1// -*- C++ -*- 2//===---------------------------- cmath -----------------------------------===// 3// 4// The LLVM Compiler Infrastructure 5// 6// This file is dual licensed under the MIT and the University of Illinois Open 7// Source Licenses. See LICENSE.TXT for details. 8// 9//===----------------------------------------------------------------------===// 10 11#ifndef _LIBCPP_CMATH 12#define _LIBCPP_CMATH 13 14/* 15 cmath synopsis 16 17Macros: 18 19 HUGE_VAL 20 HUGE_VALF // C99 21 HUGE_VALL // C99 22 INFINITY // C99 23 NAN // C99 24 FP_INFINITE // C99 25 FP_NAN // C99 26 FP_NORMAL // C99 27 FP_SUBNORMAL // C99 28 FP_ZERO // C99 29 FP_FAST_FMA // C99 30 FP_FAST_FMAF // C99 31 FP_FAST_FMAL // C99 32 FP_ILOGB0 // C99 33 FP_ILOGBNAN // C99 34 MATH_ERRNO // C99 35 MATH_ERREXCEPT // C99 36 math_errhandling // C99 37 38namespace std 39{ 40 41Types: 42 43 float_t // C99 44 double_t // C99 45 46// C90 47 48floating_point abs(floating_point x); 49 50floating_point acos (arithmetic x); 51float acosf(float x); 52long double acosl(long double x); 53 54floating_point asin (arithmetic x); 55float asinf(float x); 56long double asinl(long double x); 57 58floating_point atan (arithmetic x); 59float atanf(float x); 60long double atanl(long double x); 61 62floating_point atan2 (arithmetic y, arithmetic x); 63float atan2f(float y, float x); 64long double atan2l(long double y, long double x); 65 66floating_point ceil (arithmetic x); 67float ceilf(float x); 68long double ceill(long double x); 69 70floating_point cos (arithmetic x); 71float cosf(float x); 72long double cosl(long double x); 73 74floating_point cosh (arithmetic x); 75float coshf(float x); 76long double coshl(long double x); 77 78floating_point exp (arithmetic x); 79float expf(float x); 80long double expl(long double x); 81 82floating_point fabs (arithmetic x); 83float fabsf(float x); 84long double fabsl(long double x); 85 86floating_point floor (arithmetic x); 87float floorf(float x); 88long double floorl(long double x); 89 90floating_point fmod (arithmetic x, arithmetic y); 91float fmodf(float x, float y); 92long double fmodl(long double x, long double y); 93 94floating_point frexp (arithmetic value, int* exp); 95float frexpf(float value, int* exp); 96long double frexpl(long double value, int* exp); 97 98floating_point ldexp (arithmetic value, int exp); 99float ldexpf(float value, int exp); 100long double ldexpl(long double value, int exp); 101 102floating_point log (arithmetic x); 103float logf(float x); 104long double logl(long double x); 105 106floating_point log10 (arithmetic x); 107float log10f(float x); 108long double log10l(long double x); 109 110floating_point modf (floating_point value, floating_point* iptr); 111float modff(float value, float* iptr); 112long double modfl(long double value, long double* iptr); 113 114floating_point pow (arithmetic x, arithmetic y); 115float powf(float x, float y); 116long double powl(long double x, long double y); 117 118floating_point sin (arithmetic x); 119float sinf(float x); 120long double sinl(long double x); 121 122floating_point sinh (arithmetic x); 123float sinhf(float x); 124long double sinhl(long double x); 125 126floating_point sqrt (arithmetic x); 127float sqrtf(float x); 128long double sqrtl(long double x); 129 130floating_point tan (arithmetic x); 131float tanf(float x); 132long