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 43typedef ratio<1, 1000000000000000000000000> yocto; // not supported 44typedef ratio<1, 1000000000000000000000> zepto; // not supported 45typedef ratio<1, 1000000000000000000> atto; 46typedef ratio<1, 1000000000000000> femto; 47typedef ratio<1, 1000000000000> pico; 48typedef ratio<1, 1000000000> nano; 49typedef ratio<1, 1000000> micro; 50typedef ratio<1, 1000> milli; 51typedef ratio<1, 100> centi; 52typedef ratio<1, 10> deci; 53typedef ratio< 10, 1> deca; 54typedef ratio< 100, 1> hecto; 55typedef ratio< 1000, 1> kilo; 56typedef ratio< 1000000, 1> mega; 57typedef ratio< 1000000000, 1> giga; 58typedef ratio< 1000000000000, 1> tera; 59typedef ratio< 1000000000000000, 1> peta; 60typedef ratio< 1000000000000000000, 1> exa; 61typedef ratio< 1000000000000000000000, 1> zetta; // not supported 62typedef ratio<1000000000000000000000000, 1> yotta; // not supported 63 64 // 20.11.5, ratio comparison 65 template <class R1, class R2> inline constexpr bool ratio_equal_v 66 = ratio_equal<R1, R2>::value; // C++17 67 template <class R1, class R2> inline constexpr bool ratio_not_equal_v 68 = ratio_not_equal<R1, R2>::value; // C++17 69 template <class R1, class R2> inline constexpr bool ratio_less_v 70 = ratio_less<R1, R2>::value; // C++17 71 template <class R1, class R2> inline constexpr bool ratio_less_equal_v 72 = ratio_less_equal<R1, R2>::value; // C++17 73 template <class R1, class R2> inline constexpr bool ratio_greater_v 74 = ratio_greater<R1, R2>::value; // C++17 75 template <class R1, class R2> inline constexpr bool ratio_greater_equal_v 76 = ratio_greater_equal<R1, R2>::value; // C++17 77} 78*/ 79 80#include <__config> 81#include <climits> 82#include <cstdint> 83#include <type_traits> 84#include <version> 85 86#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER) 87#pragma GCC system_header 88#endif 89 90_LIBCPP_PUSH_MACROS 91#include <__undef_macros> 92 93 94_LIBCPP_BEGIN_NAMESPACE_STD 95 96// __static_gcd 97 98template <intmax_t _Xp, intmax_t _Yp> 99struct __static_gcd 100{ 101 static const intmax_t value = __static_gcd<_Yp, _Xp % _Yp>::value; 102}; 103 104template <intmax_t _Xp> 105struct __static_gcd<_Xp, 0> 106{ 107 static const intmax_t value = _Xp; 108}; 109 110template <> 111struct __static_gcd<0, 0> 112{ 113 static const intmax_t value = 1; 114}; 115 116// __static_lcm 117 118template <intmax_t _Xp, intmax_t _Yp> 119struct __static_lcm 120{ 121 static const intmax_t value = _Xp / __static_gcd<_Xp, _Yp>::value * _Yp; 122}; 123 124template <intmax_t _Xp> 125struct __static_abs 126{ 127 static const intmax_t value = _Xp < 0 ? -_Xp : _Xp; 128}; 129 130template <intmax_t _Xp> 131struct __static_sign 132{ 133 static const intmax_t value = _Xp == 0 ? 0 : (_Xp < 0 ? -1 : 1); 134}; 135 136template <intmax_t _Xp, intmax_t _Yp, intmax_t = __static_sign<_Yp>::value> 137class __ll_add; 138 139template <intmax_t _Xp, intmax_t _Yp> 140class __ll_add<_Xp, _Yp, 1> 141{ 142 static const intmax_t min = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)) + 1; 143 static const intmax_t max = -min; 144 145 static_assert(_Xp <= max - _Yp, "overflow in __ll_add"); 146public: 147 static const intmax_t value = _Xp + _Yp; 148}; 149 150template <intmax_t _Xp, intmax_t _Yp> 151class __ll_add<_Xp, _Yp, 0> 152{ 153public: 154 static const intmax_t value = _Xp; 155}; 156 157template <intmax_t _Xp, intmax_t _Yp> 158class __ll_add<_Xp, _Yp, -1> 159{ 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_add"); 164public: 165 static const intmax_t value = _Xp + _Yp; 166}; 167 168template <intmax_t _Xp, intmax_t _Yp, intmax_t = __static_sign<_Yp>::value> 169class __ll_sub; 170 