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); 298 299} // std 300 301*/ 302 303#include <__config> 304#include <math.h> 305#include <version> 306#include <type_traits> 307 308#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER) 309#pragma GCC system_header 310#endif 311 312_LIBCPP_PUSH_MACROS 313#include <__undef_macros> 314 315_LIBCPP_BEGIN_NAMESPACE_STD 316 317using ::signbit; 318using ::fpclassify; 319using ::isfinite; 320using ::isinf; 321using ::isnan; 322using ::isnormal; 323using ::isgreater; 324using ::isgreaterequal; 325using ::isless; 326using ::islessequal; 327using ::islessgreater; 328using ::isunordered; 329using ::isunordered; 330 331using ::float_t; 332using ::double_t; 333 334#ifndef _AIX 335using ::abs; 336#endif 337 338using ::acos; 339using ::acosf; 340using ::asin; 341using ::asinf; 342using ::atan; 343using ::atanf; 344using ::atan2; 345using ::atan2f; 346using ::ceil; 347using ::ceilf; 348using ::cos; 349using ::cosf; 350using ::cosh; 351using ::coshf; 352 353using ::exp; 354using ::expf; 355 356using ::fabs; 357using ::fabsf; 358using ::floor; 359using ::floorf; 360 361using ::fmod; 362using ::fmodf; 363 364using ::frexp; 365using ::frexpf; 366using ::ldexp; 367using ::ldexpf; 368 369using ::log; 370using ::logf; 371 372using ::log10; 373using ::log10f; 374using ::modf; 375using ::modff; 376 377using ::pow; 378using ::powf; 379 380using ::sin; 381using ::sinf; 382using ::sinh; 383using ::sinhf; 384 385using ::sqrt; 386using ::sqrtf; 387using ::tan; 388using ::tanf; 389 390using ::tanh; 391using ::tanhf; 392 393using ::acosh; 394using ::acoshf; 395using ::asinh; 396using ::asinhf; 397using ::atanh; 398using ::atanhf; 399using ::cbrt; 400using ::cbrtf; 401 402using ::copysign; 403using ::copysignf; 404 405using ::erf; 406using ::erff; 407using ::erfc; 408using ::erfcf; 409using ::exp2; 410using ::exp2f; 411using ::expm1; 412using ::expm1f; 413using ::fdim; 414using ::fdimf; 415using ::fmaf; 416using ::fma; 417using ::fmax; 418using ::fmaxf; 419using ::fmin; 420using ::fminf; 421using ::hypot; 422using ::hypotf; 423using ::ilogb; 424using ::ilogbf; 425using ::lgamma; 426using ::lgammaf; 427using ::llrint; 428using ::llrintf; 429using ::llround; 430using ::llroundf; 431using ::log1p; 432using ::log1pf; 433using ::log2; 434using ::log2f; 435using ::logb; 436using ::logbf; 437using ::lrint; 438using ::lrintf; 439using ::lround; 440using ::lroundf; 441 442using ::nan; 443using ::nanf; 444 445using ::nearbyint; 446using ::nearbyintf; 447using ::nextafter; 448using ::nextafterf; 449using ::nexttoward; 450using ::nexttowardf; 451using ::remainder; 452using ::remainderf; 453using ::remquo; 454using ::remquof; 455using ::rint; 456using ::rintf; 457using ::round; 458using ::roundf; 459using ::scalbln; 460using ::scalblnf; 461using ::scalbn; 462using ::scalbnf; 463using ::tgamma; 464using ::tgammaf; 465using ::trunc; 466using ::truncf; 467 468using ::acosl; 469using ::asinl; 470using ::atanl; 471using ::atan2l; 472using ::ceill; 473using ::cosl; 474using ::coshl; 