double tanl(long double x); 133 134floating_point tanh (arithmetic x); 135float tanhf(float x); 136long double tanhl(long double x); 137 138// C99 139 140bool signbit(arithmetic x); 141 142int fpclassify(arithmetic x); 143 144bool isfinite(arithmetic x); 145bool isinf(arithmetic x); 146bool isnan(arithmetic x); 147bool isnormal(arithmetic x); 148 149bool isgreater(arithmetic x, arithmetic y); 150bool isgreaterequal(arithmetic x, arithmetic y); 151bool isless(arithmetic x, arithmetic y); 152bool islessequal(arithmetic x, arithmetic y); 153bool islessgreater(arithmetic x, arithmetic y); 154bool isunordered(arithmetic x, arithmetic y); 155 156floating_point acosh (arithmetic x); 157float acoshf(float x); 158long double acoshl(long double x); 159 160floating_point asinh (arithmetic x); 161float asinhf(float x); 162long double asinhl(long double x); 163 164floating_point atanh (arithmetic x); 165float atanhf(float x); 166long double atanhl(long double x); 167 168floating_point cbrt (arithmetic x); 169float cbrtf(float x); 170long double cbrtl(long double x); 171 172floating_point copysign (arithmetic x, arithmetic y); 173float copysignf(float x, float y); 174long double copysignl(long double x, long double y); 175 176floating_point erf (arithmetic x); 177float erff(float x); 178long double erfl(long double x); 179 180floating_point erfc (arithmetic x); 181float erfcf(float x); 182long double erfcl(long double x); 183 184floating_point exp2 (arithmetic x); 185float exp2f(float x); 186long double exp2l(long double x); 187 188floating_point expm1 (arithmetic x); 189float expm1f(float x); 190long double expm1l(long double x); 191 192floating_point fdim (arithmetic x, arithmetic y); 193float fdimf(float x, float y); 194long double fdiml(long double x, long double y); 195 196floating_point fma (arithmetic x, arithmetic y, arithmetic z); 197float fmaf(float x, float y, float z); 198long double fmal(long double x, long double y, long double z); 199 200floating_point fmax (arithmetic x, arithmetic y); 201float fmaxf(float x, float y); 202long double fmaxl(long double x, long double y); 203 204floating_point fmin (arithmetic x, arithmetic y); 205float fminf(float x, float y); 206long double fminl(long double x, long double y); 207 208floating_point hypot (arithmetic x, arithmetic y); 209float hypotf(float x, float y); 210long double hypotl(long double x, long double y); 211 212double hypot(double x, double y, double z); // C++17 213float hypot(float x, float y, float z); // C++17 214long double hypot(long double x, long double y, long double z); // C++17 215 216int ilogb (arithmetic x); 217int ilogbf(float x); 218int ilogbl(long double x); 219 220floating_point lgamma (arithmetic x); 221float lgammaf(float x); 222long double lgammal(long double x); 223 224long long llrint (arithmetic x); 225long long llrintf(float x); 226long long llrintl(long double x); 227 228long long llround (arithmetic x); 229long long llroundf(float x); 230long long llroundl(long double x); 231 232floating_point log1p (arithmetic x); 233float log1pf(float x); 234long double log1pl(long double x); 235 236floating_point log2 (arithmetic x); 237float log2f(float x); 238long double log2l(long double x); 239 240floating_point logb (arithmetic x); 241float logbf(float x); 242long double logbl(long double x); 243 244long lrint (arithmetic x); 245long lrintf(float x); 246long lrintl(long double x); 247 248long lround (arithmetic x); 249long lroundf(float x); 250long lroundl(long double x); 251 252double nan (const char* str); 253float nanf(const char* str); 254long double nanl(const char* str); 255 256floating_point nearbyint (arithmetic x); 257float nearbyintf(float x); 258long double nearbyintl(long double x); 259 260floating_point nextafter (arithmetic x, arithmetic y); 261float nextafterf(float x, float y); 262long double nextafterl(long double x, long double y); 263 264floating_point nexttoward (arithmetic x, long double y); 265float nexttowardf(float x, long double y); 266long double nexttowardl(long double x, long double y); 267 268floating_point remainder (arithmetic x, arithmetic y); 269float remainderf(float x, float y); 270long double remainderl(long double x, long double y); 271 272floating_point remquo (arithmetic x, arithmetic y, int* pquo); 273float remquof(float x, float y, int* pquo); 274long double remquol(long double x, long double y, int* pquo); 275 276floating_point rint (arithmetic x); 277float rintf(float x); 278long double rintl(long double x); 279 280floating_point round (arithmetic x); 281float roundf(float x); 282long double roundl(long double x); 283 284floating_point scalbln (arithmetic x, long ex); 285float scalblnf(float x, long ex); 286long double scalblnl(long double x, long ex); 287 288floating_point scalbn (arithmetic x, int ex); 289float scalbnf(float x, int ex); 290long double scalbnl(long double x, int ex); 291 292floating_point tgamma (arithmetic x); 293float tgammaf(float x); 294long double tgammal(long double x); 295 296floating_point trunc (arithmetic x); 297float truncf(float x); 298long double truncl(long double x); 299 300} // std 301 302*/ 303 304#include <__config> 305#include <math.h> 306#include <version> 307#include <type_traits> 308 309#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER) 310#pragma GCC system_header 311#endif 312 313_LIBCPP_PUSH_MACROS 314#include <__undef_macros> 315 316_LIBCPP_BEGIN_NAMESPACE_STD 317 318using ::signbit; 319using ::fpclassify; 320using ::isfinite; 321using ::isinf; 322using ::isnan; 323using ::isnormal; 324using ::isgreater; 325using ::isgreaterequal; 326using ::isless; 327using ::islessequal; 328using ::islessgreater; 329using ::isunordered; 330using ::isunordered; 331 332using ::float_t; 333using ::double_t; 334 335#ifndef _AIX 336using ::abs; 337#endif 338 339using ::acos; 340using ::acosf; 341using ::asin; 342using ::asinf; 343using ::atan; 344using ::atanf; 345using ::atan2; 346using ::atan2f; 347using ::ceil; 348using ::ceilf; 349using ::cos; 350using ::cosf; 351using ::cosh; 352using ::coshf; 353 354using ::exp; 355using ::expf; 356 357using ::fabs; 358using ::fabsf; 359using ::floor; 360using ::floorf; 361 362using ::fmod; 363using ::fmodf; 364 365using ::frexp; 366using ::frexpf; 367using ::ldexp; 368using ::ldexpf; 369 370using ::log; 371using ::logf; 372 373using ::log10; 374using ::log10f; 375using ::modf; 376using ::modff; 377 378using ::pow; 379using ::powf; 380 381using ::sin; 382using ::sinf; 383using ::sinh; 384using ::sinhf; 385 386using ::sqrt; 387using ::sqrtf; 388using ::tan; 389using ::tanf; 390 391using ::tanh; 392using ::tanhf; 393 394using ::acosh; 395using ::acoshf; 396using ::asinh; 397using ::asinhf; 398using ::atanh; 399using ::atanhf; 400using ::cbrt; 401using ::cbrtf; 402 403using ::copysign; 404using ::copysignf; 405 406using ::erf; 407using ::erff; 408using ::erfc; 409using ::erfcf; 410using ::exp2; 411using ::exp2f; 412using ::expm1; 413using ::expm1f; 414using ::fdim; 415using ::fdimf; 416using ::fmaf; 417using ::fma; 418using ::fmax; 419using ::fmaxf; 420using ::fmin; 421using ::fminf; 422using ::hypot; 423using ::hypotf; 424using ::ilogb; 425using ::ilogbf; 426using ::lgamma; 427using ::lgammaf; 428using ::llrint; 429using ::llrintf; 430using ::llround; 431using ::llroundf; 432using ::log1p; 433using ::log1pf; 434using ::log2; 435using ::log2f; 436using ::logb; 437using ::logbf; 438using ::lrint; 439using ::lrintf; 440using ::lround; 441using ::lroundf; 442 443using ::nan; 444using ::nanf; 445 446using ::nearbyint; 447using ::nearbyintf; 448using ::nextafter; 449using ::nextafterf; 450using ::nexttoward; 451using ::nexttowardf; 452using ::remainder; 453using ::remainderf; 454using ::remquo; 455using ::remquof; 456using ::rint; 457using ::rintf; 458using ::round; 459using ::roundf; 460using ::scalbln; 461using ::scalblnf; 462using ::scalbn; 463using ::scalbnf; 464using ::tgamma; 465using ::tgammaf; 466using ::trunc; 467using ::truncf; 468 469using ::acosl; 470using ::asinl; 471using ::atanl; 472using ::atan2l; 473using ::ceill; 474using ::cosl; 475using ::coshl; 476using ::expl; 477using ::fabsl; 478using ::floorl; 479using ::fmodl; 480using ::frexpl; 481using ::ldexpl; 482using ::logl; 483using ::log10l; 484using ::modfl; 485using ::powl; 486using ::sinl; 487using ::sinhl; 488using ::sqrtl; 489using ::tanl; 490 491using ::tanhl; 492using ::acoshl; 493using ::asinhl; 494using ::atanhl; 495using ::cbrtl; 496 497using ::copysignl; 498 499using ::erfl; 500using ::erfcl; 501using ::exp2l; 502using ::expm1l; 503using ::fdiml; 504using ::fmal; 505using ::fmaxl; 506using ::fminl; 507using ::hypotl; 508using ::ilogbl; 509using ::lgammal; 510using ::llrintl; 511using ::llroundl; 512using ::log1pl; 513using ::log2l; 514using ::logbl; 515using ::lrintl; 516using ::lroundl; 517using ::nanl; 518using ::nearbyintl; 519using ::nextafterl; 520using ::nexttowardl; 521using ::remainderl; 522using ::remquol; 523using ::rintl; 524using ::roundl; 525using ::scalblnl; 526using ::scalbnl; 527using ::tgammal; 528using ::truncl; 529 530#if _LIBCPP_STD_VER > 14 531inline _LIBCPP_INLINE_VISIBILITY float hypot( float x, float y, float z ) { return sqrt(x*x + y*y + z*z); } 532inline _LIBCPP_INLINE_VISIBILITY double hypot( double x, double y, double z ) { return sqrt(x*x + y*y + z*z); } 533inline _LIBCPP_INLINE_VISIBILITY long double hypot( long double x, long double y, long double z ) { return sqrt(x*x + y*y + z*z); } 534 535template <class _A1, class _A2, class _A3> 536inline _LIBCPP_INLINE_VISIBILITY 537typename __lazy_enable_if 538< 539 is_arithmetic<_A1>::value && 540 is_arithmetic<_A2>::value && 541 is_arithmetic<_A3>::value, 542 __promote<_A1, _A2, _A3> 543>::type 544hypot(_A1 __lcpp_x, _A2 __lcpp_y, _A3 __lcpp_z) _NOEXCEPT 545{ 546 typedef typename __promote<_A1, _A2, _A3>::type __result_type; 547 static_assert((!