1// -*- C++ -*- 2//===---------------------------- ratio -----------------------------------===// 3// 4// The LLVM Compiler Infrastructure 5// 6// This file is dual licensed under the MIT and the University of Illinois Open 7// Source Licenses. See LICENSE.TXT for details. 8// 9//===----------------------------------------------------------------------===// 10 11#ifndef _LIBCPP_RATIO 12#define _LIBCPP_RATIO 13 14/* 15 ratio synopsis 16 17namespace std 18{ 19 20template <intmax_t N, intmax_t D = 1> 21class ratio 22{ 23public: 24 static constexpr intmax_t num; 25 static constexpr intmax_t den; 26 typedef ratio<num, den> type; 27}; 28 29// ratio arithmetic 30template <class R1, class R2> using ratio_add = ...; 31template <class R1, class R2> using ratio_subtract = ...; 32template <class R1, class R2> using ratio_multiply = ...; 33template <class R1, class R2> using ratio_divide = ...; 34 35// ratio comparison 36template <class R1, class R2> struct ratio_equal; 37template <class R1, class R2> struct ratio_not_equal; 38template <class R1, class R2> struct ratio_less; 39template <class R1, class R2> struct ratio_less_equal; 40template <class R1, class R2> struct ratio_greater; 41template <class R1, class R2> struct ratio_greater_equal; 42 43// convenience SI typedefs 44typedef ratio<1, 1000000000000000000000000> yocto; // not supported 45typedef ratio<1, 1000000000000000000000> zepto; // not supported 46typedef ratio<1, 1000000000000000000> atto; 47typedef ratio<1, 1000000000000000> femto; 48typedef ratio<1, 1000000000000> pico; 49typedef ratio<1, 1000000000> nano; 50typedef ratio<1, 1000000> micro; 51typedef ratio<1, 1000> milli; 52typedef ratio<1, 100> centi; 53typedef ratio<1, 10> deci; 54typedef ratio< 10, 1> deca; 55typedef ratio< 100, 1> hecto; 56typedef ratio< 1000, 1> kilo; 57typedef ratio< 1000000, 1> mega; 58typedef ratio< 1000000000, 1> giga; 59typedef ratio< 1000000000000, 1> tera; 60typedef ratio< 1000000000000000, 1> peta; 61typedef ratio< 1000000000000000000, 1> exa; 62typedef ratio< 1000000000000000000000, 1> zetta; // not supported 63typedef ratio<1000000000000000000000000, 1> yotta; // not supported 64 65 // 20.11.5, ratio comparison 66 template <class R1, class R2> constexpr bool ratio_equal_v 67 = ratio_equal<R1, R2>::value; // C++17 68 template <class R1, class R2> constexpr bool ratio_not_equal_v 69 = ratio_not_equal<R1, R2>::value; // C++17 70 template <class R1, class R2> constexpr bool ratio_less_v 71 = ratio_less<R1, R2>::value; // C++17 72 template <class R1, class R2> constexpr bool ratio_less_equal_v 73 = ratio_less_equal<R1, R2>::value; // C++17 74 template <class R1, class R2> constexpr bool ratio_greater_v 75 = ratio_greater<R1, R2>::value; // C++17 76 template <class R1, class R2> constexpr bool ratio_greater_equal_v 77 = ratio_greater_equal<R1, R2>::value; // C++17 78} 79*/ 80 81#include <__config> 82#include <cstdint> 83#include <climits> 84#include <type_traits> 85 86#include <__undef_min_max> 87 88#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER) 89#pragma GCC system_header 90#endif 91 92_LIBCPP_BEGIN_NAMESPACE_STD 93 94// __static_gcd 95 96template <intmax_t _Xp, intmax_t _Yp> 97struct __static_gcd 98{ 99 static const intmax_t value = __static_gcd<_Yp, _Xp % _Yp>::value; 100}; 101 102template <intmax_t _Xp> 103struct __static_gcd<_Xp, 0> 104{ 105 static const intmax_t value = _Xp; 106}; 107 108template <> 109struct __static_gcd<0, 0> 110{ 111 static const intmax_t value = 1; 112}; 113 114// __static_lcm 115 116template <intmax_t _Xp, intmax_t _Yp> 117struct __static_lcm 118{ 119 static const intmax_t value = _Xp / __static_gcd<_Xp, _Yp>::value * _Yp; 120}; 121 122template <intmax_t _Xp> 123struct __static_abs 124{ 125 static const intmax_t value = _Xp < 0 ? -_Xp : _Xp; 126}; 127 128template <intmax_t _Xp> 129struct __static_sign 130{ 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{ 140 static const intmax_t min = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)) + 1; 141 static const intmax_t max = -min; 142 143 static_assert(_Xp <= max - _Yp, "overflow in __ll_add"); 144public: 145 static const intmax_t value = _Xp + _Yp; 146}; 147 148template <intmax_t _Xp, intmax_t _Yp> 149class __ll_add<_Xp, _Yp, 0> 150{ 151public: 152 static const intmax_t value = _Xp; 153}; 154 155template <intmax_t _Xp, intmax_t _Yp> 156class __ll_add<_Xp, _Yp, -1> 157{ 158 static const intmax_t min = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)) + 1; 159 static const intmax_t max = -min; 160 161 static_assert(min - _Yp <= _Xp, "overflow in __ll_add"); 162public: 163 static const intmax_t value = _Xp + _Yp; 164}; 165 166template <intmax_t _Xp, intmax_t _Yp, intmax_t = __static_sign<_Yp>::value> 167class __ll_sub; 168 169template <intmax_t _Xp, intmax_t _Yp> 170class __ll_sub<_Xp, _Yp, 1> 171{ 172 static const intmax_t min = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)) + 1; 173 static const intmax_t max = -min; 174 175 static_assert(min + _Yp <= _Xp, "overflow in __ll_sub"); 176public: 177 static const intmax_t value = _Xp - _Yp; 178}; 179 180template <intmax_t _Xp, intmax_t _Yp> 181class __ll_sub<_Xp, _Yp, 0> 182{ 183public: 184 static const intmax_t value = _Xp; 185}; 186 187template <intmax_t _Xp, intmax_t _Yp> 188class __ll_sub<_Xp, _Yp, -1> 189{ 190 static const intmax_t min = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)) + 1; 191 static const intmax_t max = -min; 192 193 static_assert(_Xp <= max + _Yp, "overflow in __ll_sub"); 194public: 195 static const intmax_t value = _Xp - _Yp; 196}; 197 198template <intmax_t _Xp, intmax_t _Yp> 199class __ll_mul 200{ 201 static const intmax_t nan = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)); 202 static const intmax_t min = nan + 1; 203 static const intmax_t max = -min; 204 static const intmax_t __a_x = __static_abs<_Xp>::value; 205 static const intmax_t __a_y = __static_abs<_Yp>::value; 206 207 static_assert(_Xp != nan && _Yp != nan && __a_x <= max / __a_y, "overflow in __ll_mul"); 208public: 209 static const intmax_t value = _Xp * _Yp; 210}; 211 212template <intmax_t _Yp> 213class __ll_mul<0, _Yp> 214{ 215public: 216 static const intmax_t value = 0; 217}; 218 219template <intmax_t _Xp> 220class __ll_mul<_Xp, 0> 221{ 222public: 223 static const intmax_t value = 0; 224}; 225 226template <> 227class __ll_mul<0, 0> 228{ 229public: 230 static const intmax_t value = 0; 231}; 232 233// Not actually used but left here in case needed in future maintenance 