::scalbnf _LIBCPP_USING_IF_EXISTS; 482using ::tgamma _LIBCPP_USING_IF_EXISTS; 483using ::tgammaf _LIBCPP_USING_IF_EXISTS; 484using ::trunc _LIBCPP_USING_IF_EXISTS; 485using ::truncf _LIBCPP_USING_IF_EXISTS; 486 487using ::acosl _LIBCPP_USING_IF_EXISTS; 488using ::asinl _LIBCPP_USING_IF_EXISTS; 489using ::atanl _LIBCPP_USING_IF_EXISTS; 490using ::atan2l _LIBCPP_USING_IF_EXISTS; 491using ::ceill _LIBCPP_USING_IF_EXISTS; 492using ::cosl _LIBCPP_USING_IF_EXISTS; 493using ::coshl _LIBCPP_USING_IF_EXISTS; 494using ::expl _LIBCPP_USING_IF_EXISTS; 495using ::fabsl _LIBCPP_USING_IF_EXISTS; 496using ::floorl _LIBCPP_USING_IF_EXISTS; 497using ::fmodl _LIBCPP_USING_IF_EXISTS; 498using ::frexpl _LIBCPP_USING_IF_EXISTS; 499using ::ldexpl _LIBCPP_USING_IF_EXISTS; 500using ::logl _LIBCPP_USING_IF_EXISTS; 501using ::log10l _LIBCPP_USING_IF_EXISTS; 502using ::modfl _LIBCPP_USING_IF_EXISTS; 503using ::powl _LIBCPP_USING_IF_EXISTS; 504using ::sinl _LIBCPP_USING_IF_EXISTS; 505using ::sinhl _LIBCPP_USING_IF_EXISTS; 506using ::sqrtl _LIBCPP_USING_IF_EXISTS; 507using ::tanl _LIBCPP_USING_IF_EXISTS; 508 509using ::tanhl _LIBCPP_USING_IF_EXISTS; 510using ::acoshl _LIBCPP_USING_IF_EXISTS; 511using ::asinhl _LIBCPP_USING_IF_EXISTS; 512using ::atanhl _LIBCPP_USING_IF_EXISTS; 513using ::cbrtl _LIBCPP_USING_IF_EXISTS; 514 515using ::copysignl _LIBCPP_USING_IF_EXISTS; 516 517using ::erfl _LIBCPP_USING_IF_EXISTS; 518using ::erfcl _LIBCPP_USING_IF_EXISTS; 519using ::exp2l _LIBCPP_USING_IF_EXISTS; 520using ::expm1l _LIBCPP_USING_IF_EXISTS; 521using ::fdiml _LIBCPP_USING_IF_EXISTS; 522using ::fmal _LIBCPP_USING_IF_EXISTS; 523using ::fmaxl _LIBCPP_USING_IF_EXISTS; 524using ::fminl _LIBCPP_USING_IF_EXISTS; 525using ::hypotl _LIBCPP_USING_IF_EXISTS; 526using ::ilogbl _LIBCPP_USING_IF_EXISTS; 527using ::lgammal _LIBCPP_USING_IF_EXISTS; 528using ::llrintl _LIBCPP_USING_IF_EXISTS; 529using ::llroundl _LIBCPP_USING_IF_EXISTS; 530using ::log1pl _LIBCPP_USING_IF_EXISTS; 531using ::log2l _LIBCPP_USING_IF_EXISTS; 532using ::logbl _LIBCPP_USING_IF_EXISTS; 533using ::lrintl _LIBCPP_USING_IF_EXISTS; 534using ::lroundl _LIBCPP_USING_IF_EXISTS; 535using ::nanl _LIBCPP_USING_IF_EXISTS; 536using ::nearbyintl _LIBCPP_USING_IF_EXISTS; 537using ::nextafterl _LIBCPP_USING_IF_EXISTS; 538using ::nexttowardl _LIBCPP_USING_IF_EXISTS; 539using ::remainderl _LIBCPP_USING_IF_EXISTS; 540using ::remquol _LIBCPP_USING_IF_EXISTS; 541using ::rintl _LIBCPP_USING_IF_EXISTS; 542using ::roundl _LIBCPP_USING_IF_EXISTS; 543using ::scalblnl _LIBCPP_USING_IF_EXISTS; 544using ::scalbnl _LIBCPP_USING_IF_EXISTS; 545using ::tgammal _LIBCPP_USING_IF_EXISTS; 546using ::truncl _LIBCPP_USING_IF_EXISTS; 547 548#if _LIBCPP_STD_VER >= 17 549inline _LIBCPP_HIDE_FROM_ABI float hypot(float __x, float __y, float __z) { 550 return sqrt(__x * __x + __y * __y + __z * __z); 551} 552inline _LIBCPP_HIDE_FROM_ABI double hypot(double __x, double __y, double __z) { 553 return sqrt(__x * __x + __y * __y + __z * __z); 554} 555inline _LIBCPP_HIDE_FROM_ABI long double hypot(long double __x, long double __y, long double __z) { 556 return sqrt(__x * __x + __y * __y + __z * __z); 557} 558 559template <class _A1, class _A2, class _A3> 560inline _LIBCPP_HIDE_FROM_ABI 561 typename enable_if_t< is_arithmetic<_A1>::value && is_arithmetic<_A2>::value && is_arithmetic<_A3>::value, 562 __promote<_A1, _A2, _A3> >::type 563 hypot(_A1 __lcpp_x, _A2 __lcpp_y, _A3 __lcpp_z) _NOEXCEPT { 564 typedef typename __promote<_A1, _A2, _A3>::type __result_type; 565 static_assert((!