(is_same<_A1, __result_type>::value && 548 is_same<_A2, __result_type>::value && 549 is_same<_A3, __result_type>::value)), ""); 550 return hypot((__result_type)__lcpp_x, (__result_type)__lcpp_y, (__result_type)__lcpp_z); 551} 552#endif 553 554template <class _A1> 555_LIBCPP_INLINE_VISIBILITY 556_LIBCPP_CONSTEXPR typename enable_if<is_floating_point<_A1>::value, bool>::type 557__libcpp_isnan_or_builtin(_A1 __lcpp_x) _NOEXCEPT 558{ 559#if __has_builtin(__builtin_isnan) 560 return __builtin_isnan(__lcpp_x); 561#else 562 return isnan(__lcpp_x); 563#endif 564} 565 566template <class _A1> 567_LIBCPP_INLINE_VISIBILITY 568_LIBCPP_CONSTEXPR typename enable_if<!is_floating_point<_A1>::value, bool>::type 569__libcpp_isnan_or_builtin(_A1 __lcpp_x) _NOEXCEPT 570{ 571 return isnan(__lcpp_x); 572} 573 574template <class _A1> 575_LIBCPP_INLINE_VISIBILITY 576_LIBCPP_CONSTEXPR typename enable_if<is_floating_point<_A1>::value, bool>::type 577__libcpp_isinf_or_builtin(_A1 __lcpp_x) _NOEXCEPT 578{ 579#if __has_builtin(__builtin_isinf) 580 return __builtin_isinf(__lcpp_x); 581#else 582 return isinf(__lcpp_x); 583#endif 584} 585 586template <class _A1> 587_LIBCPP_INLINE_VISIBILITY 588_LIBCPP_CONSTEXPR typename enable_if<!is_floating_point<_A1>::value, bool>::type 589__libcpp_isinf_or_builtin(_A1 __lcpp_x) _NOEXCEPT 590{ 591 return isinf(__lcpp_x); 592} 593 594template <class _A1> 595_LIBCPP_INLINE_VISIBILITY 596_LIBCPP_CONSTEXPR typename enable_if<is_floating_point<_A1>::value, bool>::type 597__libcpp_isfinite_or_builtin(_A1 __lcpp_x) _NOEXCEPT 598{ 599#if __has_builtin(__builtin_isfinite) 600 return __builtin_isfinite(__lcpp_x); 601#else 602 return isfinite(__lcpp_x); 603#endif 604} 605 606template <class _A1> 607_LIBCPP_INLINE_VISIBILITY 608_LIBCPP_CONSTEXPR typename enable_if<!is_floating_point<_A1>::value, bool>::type 609__libcpp_isfinite_or_builtin(_A1 __lcpp_x) _NOEXCEPT 610{ 611 return isfinite(__lcpp_x); 612} 613 614template <class _IntT, class _FloatT, 615 bool _FloatBigger = (numeric_limits<_FloatT>::digits > numeric_limits<_IntT>::digits), 616 int _Bits = (numeric_limits<_IntT>::digits - numeric_limits<_FloatT>::digits)> 617_LIBCPP_INLINE_VISIBILITY 618_LIBCPP_CONSTEXPR _IntT __max_representable_int_for_float() _NOEXCEPT { 619 static_assert(is_floating_point<_FloatT>::value, "must be a floating point type"); 620 static_assert(is_integral<_IntT>::value, "must be an integral type"); 621 static_assert(numeric_limits<_FloatT>::radix == 2, "FloatT has incorrect radix"); 622 static_assert(is_same<_FloatT, float>::value || is_same<_FloatT, double>::value 623 || is_same<_FloatT,long double>::value, "unsupported floating point type"); 624 return _FloatBigger ? numeric_limits<_IntT>::max() : (numeric_limits<_IntT>::max() >> _Bits << _Bits); 625} 626 627// Convert a floating point number to the specified integral type after 628// clamping to the integral types representable range. 629// 630// The behavior is undefined if `__r` is NaN. 631template <class _IntT, class _RealT> 632_LIBCPP_INLINE_VISIBILITY 633_IntT __clamp_to_integral(_RealT __r) _NOEXCEPT { 634 using _Lim = std::numeric_limits<_IntT>; 635 const _IntT _MaxVal = std::__max_representable_int_for_float<_IntT, _RealT>(); 636 if (__r >= ::nextafter(static_cast<_RealT>(_MaxVal), INFINITY)) { 637 return _Lim::max(); 638 } else if (__r <= _Lim::lowest()) { 639 return _Lim::min(); 640 } 641 return static_cast<_IntT>(__r); 642} 643 644_LIBCPP_END_NAMESPACE_STD 645 646_LIBCPP_POP_MACROS 647 648#endif // _LIBCPP_CMATH 649