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#if __cplusplus < 201103L && defined(_LIBCPP_USE_FROZEN_CXX03_HEADERS) 85# include <__cxx03/ratio> 86#else 87# 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_header 95# endif 96 97_LIBCPP_PUSH_MACROS 98# include <__undef_macros> 99 100_LIBCPP_BEGIN_NAMESPACE_STD 101 102// __static_gcd 103 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_lcm 114 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 maintenance 219template <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 _LIBCPP_TEMPLATE_VIS 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_LANG 286 287template <class _R1, class _R2> 288using ratio_multiply = typename __ratio_multiply<_R1, _R2>::type; 289 290# else // _LIBCPP_CXX03_LANG 291 292template <class _R1, class _R2> 293struct _LIBCPP_TEMPLATE_VIS ratio_multiply : public __ratio_multiply<_R1, _R2>::type {}; 294 295# endif // _LIBCPP_CXX03_LANG 296 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_LANG 312 313template <class _R1, class _R2> 314using ratio_divide = typename __ratio_divide<_R1, _R2>::type; 315 316# else // _LIBCPP_CXX03_LANG 317 318template <class _R1, class _R2> 319struct _LIBCPP_TEMPLATE_VIS ratio_divide : public __ratio_divide<_R1, _R2>::type {}; 320 321# endif // _LIBCPP_CXX03_LANG 322 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_LANG 341 342template <class _R1, class _R2> 343using ratio_add = typename __ratio_add<_R1, _R2>::type; 344 345# else // _LIBCPP_CXX03_LANG 346 347template <class _R1, class _R2> 348struct _LIBCPP_TEMPLATE_VIS ratio_add : public __ratio_add<_R1, _R2>::type {}; 349 350# endif // _LIBCPP_CXX03_LANG 351 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_LANG 370 371template <class _R1, class _R2> 372using ratio_subtract = typename __ratio_subtract<_R1, _R2>::type; 373 374# else // _LIBCPP_CXX03_LANG 375 376template <class _R1, class _R2> 377struct _LIBCPP_TEMPLATE_VIS ratio_subtract : public __ratio_subtract<_R1, _R2>::type {}; 378 379# endif // _LIBCPP_CXX03_LANG 380 381// ratio_equal 382 383template <class _R1, class _R2> 384struct _LIBCPP_TEMPLATE_VIS 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 _LIBCPP_TEMPLATE_VIS 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_less 396 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 _LIBCPP_TEMPLATE_VIS 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 _LIBCPP_TEMPLATE_VIS 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 _LIBCPP_TEMPLATE_VIS 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 _LIBCPP_TEMPLATE_VIS 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 >= 17 471template <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# endif 489 490_LIBCPP_END_NAMESPACE_STD 491 492_LIBCPP_POP_MACROS 493 494# if !defined(_LIBCPP_REMOVE_TRANSITIVE_INCLUDES) && _LIBCPP_STD_VER <= 20 495# include <type_traits> 496# endif 497#endif // __cplusplus < 201103L && defined(_LIBCPP_USE_FROZEN_CXX03_HEADERS) 498 499#endif // _LIBCPP_RATIO 500