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___CXX03_RATIO 11#define _LIBCPP___CXX03_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 <__cxx03/__config> 85#include <__cxx03/__type_traits/integral_constant.h> 86#include <__cxx03/climits> 87#include <__cxx03/cstdint> 88#include <__cxx03/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 <__cxx03/__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 const intmax_t __na = __static_abs<_Num>::value; 246 static const intmax_t __da = __static_abs<_Den>::value; 247 static const intmax_t __s = __static_sign<_Num>::value * __static_sign<_Den>::value; 248 static const intmax_t __gcd = __static_gcd<__na, __da>::value; 249 250public: 251 static const intmax_t num = __s * __na / __gcd; 252 static const intmax_t den = __da / __gcd; 253 254 typedef ratio<num, den> type; 255}; 256 257template <intmax_t _Num, intmax_t _Den> 258const intmax_t ratio<_Num, _Den>::num; 259 260template <intmax_t _Num, intmax_t _Den> 261const 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 299template <class _R1, class _R2> 300struct _LIBCPP_TEMPLATE_VIS ratio_multiply : public __ratio_multiply<_R1, _R2>::type {}; 301 302template <class _R1, class _R2> 303struct __ratio_divide { 304private: 305 static const intmax_t __gcd_n1_n2 = __static_gcd<_R1::num, _R2::num>::value; 306 static const intmax_t __gcd_d1_d2 = __static_gcd<_R1::den, _R2::den>::value; 307 308 static_assert(__is_ratio<_R1>::value, "[ratio.general]/2 requires R1 to be a specialisation of the ratio template"); 309 static_assert(__is_ratio<_R2>::value, "[ratio.general]/2 requires R2 to be a specialisation of the ratio template"); 310 311public: 312 typedef typename ratio< __ll_mul<_R1::num / __gcd_n1_n2, _R2::den / __gcd_d1_d2>::value, 313 __ll_mul<_R2::num / __gcd_n1_n2, _R1::den / __gcd_d1_d2>::value >::type type; 314}; 315 316template <class _R1, class _R2> 317struct _LIBCPP_TEMPLATE_VIS ratio_divide : public __ratio_divide<_R1, _R2>::type {}; 318 319template <class _R1, class _R2> 320struct __ratio_add { 321private: 322 static const intmax_t __gcd_n1_n2 = __static_gcd<_R1::num, _R2::num>::value; 323 static const intmax_t __gcd_d1_d2 = __static_gcd<_R1::den, _R2::den>::value; 324 325 static_assert(__is_ratio<_R1>::value, "[ratio.general]/2 requires R1 to be a specialisation of the ratio template"); 326 static_assert(__is_ratio<_R2>::value, "[ratio.general]/2 requires R2 to be a specialisation of the ratio template"); 327 328public: 329 typedef typename ratio_multiply< 330 ratio<__gcd_n1_n2, _R1::den / __gcd_d1_d2>, 331 ratio< __ll_add< __ll_mul<_R1::num / __gcd_n1_n2, _R2::den / __gcd_d1_d2>::value, 332 __ll_mul<_R2::num / __gcd_n1_n2, _R1::den / __gcd_d1_d2>::value >::value, 333 _R2::den > >::type type; 334}; 335 336template <class _R1, class _R2> 337struct _LIBCPP_TEMPLATE_VIS ratio_add : public __ratio_add<_R1, _R2>::type {}; 338 339template <class _R1, class _R2> 340struct __ratio_subtract { 341private: 342 static const intmax_t __gcd_n1_n2 = __static_gcd<_R1::num, _R2::num>::value; 343 static const intmax_t __gcd_d1_d2 = __static_gcd<_R1::den, _R2::den>::value; 344 345 static_assert(__is_ratio<_R1>::value, "[ratio.general]/2 requires R1 to be a specialisation of the ratio template"); 346 static_assert(__is_ratio<_R2>::value, "[ratio.general]/2 requires R2 to be a specialisation of the ratio template"); 347 348public: 349 typedef typename ratio_multiply< 350 ratio<__gcd_n1_n2, _R1::den / __gcd_d1_d2>, 351 ratio< __ll_sub< __ll_mul<_R1::num / __gcd_n1_n2, _R2::den / __gcd_d1_d2>::value, 352 __ll_mul<_R2::num / __gcd_n1_n2, _R1::den / __gcd_d1_d2>::value >::value, 353 _R2::den > >::type type; 354}; 355 356template <class _R1, class _R2> 357struct _LIBCPP_TEMPLATE_VIS ratio_subtract : public __ratio_subtract<_R1, _R2>::type {}; 358 359// ratio_equal 360 361template <class _R1, class _R2> 362struct _LIBCPP_TEMPLATE_VIS ratio_equal : _BoolConstant<(_R1::num == _R2::num && _R1::den == _R2::den)> { 363 static_assert(__is_ratio<_R1>::value, "[ratio.general]/2 requires R1 to be a specialisation of the ratio template"); 364 