171template <intmax_t _Xp, intmax_t _Yp> 172class __ll_sub<_Xp, _Yp, 1> 173{ 174 static const intmax_t min = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)) + 1; 175 static const intmax_t max = -min; 176 177 static_assert(min + _Yp <= _Xp, "overflow in __ll_sub"); 178public: 179 static const intmax_t value = _Xp - _Yp; 180}; 181 182template <intmax_t _Xp, intmax_t _Yp> 183class __ll_sub<_Xp, _Yp, 0> 184{ 185public: 186 static const intmax_t value = _Xp; 187}; 188 189template <intmax_t _Xp, intmax_t _Yp> 190class __ll_sub<_Xp, _Yp, -1> 191{ 192 static const intmax_t min = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)) + 1; 193 static const intmax_t max = -min; 194 195 static_assert(_Xp <= max + _Yp, "overflow in __ll_sub"); 196public: 197 static const intmax_t value = _Xp - _Yp; 198}; 199 200template <intmax_t _Xp, intmax_t _Yp> 201class __ll_mul 202{ 203 static const intmax_t nan = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)); 204 static const intmax_t min = nan + 1; 205 static const intmax_t max = -min; 206 static const intmax_t __a_x = __static_abs<_Xp>::value; 207 static const intmax_t __a_y = __static_abs<_Yp>::value; 208 209 static_assert(_Xp != nan && _Yp != nan && __a_x <= max / __a_y, "overflow in __ll_mul"); 210public: 211 static const intmax_t value = _Xp * _Yp; 212}; 213 214template <intmax_t _Yp> 215class __ll_mul<0, _Yp> 216{ 217public: 218 static const intmax_t value = 0; 219}; 220 221template <intmax_t _Xp> 222class __ll_mul<_Xp, 0> 223{ 224public: 225 static const intmax_t value = 0; 226}; 227 228template <> 229class __ll_mul<0, 0> 230{ 231public: 232 static const intmax_t value = 0; 233}; 234 235// Not actually used but left here in case needed in future maintenance 236template <intmax_t _Xp, intmax_t _Yp> 237class __ll_div 238{ 239 static const intmax_t nan = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)); 240 static const intmax_t min = nan + 1; 241 static const intmax_t max = -min; 242 243 static_assert(_Xp != nan && _Yp != nan && _Yp != 0, "overflow in __ll_div"); 244public: 245 static const intmax_t value = _Xp / _Yp; 246}; 247 248template <intmax_t _Num, intmax_t _Den = 1> 249class _LIBCPP_TEMPLATE_VIS ratio 250{ 251 static_assert(__static_abs<_Num>::value >= 0, "ratio numerator is out of range"); 252 static_assert(_Den != 0, "ratio divide by 0"); 253 static_assert(__static_abs<_Den>::value > 0, "ratio denominator is out of range"); 254 static _LIBCPP_CONSTEXPR const intmax_t __na = __static_abs<_Num>::value; 255 static _LIBCPP_CONSTEXPR const intmax_t __da = __static_abs<_Den>::value; 256 static _LIBCPP_CONSTEXPR const intmax_t __s = __static_sign<_Num>::value * __static_sign<_Den>::value; 257 static _LIBCPP_CONSTEXPR const intmax_t __gcd = __static_gcd<__na, __da>::value; 258public: 259 static _LIBCPP_CONSTEXPR const intmax_t num = __s * __na / __gcd; 260 static _LIBCPP_CONSTEXPR const intmax_t den = __da / __gcd; 261 262 typedef ratio<num, den> type; 263}; 264 265template <intmax_t _Num, intmax_t _Den> 266_LIBCPP_CONSTEXPR const intmax_t ratio<_Num, _Den>::num; 267 268template <intmax_t _Num, intmax_t _Den> 269_LIBCPP_CONSTEXPR const intmax_t ratio<_Num, _Den>::den; 270 271template <class _Tp> struct __is_ratio : false_type {}; 272template <intmax_t _Num, intmax_t _Den> struct __is_ratio<ratio<_Num, _Den> > : true_type {}; 273 274typedef ratio<1LL, 1000000000000000000LL> atto; 275typedef ratio<1LL, 1000000000000000LL> femto; 276typedef ratio<1LL, 1000000000000LL> pico; 277typedef ratio<1LL, 1000000000LL> nano; 278typedef ratio<1LL, 1000000LL> micro; 279typedef ratio<1LL, 1000LL> milli; 280typedef ratio<1LL, 100LL> centi; 281typedef ratio<1LL, 