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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-exception7//8//===----------------------------------------------------------------------===//9 10#ifndef _LIBCPP_RATIO11#define _LIBCPP_RATIO12 13/*14 ratio synopsis15 16namespace std17{18 19template <intmax_t N, intmax_t D = 1>20class ratio21{22public:23 static constexpr intmax_t num;24 static constexpr intmax_t den;25 typedef ratio<num, den> type;26};27 28// ratio arithmetic29template <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 comparison35template <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 typedefs43using quecto = ratio <1, 1'000'000'000'000'000'000'000'000'000'000>; // Since C++26; not supported44using ronto = ratio <1, 1'000'000'000'000'000'000'000'000'000>; // Since C++26; not supported45typedef ratio<1, 1000000000000000000000000> yocto; // not supported46typedef ratio<1, 1000000000000000000000> zepto; // not supported47typedef 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 supported64typedef ratio<1000000000000000000000000, 1> yotta; // not supported65using ronna = ratio <1'000'000'000'000'000'000'000'000'000, 1>; // Since C++26; not supported66using quetta = ratio <1'000'000'000'000'000'000'000'000'000'000, 1>; // Since C++26; not supported67 68 // 20.11.5, ratio comparison69 template <class R1, class R2> inline constexpr bool ratio_equal_v70 = ratio_equal<R1, R2>::value; // C++1771 template <class R1, class R2> inline constexpr bool ratio_not_equal_v72 = ratio_not_equal<R1, R2>::value; // C++1773 template <class R1, class R2> inline constexpr bool ratio_less_v74 = ratio_less<R1, R2>::value; // C++1775 template <class R1, class R2> inline constexpr bool ratio_less_equal_v76 = ratio_less_equal<R1, R2>::value; // C++1777 template <class R1, class R2> inline constexpr bool ratio_greater_v78 = ratio_greater<R1, R2>::value; // C++1779 template <class R1, class R2> inline constexpr bool ratio_greater_equal_v80 = ratio_greater_equal<R1, R2>::value; // C++1781}82*/83 84#if __cplusplus < 201103L && defined(_LIBCPP_USE_FROZEN_CXX03_HEADERS)85# include <__cxx03/ratio>86#else87# include <__config>88# include <__type_traits/integral_constant.h>89# include <climits>90# include <cstdint>91# include <version>92 93# if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)94# pragma GCC system_header95# endif96 97_LIBCPP_PUSH_MACROS98# include <__undef_macros>99 100_LIBCPP_BEGIN_NAMESPACE_STD101 102// __static_gcd103 104template <intmax_t _Xp, intmax_t _Yp>105inline const intmax_t __static_gcd = __static_gcd<_Yp, _Xp % _Yp>;106 107template <intmax_t _Xp>108inline const intmax_t __static_gcd<_Xp, 0> = _Xp;109 110template <>111inline const intmax_t __static_gcd<0, 0> = 1;112 113// __static_lcm114 115template <intmax_t _Xp, intmax_t _Yp>116inline const intmax_t __static_lcm = _Xp / __static_gcd<_Xp, _Yp> * _Yp;117 118template <intmax_t _Xp>119inline const intmax_t __static_abs = _Xp < 0 ? -_Xp : _Xp;120 121template <intmax_t _Xp>122inline const intmax_t __static_sign = _Xp == 0 ? 