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 16 Macros: 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 37 namespace std 38 { 39 40 Types: 41 42 float_t // C99 43 double_t // C99 44 45 // C90 46 47 floating_point abs(floating_point x); 48 49 floating_point acos (arithmetic x); 50 float acosf(float x); 51 long double acosl(long double x); 52 53 floating_point asin (arithmetic x); 54 float asinf(float x); 55 long double asinl(long double x); 56 57 floating_point atan (arithmetic x); 58 float atanf(float x); 59 long double atanl(long double x); 60 61 floating_point atan2 (arithmetic y, arithmetic x); 62 float atan2f(float y, float x); 63 long double atan2l(long double y, long double x); 64 65 floating_point ceil (arithmetic x); 66 float ceilf(float x); 67 long double ceill(long double x); 68 69 floating_point cos (arithmetic x); 70 float cosf(float x); 71 long double cosl(long double x); 72 73 floating_point cosh (arithmetic x); 74 float coshf(float x); 75 long double coshl(long double x); 76 77 floating_point exp (arithmetic x); 78 float expf(float x); 79 long double expl(long double x); 80 81 floating_point fabs (arithmetic x); 82 float fabsf(float x); 83 long double fabsl(long double x); 84 85 floating_point floor (arithmetic x); 86 float floorf(float x); 87 long double floorl(long double x); 88 89 floating_point fmod (arithmetic x, arithmetic y); 90 float fmodf(float x, float y); 91 long double fmodl(long double x, long double y); 92 93 floating_point frexp (arithmetic value, int* exp); 94 float frexpf(float value, int* exp); 95 long double frexpl(long double value, int* exp); 96 97 floating_point ldexp (arithmetic value, int exp); 98 float ldexpf(float value, int exp); 99 long double ldexpl(long double value, int exp); 100 101 floating_point log (arithmetic x); 102 float logf(float x); 103 long double logl(long double x); 104 105 floating_point log10 (arithmetic x); 106 float log10f(float x); 107 long double log10l(long double x); 108 109 floating_point modf (floating_point value, floating_point* iptr); 110 float modff(float value, float* iptr); 111 long double modfl(long double value, long double* iptr); 112 113 floating_point pow (arithmetic x, arithmetic y); 114 float powf(float x, float y); 115 long double powl(long double x, long double y); 116 117 floating_point sin (arithmetic x); 118 float sinf(float x); 119 long double sinl(long double x); 120 121 floating_point sinh (arithmetic x); 122 float sinhf(float x); 123 long double sinhl(long double x); 124 125 floating_point sqrt (arithmetic x); 126 float sqrtf(float x); 127 long double sqrtl(long double x); 128 129 floating_point tan (arithmetic x); 130 float tanf(float x); 131 long double tanl(long double x); 132 133 floating_point tanh (arithmetic x); 134 float tanhf(float x); 135 long double tanhl(long double x); 136 137 // C99 138 139 bool signbit(arithmetic x); 140 141 int fpclassify(arithmetic x); 142 143 bool isfinite(arithmetic x); 144 bool isinf(arithmetic x); 145 bool isnan(arithmetic x); 146 bool isnormal(arithmetic x); 147 148 bool isgreater(arithmetic x, arithmetic y); 149 bool isgreaterequal(arithmetic x, arithmetic y); 150 bool isless(arithmetic x, arithmetic y); 151 bool islessequal(arithmetic x, arithmetic y); 152 bool islessgreater(arithmetic x, arithmetic y); 153 bool isunordered(arithmetic x, arithmetic y); 154 155 floating_point acosh (arithmetic x); 156 float acoshf(float x); 157 long double acoshl(long double x); 158 159 floating_point asinh (arithmetic x); 160 float asinhf(float x); 161 long double asinhl(long double x); 162 163 floating_point atanh (arithmetic x); 164 float atanhf(float x); 165 long double atanhl(long double x); 166 167 floating_point cbrt (arithmetic x); 168 float cbrtf(float x); 169 long double cbrtl(long double x); 170 171 floating_point copysign (arithmetic x, arithmetic y); 172 float copysignf(float x, float y); 173 long double copysignl(long double x, long double y); 174 175 floating_point erf (arithmetic x); 176 float erff(float x); 177 long double erfl(long double x); 178 179 floating_point erfc (arithmetic x); 180 float erfcf(float x); 181 long double erfcl(long double x); 182 183 floating_point exp2 (arithmetic x); 184 float exp2f(float x); 185 long double exp2l(long double x); 186 187 floating_point expm1 (arithmetic x); 188 float expm1f(float x); 189 long double expm1l(long double x); 190 191 floating_point fdim (arithmetic x, arithmetic y); 192 float fdimf(float x, float y); 193 long double fdiml(long double x, long double y); 194 195 floating_point fma (arithmetic x, arithmetic