(is_same<_A1, __result_type>::value && is_same<_A2, __result_type>::value && 566 is_same<_A3, __result_type>::value)), 567 ""); 568 return std::hypot((__result_type)__lcpp_x, (__result_type)__lcpp_y, (__result_type)__lcpp_z); 569} 570#endif 571 572template <class _A1, __enable_if_t<is_floating_point<_A1>::value, int> = 0> 573_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR bool __constexpr_isnan(_A1 __lcpp_x) _NOEXCEPT { 574#if __has_builtin(__builtin_isnan) 575 return __builtin_isnan(__lcpp_x); 576#else 577 return isnan(__lcpp_x); 578#endif 579} 580 581template <class _A1, __enable_if_t<!is_floating_point<_A1>::value, int> = 0> 582_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR bool __constexpr_isnan(_A1 __lcpp_x) _NOEXCEPT { 583 return std::isnan(__lcpp_x); 584} 585 586template <class _A1, __enable_if_t<is_floating_point<_A1>::value, int> = 0> 587_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR bool __constexpr_isinf(_A1 __lcpp_x) _NOEXCEPT { 588#if __has_builtin(__builtin_isinf) 589 return __builtin_isinf(__lcpp_x); 590#else 591 return isinf(__lcpp_x); 592#endif 593} 594 595template <class _A1, __enable_if_t<!is_floating_point<_A1>::value, int> = 0> 596_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR bool __constexpr_isinf(_A1 __lcpp_x) _NOEXCEPT { 597 return std::isinf(__lcpp_x); 598} 599 600template <class _A1, __enable_if_t<is_floating_point<_A1>::value, int> = 0> 601_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR bool __constexpr_isfinite(_A1 __lcpp_x) _NOEXCEPT { 602#if __has_builtin(__builtin_isfinite) 603 return __builtin_isfinite(__lcpp_x); 604#else 605 return isfinite(__lcpp_x); 606#endif 607} 608 609template <class _A1, __enable_if_t<!is_floating_point<_A1>::value, int> = 0> 610_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR bool __constexpr_isfinite(_A1 __lcpp_x) _NOEXCEPT { 611 return __builtin_isfinite(__lcpp_x); 612} 613 614_LIBCPP_CONSTEXPR inline _LIBCPP_HIDE_FROM_ABI float __constexpr_copysign(float __x, float __y) _NOEXCEPT { 615 return __builtin_copysignf(__x, __y); 616} 617 618_LIBCPP_CONSTEXPR inline _LIBCPP_HIDE_FROM_ABI double __constexpr_copysign(double __x, double __y) _NOEXCEPT { 619 return __builtin_copysign(__x, __y); 620} 621 622_LIBCPP_CONSTEXPR inline _LIBCPP_HIDE_FROM_ABI long double 623__constexpr_copysign(long double __x, long double __y) _NOEXCEPT { 624 return __builtin_copysignl(__x, __y); 625} 626 627template <class _A1, 628 class _A2, 629 __enable_if_t<std::is_arithmetic<_A1>::value && std::is_arithmetic<_A2>::value, int> = 0> 630_LIBCPP_CONSTEXPR inline _LIBCPP_HIDE_FROM_ABI typename __promote<_A1, _A2>::type 631__constexpr_copysign(_A1 __x, _A2 __y) _NOEXCEPT { 632 typedef typename std::__promote<_A1, _A2>::type __result_type; 633 static_assert((!