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; 322using ::fpclassify; 323using ::isfinite; 324using ::isinf; 325using ::isnan; 326using ::isnormal; 327using ::isgreater; 328using ::isgreaterequal; 329using ::isless; 330using ::islessequal; 331using ::islessgreater; 332using ::isunordered; 333using ::isunordered; 334 335using ::float_t; 336using ::double_t; 337 338#ifndef _AIX 339using ::abs; 340#endif 341 342using ::acos; 343using ::acosf; 344using ::asin; 345using ::asinf; 346using ::atan; 347using ::atanf; 348using ::atan2; 349using ::atan2f; 350using ::ceil; 351using ::ceilf; 352using ::cos; 353using ::cosf; 354using ::cosh; 355using ::coshf; 356 357using ::exp; 358using ::expf; 359 360using ::fabs; 361using ::fabsf; 362using ::floor; 363using ::floorf; 364 365using ::fmod; 366using ::fmodf; 367 368using ::frexp; 369using ::frexpf; 370using ::ldexp; 371using ::ldexpf; 372 373using ::log; 374using ::logf; 375 376using ::log10; 377using ::log10f; 378using ::modf; 379using ::modff; 380 381using ::pow; 382using ::powf; 383 384using ::sin; 385using ::sinf; 386using ::sinh; 387using ::sinhf; 388 389using ::sqrt; 390using ::sqrtf; 391using ::tan; 392using ::tanf; 393 394using ::tanh; 395using ::tanhf; 396 397using ::acosh; 398using ::acoshf; 399using ::asinh; 400using ::asinhf; 401using ::atanh; 402using ::atanhf; 403using ::cbrt; 404using ::cbrtf; 405 406using ::copysign; 407using ::copysignf; 408 409using ::erf; 410using ::erff; 411using ::erfc; 412using ::erfcf; 413using ::exp2; 414using ::exp2f; 415using ::expm1; 416using ::expm1f; 417using ::fdim; 418using ::fdimf; 419using ::fmaf; 420using ::fma; 421using ::fmax; 422using ::fmaxf; 423using ::fmin; 424using ::fminf; 425using ::hypot; 426using ::hypotf; 427using ::ilogb; 428using ::ilogbf; 429using ::lgamma; 430using ::lgammaf; 431using ::llrint; 432using ::llrintf; 433using ::llround; 434using ::llroundf; 435using ::log1p; 436using ::log1pf; 437using ::log2; 438using ::log2f; 439using ::logb; 440using ::logbf; 441using ::lrint; 442using ::lrintf; 443using ::lround; 444using ::lroundf; 445 446using ::nan; 447using ::nanf; 448 449using ::nearbyint; 450using ::nearbyintf; 451using ::nextafter; 452using ::nextafterf; 453using ::nexttoward; 454using ::nexttowardf; 455using ::remainder; 456using ::remainderf; 457using ::remquo; 458using ::remquof; 459using ::rint; 460using ::rintf; 461using ::round; 462using ::roundf; 463using ::scalbln; 464using ::scalblnf; 465using ::scalbn; 466using ::scalbnf; 467using ::tgamma; 468using ::tgammaf; 469using ::trunc; 470using ::truncf; 471 472using ::acosl; 473using ::asinl; 474using ::atanl; 475using ::atan2l; 476using ::ceill; 477using ::cosl; 478using ::coshl; 479using ::expl; 480using ::fabsl; 481using ::floorl; 482using ::fmodl; 483using ::frexpl; 484using ::ldexpl; 485using ::logl; 486using ::log10l; 487using ::modfl; 488using ::powl; 489using ::sinl; 490using ::sinhl; 491using ::sqrtl; 492using ::tanl; 493 494using ::tanhl; 495using ::acoshl; 496using ::asinhl; 497using ::atanhl; 498using ::cbrtl; 499 500using ::copysignl; 501 502using ::erfl; 503using ::erfcl; 504using ::exp2l; 505using ::expm1l; 506using ::fdiml; 507using ::fmal; 508using ::fmaxl; 509using ::fminl; 510using ::hypotl; 511using ::ilogbl; 512using ::lgammal; 513using ::llrintl; 514using ::llroundl; 515using ::log1pl; 516using ::log2l; 517using ::logbl; 518using ::lrintl; 519using ::lroundl; 520using ::nanl; 521using ::nearbyintl; 522using ::nextafterl; 523using ::nexttowardl; 524using ::remainderl; 525using ::remquol; 526using ::rintl; 527using ::roundl; 528using ::scalblnl; 529using ::scalbnl; 530using ::tgammal; 531using ::truncl; 532 533#if _LIBCPP_STD_VER > 14 534inline _LIBCPP_INLINE_VISIBILITY float hypot( float x, float y, float z ) { return sqrt(x*x + y*y + z*z); } 535inline _LIBCPP_INLINE_VISIBILITY double hypot( double x, double y, double z ) { return sqrt(x*x + y*y + z*z); } 536inline _LIBCPP_INLINE_VISIBILITY long double hypot( long double x, long double y, long double z ) { return sqrt(x*x + y*y + z*z); } 537 538template <class _A1, class _A2, class _A3> 539inline _LIBCPP_INLINE_VISIBILITY 540typename _EnableIf 541< 542 is_arithmetic<_A1>::value && 543 is_arithmetic<_A2>::value && 544 is_arithmetic<_A3>::value, 545 __promote<_A1, _A2, _A3> 546>::type 547hypot(_A1 __lcpp_x, _A2 __lcpp_y, _A3 __lcpp_z) _NOEXCEPT 548{ 549 typedef typename __promote<_A1, _A2, _A3>::type __result_type; 550 static_assert((!