10LL> deci; 282typedef ratio< 10LL, 1LL> deca; 283typedef ratio< 100LL, 1LL> hecto; 284typedef ratio< 1000LL, 1LL> kilo; 285typedef ratio< 1000000LL, 1LL> mega; 286typedef ratio< 1000000000LL, 1LL> giga; 287typedef ratio< 1000000000000LL, 1LL> tera; 288typedef ratio< 1000000000000000LL, 1LL> peta; 289typedef ratio<1000000000000000000LL, 1LL> exa; 290 291template <class _R1, class _R2> 292struct __ratio_multiply 293{ 294private: 295 static const intmax_t __gcd_n1_d2 = __static_gcd<_R1::num, _R2::den>::value; 296 static const intmax_t __gcd_d1_n2 = __static_gcd<_R1::den, _R2::num>::value; 297public: 298 typedef typename ratio 299 < 300 __ll_mul<_R1::num / __gcd_n1_d2, _R2::num / __gcd_d1_n2>::value, 301 __ll_mul<_R2::den / __gcd_n1_d2, _R1::den / __gcd_d1_n2>::value 302 >::type type; 303}; 304 305#ifndef _LIBCPP_CXX03_LANG 306 307template <class _R1, class _R2> using ratio_multiply 308 = typename __ratio_multiply<_R1, _R2>::type; 309 310#else // _LIBCPP_CXX03_LANG 311 312template <class _R1, class _R2> 313struct _LIBCPP_TEMPLATE_VIS ratio_multiply 314 : public __ratio_multiply<_R1, _R2>::type {}; 315 316#endif // _LIBCPP_CXX03_LANG 317 318template <class _R1, class _R2> 319struct __ratio_divide 320{ 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; 324public: 325 typedef typename ratio 326 < 327 __ll_mul<_R1::num / __gcd_n1_n2, _R2::den / __gcd_d1_d2>::value, 328 __ll_mul<_R2::num / __gcd_n1_n2, _R1::den / __gcd_d1_d2>::value 329 >::type type; 330}; 331 332#ifndef _LIBCPP_CXX03_LANG 333 334template <class _R1, class _R2> using ratio_divide 335 = typename __ratio_divide<_R1, _R2>::type; 336 337#else // _LIBCPP_CXX03_LANG 338 339template <class _R1, class _R2> 340struct _LIBCPP_TEMPLATE_VIS ratio_divide 341 : public __ratio_divide<_R1, _R2>::type {}; 342 343#endif // _LIBCPP_CXX03_LANG 344 345template <class _R1, class _R2> 346struct __ratio_add 347{ 348private: 349 static const intmax_t __gcd_n1_n2 = __static_gcd<_R1::num, _R2::num>::value; 350 static const intmax_t __gcd_d1_d2 = __static_gcd<_R1::den, _R2::den>::value; 351public: 352 typedef typename ratio_multiply 353 < 354 ratio<__gcd_n1_n2, _R1::den / __gcd_d1_d2>, 355 ratio 356 < 357 __ll_add 358 < 359 __ll_mul<_R1::num / __gcd_n1_n2, _R2::den / __gcd_d1_d2>::value, 360 __ll_mul<_R2::num / __gcd_n1_n2, _R1::den / __gcd_d1_d2>::value 361 >::value, 362 _R2::den 363 > 364 >::type type; 365}; 366 367#ifndef _LIBCPP_CXX03_LANG 368 369template <class _R1, class _R2> using ratio_add 370 = typename __ratio_add<_R1, _R2>::type; 371 372#else // _LIBCPP_CXX03_LANG 373 374template <class _R1, class _R2> 375struct _LIBCPP_TEMPLATE_VIS ratio_add 376 : public __ratio_add<_R1, _R2>::type {}; 377 378#endif // _LIBCPP_CXX03_LANG 379 380template <class _R1, class _R2> 381struct __ratio_subtract 382{ 383private: 384 static const intmax_t __gcd_n1_n2 = __static_gcd<_R1::num, _R2::num>::value; 385 static const intmax_t __gcd_d1_d2 = __static_gcd<_R1::den, _R2::den>::value; 386public: 387 typedef typename ratio_multiply 388 < 389 ratio<__gcd_n1_n2, _R1::den / __gcd_d1_d2>, 390 ratio 391 < 392 __ll_sub 393 < 394 __ll_mul<_R1::num / __gcd_n1_n2, _R2::den / __gcd_d1_d2>::value, 395 __ll_mul<_R2::num / __gcd_n1_n2, _R1::den / __gcd_d1_d2>::value 396 >::value, 397 _R2::den 398 > 399 >::type type; 400}; 401 402#ifndef _LIBCPP_CXX03_LANG 403 404template <class _R1, class _R2> using ratio_subtract 405 = typename __ratio_subtract<_R1, _R2>::type; 406 407#else // _LIBCPP_CXX03_LANG 408 409template <class _R1, class _R2> 410struct _LIBCPP_TEMPLATE_VIS ratio_subtract 411 : public __ratio_subtract<_R1, _R2>::type {}; 412 413#endif // _LIBCPP_CXX03_LANG 414 415// ratio_equal 