(std::_IsSame<_A1, __result_type>::value && std::_IsSame<_A2, __result_type>::value)), ""); 634 return __builtin_copysign((__result_type)__x, (__result_type)__y); 635} 636 637inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR float __constexpr_fabs(float __x) _NOEXCEPT { 638 return __builtin_fabsf(__x); 639} 640 641inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR double __constexpr_fabs(double __x) _NOEXCEPT { 642 return __builtin_fabs(__x); 643} 644 645inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR long double __constexpr_fabs(long double __x) _NOEXCEPT { 646 return __builtin_fabsl(__x); 647} 648 649template <class _Tp, __enable_if_t<is_integral<_Tp>::value, int> = 0> 650_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR double __constexpr_fabs(_Tp __x) _NOEXCEPT { 651 return __builtin_fabs(static_cast<double>(__x)); 652} 653 654inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14 float __constexpr_fmax(float __x, float __y) _NOEXCEPT { 655#if !__has_constexpr_builtin(__builtin_fmaxf) 656 if (__libcpp_is_constant_evaluated()) { 657 if (std::__constexpr_isnan(__x)) 658 return __y; 659 if (std::__constexpr_isnan(__y)) 660 return __x; 661 return __x < __y ? __y : __x; 662 } 663#endif 664 return __builtin_fmaxf(__x, __y); 665} 666 667inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14 double __constexpr_fmax(double __x, double __y) _NOEXCEPT { 668#if !__has_constexpr_builtin(__builtin_fmax) 669 if (__libcpp_is_constant_evaluated()) { 670 if (std::__constexpr_isnan(__x)) 671 return __y; 672 if (std::__constexpr_isnan(__y)) 673 return __x; 674 return __x < __y ? __y : __x; 675 } 676#endif 677 return __builtin_fmax(__x, __y); 678} 679 680inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14 long double 681__constexpr_fmax(long double __x, long double __y) _NOEXCEPT { 682#if !__has_constexpr_builtin(__builtin_fmaxl) 683 if (__libcpp_is_constant_evaluated()) { 684 if (std::__constexpr_isnan(__x)) 685 return __y; 686 if (std::__constexpr_isnan(__y)) 687 return __x; 688 return __x < __y ? __y : __x; 689 } 690#endif 691 return __builtin_fmaxl(__x, __y); 692} 693 694template <class _Tp, class _Up, __enable_if_t<is_arithmetic<_Tp>::value && is_arithmetic<_Up>::value, int> = 0> 695_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14 typename __promote<_Tp, _Up>::type 696__constexpr_fmax(_Tp __x, _Up __y) _NOEXCEPT { 697 using __result_type = typename __promote<_Tp, _Up>::type; 698 return std::__constexpr_fmax(static_cast<__result_type>(__x), static_cast<__result_type>(__y)); 699} 700 701template <class _Tp> 702_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14 _Tp __constexpr_logb(_Tp __x) { 703#if !