1// -*- C++ -*- 2//===---------------------------- cmath -----------------------------------===// 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 <__config> 308#include <math.h> 309#include <version> 310#include <type_traits> 311 312#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER) 313#pragma GCC system_header 314#endif 315 316_LIBCPP_PUSH_MACROS 317#include <__undef_macros> 318 319_LIBCPP_BEGIN_NAMESPACE_STD 320 321using ::signbit _LIBCPP_USING_IF_EXISTS; 322using ::fpclassify _LIBCPP_USING_IF_EXISTS; 323using ::isfinite _LIBCPP_USING_IF_EXISTS; 324using ::isinf _LIBCPP_USING_IF_EXISTS; 325using ::isnan _LIBCPP_USING_IF_EXISTS; 326using ::isnormal _LIBCPP_USING_IF_EXISTS; 327using ::isgreater _LIBCPP_USING_IF_EXISTS; 328using ::isgreaterequal _LIBCPP_USING_IF_EXISTS; 329using ::isless _LIBCPP_USING_IF_EXISTS; 330using ::islessequal _LIBCPP_USING_IF_EXISTS; 331using ::islessgreater _LIBCPP_USING_IF_EXISTS; 332using ::isunordered _LIBCPP_USING_IF_EXISTS; 333using ::isunordered _LIBCPP_USING_IF_EXISTS; 334 335using ::float_t _LIBCPP_USING_IF_EXISTS; 336using ::double_t _LIBCPP_USING_IF_EXISTS; 337 338using ::abs _LIBCPP_USING_IF_EXISTS; 339 340using ::acos _LIBCPP_USING_IF_EXISTS; 341using ::acosf _LIBCPP_USING_IF_EXISTS; 342using ::asin _LIBCPP_USING_IF_EXISTS; 343using ::asinf _LIBCPP_USING_IF_EXISTS; 344using ::atan _LIBCPP_USING_IF_EXISTS; 345using ::atanf _LIBCPP_USING_IF_EXISTS; 346using ::atan2 _LIBCPP_USING_IF_EXISTS; 347using ::atan2f _LIBCPP_USING_IF_EXISTS; 348using ::ceil _LIBCPP_USING_IF_EXISTS; 349using ::ceilf _LIBCPP_USING_IF_EXISTS; 350using ::cos _LIBCPP_USING_IF_EXISTS; 351using ::cosf _LIBCPP_USING_IF_EXISTS; 352using ::cosh _LIBCPP_USING_IF_EXISTS; 353using ::coshf _LIBCPP_USING_IF_EXISTS; 354 355using ::exp _LIBCPP_USING_IF_EXISTS; 356using ::expf _LIBCPP_USING_IF_EXISTS; 357 358using ::fabs _LIBCPP_USING_IF_EXISTS; 359using ::fabsf _LIBCPP_USING_IF_EXISTS; 360using ::floor _LIBCPP_USING_IF_EXISTS; 361using ::floorf _LIBCPP_USING_IF_EXISTS; 362 363using ::fmod _LIBCPP_USING_IF_EXISTS; 364using ::fmodf _LIBCPP_USING_IF_EXISTS; 365 366using ::frexp _LIBCPP_USING_IF_EXISTS; 367using ::frexpf _LIBCPP_USING_IF_EXISTS; 368using ::ldexp _LIBCPP_USING_IF_EXISTS; 369using ::ldexpf _LIBCPP_USING_IF_EXISTS; 370 371using ::log _LIBCPP_USING_IF_EXISTS; 372using ::logf _LIBCPP_USING_IF_EXISTS; 373 374using ::log10 _LIBCPP_USING_IF_EXISTS; 375using ::log10f _LIBCPP_USING_IF_EXISTS; 376using ::modf _LIBCPP_USING_IF_EXISTS; 377using ::modff _LIBCPP_USING_IF_EXISTS; 378 379using ::pow _LIBCPP_USING_IF_EXISTS; 380using ::powf _LIBCPP_USING_IF_EXISTS; 381 382using ::sin _LIBCPP_USING_IF_EXISTS; 383using ::sinf _LIBCPP_USING_IF_EXISTS; 384using ::sinh _LIBCPP_USING_IF_EXISTS; 