234template <intmax_t _Xp, intmax_t _Yp> 235class __ll_div 236{ 237 static const intmax_t nan = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)); 238 static const intmax_t min = nan + 1; 239 static const intmax_t max = -min; 240 241 static_assert(_Xp != nan && _Yp != nan && _Yp != 0, "overflow in __ll_div"); 242public: 243 static const intmax_t value = _Xp / _Yp; 244}; 245 246template <intmax_t _Num, intmax_t _Den = 1> 247class _LIBCPP_TEMPLATE_VIS ratio 248{ 249 static_assert(__static_abs<_Num>::value >= 0, "ratio numerator is out of range"); 250 static_assert(_Den != 0, "ratio divide by 0"); 251 static_assert(__static_abs<_Den>::value > 0, "ratio denominator is out of range"); 252 static _LIBCPP_CONSTEXPR const intmax_t __na = __static_abs<_Num>::value; 253 static _LIBCPP_CONSTEXPR const intmax_t __da = __static_abs<_Den>::value; 254 static _LIBCPP_CONSTEXPR const intmax_t __s = __static_sign<_Num>::value * __static_sign<_Den>::value; 255 static _LIBCPP_CONSTEXPR const intmax_t __gcd = __static_gcd<__na, __da>::value; 256public: 257 static _LIBCPP_CONSTEXPR const intmax_t num = __s * __na / __gcd; 258 static _LIBCPP_CONSTEXPR const intmax_t den = __da / __gcd; 259 260 typedef ratio<num, den> type; 261}; 262 263template <intmax_t _Num, intmax_t _Den> 264_LIBCPP_CONSTEXPR const intmax_t ratio<_Num, _Den>::num; 265 266template <intmax_t _Num, intmax_t _Den> 267_LIBCPP_CONSTEXPR const intmax_t ratio<_Num, _Den>::den; 268 269template <class _Tp> struct __is_ratio : false_type {}; 270template <intmax_t _Num, intmax_t _Den> struct __is_ratio<ratio<_Num, _Den> > : true_type {}; 271 272typedef ratio<1LL, 1000000000000000000LL> atto; 273typedef ratio<1LL, 1000000000000000LL> femto; 274typedef ratio<1LL, 1000000000000LL> pico; 275typedef ratio<1LL, 1000000000LL> nano; 276typedef ratio<1LL, 1000000LL> micro; 277typedef ratio<1LL, 1000LL> milli; 278typedef ratio<1LL, 100LL> centi; 279typedef ratio<1LL, 10LL> deci; 280typedef ratio< 10LL, 1LL> deca; 281typedef ratio< 100LL, 1LL> hecto; 282typedef ratio< 1000LL, 1LL> kilo; 283typedef ratio< 1000000LL, 1LL> mega; 284typedef ratio< 1000000000LL, 1LL> giga; 285typedef ratio< 1000000000000LL, 1LL> tera; 286typedef ratio< 1000000000000000LL, 1LL> peta; 287typedef ratio<1000000000000000000LL, 1LL> exa; 288 289template <class _R1, class _R2> 290struct __ratio_multiply 291{ 292private: 293 static const intmax_t __gcd_n1_d2 = __static_gcd<_R1::num, _R2::den>::value; 294 static const intmax_t __gcd_d1_n2 = __static_gcd<_R1::den, _R2::num>::value; 295public: 296 typedef typename ratio 297 < 298 __ll_mul<_R1::num / __gcd_n1_d2, _R2::num / __gcd_d1_n2>::value, 299 __ll_mul<_R2::den / __gcd_n1_d2, _R1::den / __gcd_d1_n2>::value 300 >::type type; 301}; 302 303#ifndef _LIBCPP_CXX03_LANG 304 305template <class _R1, class _R2> using ratio_multiply 306 = typename __ratio_multiply<_R1, _R2>::type; 307 308#else // _LIBCPP_CXX03_LANG 309 310template <class _R1, class _R2> 311struct _LIBCPP_TEMPLATE_VIS ratio_multiply 312 : public __ratio_multiply<_R1, _R2>::type {}; 313 314#endif // _LIBCPP_CXX03_LANG 315 316template <class _R1, class _R2> 317struct __ratio_divide 318{ 319private: 320 static const intmax_t __gcd_n1_n2 = __static_gcd<_R1::num, _R2::num>::value; 