1// -*- C++ -*- 2//===----------------------------------------------------------------------===// 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_RATIO 11#define _LIBCPP_RATIO 12 13/* 14 ratio synopsis 15 16namespace std 17{ 18 19template <intmax_t N, intmax_t D = 1> 20class ratio 21{ 22public: 23 static constexpr intmax_t num; 24 static constexpr intmax_t den; 25 typedef ratio<num, den> type; 26}; 27 28// ratio arithmetic 29template <class R1, class R2> using ratio_add = ...; 30template <class R1, class R2> using ratio_subtract = ...; 31template <class R1, class R2> using ratio_multiply = ...; 32template <class R1, class R2> using ratio_divide = ...; 33 34// ratio comparison 35template <class R1, class R2> struct ratio_equal; 36template <class R1, class R2> struct ratio_not_equal; 37template <class R1, class R2> struct ratio_less; 38template <class R1, class R2> struct ratio_less_equal; 39template <class R1, class R2> struct ratio_greater; 40template <class R1, class R2> struct ratio_greater_equal; 41 42// convenience SI typedefs 43using quecto = ratio <1, 1'000'000'000'000'000'000'000'000'000'000>; // Since C++26; not supported 44using ronto = ratio <1, 1'000'000'000'000'000'000'000'000'000>; // Since C++26; not supported 45typedef ratio<1, 1000000000000000000000000> yocto; // not supported 46typedef ratio<1, 1000000000000000000000> zepto; // not supported 47typedef ratio<1, 1000000000000000000> atto; 48typedef ratio<1, 1000000000000000> femto; 49typedef ratio<1, 1000000000000> pico; 50typedef ratio<1, 1000000000> nano; 51typedef ratio<1, 1000000> micro; 52typedef ratio<1, 1000> milli; 53typedef ratio<1, 100> centi; 54typedef ratio<1, 10> deci; 55typedef ratio< 10, 1> deca; 56typedef ratio< 100, 1> hecto; 57typedef ratio< 1000, 1> kilo; 58typedef ratio< 1000000, 1> mega; 59typedef ratio< 1000000000, 1> giga; 60typedef ratio< 1000000000000, 1> tera; 61typedef ratio< 1000000000000000, 1> peta; 62typedef ratio< 1000000000000000000, 1> exa; 63typedef ratio< 1000000000000000000000, 1> zetta; // not supported 64typedef ratio<1000000000000000000000000, 1> yotta; // not supported 65using ronna = ratio <1'000'000'000'000'000'000'000'000'000, 1>; // Since C++26; not supported 66using quetta = ratio <1'000'000'000'000'000'000'000'000'000'000, 1>; // Since C++26; not supported 67 68 // 20.11.5, ratio comparison 69 template <class R1, class R2> inline constexpr bool ratio_equal_v 70 = ratio_equal<R1, R2>::value; // C++17 71 template <class R1, class R2> inline constexpr bool ratio_not_equal_v 72 = ratio_not_equal<R1, R2>::value; // C++17 73 template <class R1, class R2> inline constexpr bool ratio_less_v 74 = ratio_less<R1, R2>::value; // C++17 75 template <class R1, class R2> inline constexpr bool ratio_less_equal_v 76 = ratio_less_equal<R1, R2>::value; // C++17 77 template <class R1, class R2> inline constexpr bool ratio_greater_v 78 = ratio_greater<R1, R2>::value; // C++17 79 template <class R1, class R2> inline constexpr bool ratio_greater_equal_v 80 = ratio_greater_equal<R1, R2>::value; // C++17 81} 82*/ 83 84#include <__assert> // all public C++ headers provide the assertion handler 85#include <__config> 86#include <__type_traits/integral_constant.h> 87#include <climits> 88#include <cstdint> 89#include <version> 90 