385using ::sinhf _LIBCPP_USING_IF_EXISTS; 386 387using ::sqrt _LIBCPP_USING_IF_EXISTS; 388using ::sqrtf _LIBCPP_USING_IF_EXISTS; 389using ::tan _LIBCPP_USING_IF_EXISTS; 390using ::tanf _LIBCPP_USING_IF_EXISTS; 391 392using ::tanh _LIBCPP_USING_IF_EXISTS; 393using ::tanhf _LIBCPP_USING_IF_EXISTS; 394 395using ::acosh _LIBCPP_USING_IF_EXISTS; 396using ::acoshf _LIBCPP_USING_IF_EXISTS; 397using ::asinh _LIBCPP_USING_IF_EXISTS; 398using ::asinhf _LIBCPP_USING_IF_EXISTS; 399using ::atanh _LIBCPP_USING_IF_EXISTS; 400using ::atanhf _LIBCPP_USING_IF_EXISTS; 401using ::cbrt _LIBCPP_USING_IF_EXISTS; 402using ::cbrtf _LIBCPP_USING_IF_EXISTS; 403 404using ::copysign _LIBCPP_USING_IF_EXISTS; 405using ::copysignf _LIBCPP_USING_IF_EXISTS; 406 407using ::erf _LIBCPP_USING_IF_EXISTS; 408using ::erff _LIBCPP_USING_IF_EXISTS; 409using ::erfc _LIBCPP_USING_IF_EXISTS; 410using ::erfcf _LIBCPP_USING_IF_EXISTS; 411using ::exp2 _LIBCPP_USING_IF_EXISTS; 412using ::exp2f _LIBCPP_USING_IF_EXISTS; 413using ::expm1 _LIBCPP_USING_IF_EXISTS; 414using ::expm1f _LIBCPP_USING_IF_EXISTS; 415using ::fdim _LIBCPP_USING_IF_EXISTS; 416using ::fdimf _LIBCPP_USING_IF_EXISTS; 417using ::fmaf _LIBCPP_USING_IF_EXISTS; 418using ::fma _LIBCPP_USING_IF_EXISTS; 419using ::fmax _LIBCPP_USING_IF_EXISTS; 420using ::fmaxf _LIBCPP_USING_IF_EXISTS; 421using ::fmin _LIBCPP_USING_IF_EXISTS; 422using ::fminf _LIBCPP_USING_IF_EXISTS; 423using ::hypot _LIBCPP_USING_IF_EXISTS; 424using ::hypotf _LIBCPP_USING_IF_EXISTS; 425using ::ilogb _LIBCPP_USING_IF_EXISTS; 426using ::ilogbf _LIBCPP_USING_IF_EXISTS; 427using ::lgamma _LIBCPP_USING_IF_EXISTS; 428using ::lgammaf _LIBCPP_USING_IF_EXISTS; 429using ::llrint _LIBCPP_USING_IF_EXISTS; 430using ::llrintf _LIBCPP_USING_IF_EXISTS; 431using ::llround _LIBCPP_USING_IF_EXISTS; 432using ::llroundf _LIBCPP_USING_IF_EXISTS; 433using ::log1p _LIBCPP_USING_IF_EXISTS; 434using ::log1pf _LIBCPP_USING_IF_EXISTS; 435using ::log2 _LIBCPP_USING_IF_EXISTS; 436using ::log2f _LIBCPP_USING_IF_EXISTS; 437using ::logb _LIBCPP_USING_IF_EXISTS; 438using ::logbf _LIBCPP_USING_IF_EXISTS; 439using ::lrint _LIBCPP_USING_IF_EXISTS; 440using ::lrintf _LIBCPP_USING_IF_EXISTS; 441using ::lround _LIBCPP_USING_IF_EXISTS; 442using ::lroundf _LIBCPP_USING_IF_EXISTS; 443 444using ::nan _LIBCPP_USING_IF_EXISTS; 445using ::nanf _LIBCPP_USING_IF_EXISTS; 446 447using ::nearbyint _LIBCPP_USING_IF_EXISTS; 448using ::nearbyintf _LIBCPP_USING_IF_EXISTS; 449using ::nextafter _LIBCPP_USING_IF_EXISTS; 450using ::nextafterf _LIBCPP_USING_IF_EXISTS; 451using ::nexttoward _LIBCPP_USING_IF_EXISTS; 452using ::nexttowardf _LIBCPP_USING_IF_EXISTS; 453using ::remainder _LIBCPP_USING_IF_EXISTS; 454using ::remainderf _LIBCPP_USING_IF_EXISTS; 