y, arithmetic z); 196 float fmaf(float x, float y, float z); 197 long double fmal(long double x, long double y, long double z); 198 199 floating_point fmax (arithmetic x, arithmetic y); 200 float fmaxf(float x, float y); 201 long double fmaxl(long double x, long double y); 202 203 floating_point fmin (arithmetic x, arithmetic y); 204 float fminf(float x, float y); 205 long double fminl(long double x, long double y); 206 207 floating_point hypot (arithmetic x, arithmetic y); 208 float hypotf(float x, float y); 209 long double hypotl(long double x, long double y); 210 211 double hypot(double x, double y, double z); // C++17 212 float hypot(float x, float y, float z); // C++17 213 long double hypot(long double x, long double y, long double z); // C++17 214 215 int ilogb (arithmetic x); 216 int ilogbf(float x); 217 int ilogbl(long double x); 218 219 floating_point lgamma (arithmetic x); 220 float lgammaf(float x); 221 long double lgammal(long double x); 222 223 long long llrint (arithmetic x); 224 long long llrintf(float x); 225 long long llrintl(long double x); 226 227 long long llround (arithmetic x); 228 long long llroundf(float x); 229 long long llroundl(long double x); 230 231 floating_point log1p (arithmetic x); 232 float log1pf(float x); 233 long double log1pl(long double x); 234 235 floating_point log2 (arithmetic x); 236 float log2f(float x); 237 long double log2l(long double x); 238 239 floating_point logb (arithmetic x); 240 float logbf(float x); 241 long double logbl(long double x); 242 243 long lrint (arithmetic x); 244 long lrintf(float x); 245 long lrintl(long double x); 246 247 long lround (arithmetic x); 248 long lroundf(float x); 249 long lroundl(long double x); 250 251 double nan (const char* str); 252 float nanf(const char* str); 253 long double nanl(const char* str); 254 255 floating_point nearbyint (arithmetic x); 256 float nearbyintf(float x); 257 long double nearbyintl(long double x); 258 259 floating_point nextafter (arithmetic x, arithmetic y); 260 float nextafterf(float x, float y); 261 long double nextafterl(long double x, long double y); 262 263 floating_point nexttoward (arithmetic x, long double y); 264 float nexttowardf(float x, long double y); 265 long double nexttowardl(long double x, long double y); 266 267 floating_point remainder (arithmetic x, arithmetic y); 268 float remainderf(float x, float y); 269 long double remainderl(long double x, long double y); 270 271 floating_point remquo (arithmetic x, arithmetic y, int* pquo); 272 float remquof(float x, float y, int* pquo); 273 long double remquol(long double x, long double y, int* pquo); 274 275 floating_point rint (arithmetic x); 276 float rintf(float x); 277 long double rintl(long double x); 278 279 floating_point round (arithmetic x); 280 float roundf(float x); 281 long double roundl(long double x); 282 283 floating_point scalbln (arithmetic x, long ex); 284 float scalblnf(float x, long ex); 285 long double scalblnl(long double x, long ex); 286 287 floating_point scalbn (arithmetic x, int ex); 288 float scalbnf(float x, int ex); 289 long double scalbnl(long double x, int ex); 290 291 floating_point tgamma (arithmetic x); 292 float tgammaf(float x); 293 long double tgammal(long double x); 294 295 floating_point trunc (arithmetic x); 296 float truncf(float x); 297 long double truncl(long double x); 298 299 constexpr float lerp(float a, float b, float t) noexcept; // C++20 300 constexpr double lerp(double a, double b, double t) noexcept; // C++20 301 constexpr 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 320 321 using ::signbit; 322 using ::fpclassify; 323 using ::isfinite; 324 using ::isinf; 325 using ::isnan; 326 using ::isnormal; 327 using ::isgreater; 328 using ::isgreaterequal; 329 using ::isless; 330 using ::islessequal; 331 using ::islessgreater; 332 using ::isunordered; 333 using ::isunordered; 334 335 using ::float_t; 336 using ::double_t; 337 338 using ::abs; 339 340 using ::acos; 341 using ::acosf; 342 using ::asin; 343 using ::asinf; 344 using ::atan; 345 using ::atanf; 346 using ::atan2; 347 using ::atan2f; 348 using ::ceil; 349 using ::ceilf; 350 using ::cos; 351 using ::cosf; 352 using ::cosh; 353 using ::coshf; 354 355 using ::exp; 356 using ::expf; 357 358 using ::fabs; 359 using ::fabsf; 360 using ::floor; 361 using ::floorf; 362 363 using ::fmod; 364 using ::fmodf; 365 366 using ::frexp; 367 using ::frexpf; 368 using ::ldexp; 369 using ::ldexpf; 370 371 using ::log; 372 using ::logf; 373 374 using ::log10; 375 using ::log10f; 376 using ::modf; 377 using ::modff; 378 379 using ::pow; 380 using ::powf; 381 