(is_same<_A1, __result_type>::value && 551 is_same<_A2, __result_type>::value && 552 is_same<_A3, __result_type>::value)), ""); 553 return hypot((__result_type)__lcpp_x, (__result_type)__lcpp_y, (__result_type)__lcpp_z); 554} 555#endif 556 557template <class _A1> 558_LIBCPP_INLINE_VISIBILITY 559_LIBCPP_CONSTEXPR typename enable_if<is_floating_point<_A1>::value, bool>::type 560__libcpp_isnan_or_builtin(_A1 __lcpp_x) _NOEXCEPT 561{ 562#if __has_builtin(__builtin_isnan) 563 return __builtin_isnan(__lcpp_x); 564#else 565 return isnan(__lcpp_x); 566#endif 567} 568 569template <class _A1> 570_LIBCPP_INLINE_VISIBILITY 571_LIBCPP_CONSTEXPR typename enable_if<!is_floating_point<_A1>::value, bool>::type 572__libcpp_isnan_or_builtin(_A1 __lcpp_x) _NOEXCEPT 573{ 574 return isnan(__lcpp_x); 575} 576 577template <class _A1> 578_LIBCPP_INLINE_VISIBILITY 579_LIBCPP_CONSTEXPR typename enable_if<is_floating_point<_A1>::value, bool>::type 580__libcpp_isinf_or_builtin(_A1 __lcpp_x) _NOEXCEPT 581{ 582#if __has_builtin(__builtin_isinf) 583 return __builtin_isinf(__lcpp_x); 584#else 585 return isinf(__lcpp_x); 586#endif 587} 588 589template <class _A1> 590_LIBCPP_INLINE_VISIBILITY 591_LIBCPP_CONSTEXPR typename enable_if<!is_floating_point<_A1>::value, bool>::type 592__libcpp_isinf_or_builtin(_A1 __lcpp_x) _NOEXCEPT 593{ 594 return isinf(__lcpp_x); 595} 596 597template <class _A1> 598_LIBCPP_INLINE_VISIBILITY 599_LIBCPP_CONSTEXPR typename enable_if<is_floating_point<_A1>::value, bool>::type 600__libcpp_isfinite_or_builtin(_A1 __lcpp_x) _NOEXCEPT 601{ 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> 610_LIBCPP_INLINE_VISIBILITY 611_LIBCPP_CONSTEXPR typename enable_if<!is_floating_point<_A1>::value, bool>::type 612__libcpp_isfinite_or_builtin(_A1 __lcpp_x) _NOEXCEPT 613{ 614 return isfinite(__lcpp_x); 615} 616 617#if _LIBCPP_STD_VER > 17 618template <typename _Fp> 619constexpr 620_Fp __lerp(_Fp __a, _Fp __b, _Fp __t) noexcept { 621 if ((__a <= 0 && __b >= 0) || (__a >= 0 && __b <= 0)) 622 return __t * __b + (1 - __t) * __a; 623 624 if (__t == 1) return __b; 625 const _Fp __x = __a + __t * (__b - __a); 626 if (__t > 1 == __b > __a) 627 return __b < __x ? __x : __b; 628 else 629 return __x < __b ? __x : __b; 630} 631 632constexpr float 633lerp(float __a, float __b, float __t) _NOEXCEPT { return __lerp(__a, __b, __t); } 634 635constexpr double 636lerp(double __a, double __b, double __t) _NOEXCEPT { return __lerp(__a, __b, __t); } 637 638constexpr long double 639lerp(long double __a, long double __b, long double __t) _NOEXCEPT { return __lerp(__a, __b, __t); } 640 641#endif // _LIBCPP_STD_VER > 17 642 643template <class _IntT, class _FloatT, 644 bool _FloatBigger = (numeric_limits<_FloatT>::digits > numeric_limits<_IntT>::digits), 645 int _Bits = (numeric_limits<_IntT>::digits - numeric_limits<_FloatT>::digits)> 646_LIBCPP_INLINE_VISIBILITY 647_LIBCPP_CONSTEXPR _IntT __max_representable_int_for_float() _NOEXCEPT { 648 static_assert(is_floating_point<_FloatT>::value, "must be a floating point type"); 649 static_assert(is_integral<_IntT>::value, "must be an integral type"); 650 static_assert(numeric_limits<_FloatT>::radix == 2, "FloatT has incorrect radix"); 651 static_assert((_IsSame<_FloatT, float>::value || _IsSame<_FloatT, double>::value 652 || _IsSame<_FloatT,long double>::value), "unsupported floating point type"); 653 return _FloatBigger ? numeric_limits<_IntT>::max() : (numeric_limits<_IntT>::max() >> _Bits << _Bits); 654} 655 656// Convert a floating point number to the specified integral type after 657// clamping to the integral types representable range. 658// 659// The behavior is undefined if `__r` is NaN. 660template <class _IntT, class _RealT> 661_LIBCPP_INLINE_VISIBILITY 662_IntT __clamp_to_integral(_RealT __r) _NOEXCEPT { 663 using _Lim = std::numeric_limits<_IntT>; 664 const _IntT _MaxVal = std::__max_representable_int_for_float<_IntT, _RealT>(); 665 if (__r >= ::nextafter(static_cast<_RealT>(_MaxVal), INFINITY)) { 666 return _Lim::max(); 667 } else if (__r <= _Lim::lowest()) { 668 return _Lim::min(); 669 } 670 return static_cast<_IntT>(__r); 671} 672 673_LIBCPP_END_NAMESPACE_STD 674 675_LIBCPP_POP_MACROS 676 677#endif // _LIBCPP_CMATH 678