455using ::remquo _LIBCPP_USING_IF_EXISTS; 456using ::remquof _LIBCPP_USING_IF_EXISTS; 457using ::rint _LIBCPP_USING_IF_EXISTS; 458using ::rintf _LIBCPP_USING_IF_EXISTS; 459using ::round _LIBCPP_USING_IF_EXISTS; 460using ::roundf _LIBCPP_USING_IF_EXISTS; 461using ::scalbln _LIBCPP_USING_IF_EXISTS; 462using ::scalblnf _LIBCPP_USING_IF_EXISTS; 463using ::scalbn _LIBCPP_USING_IF_EXISTS; 464using ::scalbnf _LIBCPP_USING_IF_EXISTS; 465using ::tgamma _LIBCPP_USING_IF_EXISTS; 466using ::tgammaf _LIBCPP_USING_IF_EXISTS; 467using ::trunc _LIBCPP_USING_IF_EXISTS; 468using ::truncf _LIBCPP_USING_IF_EXISTS; 469 470using ::acosl _LIBCPP_USING_IF_EXISTS; 471using ::asinl _LIBCPP_USING_IF_EXISTS; 472using ::atanl _LIBCPP_USING_IF_EXISTS; 473using ::atan2l _LIBCPP_USING_IF_EXISTS; 474using ::ceill _LIBCPP_USING_IF_EXISTS; 475using ::cosl _LIBCPP_USING_IF_EXISTS; 476using ::coshl _LIBCPP_USING_IF_EXISTS; 477using ::expl _LIBCPP_USING_IF_EXISTS; 478using ::fabsl _LIBCPP_USING_IF_EXISTS; 479using ::floorl _LIBCPP_USING_IF_EXISTS; 480using ::fmodl _LIBCPP_USING_IF_EXISTS; 481using ::frexpl _LIBCPP_USING_IF_EXISTS; 482using ::ldexpl _LIBCPP_USING_IF_EXISTS; 483using ::logl _LIBCPP_USING_IF_EXISTS; 484using ::log10l _LIBCPP_USING_IF_EXISTS; 485using ::modfl _LIBCPP_USING_IF_EXISTS; 486using ::powl _LIBCPP_USING_IF_EXISTS; 487using ::sinl _LIBCPP_USING_IF_EXISTS; 488using ::sinhl _LIBCPP_USING_IF_EXISTS; 489using ::sqrtl _LIBCPP_USING_IF_EXISTS; 490using ::tanl _LIBCPP_USING_IF_EXISTS; 491 492using ::tanhl _LIBCPP_USING_IF_EXISTS; 493using ::acoshl _LIBCPP_USING_IF_EXISTS; 494using ::asinhl _LIBCPP_USING_IF_EXISTS; 495using ::atanhl _LIBCPP_USING_IF_EXISTS; 496using ::cbrtl _LIBCPP_USING_IF_EXISTS; 497 498using ::copysignl _LIBCPP_USING_IF_EXISTS; 499 500using ::erfl _LIBCPP_USING_IF_EXISTS; 501using ::erfcl _LIBCPP_USING_IF_EXISTS; 502using ::exp2l _LIBCPP_USING_IF_EXISTS; 503using ::expm1l _LIBCPP_USING_IF_EXISTS; 504using ::fdiml _LIBCPP_USING_IF_EXISTS; 505using ::fmal _LIBCPP_USING_IF_EXISTS; 506using ::fmaxl _LIBCPP_USING_IF_EXISTS; 507using ::fminl _LIBCPP_USING_IF_EXISTS; 508using ::hypotl _LIBCPP_USING_IF_EXISTS; 509using ::ilogbl _LIBCPP_USING_IF_EXISTS; 510using ::lgammal _LIBCPP_USING_IF_EXISTS; 511using ::llrintl _LIBCPP_USING_IF_EXISTS; 512using ::llroundl _LIBCPP_USING_IF_EXISTS; 513using ::log1pl _LIBCPP_USING_IF_EXISTS; 514using ::log2l _LIBCPP_USING_IF_EXISTS; 515using ::logbl _LIBCPP_USING_IF_EXISTS; 516using ::lrintl _LIBCPP_USING_IF_EXISTS; 517using ::lroundl _LIBCPP_USING_IF_EXISTS; 518using ::nanl _LIBCPP_USING_IF_EXISTS; 519using ::nearbyintl _LIBCPP_USING_IF_EXISTS; 520using ::nextafterl _LIBCPP_USING_IF_EXISTS; 521using ::nexttowardl _LIBCPP_USING_IF_EXISTS; 522using ::remainderl _LIBCPP_USING_IF_EXISTS; 523using ::remquol _LIBCPP_USING_IF_EXISTS; 524using ::rintl _LIBCPP_USING_IF_EXISTS; 525using ::roundl _LIBCPP_USING_IF_EXISTS; 526using ::scalblnl _LIBCPP_USING_IF_EXISTS; 527using ::scalbnl _LIBCPP_USING_IF_EXISTS; 528using ::tgammal _LIBCPP_USING_IF_EXISTS; 529using ::truncl _LIBCPP_USING_IF_EXISTS; 530 531#if _LIBCPP_STD_VER > 14 532inline _LIBCPP_INLINE_VISIBILITY float hypot( float x, float y, float z ) { return sqrt(x*x + y*y + z*z); } 533inline _LIBCPP_INLINE_VISIBILITY double hypot( double x, double y, double z ) { return sqrt(x*x + y*y + z*z); } 534inline _LIBCPP_INLINE_VISIBILITY long double hypot( long double x, long double y, long double z ) { return sqrt(x*x + y*y + z*z); } 535 536template <class _A1, class _A2, class _A3> 537inline _LIBCPP_INLINE_VISIBILITY 538typename _EnableIf 539< 540 is_arithmetic<_A1>::value && 541 is_arithmetic<_A2>::value && 542 is_arithmetic<_A3>::value, 543 __promote<_A1, _A2, _A3> 544>::type 545hypot(_A1 __lcpp_x, _A2 __lcpp_y, _A3 __lcpp_z) _NOEXCEPT 546{ 547 typedef typename __promote<_A1, _A2, _A3>::type __result_type; 548 static_assert((!(is_same<_A1, __result_type>::value && 549 is_same<_A2, __result_type>::value && 550 is_same<_A3, __result_type>::value)), ""); 551 return hypot((__result_type)__lcpp_x, (__result_type)__lcpp_y, (__result_type)__lcpp_z); 552} 553#endif 554 555template <class _A1> 556_LIBCPP_INLINE_VISIBILITY 557_LIBCPP_CONSTEXPR typename enable_if<is_floating_point<_A1>::value, bool>::type 558__libcpp_isnan_or_builtin(_A1 __lcpp_x) _NOEXCEPT 559{ 560#if __has_builtin(__builtin_isnan) 561 return __builtin_isnan(__lcpp_x); 562#else 563 return isnan(__lcpp_x); 564#endif 565} 566 567template <class _A1> 568_LIBCPP_INLINE_VISIBILITY 569_LIBCPP_CONSTEXPR typename enable_if<!is_floating_point<_A1>::value, bool>::type 570__libcpp_isnan_or_builtin(_A1 __lcpp_x) _NOEXCEPT 571{ 572 return isnan(__lcpp_x); 573} 574 575template <class _A1> 576_LIBCPP_INLINE_VISIBILITY 577_LIBCPP_CONSTEXPR typename enable_if<is_floating_point<_A1>::value, bool>::type 578__libcpp_isinf_or_builtin(_A1 __lcpp_x) _NOEXCEPT 579{ 580#if __has_builtin(__builtin_isinf) 581 return __builtin_isinf(__lcpp_x); 582#else 583 return isinf(__lcpp_x); 584#endif 585} 586 587template <class _A1> 588_LIBCPP_INLINE_VISIBILITY 589_LIBCPP_CONSTEXPR typename enable_if<!is_floating_point<_A1>::value, bool>::type 590__libcpp_isinf_or_builtin(_A1 __lcpp_x) _NOEXCEPT 591{ 592 return isinf(__lcpp_x); 593} 594 595template <class _A1> 596_LIBCPP_INLINE_VISIBILITY 597_LIBCPP_CONSTEXPR typename enable_if<is_floating_point<_A1>::value, bool>::type 598__libcpp_isfinite_or_builtin(_A1 __lcpp_x) _NOEXCEPT 599{ 600#if __has_builtin(__builtin_isfinite) 