1// -*- C++ -*- 2//===---------------------------- ratio -----------------------------------===// 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 85#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER) 86#pragma GCC system_header 87#endif 88 89_LIBCPP_PUSH_MACROS 90#include <__undef_macros> 91 92 93_LIBCPP_BEGIN_NAMESPACE_STD 94 95// __static_gcd 96 97template <intmax_t _Xp, intmax_t _Yp> 98struct __static_gcd 99{ 100 static const intmax_t value = __static_gcd<_Yp, _Xp % _Yp>::value; 101}; 102 103template <intmax_t _Xp> 104struct __static_gcd<_Xp, 0> 105{ 106 static const intmax_t value = _Xp; 107}; 108 109template <> 110struct __static_gcd<0, 0> 111{ 112 static const intmax_t value = 1; 113}; 114 115// __static_lcm 116 117template <intmax_t _Xp, intmax_t _Yp> 118struct __static_lcm 119{ 120 static const intmax_t value = _Xp / __static_gcd<_Xp, _Yp>::value * _Yp; 121}; 122 123template <intmax_t _Xp> 124struct __static_abs 125{ 126 static const intmax_t value = _Xp < 0 ? -_Xp : _Xp; 127}; 128 129template <intmax_t _Xp> 130struct __static_sign 131{ 132 static const intmax_t value = _Xp == 0 ? 0 : (_Xp < 0 ? -1 : 1); 133}; 134 135template <intmax_t _Xp, intmax_t _Yp, intmax_t = __static_sign<_Yp>::value> 136class __ll_add; 137 138template <intmax_t _Xp, intmax_t _Yp> 139class __ll_add<_Xp, _Yp, 1> 140{ 141 static const intmax_t min = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)) + 1; 142 static const intmax_t max = -min; 143 144 static_assert(_Xp <= max - _Yp, "overflow in __ll_add"); 145public: 146 static const intmax_t value = _Xp + _Yp; 147}; 148 149template <intmax_t _Xp, intmax_t _Yp> 150class __ll_add<_Xp, _Yp, 0> 151{ 152public: 153 static const intmax_t value = _Xp; 154}; 155 156template <intmax_t _Xp, intmax_t _Yp> 157class __ll_add<_Xp, _Yp, -1> 158{ 159 static const intmax_t min = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)) + 1; 160 static const intmax_t max = -min; 161 162 static_assert(min - _Yp <= _Xp, "overflow in __ll_add"); 163public: 164 static const intmax_t value = _Xp + _Yp; 165}; 166 167template <intmax_t _Xp, intmax_t _Yp, intmax_t = __static_sign<_Yp>::value> 168class __ll_sub; 169 170template <intmax_t _Xp, intmax_t _Yp> 171class __ll_sub<_Xp, _Yp, 1> 172{ 173 static const intmax_t min = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)) + 1; 174 static const intmax_t max = -min; 175 176 static_assert(min + _Yp <= _Xp, "overflow in __ll_sub"); 177public: 178 static const intmax_t value = _Xp - _Yp; 179}; 180 181template <intmax_t _Xp, intmax_t _Yp> 182class __ll_sub<_Xp, _Yp, 0> 183{ 184public: 185 static const intmax_t value = _Xp; 186}; 187 188template <intmax_t _Xp, intmax_t _Yp> 189class __ll_sub<_Xp, _Yp, -1> 190{ 191 static const intmax_t min = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)) + 1; 192 static const intmax_t max = -min; 193 194 static_assert(_Xp <= max + _Yp, "overflow in __ll_sub"); 195public: 196 static const intmax_t value = _Xp - _Yp; 197}; 198 199template <intmax_t _Xp, intmax_t _Yp> 200class __ll_mul 201{ 202 static const intmax_t nan = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)); 203 static const intmax_t min = nan + 1; 204 static const intmax_t max = -min; 205 static const intmax_t __a_x = __static_abs<_Xp>::value; 206 static const intmax_t __a_y = __static_abs<_Yp>::value; 207 208 static_assert(_Xp != nan && _Yp != nan && __a_x <= max / __a_y, "overflow in __ll_mul"); 209public: 210 static const intmax_t value = _Xp * _Yp; 211}; 212 213template <intmax_t _Yp> 214class __ll_mul<0, _Yp> 215{ 216public: 217 static const intmax_t value = 0; 218}; 219 220template <intmax_t _Xp> 221class __ll_mul<_Xp, 0> 222{ 223public: 224 static const intmax_t value = 0; 225}; 226 227template <> 228class __ll_mul<0, 0> 229{ 230public: 231 static const intmax_t value = 0; 232}; 233 234// Not actually used but left here in case needed in future maintenance 235template <intmax_t _Xp, intmax_t _Yp> 236class __ll_div 237{ 238 static const intmax_t nan = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)); 239 static const intmax_t min = nan + 1; 240 static const intmax_t max = -min; 241 242 static_assert(_Xp != nan && _Yp != nan && _Yp != 0, "overflow in __ll_div"); 243public: 244 static const intmax_t value = _Xp / _Yp; 245}; 246 247template <intmax_t _Num, intmax_t _Den = 1> 248class _LIBCPP_TEMPLATE_VIS ratio 249{ 250 static_assert(__static_abs<_Num>::value >= 0, "ratio numerator is out of range"); 251 static_assert(_Den != 0, "ratio divide by 0"); 252 static_assert(__static_abs<_Den>::value > 0, "ratio denominator is out of range"); 253 static _LIBCPP_CONSTEXPR const intmax_t __na = __static_abs<_Num>::value; 254 static _LIBCPP_CONSTEXPR const intmax_t __da = __static_abs<_Den>::value; 255 static _LIBCPP_CONSTEXPR const intmax_t __s = __static_sign<_Num>::value * __static_sign<_Den>::value; 256 static _LIBCPP_CONSTEXPR const intmax_t __gcd = __static_gcd<__na, __da>::value; 257public: 258 static _LIBCPP_CONSTEXPR const intmax_t num = __s * __na / __gcd; 259 static _LIBCPP_CONSTEXPR const intmax_t den = __da / __gcd; 260 261 typedef ratio<num, den> type; 262}; 263 264template <intmax_t _Num, intmax_t _Den> 265_LIBCPP_CONSTEXPR const intmax_t ratio<_Num, _Den>::num; 266 267template <intmax_t _Num, intmax_t _Den> 268_LIBCPP_CONSTEXPR const intmax_t ratio<_Num, _Den>::den; 269 270template <class _Tp> struct __is_ratio : false_type {}; 271template <intmax_t _Num, intmax_t _Den> struct __is_ratio<ratio<_Num, _Den> > : true_type {}; 272 273typedef ratio<1LL, 1000000000000000000LL> atto; 274typedef ratio<1LL, 1000000000000000LL> femto; 275typedef ratio<1LL, 1000000000000LL> pico; 276typedef ratio<1LL, 1000000000LL> nano; 277typedef ratio<1LL, 1000000LL> micro; 278typedef ratio<1LL, 1000LL> milli; 279typedef ratio<1LL, 100LL> centi; 280typedef ratio<1LL, 10LL> deci; 281typedef ratio< 10LL, 1LL> deca; 282typedef ratio< 100LL, 1LL> hecto; 283typedef ratio< 1000LL, 1LL> kilo; 284typedef ratio< 1000000LL, 1LL> mega; 285typedef ratio< 1000000000LL, 1LL> giga; 286typedef ratio< 1000000000000LL, 1LL> tera; 287typedef ratio< 1000000000000000LL, 1LL> peta; 288typedef ratio<1000000000000000000LL, 1LL> exa; 289 290template <class _R1, class _R2> 291struct __ratio_multiply 292{ 293private: 294 static const intmax_t __gcd_n1_d2 = __static_gcd<_R1::num, _R2::den>::value; 295 static const intmax_t __gcd_d1_n2 = __static_gcd<_R1::den, _R2::num>::value; 296public: 297 typedef typename ratio 298 < 299 __ll_mul<_R1::num / __gcd_n1_d2, _R2::num / __gcd_d1_n2>::value, 300 __ll_mul<_R2::den / __gcd_n1_d2, _R1::den / __gcd_d1_n2>::value 301 >::type type; 302}; 303 304#ifndef _LIBCPP_CXX03_LANG 305 306template <class _R1, class _R2> using ratio_multiply 307 = typename __ratio_multiply<_R1, _R2>::type; 308 309#else // _LIBCPP_CXX03_LANG 310 311template <class _R1, class _R2> 312struct _LIBCPP_TEMPLATE_VIS ratio_multiply 313 : public __ratio_multiply<_R1, _R2>::type {}; 314 315#endif // _LIBCPP_CXX03_LANG 316 317template <class _R1, class _R2> 318struct __ratio_divide 319{ 320private: 321 static const intmax_t __gcd_n1_n2 = __static_gcd<_R1::num, _R2::num>::value; 322 static const intmax_t __gcd_d1_d2 = __static_gcd<_R1::den, _R2::den>::value; 323public: 324 typedef typename ratio 325 < 326 __ll_mul<_R1::num / __gcd_n1_n2, _R2::den / __gcd_d1_d2>::value, 327 __ll_mul<_R2::num / __gcd_n1_n2, _R1::den / __gcd_d1_d2>::value 328 >::type type; 329}; 330 331#ifndef _LIBCPP_CXX03_LANG 332 333template <class _R1, class _R2> using ratio_divide 334 = typename __ratio_divide<_R1, _R2>::type; 335 336#else // _LIBCPP_CXX03_LANG 337 338template <class _R1, class _R2> 339struct _LIBCPP_TEMPLATE_VIS ratio_divide 340 : public __ratio_divide<_R1, _R2>::type {}; 341 342#endif // _LIBCPP_CXX03_LANG 343 344template <class _R1, class _R2> 345struct __ratio_add 346{ 347private: 348 static const intmax_t __gcd_n1_n2 = __static_gcd<_R1::num, _R2::num>::value; 349 static const intmax_t __gcd_d1_d2 = __static_gcd<_R1::den, _R2::den>::value; 350public: 351 typedef typename ratio_multiply 352 < 353 ratio<__gcd_n1_n2, _R1::den / __gcd_d1_d2>, 354 ratio 355 < 356 __ll_add 357 < 358 __ll_mul<_R1::num / __gcd_n1_n2, _R2::den / __gcd_d1_d2>::value, 359 __ll_mul<_R2::num / __gcd_n1_n2, _R1::den / __gcd_d1_d2>::value 360 >::value, 361 _R2::den 362 > 363 >::type type; 364}; 365 366#ifndef _LIBCPP_CXX03_LANG 367 368template <class _R1, class _R2> using ratio_add 369 = typename __ratio_add<_R1, _R2>::type; 370 371#else // _LIBCPP_CXX03_LANG 372 373template <class _R1, class _R2> 374struct _LIBCPP_TEMPLATE_VIS ratio_add 375 : public __ratio_add<_R1, _R2>::type {}; 376 377#endif // _LIBCPP_CXX03_LANG 378 379template <class _R1, class _R2> 380struct __ratio_subtract 381{ 382private: 383 static const intmax_t __gcd_n1_n2 = __static_gcd<_R1::num, _R2::num>::value; 384 static const intmax_t __gcd_d1_d2 = __static_gcd<_R1::den, _R2::den>::value; 385public: 386 typedef typename ratio_multiply 387 < 388 ratio<__gcd_n1_n2, _R1::den / __gcd_d1_d2>, 389 ratio 390 < 391 __ll_sub 392 < 393 __ll_mul<_R1::num / __gcd_n1_n2, _R2::den / __gcd_d1_d2>::value, 394 __ll_mul<_R2::num / __gcd_n1_n2, _R1::den / __gcd_d1_d2>::value 395 >::value, 396 _R2::den 397 > 398 >::type type; 399}; 400 401#ifndef _LIBCPP_CXX03_LANG 402 403template <class _R1, class _R2> using ratio_subtract 404 = typename __ratio_subtract<_R1, _R2>::type; 405 406#else // _LIBCPP_CXX03_LANG 407 408template <class _R1, class _R2> 409struct _LIBCPP_TEMPLATE_VIS ratio_subtract 410 : public __ratio_subtract<_R1, _R2>::type {}; 411 412#endif // _LIBCPP_CXX03_LANG 413 414// ratio_equal 415 416template <class _R1, class _R2> 417struct _LIBCPP_TEMPLATE_VIS ratio_equal 418 : public _LIBCPP_BOOL_CONSTANT((_R1::num == _R2::num && _R1::den == _R2::den)) {}; 419 420template <class _R1, class _R2> 421struct _LIBCPP_TEMPLATE_VIS ratio_not_equal 422 : public _LIBCPP_BOOL_CONSTANT((!ratio_equal<_R1, _R2>::value)) {}; 423 424// ratio_less 425 426template <class _R1, class _R2, bool _Odd = false, 427 intmax_t _Q1 = _R1::num / _R1::den, intmax_t _M1 = _R1::num % _R1::den, 428 intmax_t _Q2 = _R2::num / _R2::den, intmax_t _M2 = _R2::num % _R2::den> 429struct __ratio_less1 430{ 431 static const bool value = _Odd ? _Q2 < _Q1 : _Q1 < _Q2; 432}; 433 434template <class _R1, class _R2, bool _Odd, intmax_t _Qp> 435struct __ratio_less1<_R1, _R2, _Odd, _Qp, 0, _Qp, 0> 436{ 437 static const bool value = false; 438}; 439 440template <class _R1, class _R2, bool _Odd, intmax_t _Qp, intmax_t _M2> 441struct __ratio_less1<_R1, _R2, _Odd, _Qp, 0, _Qp, _M2> 442{ 443 static const bool value = !