475using ::expl; 476using ::fabsl; 477using ::floorl; 478using ::fmodl; 479using ::frexpl; 480using ::ldexpl; 481using ::logl; 482using ::log10l; 483using ::modfl; 484using ::powl; 485using ::sinl; 486using ::sinhl; 487using ::sqrtl; 488using ::tanl; 489 490using ::tanhl; 491using ::acoshl; 492using ::asinhl; 493using ::atanhl; 494using ::cbrtl; 495 496using ::copysignl; 497 498using ::erfl; 499using ::erfcl; 500using ::exp2l; 501using ::expm1l; 502using ::fdiml; 503using ::fmal; 504using ::fmaxl; 505using ::fminl; 506using ::hypotl; 507using ::ilogbl; 508using ::lgammal; 509using ::llrintl; 510using ::llroundl; 511using ::log1pl; 512using ::log2l; 513using ::logbl; 514using ::lrintl; 515using ::lroundl; 516using ::nanl; 517using ::nearbyintl; 518using ::nextafterl; 519using ::nexttowardl; 520using ::remainderl; 521using ::remquol; 522using ::rintl; 523using ::roundl; 524using ::scalblnl; 525using ::scalbnl; 526using ::tgammal; 527using ::truncl; 528 529#if _LIBCPP_STD_VER > 14 530inline _LIBCPP_INLINE_VISIBILITY float hypot( float x, float y, float z ) { return sqrt(x*x + y*y + z*z); } 531inline _LIBCPP_INLINE_VISIBILITY double hypot( double x, double y, double z ) { return sqrt(x*x + y*y + z*z); } 532inline _LIBCPP_INLINE_VISIBILITY long double hypot( long double x, long double y, long double z ) { return sqrt(x*x + y*y + z*z); } 533 534template <class _A1, class _A2, class _A3> 535inline _LIBCPP_INLINE_VISIBILITY 536typename _EnableIf 537< 538 is_arithmetic<_A1>::value && 539 is_arithmetic<_A2>::value && 540 is_arithmetic<_A3>::value, 541 __promote<_A1, _A2, _A3> 542>::type 543hypot(_A1 __lcpp_x, _A2 __lcpp_y, _A3 __lcpp_z) _NOEXCEPT 544{ 545 typedef typename __promote<_A1, _A2, _A3>::type __result_type; 546 static_assert((!(is_same<_A1, __result_type>::value && 547 is_same<_A2, __result_type>::value && 548 is_same<_A3, __result_type>::value)), ""); 549 return hypot((__result_type)__lcpp_x, (__result_type)__lcpp_y, (__result_type)__lcpp_z); 550} 551#endif 552 553template <class _A1> 554_LIBCPP_INLINE_VISIBILITY 555_LIBCPP_CONSTEXPR typename enable_if<is_floating_point<_A1>::value, bool>::type 556__libcpp_isnan_or_builtin(_A1 __lcpp_x) _NOEXCEPT 557{ 558#if __has_builtin(__builtin_isnan) 559 return __builtin_isnan(__lcpp_x); 560#else 561 return isnan(__lcpp_x); 562#endif 563} 564 565template <class _A1> 566_LIBCPP_INLINE_VISIBILITY 567_LIBCPP_CONSTEXPR typename enable_if<!is_floating_point<_A1>::value, bool>::type 568__libcpp_isnan_or_builtin(_A1 __lcpp_x) _NOEXCEPT 569{ 570 return isnan(__lcpp_x); 571} 572 573template <class _A1> 574_LIBCPP_INLINE_VISIBILITY 575_LIBCPP_CONSTEXPR typename enable_if<is_floating_point<_A1>::value, bool>::type 576__libcpp_isinf_or_builtin(_A1 __lcpp_x) _NOEXCEPT 577{ 578#if __has_builtin(__builtin_isinf) 579 return __builtin_isinf(__lcpp_x); 580#else 581 return isinf(__lcpp_x); 582#endif 583} 584 585template <class _A1> 586_LIBCPP_INLINE_VISIBILITY 587_LIBCPP_CONSTEXPR typename enable_if<!is_floating_point<_A1>::value, bool>::type 588__libcpp_isinf_or_builtin(_A1 __lcpp_x) _NOEXCEPT 589{ 590 return isinf(__lcpp_x); 591} 592 593template <class _A1> 594_LIBCPP_INLINE_VISIBILITY 595_LIBCPP_CONSTEXPR typename enable_if<is_floating_point<_A1>::value, bool>::type 596__libcpp_isfinite_or_builtin(_A1 __lcpp_x) _NOEXCEPT 597{ 598#if __has_builtin(__builtin_isfinite) 599 return __builtin_isfinite(__lcpp_x); 600#else 601 return isfinite(__lcpp_x); 602#endif 603} 604 605template <class _A1> 606_LIBCPP_INLINE_VISIBILITY 607_LIBCPP_CONSTEXPR typename enable_if<!is_floating_point<_A1>::value, bool>::type 608__libcpp_isfinite_or_builtin(_A1 __lcpp_x) _NOEXCEPT 609{ 610 return isfinite(__lcpp_x); 611} 612 613#if _LIBCPP_STD_VER > 17 614template <typename _Fp> 615constexpr 616_Fp __lerp(_Fp __a, _Fp __b, _Fp __t) noexcept { 617 if ((__a <= 0 && __b >= 0) || (__a >= 0 && __b <= 0)) 618 return __t * __b + (1 - __t) * __a; 619 620 if (__t == 1) return __b; 621 const _Fp __x = __a + __t * (__b - __a); 622 if (__t > 1 == __b > __a) 623 return __b < __x ? __x : __b; 624 else 625 return __x < __b ? __x : __b; 626} 627 628constexpr float 629lerp(float __a, float __b, float __t) _NOEXCEPT { return __lerp(__a, __b, __t); } 630 631constexpr double 632lerp(double __a, double __b, double __t) _NOEXCEPT { return __lerp(__a, __b, __t); } 633 634constexpr long double 635lerp(long double __a, long double __b, long double __t) _NOEXCEPT { return __lerp(__a, __b, __t); } 636 637#endif // _LIBCPP_STD_VER > 17 638 639template <class _IntT, class _FloatT, 640 bool _FloatBigger = (numeric_limits<_FloatT>::digits > numeric_limits<_IntT>::digits), 641 int _Bits = (numeric_limits<_IntT>::digits - numeric_limits<_FloatT>::digits)> 642_LIBCPP_INLINE_VISIBILITY 643_LIBCPP_CONSTEXPR _IntT __max_representable_int_for_float() _NOEXCEPT { 644 static_assert(is_floating_point<_FloatT>::value, "must be a floating point type"); 645 static_assert(is_integral<_IntT>::value, "must be an integral type"); 646 static_assert(numeric_limits<_FloatT>::radix == 2, "FloatT has incorrect radix"); 647 static_assert((_IsSame<_FloatT, float>::value || _IsSame<_FloatT, double>::value 648 || _IsSame<_FloatT,long double>::value), "unsupported floating point type"); 649 return _FloatBigger ? numeric_limits<_IntT>::max() : (numeric_limits<_IntT>::max() >> _Bits << _Bits); 650} 651 652// Convert a floating point number to the specified integral type after 653// clamping to the integral types representable range. 654// 655// The behavior is undefined if `__r` is NaN. 656template <class _IntT, class _RealT> 657_LIBCPP_INLINE_VISIBILITY 658_IntT __clamp_to_integral(_RealT __r) _NOEXCEPT { 659 using _Lim = std::numeric_limits<_IntT>; 660 const _IntT _MaxVal = std::__max_representable_int_for_float<_IntT, _RealT>(); 661 if (__r >= ::nextafter(static_cast<_RealT>(_MaxVal), INFINITY)) { 662 return _Lim::max(); 663 } else if (__r <= _Lim::lowest()) { 664 return _Lim::min(); 665 } 666 return static_cast<_IntT>(__r); 667} 668 669_LIBCPP_END_NAMESPACE_STD 670 671_LIBCPP_POP_MACROS 672 673#endif // _LIBCPP_CMATH 674