91#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER) 92# pragma GCC system_header 93#endif 94 95_LIBCPP_PUSH_MACROS 96#include <__undef_macros> 97 98 99_LIBCPP_BEGIN_NAMESPACE_STD 100 101// __static_gcd 102 103template <intmax_t _Xp, intmax_t _Yp> 104struct __static_gcd 105{ 106 static const intmax_t value = __static_gcd<_Yp, _Xp % _Yp>::value; 107}; 108 109template <intmax_t _Xp> 110struct __static_gcd<_Xp, 0> 111{ 112 static const intmax_t value = _Xp; 113}; 114 115template <> 116struct __static_gcd<0, 0> 117{ 118 static const intmax_t value = 1; 119}; 120 121// __static_lcm 122 123template <intmax_t _Xp, intmax_t _Yp> 124struct __static_lcm 125{ 126 static const intmax_t value = _Xp / __static_gcd<_Xp, _Yp>::value * _Yp; 127}; 128 129template <intmax_t _Xp> 130struct __static_abs 131{ 132 static const intmax_t value = _Xp < 0 ? -_Xp : _Xp; 133}; 134 135template <intmax_t _Xp> 136struct __static_sign 137{ 138 static const intmax_t value = _Xp == 0 ? 0 : (_Xp < 0 ? -1 : 1); 139}; 140 141template <intmax_t _Xp, intmax_t _Yp, intmax_t = __static_sign<_Yp>::value> 142class __ll_add; 143 144template <intmax_t _Xp, intmax_t _Yp> 145class __ll_add<_Xp, _Yp, 1> 146{ 147 static const intmax_t min = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)) + 1; 148 static const intmax_t max = -min; 149 150 static_assert(_Xp <= max - _Yp, "overflow in __ll_add"); 151public: 152 static const intmax_t value = _Xp + _Yp; 153}; 154 155template <intmax_t _Xp, intmax_t _Yp> 156class __ll_add<_Xp, _Yp, 0> 157{ 158public: 159 static const intmax_t value = _Xp; 160}; 161 162template <intmax_t _Xp, intmax_t _Yp> 163class __ll_add<_Xp, _Yp, -1> 164{ 165 static const intmax_t min = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)) + 1; 166 static const intmax_t max = -min; 167 168 static_assert(min - _Yp <= _Xp, "overflow in __ll_add"); 169public: 170 static const intmax_t value = _Xp + _Yp; 171}; 172 173template <intmax_t _Xp, intmax_t _Yp, intmax_t = __static_sign<_Yp>::value> 174class __ll_sub; 175 176template <intmax_t _Xp, intmax_t _Yp> 177class __ll_sub<_Xp, _Yp, 1> 178{ 179 static const intmax_t min = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)) + 1; 180 static const intmax_t max = -min; 181 182 static_assert(min + _Yp <= _Xp, "overflow in __ll_sub"); 183public: 184 static const intmax_t value = _Xp - _Yp; 185}; 186 187template <intmax_t _Xp, intmax_t _Yp> 188class __ll_sub<_Xp, _Yp, 0> 189{ 190public: 191 static const intmax_t value = _Xp; 192}; 193 194template <intmax_t _Xp, intmax_t _Yp> 195class __ll_sub<_Xp, _Yp, -1> 196{ 197 static const intmax_t min = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)) + 1; 198 static const intmax_t max = -min; 199 200 static_assert(_Xp <= max + _Yp, "overflow in __ll_sub"); 201public: 202 static const intmax_t value = _Xp - _Yp; 203}; 204 205template <intmax_t _Xp, intmax_t _Yp> 206class __ll_mul 207{ 208 static const intmax_t nan = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)); 209 static const intmax_t min = nan + 1; 210 static const intmax_t max = -min; 211 static const intmax_t __a_x = __static_abs<_Xp>::value; 212 static const intmax_t __a_y = __static_abs<_Yp>::value; 213 214 static_assert(_Xp != nan && _Yp != nan && __a_x <= max / __a_y, "overflow in __ll_mul"); 215public: 