_Odd; 444}; 445 446template <class _R1, class _R2, bool _Odd, intmax_t _Qp, intmax_t _M1> 447struct __ratio_less1<_R1, _R2, _Odd, _Qp, _M1, _Qp, 0> 448{ 449 static const bool value = _Odd; 450}; 451 452template <class _R1, class _R2, bool _Odd, intmax_t _Qp, intmax_t _M1, 453 intmax_t _M2> 454struct __ratio_less1<_R1, _R2, _Odd, _Qp, _M1, _Qp, _M2> 455{ 456 static const bool value = __ratio_less1<ratio<_R1::den, _M1>, 457 ratio<_R2::den, _M2>, !_Odd>::value; 458}; 459 460template <class _R1, class _R2, intmax_t _S1 = __static_sign<_R1::num>::value, 461 intmax_t _S2 = __static_sign<_R2::num>::value> 462struct __ratio_less 463{ 464 static const bool value = _S1 < _S2; 465}; 466 467template <class _R1, class _R2> 468struct __ratio_less<_R1, _R2, 1LL, 1LL> 469{ 470 static const bool value = __ratio_less1<_R1, _R2>::value; 471}; 472 473template <class _R1, class _R2> 474struct __ratio_less<_R1, _R2, -1LL, -1LL> 475{ 476 static const bool value = __ratio_less1<ratio<-_R2::num, _R2::den>, ratio<-_R1::num, _R1::den> >::value; 477}; 478 479template <class _R1, class _R2> 480struct _LIBCPP_TEMPLATE_VIS ratio_less 481 : public _LIBCPP_BOOL_CONSTANT((__ratio_less<_R1, _R2>::value)) {}; 482 483template <class _R1, class _R2> 484struct _LIBCPP_TEMPLATE_VIS ratio_less_equal 485 : public _LIBCPP_BOOL_CONSTANT((!ratio_less<_R2, _R1>::value)) {}; 486 487template <class _R1, class _R2> 488struct _LIBCPP_TEMPLATE_VIS ratio_greater 489 : public _LIBCPP_BOOL_CONSTANT((ratio_less<_R2, _R1>::value)) {}; 490 491template <class _R1, class _R2> 492struct _LIBCPP_TEMPLATE_VIS ratio_greater_equal 493 : public _LIBCPP_BOOL_CONSTANT((!ratio_less<_R1, _R2>::value)) {}; 494 495template <class _R1, class _R2> 496struct __ratio_gcd 497{ 498 typedef ratio<__static_gcd<_R1::num, _R2::num>::value, 499 __static_lcm<_R1::den, _R2::den>::value> type; 500}; 501 502#if _LIBCPP_STD_VER > 14 && !defined(_LIBCPP_HAS_NO_VARIABLE_TEMPLATES) 503template <class _R1, class _R2> 504_LIBCPP_INLINE_VAR _LIBCPP_CONSTEXPR bool ratio_equal_v 505 = ratio_equal<_R1, _R2>::value; 506 507template <class _R1, class _R2> 508_LIBCPP_INLINE_VAR _LIBCPP_CONSTEXPR bool ratio_not_equal_v 509 = ratio_not_equal<_R1, _R2>::value; 510 511template <class _R1, class _R2> 512_LIBCPP_INLINE_VAR _LIBCPP_CONSTEXPR bool ratio_less_v 513 = ratio_less<_R1, _R2>::value; 514 515template <class _R1, class _R2> 516_LIBCPP_INLINE_VAR _LIBCPP_CONSTEXPR bool ratio_less_equal_v 517 = ratio_less_equal<_R1, _R2>::value; 518 519template <class _R1, class _R2> 520_LIBCPP_INLINE_VAR _LIBCPP_CONSTEXPR bool ratio_greater_v 521 = ratio_greater<_R1, _R2>::value; 522 523template <class _R1, class _R2> 524_LIBCPP_INLINE_VAR _LIBCPP_CONSTEXPR bool ratio_greater_equal_v 525 = ratio_greater_equal<_R1, _R2>::value; 526#endif 527 528_LIBCPP_END_NAMESPACE_STD 529 530_LIBCPP_POP_MACROS 531 532#endif // _LIBCPP_RATIO 533