0 : (_Xp < 0 ? -1 : 1);123 124template <intmax_t _Xp, intmax_t _Yp, intmax_t = __static_sign<_Yp> >125class __ll_add;126 127template <intmax_t _Xp, intmax_t _Yp>128class __ll_add<_Xp, _Yp, 1> {129 static const intmax_t min = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)) + 1;130 static const intmax_t max = -min;131 132 static_assert(_Xp <= max - _Yp, "overflow in __ll_add");133 134public:135 static const intmax_t value = _Xp + _Yp;136};137 138template <intmax_t _Xp, intmax_t _Yp>139class __ll_add<_Xp, _Yp, 0> {140public:141 static const intmax_t value = _Xp;142};143 144template <intmax_t _Xp, intmax_t _Yp>145class __ll_add<_Xp, _Yp, -1> {146 static const intmax_t min = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)) + 1;147 static const intmax_t max = -min;148 149 static_assert(min - _Yp <= _Xp, "overflow in __ll_add");150 151public:152 static const intmax_t value = _Xp + _Yp;153};154 155template <intmax_t _Xp, intmax_t _Yp, intmax_t = __static_sign<_Yp> >156class __ll_sub;157 158template <intmax_t _Xp, intmax_t _Yp>159class __ll_sub<_Xp, _Yp, 1> {160 static const intmax_t min = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)) + 1;161 static const intmax_t max = -min;162 163 static_assert(min + _Yp <= _Xp, "overflow in __ll_sub");164 165public:166 static const intmax_t value = _Xp - _Yp;167};168 169template <intmax_t _Xp, intmax_t _Yp>170class __ll_sub<_Xp, _Yp, 0> {171public:172 static const intmax_t value = _Xp;173};174 175template <intmax_t _Xp, intmax_t _Yp>176class __ll_sub<_Xp, _Yp, -1> {177 static const intmax_t min = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)) + 1;178 static const intmax_t max = -min;179 180 static_assert(_Xp <= max + _Yp, "overflow in __ll_sub");181 182public:183 static const intmax_t value = _Xp - _Yp;184};185 186template <intmax_t _Xp, intmax_t _Yp>187class __ll_mul {188 static const intmax_t nan = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1));189 static const intmax_t min = nan + 1;190 static const intmax_t max = -min;191 static const intmax_t __a_x = __static_abs<_Xp>;192 static const intmax_t __a_y = __static_abs<_Yp>;193 194 static_assert(_Xp != nan && _Yp != nan && __a_x <= max / __a_y, "overflow in __ll_mul");195 196public:197 static const intmax_t value = _Xp * _Yp;198};199 200template <intmax_t _Yp>201class __ll_mul<0, _Yp> {202public:203 static const intmax_t value = 0;204};205 206template <intmax_t _Xp>207class __ll_mul<_Xp, 0> {208public:209 static const intmax_t value = 0;210};211 212template <>213class __ll_mul<0, 0> {214public:215 static const intmax_t value = 0;216};217 218// Not actually used but left here in case needed in future maintenance219template <intmax_t _Xp, intmax_t _Yp>220class __ll_div {221 static const intmax_t nan = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1));222 static const intmax_t min = nan + 1;223 static const intmax_t max = -min;224 225 static_assert(_Xp != nan && _Yp != nan && _Yp != 0, "overflow in __ll_div");226 227public:228 static const intmax_t value = _Xp / _Yp;229};230 231template <intmax_t _Num, intmax_t _Den = 1>232class ratio {233 static_assert(__static_abs<_Num> >= 0, "ratio numerator is out of range");234 static_assert(_Den != 0, "ratio divide by 0");235 static_assert(__static_abs<_Den> > 0, "ratio denominator is out of range");236 static _LIBCPP_CONSTEXPR const intmax_t __na = __static_abs<_Num>;237 static _LIBCPP_CONSTEXPR const intmax_t __da = __static_abs<_Den>;238 static _LIBCPP_CONSTEXPR const intmax_t __s = __static_sign<_Num> * __static_sign<_Den>;239 static _LIBCPP_CONSTEXPR