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