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 <limits> 307#include <type_traits> 308 309#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER) 310#pragma GCC system_header 311#endif 312 313_LIBCPP_BEGIN_NAMESPACE_STD 314 315using ::signbit; 316using ::fpclassify; 317using ::isfinite; 318using ::isinf; 319using ::isnan; 320using ::isnormal; 321using ::isgreater; 322using ::isgreaterequal; 323using ::isless; 324using ::islessequal; 325using ::islessgreater; 326using ::isunordered; 327using ::isunordered; 328 329using ::float_t; 330using ::double_t; 331 332#ifndef _AIX 333using ::abs; 334#endif 335 336using ::acos; 337using ::acosf; 338using ::asin; 339using ::asinf; 340using ::atan; 341using ::atanf; 342using ::atan2; 343using ::atan2f; 344using ::ceil; 345using ::ceilf; 346using ::cos; 347using ::cosf; 348using ::cosh; 349using ::coshf; 350 351using ::exp; 352using ::expf; 353 354using ::fabs; 355using ::fabsf; 356using ::floor; 357using ::floorf; 358 359using ::fmod; 360using ::fmodf; 361 362using ::frexp; 363using ::frexpf; 364using ::ldexp; 365using ::ldexpf; 366 367using ::log; 368using ::logf; 369 370using ::log10; 371using ::log10f; 372using ::modf; 373using ::modff; 374 375using ::pow; 376using ::powf; 377 378using ::sin; 379using ::sinf; 380using ::sinh; 381using ::sinhf; 382 383using ::sqrt; 384using ::sqrtf; 385using ::tan; 386using ::tanf; 387 388using ::tanh; 389using ::tanhf; 390 391using ::acosh; 392using ::acoshf; 393using ::asinh; 394using ::asinhf; 395using ::atanh; 396using ::atanhf; 397using ::cbrt; 398using ::cbrtf; 399 400using ::copysign; 401using ::copysignf; 402 403#if !(defined(_LIBCPP_MSVCRT) && ((_VC_CRT_MAJOR_VERSION-0) < 14)) 404using ::erf; 405using ::erff; 406using ::erfc; 407using ::erfcf; 408using ::exp2; 409using ::exp2f; 410using ::expm1; 411using ::expm1f; 412using ::fdim; 413using ::fdimf; 414using ::fmaf; 415using ::fma; 416using ::fmax; 417using ::fmaxf; 418using ::fmin; 419using ::fminf; 420using ::hypot; 421using ::hypotf; 422using ::ilogb; 423using ::ilogbf; 424using ::lgamma; 425using ::lgammaf; 426using ::llrint; 427using ::llrintf; 428using ::llround; 429using ::llroundf; 430using ::log1p; 431using ::log1pf; 432using ::log2; 433using ::log2f; 434using ::logb; 435using ::logbf; 436using ::lrint; 437using ::lrintf; 438using ::lround; 439using ::lroundf; 440#endif // !(defined(_LIBCPP_MSVCRT) && ((_VC_CRT_MAJOR_VERSION-0) < 14)) 441 442using ::nan; 443using ::nanf; 444 445#if !(defined(_LIBCPP_MSVCRT) && ((_VC_CRT_MAJOR_VERSION-0) < 14)) 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#endif // !(defined(_LIBCPP_MSVCRT) && ((_VC_CRT_MAJOR_VERSION-0) < 14)) 469 470using ::acosl; 471using ::asinl; 472using ::atanl; 473using ::atan2l; 474using ::ceill; 475using ::cosl; 476using ::coshl; 477using ::expl; 478using ::fabsl; 479using ::floorl; 480using ::fmodl; 481using ::frexpl; 482using ::ldexpl; 483using ::logl; 484using ::log10l; 485using ::modfl; 486using ::powl; 487using ::sinl; 488using ::sinhl; 489using ::sqrtl; 490using ::tanl; 491 492using ::tanhl; 493using ::acoshl; 494using ::asinhl; 495using ::atanhl; 496using ::cbrtl; 497 498using ::copysignl; 499 500#if !