216 static const intmax_t value = _Xp * _Yp; 217}; 218 219template <intmax_t _Yp> 220class __ll_mul<0, _Yp> 221{ 222public: 223 static const intmax_t value = 0; 224}; 225 226template <intmax_t _Xp> 227class __ll_mul<_Xp, 0> 228{ 229public: 230 static const intmax_t value = 0; 231}; 232 233template <> 234class __ll_mul<0, 0> 235{ 236public: 237 static const intmax_t value = 0; 238}; 239 240// Not actually used but left here in case needed in future maintenance 241template <intmax_t _Xp, intmax_t _Yp> 242class __ll_div 243{ 244 static const intmax_t nan = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)); 245 static const intmax_t min = nan + 1; 246 static const intmax_t max = -min; 247 248 static_assert(_Xp != nan && _Yp != nan && _Yp != 0, "overflow in __ll_div"); 249public: 250 static const intmax_t value = _Xp / _Yp; 251}; 252 253template <intmax_t _Num, intmax_t _Den = 1> 254class _LIBCPP_TEMPLATE_VIS ratio 255{ 256 static_assert(__static_abs<_Num>::value >= 0, "ratio numerator is out of range"); 257 static_assert(_Den != 0, "ratio divide by 0"); 258 static_assert(__static_abs<_Den>::value > 0, "ratio denominator is out of range"); 259 static _LIBCPP_CONSTEXPR const intmax_t __na = __static_abs<_Num>::value; 260 static _LIBCPP_CONSTEXPR const intmax_t __da = __static_abs<_Den>::value; 261 static _LIBCPP_CONSTEXPR const intmax_t __s = __static_sign<_Num>::value * __static_sign<_Den>::value; 262 static _LIBCPP_CONSTEXPR const intmax_t __gcd = __static_gcd<__na, __da>::value; 263public: 264 static _LIBCPP_CONSTEXPR const intmax_t num = __s * __na / __gcd; 265 static _LIBCPP_CONSTEXPR const intmax_t den = __da / __gcd; 266 267 typedef ratio<num, den> type; 268}; 269 270template <intmax_t _Num, intmax_t _Den> 271_LIBCPP_CONSTEXPR const intmax_t ratio<_Num, _Den>::num; 272 273template <intmax_t _Num, intmax_t _Den> 274_LIBCPP_CONSTEXPR const intmax_t ratio<_Num, _Den>::den; 275 276template <class _Tp> struct __is_ratio : false_type {}; 277template <intmax_t _Num, intmax_t _Den> struct __is_ratio<ratio<_Num, _Den> > : true_type {}; 278 279typedef ratio<1LL, 1000000000000000000LL> atto; 280typedef ratio<1LL, 1000000000000000LL> femto; 281typedef ratio<1LL, 1000000000000LL> pico; 282typedef ratio<1LL, 1000000000LL> nano; 283typedef ratio<1LL, 1000000LL> micro; 284typedef ratio<1LL, 1000LL> milli; 285typedef ratio<1LL, 100LL> centi; 286typedef ratio<1LL, 10LL> deci; 287typedef ratio< 10LL, 1LL> deca; 288typedef ratio< 100LL, 1LL> hecto; 289typedef ratio< 1000LL, 1LL> kilo; 290typedef ratio< 1000000LL, 1LL> mega; 291typedef ratio< 1000000000LL, 1LL> giga; 292typedef ratio< 1000000000000LL, 1LL> tera; 293typedef ratio< 1000000000000000LL, 1LL> peta; 294typedef ratio<1000000000000000000LL, 1LL> exa; 295 296template <class _R1, class _R2> 297struct __ratio_multiply 298{ 299private: 300 static const intmax_t __gcd_n1_d2 = __static_gcd<_R1::num, _R2::den>::value; 301 static const intmax_t __gcd_d1_n2 = __static_gcd<_R1::den, _R2::num>::value; 302public: 303 typedef typename ratio 304 < 305 __ll_mul<_R1::num / __gcd_n1_d2, _R2::num / __gcd_d1_n2>::value, 306 __ll_mul<_R2::den / __gcd_n1_d2, _R1::den / __gcd_d1_n2>::value 307 >::type type; 308}; 309 310#ifndef _LIBCPP_CXX03_LANG 311 312template <class _R1, class _R2> using ratio_multiply 