const intmax_t __gcd = __static_gcd<__na, __da>;240 241public:242 static inline _LIBCPP_CONSTEXPR const intmax_t num = __s * __na / __gcd;243 static inline _LIBCPP_CONSTEXPR const intmax_t den = __da / __gcd;244 245 typedef ratio<num, den> type;246};247 248template <class _Tp>249inline const bool __is_ratio_v = false;250 251template <intmax_t _Num, intmax_t _Den>252inline const bool __is_ratio_v<ratio<_Num, _Den> > = true;253 254typedef ratio<1LL, 1000000000000000000LL> atto;255typedef ratio<1LL, 1000000000000000LL> femto;256typedef ratio<1LL, 1000000000000LL> pico;257typedef ratio<1LL, 1000000000LL> nano;258typedef ratio<1LL, 1000000LL> micro;259typedef ratio<1LL, 1000LL> milli;260typedef ratio<1LL, 100LL> centi;261typedef ratio<1LL, 10LL> deci;262typedef ratio< 10LL, 1LL> deca;263typedef ratio< 100LL, 1LL> hecto;264typedef ratio< 1000LL, 1LL> kilo;265typedef ratio< 1000000LL, 1LL> mega;266typedef ratio< 1000000000LL, 1LL> giga;267typedef ratio< 1000000000000LL, 1LL> tera;268typedef ratio< 1000000000000000LL, 1LL> peta;269typedef ratio<1000000000000000000LL, 1LL> exa;270 271template <class _R1, class _R2>272struct __ratio_multiply {273private:274 static const intmax_t __gcd_n1_d2 = __static_gcd<_R1::num, _R2::den>;275 static const intmax_t __gcd_d1_n2 = __static_gcd<_R1::den, _R2::num>;276 277 static_assert(__is_ratio_v<_R1>, "[ratio.general]/2 requires R1 to be a specialisation of the ratio template");278 static_assert(__is_ratio_v<_R2>, "[ratio.general]/2 requires R2 to be a specialisation of the ratio template");279 280public:281 typedef typename ratio< __ll_mul<_R1::num / __gcd_n1_d2, _R2::num / __gcd_d1_n2>::value,282 __ll_mul<_R2::den / __gcd_n1_d2, _R1::den / __gcd_d1_n2>::value >::type type;283};284 285# ifndef _LIBCPP_CXX03_LANG286 287template <class _R1, class _R2>288using ratio_multiply = typename __ratio_multiply<_R1, _R2>::type;289 290# else // _LIBCPP_CXX03_LANG291 292template <class _R1, class _R2>293struct ratio_multiply : public __ratio_multiply<_R1, _R2>::type {};294 295# endif // _LIBCPP_CXX03_LANG296 297template <class _R1, class _R2>298struct __ratio_divide {299private:300 static const intmax_t __gcd_n1_n2 = __static_gcd<_R1::num, _R2::num>;301 static const intmax_t __gcd_d1_d2 = __static_gcd<_R1::den, _R2::den>;302 303 static_assert(__is_ratio_v<_R1>, "[ratio.general]/2 requires R1 to be a specialisation of the ratio template");304 static_assert(__is_ratio_v<_R2>, "[ratio.general]/2 requires R2 to be a specialisation of the ratio template");305 306public:307 typedef typename ratio< __ll_mul<_R1::num / __gcd_n1_n2, _R2::den / __gcd_d1_d2>::value,308 __ll_mul<_R2::num / __gcd_n1_n2, _R1::den / __gcd_d1_d2>::value >::type type;309};310 311# ifndef _LIBCPP_CXX03_LANG312 313template <class _R1, class _R2>314using ratio_divide = typename __ratio_divide<_R1, _R2>::type;315 316# else // _LIBCPP_CXX03_LANG317 318template <class _R1, class _R2>319struct ratio_divide : public __ratio_divide<_R1, _R2>::type {};320 321# endif // _LIBCPP_CXX03_LANG322 323template <class _R1, class _R2>324struct __ratio_add {325private:326 static const intmax_t __gcd_n1_n2 = __static_gcd<_R1::num, _R2::num>;327 static const intmax_t __gcd_d1_d2 = __static_gcd<_R1::den, _R2::den>;328 329 static_assert(__is_ratio_v<_R1>, "[ratio.general]/2 requires R1 to be a