(defined(_LIBCPP_MSVCRT) && ((_VC_CRT_MAJOR_VERSION-0) < 14)) 501using ::erfl; 502using ::erfcl; 503using ::exp2l; 504using ::expm1l; 505using ::fdiml; 506using ::fmal; 507using ::fmaxl; 508using ::fminl; 509using ::hypotl; 510using ::ilogbl; 511using ::lgammal; 512using ::llrintl; 513using ::llroundl; 514using ::log1pl; 515using ::log2l; 516using ::logbl; 517using ::lrintl; 518using ::lroundl; 519using ::nanl; 520using ::nearbyintl; 521using ::nextafterl; 522using ::nexttowardl; 523using ::remainderl; 524using ::remquol; 525using ::rintl; 526using ::roundl; 527using ::scalblnl; 528using ::scalbnl; 529using ::tgammal; 530using ::truncl; 531#endif // !(defined(_LIBCPP_MSVCRT) && ((_VC_CRT_MAJOR_VERSION-0) < 14)) 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 __lazy_enable_if 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_ALWAYS_INLINE 559_LIBCPP_CONSTEXPR typename enable_if<is_floating_point<_A1>::value, bool>::type 560__libcpp_isnan(_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_ALWAYS_INLINE 571_LIBCPP_CONSTEXPR typename enable_if<!is_floating_point<_A1>::value, bool>::type 572__libcpp_isnan(_A1 __lcpp_x) _NOEXCEPT 573{ 574 return isnan(__lcpp_x); 575} 576 577template <class _A1> 578_LIBCPP_ALWAYS_INLINE 579_LIBCPP_CONSTEXPR typename enable_if<is_floating_point<_A1>::value, bool>::type 580__libcpp_isinf(_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_ALWAYS_INLINE 591_LIBCPP_CONSTEXPR typename enable_if<!is_floating_point<_A1>::value, bool>::type 592__libcpp_isinf(_A1 __lcpp_x) _NOEXCEPT 593{ 594 return isinf(__lcpp_x); 595} 596 597template <class _A1> 598_LIBCPP_ALWAYS_INLINE 599_LIBCPP_CONSTEXPR typename enable_if<is_floating_point<_A1>::value, bool>::type 600__libcpp_isfinite(_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_ALWAYS_INLINE 611_LIBCPP_CONSTEXPR typename enable_if<!is_floating_point<_A1>::value, bool>::type 612__libcpp_isfinite(_A1 __lcpp_x) _NOEXCEPT 613{ 614 return isfinite(__lcpp_x); 615} 616 617template <class _IntT, class _FloatT, 618 bool _FloatBigger = (numeric_limits<_FloatT>::digits > numeric_limits<_IntT>::digits), 619 int _Bits = (numeric_limits<_IntT>::digits - numeric_limits<_FloatT>::digits)> 620_LIBCPP_INLINE_VISIBILITY 621_LIBCPP_CONSTEXPR _IntT __max_representable_int_for_float() _NOEXCEPT { 622 static_assert(is_floating_point<_FloatT>::value, "must be a floating point type"); 623 static_assert(is_integral<_IntT>::value, "must be an integral type"); 624 static_assert(numeric_limits<_FloatT>::radix == 2, "FloatT has incorrect radix"); 625 static_assert(is_same<_FloatT, float>::value || is_same<_FloatT, double>::value 626 || is_same<_FloatT,long double>::value, "unsupported floating point type"); 627 return _FloatBigger ? numeric_limits<_IntT>::max() : (numeric_limits<_IntT>::max() >> _Bits << _Bits); 628} 629 630// Convert a floating point number to the specified integral type after 631// clamping to the integral types representable range. 632// 633// The behavior is undefined if `__r` is NaN. 634template <class _IntT, class _RealT> 635_LIBCPP_INLINE_VISIBILITY 636_IntT __clamp_to_integral(_RealT __r) _NOEXCEPT { 637 using _Lim = std::numeric_limits<_IntT>; 638 const _IntT _MaxVal = std::__max_representable_int_for_float<_IntT, _RealT>(); 639 if (__r >= ::nextafter(static_cast<_RealT>(_MaxVal), INFINITY)) { 640 return _Lim::max(); 641 } else if (__r <= _Lim::lowest()) { 642 return _Lim::min(); 643 } 644 return static_cast<_IntT>(__r); 645} 646 647_LIBCPP_END_NAMESPACE_STD 648 649#endif // _LIBCPP_CMATH 650