__has_constexpr_builtin(__builtin_logb) 704 if (__libcpp_is_constant_evaluated()) { 705 if (__x == _Tp(0)) { 706 // raise FE_DIVBYZERO 707 return -numeric_limits<_Tp>::infinity(); 708 } 709 710 if (std::__constexpr_isinf(__x)) 711 return numeric_limits<_Tp>::infinity(); 712 713 if (std::__constexpr_isnan(__x)) 714 return numeric_limits<_Tp>::quiet_NaN(); 715 716 __x = std::__constexpr_fabs(__x); 717 unsigned long long __exp = 0; 718 while (__x >= numeric_limits<_Tp>::radix) { 719 __x /= numeric_limits<_Tp>::radix; 720 __exp += 1; 721 } 722 return _Tp(__exp); 723 } 724#endif // !__has_constexpr_builtin(__builtin_logb) 725 return __builtin_logb(__x); 726} 727 728template <class _Tp> 729_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 _Tp __constexpr_scalbn(_Tp __x, int __exp) { 730#if !__has_constexpr_builtin(__builtin_scalbln) 731 if (__libcpp_is_constant_evaluated()) { 732 if (__x == _Tp(0)) 733 return __x; 734 735 if (std::__constexpr_isinf(__x)) 736 return __x; 737 738 if (__exp == _Tp(0)) 739 return __x; 740 741 if (std::__constexpr_isnan(__x)) 742 return numeric_limits<_Tp>::quiet_NaN(); 743 744 _Tp __mult(1); 745 if (__exp > 0) { 746 __mult = numeric_limits<_Tp>::radix; 747 --__exp; 748 } else { 749 ++__exp; 750 __exp = -__exp; 751 __mult /= numeric_limits<_Tp>::radix; 752 } 753 754 while (__exp > 0) { 755 if (!(__exp & 1)) { 756 __mult *= __mult; 757 __exp >>= 1; 758 } else { 759 __x *= __mult; 760 --__exp; 761 } 762 } 763 return __x; 764 } 765#endif // !__has_constexpr_builtin(__builtin_scalbln) 766 return __builtin_scalbn(__x, __exp); 767} 768 769#if _LIBCPP_STD_VER >= 20 770template <typename _Fp> 771_LIBCPP_HIDE_FROM_ABI constexpr _Fp __lerp(_Fp __a, _Fp __b, _Fp __t) noexcept { 772 if ((__a <= 0 && __b >= 0) || (__a >= 0 && __b <= 0)) 773 return __t * __b + (1 - __t) * __a; 774 775 if (__t == 1) 776 return __b; 777 const _Fp __x = __a + __t * (__b - __a); 778 if ((__t > 1) == (__b > __a)) 779 return __b < __x ? __x : __b; 780 else 781 return __x < __b ? __x : __b; 782} 783 784_LIBCPP_HIDE_FROM_ABI inline constexpr float lerp(float __a, float __b, float __t) _NOEXCEPT { 785 return __lerp(__a, __b, __t); 786} 787 788_LIBCPP_HIDE_FROM_ABI inline constexpr double lerp(double __a, double __b, double __t) _NOEXCEPT { 789 return __lerp(__a, __b, __t); 790} 791 792_LIBCPP_HIDE_FROM_ABI inline constexpr long double lerp(long double __a, long double __b, long double __t) _NOEXCEPT { 793 return __lerp(__a, __b, __t); 794} 795 796template <class _A1, class _A2, class _A3> 797inline _LIBCPP_HIDE_FROM_ABI constexpr 798 typename enable_if_t< is_arithmetic<_A1>::value && is_arithmetic<_A2>::value && is_arithmetic<_A3>::value, 799 __promote<_A1, _A2, _A3> >::type 800 lerp(_A1 __a, _A2 __b, _A3 __t) noexcept { 801 typedef typename __promote<_A1, _A2, _A3>::type __result_type; 802 static_assert(!( 803 _IsSame<_A1, __result_type>::value && _IsSame<_A2, __result_type>::value && _IsSame<_A3, __result_type>::value)); 804 return std::__lerp((__result_type)__a, (__result_type)__b, (__result_type)__t); 805} 806#endif // _LIBCPP_STD_VER >= 20 807 808_LIBCPP_END_NAMESPACE_STD 809 810_LIBCPP_POP_MACROS 811 812#if !defined(_LIBCPP_REMOVE_TRANSITIVE_INCLUDES) && _LIBCPP_STD_VER <= 20 813# include <type_traits> 814#endif 815 816#endif // _LIBCPP_CMATH 817