static_assert(__is_ratio<_R2>::value, "[ratio.general]/2 requires R2 to be a specialisation of the ratio template"); 365}; 366 367template <class _R1, class _R2> 368struct _LIBCPP_TEMPLATE_VIS ratio_not_equal : _BoolConstant<!ratio_equal<_R1, _R2>::value> { 369 static_assert(__is_ratio<_R1>::value, "[ratio.general]/2 requires R1 to be a specialisation of the ratio template"); 370 static_assert(__is_ratio<_R2>::value, "[ratio.general]/2 requires R2 to be a specialisation of the ratio template"); 371}; 372 373// ratio_less 374 375template <class _R1, 376 class _R2, 377 bool _Odd = false, 378 intmax_t _Q1 = _R1::num / _R1::den, 379 intmax_t _M1 = _R1::num % _R1::den, 380 intmax_t _Q2 = _R2::num / _R2::den, 381 intmax_t _M2 = _R2::num % _R2::den> 382struct __ratio_less1 { 383 static const bool value = _Odd ? _Q2 < _Q1 : _Q1 < _Q2; 384}; 385 386template <class _R1, class _R2, bool _Odd, intmax_t _Qp> 387struct __ratio_less1<_R1, _R2, _Odd, _Qp, 0, _Qp, 0> { 388 static const bool value = false; 389}; 390 391template <class _R1, class _R2, bool _Odd, intmax_t _Qp, intmax_t _M2> 392struct __ratio_less1<_R1, _R2, _Odd, _Qp, 0, _Qp, _M2> { 393 static const bool value = !_Odd; 394}; 395 396template <class _R1, class _R2, bool _Odd, intmax_t _Qp, intmax_t _M1> 397struct __ratio_less1<_R1, _R2, _Odd, _Qp, _M1, _Qp, 0> { 398 static const bool value = _Odd; 399}; 400 401template <class _R1, class _R2, bool _Odd, intmax_t _Qp, intmax_t _M1, intmax_t _M2> 402struct __ratio_less1<_R1, _R2, _Odd, _Qp, _M1, _Qp, _M2> { 403 static const bool value = __ratio_less1<ratio<_R1::den, _M1>, ratio<_R2::den, _M2>, !_Odd>::value; 404}; 405 406template <class _R1, 407 class _R2, 408 intmax_t _S1 = __static_sign<_R1::num>::value, 409 intmax_t _S2 = __static_sign<_R2::num>::value> 410struct __ratio_less { 411 static const bool value = _S1 < _S2; 412}; 413 414template <class _R1, class _R2> 415struct __ratio_less<_R1, _R2, 1LL, 1LL> { 416 static const bool value = __ratio_less1<_R1, _R2>::value; 417}; 418 419template <class _R1, class _R2> 420struct __ratio_less<_R1, _R2, -1LL, -1LL> { 421 static const bool value = __ratio_less1<ratio<-_R2::num, _R2::den>, ratio<-_R1::num, _R1::den> >::value; 422}; 423 424template <class _R1, class _R2> 425struct _LIBCPP_TEMPLATE_VIS ratio_less : _BoolConstant<__ratio_less<_R1, _R2>::value> { 426 static_assert(__is_ratio<_R1>::value, "[ratio.general]/2 requires R1 to be a specialisation of the ratio template"); 427 static_assert(__is_ratio<_R2>::value, "[ratio.general]/2 requires R2 to be a specialisation of the ratio template"); 428}; 429 430template <class _R1, class _R2> 431struct _LIBCPP_TEMPLATE_VIS ratio_less_equal : _BoolConstant<!ratio_less<_R2, _R1>::value> { 432 static_assert(__is_ratio<_R1>::value, "[ratio.general]/2 requires R1 to be a specialisation of the ratio template"); 433 static_assert(__is_ratio<_R2>::value, "[ratio.general]/2 requires R2 to be a specialisation of the ratio template"); 434}; 435 436template <class _R1, class _R2> 437struct _LIBCPP_TEMPLATE_VIS ratio_greater : _BoolConstant<ratio_less<_R2, _R1>::value> { 438 static_assert(__is_ratio<_R1>::value, "[ratio.general]/2 requires R1 to be a specialisation of the ratio template"); 439 static_assert(__is_ratio<_R2>::value, "[ratio.general]/2 requires R2 to be a specialisation of the ratio template"); 440}; 441 442template <class _R1, class _R2> 443struct _LIBCPP_TEMPLATE_VIS ratio_greater_equal : _BoolConstant<!ratio_less<_R1, _R2>::value> { 444 static_assert(__is_ratio<_R1>::value, "[ratio.general]/2 requires R1 to be a specialisation of the ratio template"); 445 static_assert(__is_ratio<_R2>::value, "[ratio.general]/2 requires R2 to be a specialisation of the ratio template"); 446}; 447 448template <class _R1, class _R2> 449struct __ratio_gcd { 450 typedef ratio<__static_gcd<_R1::num, _R2::num>::value, __static_lcm<_R1::den, _R2::den>::value> type; 451}; 452 453_LIBCPP_END_NAMESPACE_STD 454 455_LIBCPP_POP_MACROS 456 457#if !defined(_LIBCPP_REMOVE_TRANSITIVE_INCLUDES) 458# include <__cxx03/type_traits> 459#endif 460 461#endif // _LIBCPP___CXX03_RATIO 462