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 <__assert> // all public C++ headers provide the assertion handler 81#include <__config> 82#include <__type_traits/integral_constant.h> 83#include <climits> 84#include <cstdint> 85#include <version> 86 87#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER) 88# pragma GCC system_header 89#endif 90 91_LIBCPP_PUSH_MACROS 92#include <__undef_macros> 93 94 95_LIBCPP_BEGIN_NAMESPACE_STD 96 97// __static_gcd 98 99template <intmax_t _Xp, intmax_t _Yp> 100struct __static_gcd 101{ 102 static const intmax_t value = __static_gcd<_Yp, _Xp % _Yp>::value; 103}; 104 105template <intmax_t _Xp> 106struct __static_gcd<_Xp, 0> 107{ 108 static const intmax_t value = _Xp; 109}; 110 111template <> 112struct __static_gcd<0, 0> 113{ 114 static const intmax_t value = 1; 115}; 116 117// __static_lcm 118 119template <intmax_t _Xp, intmax_t _Yp> 120struct __static_lcm 121{ 122 static const intmax_t value = _Xp / __static_gcd<_Xp, _Yp>::value * _Yp; 123}; 124 125template <intmax_t _Xp> 126struct __static_abs 127{ 128 static const intmax_t value = _Xp < 0 ? -_Xp : _Xp; 129}; 130 131template <intmax_t _Xp> 132struct __static_sign 133{ 134 static const intmax_t value = _Xp == 0 ? 0 : (_Xp < 0 ? -1 : 1); 135}; 136 137template <intmax_t _Xp, intmax_t _Yp, intmax_t = __static_sign<_Yp>::value> 138class __ll_add; 139 140template <intmax_t _Xp, intmax_t _Yp> 141class __ll_add<_Xp, _Yp, 1> 142{ 143 static const intmax_t min = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)) + 1; 144 static const intmax_t max = -min; 145 146 static_assert(_Xp <= max - _Yp, "overflow in __ll_add"); 147public: 148 static const intmax_t value = _Xp + _Yp; 149}; 150 151template <intmax_t _Xp, intmax_t _Yp> 152class __ll_add<_Xp, _Yp, 0> 153{ 154public: 155 static const intmax_t value = _Xp; 156}; 157 158template <intmax_t _Xp, intmax_t _Yp> 159class __ll_add<_Xp, _Yp, -1> 160{ 161 static const intmax_t min = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)) + 1; 162 static const intmax_t max = -min; 163 164 static_assert(min - _Yp <= _Xp, "overflow in __ll_add"); 165public: 166 static const intmax_t value = _Xp + _Yp; 167}; 168 169template <intmax_t _Xp, intmax_t _Yp, intmax_t = __static_sign<_Yp>::value> 170class __ll_sub; 171 172template <intmax_t _Xp, intmax_t _Yp> 173class __ll_sub<_Xp, _Yp, 1> 174{ 175 static const intmax_t min = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)) + 1; 176 static const intmax_t max = -min; 177 178 static_assert(min + _Yp <= _Xp, "overflow in __ll_sub"); 179public: 180 static const intmax_t value = _Xp - _Yp; 181}; 182 183template <intmax_t _Xp, intmax_t _Yp> 184class __ll_sub<_Xp, _Yp, 0> 185{ 186public: 187 static const intmax_t value = _Xp; 188}; 189 190template <intmax_t _Xp, intmax_t _Yp> 191class __ll_sub<_Xp, _Yp, -1> 192{ 193 static const intmax_t min = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)) + 1; 194 static const intmax_t max = -min; 195 196 static_assert(_Xp <= max + _Yp, "overflow in __ll_sub"); 197public: 198 static const intmax_t value = _Xp - _Yp; 199}; 200 201template <intmax_t _Xp, intmax_t _Yp> 202class __ll_mul 203{ 204 static const intmax_t nan = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)); 205 static const intmax_t min = nan + 1; 206 static const intmax_t max = -min; 207 static const intmax_t __a_x = __static_abs<_Xp>::value; 208 static const intmax_t __a_y = __static_abs<_Yp>::value; 209 210 static_assert(_Xp != nan && _Yp != nan && __a_x <= max / __a_y, "overflow in __ll_mul"); 211public: 212 static const intmax_t value = _Xp * _Yp; 213}; 214 215template <intmax_t _Yp> 216class __ll_mul<0, _Yp> 217{ 218public: 219 static const intmax_t value = 0; 220}; 221 222template <intmax_t _Xp> 223class __ll_mul<_Xp, 0> 224{ 225public: 226 static const intmax_t value = 0; 227}; 228 229template <> 230class __ll_mul<0, 0> 231{ 232public: 233 static const intmax_t value = 0; 234}; 235 236// Not actually used but left here in case needed in future maintenance 237template <intmax_t _Xp, intmax_t _Yp> 238class __ll_div 239{ 240 static const intmax_t nan = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)); 241 static const intmax_t min = nan + 1; 242 static const intmax_t max = -min; 243 244 static_assert(_Xp != nan && _Yp != nan && _Yp != 0, "overflow in __ll_div"); 245public: 246 static const intmax_t value = _Xp / _Yp; 247}; 248 249template <intmax_t _Num, intmax_t _Den = 1> 250class _LIBCPP_TEMPLATE_VIS ratio 251{ 252 static_assert(__static_abs<_Num>::value >= 0, "ratio numerator is out of range"); 253 static_assert(_Den != 0, "ratio divide by 0"); 254 static_assert(__static_abs<_Den>::value > 0, "ratio denominator is out of range"); 255 static _LIBCPP_CONSTEXPR const intmax_t __na = __static_abs<_Num>::value; 256 static _LIBCPP_CONSTEXPR const intmax_t __da = __static_abs<_Den>::value; 257 static _LIBCPP_CONSTEXPR const intmax_t __s = __static_sign<_Num>::value * __static_sign<_Den>::value; 258 static _LIBCPP_CONSTEXPR const intmax_t __gcd = __static_gcd<__na, __da>::value; 259public: 260 static _LIBCPP_CONSTEXPR const intmax_t num = __s * __na / __gcd; 261 static _LIBCPP_CONSTEXPR const intmax_t den = __da / __gcd; 262 263 typedef ratio<num, den> type; 264}; 265 266template <intmax_t _Num, intmax_t _Den> 267_LIBCPP_CONSTEXPR const intmax_t ratio<_Num, _Den>::num; 268 269template <intmax_t _Num, intmax_t _Den> 270_LIBCPP_CONSTEXPR const intmax_t ratio<_Num, _Den>::den; 271 272template <class _Tp> struct __is_ratio : false_type {}; 273template <intmax_t _Num, intmax_t _Den> struct __is_ratio<ratio<_Num, _Den> > : true_type {}; 274 275typedef ratio<1LL, 1000000000000000000LL> atto; 276typedef ratio<1LL, 1000000000000000LL> femto; 277typedef ratio<1LL, 1000000000000LL> pico; 278typedef ratio<1LL, 1000000000LL> nano; 279typedef ratio<1LL, 1000000LL> micro; 280typedef ratio<1LL, 1000LL> milli; 281typedef ratio<1LL, 100LL> centi; 282typedef ratio<1LL, 10LL> deci; 283typedef ratio< 10LL, 1LL> deca; 284typedef ratio< 100LL, 1LL> hecto; 285typedef ratio< 1000LL, 1LL> kilo; 286typedef ratio< 1000000LL, 1LL> mega; 287typedef ratio< 1000000000LL, 1LL> giga; 288typedef ratio< 1000000000000LL, 1LL> tera; 289typedef ratio< 1000000000000000LL, 1LL> peta; 290typedef ratio<1000000000000000000LL, 1LL> exa; 291 292template <class _R1, class _R2> 293struct __ratio_multiply 294{ 295private: 296 static const intmax_t __gcd_n1_d2 = __static_gcd<_R1::num, _R2::den>::value; 297 static const intmax_t __gcd_d1_n2 = __static_gcd<_R1::den, _R2::num>::value; 298public: 299 typedef typename ratio 300 < 301 __ll_mul<_R1::num / __gcd_n1_d2, _R2::num / __gcd_d1_n2>::value, 302 __ll_mul<_R2::den / __gcd_n1_d2, _R1::den / __gcd_d1_n2>::value 303 >::type type; 304}; 305 306#ifndef _LIBCPP_CXX03_LANG 307 308template <class _R1, class _R2> using ratio_multiply 309 = typename __ratio_multiply<_R1, _R2>::type; 310 311#else // _LIBCPP_CXX03_LANG 312 313template <class _R1, class _R2> 314struct _LIBCPP_TEMPLATE_VIS ratio_multiply 315 : public __ratio_multiply<_R1, _R2>::type {}; 316 317#endif // _LIBCPP_CXX03_LANG 318 319template <class _R1, class _R2> 320struct __ratio_divide 321{ 322private: 323 static const intmax_t __gcd_n1_n2 = __static_gcd<_R1::num, _R2::num>::value; 324 static const intmax_t __gcd_d1_d2 = __static_gcd<_R1::den, _R2::den>::value; 325public: 326 typedef typename ratio 327 < 328 __ll_mul<_R1::num / __gcd_n1_n2, _R2::den / __gcd_d1_d2>::value, 329 __ll_mul<_R2::num / __gcd_n1_n2, _R1::den / __gcd_d1_d2>::value 330 >::type type; 331}; 332 333#ifndef _LIBCPP_CXX03_LANG 334 335template <class _R1, class _R2> using ratio_divide 336 = typename __ratio_divide<_R1, _R2>::type; 337 338#else // _LIBCPP_CXX03_LANG 339 340template <class _R1, class _R2> 341struct _LIBCPP_TEMPLATE_VIS ratio_divide 342 : public __ratio_divide<_R1, _R2>::type {}; 343 344#endif // _LIBCPP_CXX03_LANG 345 346template <class _R1, class _R2> 347struct __ratio_add 348{ 349private: 350 static const intmax_t __gcd_n1_n2 = __static_gcd<_R1::num, _R2::num>::value; 351 static const intmax_t __gcd_d1_d2 = __static_gcd<_R1::den, _R2::den>::value; 352public: 353 typedef typename ratio_multiply 354 < 355 ratio<__gcd_n1_n2, _R1::den / __gcd_d1_d2>, 356 ratio 357 < 358 __ll_add 359 < 360 __ll_mul<_R1::num / __gcd_n1_n2, _R2::den / __gcd_d1_d2>::value, 361 __ll_mul<_R2::num / __gcd_n1_n2, _R1::den / __gcd_d1_d2>::value 362 >::value, 363 _R2::den 364 > 365 >::type type; 366}; 367 368#ifndef _LIBCPP_CXX03_LANG 369 370template <class _R1, class _R2> using ratio_add 371 = typename __ratio_add<_R1, _R2>::type; 372 373#else // _LIBCPP_CXX03_LANG 374 375template <class _R1, class _R2> 376struct _LIBCPP_TEMPLATE_VIS ratio_add 377 : public __ratio_add<_R1, _R2>::type {}; 378 379#endif // _LIBCPP_CXX03_LANG 380 381template <class _R1, class _R2> 382struct __ratio_subtract 383{ 384private: 385 static const intmax_t __gcd_n1_n2 = __static_gcd<_R1::num, _R2::num>::value; 386 static const intmax_t __gcd_d1_d2 = __static_gcd<_R1::den, _R2::den>::value; 387public: 388 typedef typename ratio_multiply 389 < 390 ratio<__gcd_n1_n2, _R1::den / __gcd_d1_d2>, 391 ratio 392 < 393 __ll_sub 394 < 395 __ll_mul<_R1::num / __gcd_n1_n2, _R2::den / __gcd_d1_d2>::value, 396 __ll_mul<_R2::num / __gcd_n1_n2, _R1::den / __gcd_d1_d2>::value 397 >::value, 398 _R2::den 399 > 400 >::type type; 401}; 402 403#ifndef _LIBCPP_CXX03_LANG 404 405template <class _R1, class _R2> using ratio_subtract 406 = typename __ratio_subtract<_R1, _R2>::type; 407 408#else // _LIBCPP_CXX03_LANG 409 410template <class _R1, class _R2> 411struct _LIBCPP_TEMPLATE_VIS ratio_subtract 412 : public __ratio_subtract<_R1, _R2>::type {}; 413 414#endif // _LIBCPP_CXX03_LANG 415 416// ratio_equal 417 418template <class _R1, class _R2> 419struct _LIBCPP_TEMPLATE_VIS ratio_equal 420 : _BoolConstant<(_R1::num == _R2::num && _R1::den == _R2::den)> {}; 421 422template <class _R1, class _R2> 423struct _LIBCPP_TEMPLATE_VIS ratio_not_equal 424 : _BoolConstant<!ratio_equal<_R1, _R2>::value> {}; 425 426// ratio_less 427 428template <class _R1, class _R2, bool _Odd = false, 429 intmax_t _Q1 = _R1::num / _R1::den, intmax_t _M1 = _R1::num % _R1::den, 430 intmax_t _Q2 = _R2::num / _R2::den, intmax_t _M2 = _R2::num % _R2::den> 431struct __ratio_less1 432{ 433 static const bool value = _Odd ? _Q2 < _Q1 : _Q1 < _Q2; 434}; 435 436template <class _R1, class _R2, bool _Odd, intmax_t _Qp> 437struct __ratio_less1<_R1, _R2, _Odd, _Qp, 0, _Qp, 0> 438{ 439 static const bool value = false; 440}; 441 442template <class _R1, class _R2, bool _Odd, intmax_t _Qp, intmax_t _M2> 443struct __ratio_less1<_R1, _R2, _Odd, _Qp, 0, _Qp, _M2> 444{ 445 static const bool value = !_Odd; 446}; 447 448template <class _R1, class _R2, bool _Odd, intmax_t _Qp, intmax_t _M1> 449struct __ratio_less1<_R1, _R2, _Odd, _Qp, _M1, _Qp, 0> 450{ 451 static const bool value = _Odd; 452}; 453 454template <class _R1, class _R2, bool _Odd, intmax_t _Qp, intmax_t _M1, 455 intmax_t _M2> 456struct __ratio_less1<_R1, _R2, _Odd, _Qp, _M1, _Qp, _M2> 457{ 458 static const bool value = __ratio_less1<ratio<_R1::den, _M1>, 459 ratio<_R2::den, _M2>, !_Odd>::value; 460}; 461 462template <class _R1, class _R2, intmax_t _S1 = __static_sign<_R1::num>::value, 463 intmax_t _S2 = __static_sign<_R2::num>::value> 464struct __ratio_less 465{ 466 static const bool value = _S1 < _S2; 467}; 468 469template <class _R1, class _R2> 470struct __ratio_less<_R1, _R2, 1LL, 1LL> 471{ 472 static const bool value = __ratio_less1<_R1, _R2>::value; 473}; 474 475template <class _R1, class _R2> 476struct __ratio_less<_R1, _R2, -1LL, -1LL> 477{ 478 static const bool value = __ratio_less1<ratio<-_R2::num, _R2::den>, ratio<-_R1::num, _R1::den> >::value; 479}; 480 481template <class _R1, class _R2> 482struct _LIBCPP_TEMPLATE_VIS ratio_less 483 : _BoolConstant<__ratio_less<_R1, _R2>::value> {}; 484 485template <class _R1, class _R2> 486struct _LIBCPP_TEMPLATE_VIS ratio_less_equal 487 : _BoolConstant<!ratio_less<_R2, _R1>::value> {}; 488 489template <class _R1, class _R2> 490struct _LIBCPP_TEMPLATE_VIS ratio_greater 491 : _BoolConstant<ratio_less<_R2, _R1>::value> {}; 492 493template <class _R1, class _R2> 494struct _LIBCPP_TEMPLATE_VIS ratio_greater_equal 495 : _BoolConstant<!ratio_less<_R1, _R2>::value> {}; 496 497template <class _R1, class _R2> 498struct __ratio_gcd 499{ 500 typedef ratio<__static_gcd<_R1::num, _R2::num>::value, 501 __static_lcm<_R1::den, _R2::den>::value> type; 502}; 503 504#if _LIBCPP_STD_VER > 14 505template <class _R1, class _R2> 506inline constexpr bool ratio_equal_v = ratio_equal<_R1, _R2>::value; 507 508template <class _R1, class _R2> 509inline constexpr bool ratio_not_equal_v = ratio_not_equal<_R1, _R2>::value; 510 511template <class _R1, class _R2> 512inline constexpr bool ratio_less_v = ratio_less<_R1, _R2>::value; 513 514template <class _R1, class _R2> 515inline constexpr bool ratio_less_equal_v = ratio_less_equal<_R1, _R2>::value; 516 517template <class _R1, class _R2> 518inline constexpr bool ratio_greater_v = ratio_greater<_R1, _R2>::value; 519 520template <class _R1, class _R2> 521inline constexpr bool ratio_greater_equal_v = ratio_greater_equal<_R1, _R2>::value; 522#endif 523 524_LIBCPP_END_NAMESPACE_STD 525 526_LIBCPP_POP_MACROS 527 528#if !defined(_LIBCPP_REMOVE_TRANSITIVE_INCLUDES) && _LIBCPP_STD_VER <= 20 529# include <type_traits> 530#endif 531 532#endif // _LIBCPP_RATIO 533