382 using ::sin; 383 using ::sinf; 384 using ::sinh; 385 using ::sinhf; 386 387 using ::sqrt; 388 using ::sqrtf; 389 using ::tan; 390 using ::tanf; 391 392 using ::tanh; 393 using ::tanhf; 394 395 using ::acosh; 396 using ::acoshf; 397 using ::asinh; 398 using ::asinhf; 399 using ::atanh; 400 using ::atanhf; 401 using ::cbrt; 402 using ::cbrtf; 403 404 using ::copysign; 405 using ::copysignf; 406 407 using ::erf; 408 using ::erff; 409 using ::erfc; 410 using ::erfcf; 411 using ::exp2; 412 using ::exp2f; 413 using ::expm1; 414 using ::expm1f; 415 using ::fdim; 416 using ::fdimf; 417 using ::fmaf; 418 using ::fma; 419 using ::fmax; 420 using ::fmaxf; 421 using ::fmin; 422 using ::fminf; 423 using ::hypot; 424 using ::hypotf; 425 using ::ilogb; 426 using ::ilogbf; 427 using ::lgamma; 428 using ::lgammaf; 429 using ::llrint; 430 using ::llrintf; 431 using ::llround; 432 using ::llroundf; 433 using ::log1p; 434 using ::log1pf; 435 using ::log2; 436 using ::log2f; 437 using ::logb; 438 using ::logbf; 439 using ::lrint; 440 using ::lrintf; 441 using ::lround; 442 using ::lroundf; 443 444 using ::nan; 445 using ::nanf; 446 447 using ::nearbyint; 448 using ::nearbyintf; 449 using ::nextafter; 450 using ::nextafterf; 451 using ::nexttoward; 452 using ::nexttowardf; 453 using ::remainder; 454 using ::remainderf; 455 using ::remquo; 456 using ::remquof; 457 using ::rint; 458 using ::rintf; 459 using ::round; 460 using ::roundf; 461 using ::scalbln; 462 using ::scalblnf; 463 using ::scalbn; 464 using ::scalbnf; 465 using ::tgamma; 466 using ::tgammaf; 467 using ::trunc; 468 using ::truncf; 469 470 using ::acosl; 471 using ::asinl; 472 using ::atanl; 473 using ::atan2l; 474 using ::ceill; 475 using ::cosl; 476 using ::coshl; 477 using ::expl; 478 using ::fabsl; 479 using ::floorl; 480 using ::fmodl; 481 using ::frexpl; 482 using ::ldexpl; 483 using ::logl; 484 using ::log10l; 485 using ::modfl; 486 using ::powl; 487 using ::sinl; 488 using ::sinhl; 489 using ::sqrtl; 490 using ::tanl; 491 492 using ::tanhl; 493 using ::acoshl; 494 using ::asinhl; 495 using ::atanhl; 496 using ::cbrtl; 497 498 using ::copysignl; 499 500 using ::erfl; 501 using ::erfcl; 502 using ::exp2l; 503 using ::expm1l; 504 using ::fdiml; 505 using ::fmal; 506 using ::fmaxl; 507 using ::fminl; 508 using ::hypotl; 509 using ::ilogbl; 510 using ::lgammal; 511 using ::llrintl; 512 using ::llroundl; 513 using ::log1pl; 514 using ::log2l; 515 using ::logbl; 516 using ::lrintl; 517 using ::lroundl; 518 using ::nanl; 519 using ::nearbyintl; 520 using ::nextafterl; 521 using ::nexttowardl; 522 using ::remainderl; 523 using ::remquol; 524 using ::rintl; 525 using ::roundl; 526 using ::scalblnl; 527 using ::scalbnl; 528 using ::tgammal; 529 using ::truncl; 530 531 #if _LIBCPP_STD_VER > 14 532 inline _LIBCPP_INLINE_VISIBILITY float hypot( float x, float y, float z ) { return sqrt(x*x + y*y + z*z); } 533 inline _LIBCPP_INLINE_VISIBILITY double hypot( double x, double y, double z ) { return sqrt(x*x + y*y + z*z); } 534 inline _LIBCPP_INLINE_VISIBILITY long double hypot( long double x, long double y, long double z ) { return sqrt(x*x + y*y + z*z); } 535 536 template <class _A1, class _A2, class _A3> 537 inline _LIBCPP_INLINE_VISIBILITY 538 typename _EnableIf 539 < 540 is_arithmetic<_A1>::value && 541 is_arithmetic<_A2>::value && 542 is_arithmetic<_A3>::value, 543 __promote<_A1, _A2, _A3> 544 >::type 545 hypot(_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 554 555 template <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 } 566 567 template <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 } 574 575 template <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 } 586 587 template <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 } 594 595 template <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 } 606 607 template <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 > 17 616 template <typename _Fp> 617 constexpr 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 } 629 630 constexpr float 631 lerp(float __a, float __b, float __t) _NOEXCEPT { return __lerp(__a, __b, __t); } 632 633 constexpr double 634 lerp(double __a, double __b, double __t) _NOEXCEPT { return __lerp(__a, __b, __t); } 635 636 constexpr long double 637 lerp(long double __a, long double __b, long double __t) _NOEXCEPT { return __lerp(__a, __b, __t); } 638 639 #endif // _LIBCPP_STD_VER > 17 640 641 template <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. 658 template <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
Indexes created Mon Oct 26 00:26:21 UTC 2026