416 417template <class _R1, class _R2> 418struct _LIBCPP_TEMPLATE_VIS ratio_equal 419 : public _LIBCPP_BOOL_CONSTANT((_R1::num == _R2::num && _R1::den == _R2::den)) {}; 420 421template <class _R1, class _R2> 422struct _LIBCPP_TEMPLATE_VIS ratio_not_equal 423 : public _LIBCPP_BOOL_CONSTANT((!ratio_equal<_R1, _R2>::value)) {}; 424 425// ratio_less 426 427template <class _R1, class _R2, bool _Odd = false, 428 intmax_t _Q1 = _R1::num / _R1::den, intmax_t _M1 = _R1::num % _R1::den, 429 intmax_t _Q2 = _R2::num / _R2::den, intmax_t _M2 = _R2::num % _R2::den> 430struct __ratio_less1 431{ 432 static const bool value = _Odd ? _Q2 < _Q1 : _Q1 < _Q2; 433}; 434 435template <class _R1, class _R2, bool _Odd, intmax_t _Qp> 436struct __ratio_less1<_R1, _R2, _Odd, _Qp, 0, _Qp, 0> 437{ 438 static const bool value = false; 439}; 440 441template <class _R1, class _R2, bool _Odd, intmax_t _Qp, intmax_t _M2> 442struct __ratio_less1<_R1, _R2, _Odd, _Qp, 0, _Qp, _M2> 443{ 444 static const bool value = !_Odd; 445}; 446 447template <class _R1, class _R2, bool _Odd, intmax_t _Qp, intmax_t _M1> 448struct __ratio_less1<_R1, _R2, _Odd, _Qp, _M1, _Qp, 0> 449{ 450 static const bool value = _Odd; 451}; 452 453template <class _R1, class _R2, bool _Odd, intmax_t _Qp, intmax_t _M1, 454 intmax_t _M2> 455struct __ratio_less1<_R1, _R2, _Odd, _Qp, _M1, _Qp, _M2> 456{ 457 static const bool value = __ratio_less1<ratio<_R1::den, _M1>, 458 ratio<_R2::den, _M2>, !_Odd>::value; 459}; 460 461template <class _R1, class _R2, intmax_t _S1 = __static_sign<_R1::num>::value, 462 intmax_t _S2 = __static_sign<_R2::num>::value> 463struct __ratio_less 464{ 465 static const bool value = _S1 < _S2; 466}; 467 468template <class _R1, class _R2> 469struct __ratio_less<_R1, _R2, 1LL, 1LL> 470{ 471 static const bool value = __ratio_less1<_R1, _R2>::value; 472}; 473 474template <class _R1, class _R2> 475struct __ratio_less<_R1, _R2, -1LL, -1LL> 476{ 477 static const bool value = __ratio_less1<ratio<-_R2::num, _R2::den>, ratio<-_R1::num, _R1::den> >::value; 478}; 479 480template <class _R1, class _R2> 481struct _LIBCPP_TEMPLATE_VIS ratio_less 482 : public _LIBCPP_BOOL_CONSTANT((__ratio_less<_R1, _R2>::value)) {}; 483 484template <class _R1, class _R2> 485struct _LIBCPP_TEMPLATE_VIS ratio_less_equal 486 : public _LIBCPP_BOOL_CONSTANT((!ratio_less<_R2, _R1>::value)) {}; 487 488template <class _R1, class _R2> 489struct _LIBCPP_TEMPLATE_VIS ratio_greater 490 : public _LIBCPP_BOOL_CONSTANT((ratio_less<_R2, _R1>::value)) {}; 491 492template <class _R1, class _R2> 493struct _LIBCPP_TEMPLATE_VIS ratio_greater_equal 494 : public _LIBCPP_BOOL_CONSTANT((!ratio_less<_R1, _R2>::value)) {}; 495 496template <class _R1, class _R2> 497struct __ratio_gcd 498{ 499 typedef ratio<__static_gcd<_R1::num, _R2::num>::value, 500 __static_lcm<_R1::den, _R2::den>::value> type; 501}; 502 503#if _LIBCPP_STD_VER > 14 504template <class _R1, class _R2> 505inline constexpr bool ratio_equal_v = ratio_equal<_R1, _R2>::value; 506 507template <class _R1, class _R2> 508inline constexpr bool ratio_not_equal_v = ratio_not_equal<_R1, _R2>::value; 509 510template <class _R1, class _R2> 511inline constexpr bool ratio_less_v = ratio_less<_R1, _R2>::value; 512 513template <class _R1, class _R2> 514inline constexpr bool ratio_less_equal_v = ratio_less_equal<_R1, _R2>::value; 515 516template <class _R1, class _R2> 517inline constexpr bool ratio_greater_v = ratio_greater<_R1, _R2>::value; 518 519template <class _R1, class _R2> 520inline constexpr bool ratio_greater_equal_v = ratio_greater_equal<_R1, _R2>::value; 521#endif 522 523_LIBCPP_END_NAMESPACE_STD 524 525_LIBCPP_POP_MACROS 526 527#endif // _LIBCPP_RATIO 528