specialisation of the ratio template");330 static_assert(__is_ratio_v<_R2>, "[ratio.general]/2 requires R2 to be a specialisation of the ratio template");331 332public:333 typedef typename ratio_multiply<334 ratio<__gcd_n1_n2, _R1::den / __gcd_d1_d2>,335 ratio< __ll_add< __ll_mul<_R1::num / __gcd_n1_n2, _R2::den / __gcd_d1_d2>::value,336 __ll_mul<_R2::num / __gcd_n1_n2, _R1::den / __gcd_d1_d2>::value >::value,337 _R2::den > >::type type;338};339 340# ifndef _LIBCPP_CXX03_LANG341 342template <class _R1, class _R2>343using ratio_add = typename __ratio_add<_R1, _R2>::type;344 345# else // _LIBCPP_CXX03_LANG346 347template <class _R1, class _R2>348struct ratio_add : public __ratio_add<_R1, _R2>::type {};349 350# endif // _LIBCPP_CXX03_LANG351 352template <class _R1, class _R2>353struct __ratio_subtract {354private:355 static const intmax_t __gcd_n1_n2 = __static_gcd<_R1::num, _R2::num>;356 static const intmax_t __gcd_d1_d2 = __static_gcd<_R1::den, _R2::den>;357 358 static_assert(__is_ratio_v<_R1>, "[ratio.general]/2 requires R1 to be a specialisation of the ratio template");359 static_assert(__is_ratio_v<_R2>, "[ratio.general]/2 requires R2 to be a specialisation of the ratio template");360 361public:362 typedef typename ratio_multiply<363 ratio<__gcd_n1_n2, _R1::den / __gcd_d1_d2>,364 ratio< __ll_sub< __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 >::value,366 _R2::den > >::type type;367};368 369# ifndef _LIBCPP_CXX03_LANG370 371template <class _R1, class _R2>372using ratio_subtract = typename __ratio_subtract<_R1, _R2>::type;373 374# else // _LIBCPP_CXX03_LANG375 376template <class _R1, class _R2>377struct ratio_subtract : public __ratio_subtract<_R1, _R2>::type {};378 379# endif // _LIBCPP_CXX03_LANG380 381// ratio_equal382 383template <class _R1, class _R2>384struct ratio_equal : _BoolConstant<(_R1::num == _R2::num && _R1::den == _R2::den)> {385 static_assert(__is_ratio_v<_R1>, "[ratio.general]/2 requires R1 to be a specialisation of the ratio template");386 static_assert(__is_ratio_v<_R2>, "[ratio.general]/2 requires R2 to be a specialisation of the ratio template");387};388 389template <class _R1, class _R2>390struct ratio_not_equal : _BoolConstant<!ratio_equal<_R1, _R2>::value> {391 static_assert(__is_ratio_v<_R1>, "[ratio.general]/2 requires R1 to be a specialisation of the ratio template");392 static_assert(__is_ratio_v<_R2>, "[ratio.general]/2 requires R2 to be a specialisation of the ratio template");393};394 395// ratio_less396 397template <class _R1,398 class _R2,399 bool _Odd = false,400 intmax_t _Q1 = _R1::num / _R1::den,401 intmax_t _M1 = _R1::num % _R1::den,402 intmax_t _Q2 = _R2::num / _R2::den,403 intmax_t _M2 = _R2::num % _R2::den>404struct __ratio_less1 {405 static const bool value = _Odd ? _Q2 < _Q1 : _Q1 < _Q2;406};407 408template <class _R1, class _R2, bool _Odd, intmax_t _Qp>409struct __ratio_less1<_R1, _R2, _Odd, _Qp, 0, _Qp, 0> {410 static const bool value = false;411};412 413template <class _R1, class _R2, bool _Odd, intmax_t _Qp, intmax_t _M2>414struct __ratio_less1<_R1, _R2, _Odd, _Qp, 0, _Qp, _M2> {415 static const bool value = !