313 = typename __ratio_multiply<_R1, _R2>::type; 314 315#else // _LIBCPP_CXX03_LANG 316 317template <class _R1, class _R2> 318struct _LIBCPP_TEMPLATE_VIS ratio_multiply 319 : public __ratio_multiply<_R1, _R2>::type {}; 320 321#endif // _LIBCPP_CXX03_LANG 322 323template <class _R1, class _R2> 324struct __ratio_divide 325{ 326private: 327 static const intmax_t __gcd_n1_n2 = __static_gcd<_R1::num, _R2::num>::value; 328 static const intmax_t __gcd_d1_d2 = __static_gcd<_R1::den, _R2::den>::value; 329public: 330 typedef typename ratio 331 < 332 __ll_mul<_R1::num / __gcd_n1_n2, _R2::den / __gcd_d1_d2>::value, 333 __ll_mul<_R2::num / __gcd_n1_n2, _R1::den / __gcd_d1_d2>::value 334 >::type type; 335}; 336 337#ifndef _LIBCPP_CXX03_LANG 338 339template <class _R1, class _R2> using ratio_divide 340 = typename __ratio_divide<_R1, _R2>::type; 341 342#else // _LIBCPP_CXX03_LANG 343 344template <class _R1, class _R2> 345struct _LIBCPP_TEMPLATE_VIS ratio_divide 346 : public __ratio_divide<_R1, _R2>::type {}; 347 348#endif // _LIBCPP_CXX03_LANG 349 350template <class _R1, class _R2> 351struct __ratio_add 352{ 353private: 354 static const intmax_t __gcd_n1_n2 = __static_gcd<_R1::num, _R2::num>::value; 355 static const intmax_t __gcd_d1_d2 = __static_gcd<_R1::den, _R2::den>::value; 356public: 357 typedef typename ratio_multiply 358 < 359 ratio<__gcd_n1_n2, _R1::den / __gcd_d1_d2>, 360 ratio 361 < 362 __ll_add 363 < 364 __ll_mul<_R1::num / __gcd_n1_n2, _R2::den / __gcd_d1_d2>::value, 365 __ll_mul<_R2::num / __gcd_n1_n2, _R1::den / __gcd_d1_d2>::value 366 >::value, 367 _R2::den 368 > 369 >::type type; 370}; 371 372#ifndef _LIBCPP_CXX03_LANG 373 374template <class _R1, class _R2> using ratio_add 375 = typename __ratio_add<_R1, _R2>::type; 376 377#else // _LIBCPP_CXX03_LANG 378 379template <class _R1, class _R2> 380struct _LIBCPP_TEMPLATE_VIS ratio_add 381 : public __ratio_add<_R1, _R2>::type {}; 382 383#endif // _LIBCPP_CXX03_LANG 384 385template <class _R1, class _R2> 386struct __ratio_subtract 387{ 388private: 389 static const intmax_t __gcd_n1_n2 = __static_gcd<_R1::num, _R2::num>::value; 390 static const intmax_t __gcd_d1_d2 = __static_gcd<_R1::den, _R2::den>::value; 391public: 392 typedef typename ratio_multiply 393 < 394 ratio<__gcd_n1_n2, _R1::den / __gcd_d1_d2>, 395 ratio 396 < 397 __ll_sub 398 < 399 __ll_mul<_R1::num / __gcd_n1_n2, _R2::den / __gcd_d1_d2>::value, 400 __ll_mul<_R2::num / __gcd_n1_n2, _R1::den / __gcd_d1_d2>::value 401 >::value, 402 _R2::den 403 > 404 >::type type; 405}; 406 407#ifndef _LIBCPP_CXX03_LANG 408 409template <class _R1, class _R2> using ratio_subtract 410 = typename __ratio_subtract<_R1, _R2>::type; 411 412#else // _LIBCPP_CXX03_LANG 413 414template <class _R1, class _R2> 415struct _LIBCPP_TEMPLATE_VIS ratio_subtract 416 : public __ratio_subtract<_R1, _R2>::type {}; 417 418#endif // _LIBCPP_CXX03_LANG 419 420// ratio_equal 421 422template <class _R1, class _R2> 423struct _LIBCPP_TEMPLATE_VIS ratio_equal 424 : _BoolConstant<(_R1::num == _R2::num && _R1::den == _R2::den)> {}; 425 426template <class _R1, class _R2> 427struct _LIBCPP_TEMPLATE_VIS ratio_not_equal 428 : _BoolConstant<!ratio_equal<_R1, _R2>::value> {}; 429 430// ratio_less 431 432template <class _R1, class _R2, bool _Odd = false, 433 intmax_t _Q1 = _R1::num / _R1::den, intmax_t _M1 = _R1::num % _R1::den, 434 intmax_t _Q2 = _R2::num / _R2::den, intmax_t _M2 = _R2::num % _R2::den> 435struct __ratio_less1 436{ 437 static const bool value = _Odd ? _Q2 < _Q1 : _Q1 < _Q2; 438}; 439 440template <class _R1, class _R2, bool _Odd, intmax_t _Qp> 441struct __ratio_less1<_R1, _R2, _Odd, _Qp, 0, _Qp, 0> 442{ 443 static const bool value = false; 444}; 445 446template <class _R1, class _R2, bool _Odd, intmax_t _Qp, intmax_t _M2> 447struct __ratio_less1<_R1, _R2, _Odd, _Qp, 0, _Qp, _M2> 448{ 449 static const bool value = !_Odd; 450}; 451 452template <class _R1, class _R2, bool _Odd, intmax_t _Qp, intmax_t _M1> 453struct __ratio_less1<_R1, _R2, _Odd, _Qp, _M1, _Qp, 0> 454{ 455 static const bool value = _Odd; 456}; 457 458template <class _R1, class _R2, bool _Odd, intmax_t _Qp, intmax_t _M1, 459 intmax_t _M2> 460struct __ratio_less1<_R1, _R2, _Odd, _Qp, _M1, _Qp, _M2> 461{ 462 static const bool value = __ratio_less1<ratio<_R1::den, _M1>, 463 ratio<_R2::den, _M2>, !_Odd>::value; 464}; 465 466template <class _R1, class _R2, intmax_t _S1 = __static_sign<_R1::num>::value, 467 intmax_t _S2 = __static_sign<_R2::num>::value> 468struct __ratio_less 469{ 470 static const bool value = _S1 < _S2; 471}; 472 473template <class _R1, class _R2> 474struct __ratio_less<_R1, _R2, 1LL, 1LL> 475{ 476 static const bool value = __ratio_less1<_R1, _R2>::value; 477}; 478 479template <class _R1, class _R2> 480struct __ratio_less<_R1, _R2, -1LL, -1LL> 481{ 482 static const bool value = __ratio_less1<ratio<-_R2::num, _R2::den>, ratio<-_R1::num, _R1::den> >::value; 483}; 484 485template <class _R1, class _R2> 486struct _LIBCPP_TEMPLATE_VIS ratio_less 487 : _BoolConstant<__ratio_less<_R1, _R2>::value> {}; 488 489template <class _R1, class _R2> 490struct _LIBCPP_TEMPLATE_VIS ratio_less_equal 491 : _BoolConstant<!ratio_less<_R2, _R1>::value> {}; 492 493template <class _R1, class _R2> 494struct _LIBCPP_TEMPLATE_VIS ratio_greater 495 : _BoolConstant<ratio_less<_R2, _R1>::value> {}; 496 497template <class _R1, class _R2> 498struct _LIBCPP_TEMPLATE_VIS ratio_greater_equal 499 : _BoolConstant<!ratio_less<_R1, _R2>::value> {}; 500 501template <class _R1, class _R2> 502struct __ratio_gcd 503{ 504 typedef ratio<__static_gcd<_R1::num, _R2::num>::value, 505 __static_lcm<_R1::den, _R2::den>::value> type; 506}; 507 508#if _LIBCPP_STD_VER >= 17 509template <class _R1, class _R2> 510inline constexpr bool ratio_equal_v = ratio_equal<_R1, _R2>::value; 511 512template <class _R1, class _R2> 513inline constexpr bool ratio_not_equal_v = ratio_not_equal<_R1, _R2>::value; 514 515template <class _R1, class _R2> 516inline constexpr bool ratio_less_v = ratio_less<_R1, _R2>::value; 517 518template <class _R1, class _R2> 519inline constexpr bool ratio_less_equal_v = ratio_less_equal<_R1, _R2>::value; 520 521template <class _R1, class _R2> 522inline constexpr bool ratio_greater_v = ratio_greater<_R1, _R2>::value; 523 524template <class _R1, class _R2> 525inline constexpr bool ratio_greater_equal_v = ratio_greater_equal<_R1, _R2>::value; 526#endif 527 528_LIBCPP_END_NAMESPACE_STD 529 530_LIBCPP_POP_MACROS 531 532#if !defined(_LIBCPP_REMOVE_TRANSITIVE_INCLUDES) && _LIBCPP_STD_VER <= 20 533# include <type_traits> 534#endif 535 536#endif // _LIBCPP_RATIO 537