601 return __builtin_isfinite(__lcpp_x); 602#else 603 return isfinite(__lcpp_x); 604#endif 605} 606 607template <class _A1> 608_LIBCPP_INLINE_VISIBILITY 609_LIBCPP_CONSTEXPR typename enable_if<!is_floating_point<_A1>::value, bool>::type 610__libcpp_isfinite_or_builtin(_A1 __lcpp_x) _NOEXCEPT 611{ 612 return isfinite(__lcpp_x); 613} 614 615#if _LIBCPP_STD_VER > 17 616template <typename _Fp> 617constexpr 618_Fp __lerp(_Fp __a, _Fp __b, _Fp __t) noexcept { 619 if ((__a <= 0 && __b >= 0) || (__a >= 0 && __b <= 0)) 620 return __t * __b + (1 - __t) * __a; 621 622 if (__t == 1) return __b; 623 const _Fp __x = __a + __t * (__b - __a); 624 if ((__t > 1) == (__b > __a)) 625 return __b < __x ? __x : __b; 626 else 627 return __x < __b ? __x : __b; 628} 629 630constexpr float 631lerp(float __a, float __b, float __t) _NOEXCEPT { return __lerp(__a, __b, __t); } 632 633constexpr double 634lerp(double __a, double __b, double __t) _NOEXCEPT { return __lerp(__a, __b, __t); } 635 636constexpr long double 637lerp(long double __a, long double __b, long double __t) _NOEXCEPT { return __lerp(__a, __b, __t); } 638 639#endif // _LIBCPP_STD_VER > 17 640 641template <class _IntT, class _FloatT, 642 bool _FloatBigger = (numeric_limits<_FloatT>::digits > numeric_limits<_IntT>::digits), 643 int _Bits = (numeric_limits<_IntT>::digits - numeric_limits<_FloatT>::digits)> 644_LIBCPP_INLINE_VISIBILITY 645_LIBCPP_CONSTEXPR _IntT __max_representable_int_for_float() _NOEXCEPT { 646 static_assert(is_floating_point<_FloatT>::value, "must be a floating point type"); 647 static_assert(is_integral<_IntT>::value, "must be an integral type"); 648 static_assert(numeric_limits<_FloatT>::radix == 2, "FloatT has incorrect radix"); 649 static_assert((_IsSame<_FloatT, float>::value || _IsSame<_FloatT, double>::value 650 || _IsSame<_FloatT,long double>::value), "unsupported floating point type"); 651 return _FloatBigger ? numeric_limits<_IntT>::max() : (numeric_limits<_IntT>::max() >> _Bits << _Bits); 652} 653 654// Convert a floating point number to the specified integral type after 655// clamping to the integral types representable range. 656// 657// The behavior is undefined if `__r` is NaN. 658template <class _IntT, class _RealT> 659_LIBCPP_INLINE_VISIBILITY 660_IntT __clamp_to_integral(_RealT __r) _NOEXCEPT { 661 using _Lim = numeric_limits<_IntT>; 662 const _IntT _MaxVal = __max_representable_int_for_float<_IntT, _RealT>(); 663 if (__r >= ::nextafter(static_cast<_RealT>(_MaxVal), INFINITY)) { 664 return _Lim::max(); 665 } else if (__r <= _Lim::lowest()) { 666 return _Lim::min(); 667 } 668 return static_cast<_IntT>(__r); 669} 670 671_LIBCPP_END_NAMESPACE_STD 672 673_LIBCPP_POP_MACROS 674 675#endif // _LIBCPP_CMATH 676