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