_Odd;416};417 418template <class _R1, class _R2, bool _Odd, intmax_t _Qp, intmax_t _M1>419struct __ratio_less1<_R1, _R2, _Odd, _Qp, _M1, _Qp, 0> {420 static const bool value = _Odd;421};422 423template <class _R1, class _R2, bool _Odd, intmax_t _Qp, intmax_t _M1, intmax_t _M2>424struct __ratio_less1<_R1, _R2, _Odd, _Qp, _M1, _Qp, _M2> {425 static const bool value = __ratio_less1<ratio<_R1::den, _M1>, ratio<_R2::den, _M2>, !_Odd>::value;426};427 428template <class _R1, class _R2, intmax_t _S1 = __static_sign<_R1::num>, intmax_t _S2 = __static_sign<_R2::num> >429struct __ratio_less {430 static const bool value = _S1 < _S2;431};432 433template <class _R1, class _R2>434struct __ratio_less<_R1, _R2, 1LL, 1LL> {435 static const bool value = __ratio_less1<_R1, _R2>::value;436};437 438template <class _R1, class _R2>439struct __ratio_less<_R1, _R2, -1LL, -1LL> {440 static const bool value = __ratio_less1<ratio<-_R2::num, _R2::den>, ratio<-_R1::num, _R1::den> >::value;441};442 443template <class _R1, class _R2>444struct ratio_less : _BoolConstant<__ratio_less<_R1, _R2>::value> {445 static_assert(__is_ratio_v<_R1>, "[ratio.general]/2 requires R1 to be a specialisation of the ratio template");446 static_assert(__is_ratio_v<_R2>, "[ratio.general]/2 requires R2 to be a specialisation of the ratio template");447};448 449template <class _R1, class _R2>450struct ratio_less_equal : _BoolConstant<!ratio_less<_R2, _R1>::value> {451 static_assert(__is_ratio_v<_R1>, "[ratio.general]/2 requires R1 to be a specialisation of the ratio template");452 static_assert(__is_ratio_v<_R2>, "[ratio.general]/2 requires R2 to be a specialisation of the ratio template");453};454 455template <class _R1, class _R2>456struct ratio_greater : _BoolConstant<ratio_less<_R2, _R1>::value> {457 static_assert(__is_ratio_v<_R1>, "[ratio.general]/2 requires R1 to be a specialisation of the ratio template");458 static_assert(__is_ratio_v<_R2>, "[ratio.general]/2 requires R2 to be a specialisation of the ratio template");459};460 461template <class _R1, class _R2>462struct ratio_greater_equal : _BoolConstant<!ratio_less<_R1, _R2>::value> {463 static_assert(__is_ratio_v<_R1>, "[ratio.general]/2 requires R1 to be a specialisation of the ratio template");464 static_assert(__is_ratio_v<_R2>, "[ratio.general]/2 requires R2 to be a specialisation of the ratio template");465};466 467template <class _R1, class _R2>468using __ratio_gcd _LIBCPP_NODEBUG = ratio<__static_gcd<_R1::num, _R2::num>, __static_lcm<_R1::den, _R2::den> >;469 470# if _LIBCPP_STD_VER >= 17471template <class _R1, class _R2>472inline constexpr bool ratio_equal_v = ratio_equal<_R1, _R2>::value;473 474template <class _R1, class _R2>475inline constexpr bool ratio_not_equal_v = ratio_not_equal<_R1, _R2>::value;476 477template <class _R1, class _R2>478inline constexpr bool ratio_less_v = ratio_less<_R1, _R2>::value;479 480template <class _R1, class _R2>481inline constexpr bool ratio_less_equal_v = ratio_less_equal<_R1, _R2>::value;482 483template <class _R1, class _R2>484inline constexpr bool ratio_greater_v = ratio_greater<_R1, _R2>::value;485 486template <class _R1, class _R2>487inline constexpr bool ratio_greater_equal_v = ratio_greater_equal<_R1, _R2>::value;488# endif489 490_LIBCPP_END_NAMESPACE_STD491 492_LIBCPP_POP_MACROS493 494# if !defined(_LIBCPP_REMOVE_TRANSITIVE_INCLUDES) && _LIBCPP_STD_VER <= 20495# include <type_traits>496# endif497#endif // __cplusplus < 201103L && defined(_LIBCPP_USE_FROZEN_CXX03_HEADERS)498 499#endif // _LIBCPP_RATIO500