321 static const intmax_t __gcd_d1_d2 = __static_gcd<_R1::den, _R2::den>::value; 322public: 323 typedef typename ratio 324 < 325 __ll_mul<_R1::num / __gcd_n1_n2, _R2::den / __gcd_d1_d2>::value, 326 __ll_mul<_R2::num / __gcd_n1_n2, _R1::den / __gcd_d1_d2>::value 327 >::type type; 328}; 329 330#ifndef _LIBCPP_CXX03_LANG 331 332template <class _R1, class _R2> using ratio_divide 333 = typename __ratio_divide<_R1, _R2>::type; 334 335#else // _LIBCPP_CXX03_LANG 336 337template <class _R1, class _R2> 338struct _LIBCPP_TEMPLATE_VIS ratio_divide 339 : public __ratio_divide<_R1, _R2>::type {}; 340 341#endif // _LIBCPP_CXX03_LANG 342 343template <class _R1, class _R2> 344struct __ratio_add 345{ 346private: 347 static const intmax_t __gcd_n1_n2 = __static_gcd<_R1::num, _R2::num>::value; 348 static const intmax_t __gcd_d1_d2 = __static_gcd<_R1::den, _R2::den>::value; 349public: 350 typedef typename ratio_multiply 351 < 352 ratio<__gcd_n1_n2, _R1::den / __gcd_d1_d2>, 353 ratio 354 < 355 __ll_add 356 < 357 __ll_mul<_R1::num / __gcd_n1_n2, _R2::den / __gcd_d1_d2>::value, 358 __ll_mul<_R2::num / __gcd_n1_n2, _R1::den / __gcd_d1_d2>::value 359 >::value, 360 _R2::den 361 > 362 >::type type; 363}; 364 365#ifndef _LIBCPP_CXX03_LANG 366 367template <class _R1, class _R2> using ratio_add 368 = typename __ratio_add<_R1, _R2>::type; 369 370#else // _LIBCPP_CXX03_LANG 371 372template <class _R1, class _R2> 373struct _LIBCPP_TEMPLATE_VIS ratio_add 374 : public __ratio_add<_R1, _R2>::type {}; 375 376#endif // _LIBCPP_CXX03_LANG 377 378template <class _R1, class _R2> 379struct __ratio_subtract 380{ 381private: 382 static const intmax_t __gcd_n1_n2 = __static_gcd<_R1::num, _R2::num>::value; 383 static const intmax_t __gcd_d1_d2 = __static_gcd<_R1::den, _R2::den>::value; 384public: 385 typedef typename ratio_multiply 386 < 387 ratio<__gcd_n1_n2, _R1::den / __gcd_d1_d2>, 388 ratio 389 < 390 __ll_sub 391 < 392 __ll_mul<_R1::num / __gcd_n1_n2, _R2::den / __gcd_d1_d2>::value, 393 __ll_mul<_R2::num / __gcd_n1_n2, _R1::den / __gcd_d1_d2>::value 394 >::value, 395 _R2::den 396 > 397 >::type type; 398}; 399 400#ifndef _LIBCPP_CXX03_LANG 401 402template <class _R1, class _R2> using ratio_subtract 403 = typename __ratio_subtract<_R1, _R2>::type; 404 405#else // _LIBCPP_CXX03_LANG 406 407template <class _R1, class _R2> 408struct _LIBCPP_TEMPLATE_VIS ratio_subtract 409 : public __ratio_subtract<_R1, _R2>::type {}; 410 411#endif // _LIBCPP_CXX03_LANG 412 413// ratio_equal 414 415template <class _R1, class _R2> 416struct _LIBCPP_TEMPLATE_VIS ratio_equal 417 : public _LIBCPP_BOOL_CONSTANT((_R1::num == _R2::num && _R1::den == _R2::den)) {}; 418 419template <class _R1, class _R2> 420struct _LIBCPP_TEMPLATE_VIS ratio_not_equal 421 : public _LIBCPP_BOOL_CONSTANT((!ratio_equal<_R1, _R2>::value)) {}; 422 423// ratio_less 424 425template <class _R1, class _R2, bool _Odd = false, 426 intmax_t _Q1 = _R1::num / _R1::den, intmax_t _M1 = _R1::num % _R1::den, 427 intmax_t _Q2 = _R2::num / _R2::den, intmax_t _M2 = _R2::num % _R2::den> 428struct __ratio_less1 429{ 430 static const bool value = _Odd ? _Q2 < _Q1 : _Q1 < _Q2; 431}; 432 433template <class _R1, class _R2, bool _Odd, intmax_t _Qp> 434struct __ratio_less1<_R1, _R2, _Odd, _Qp, 0, _Qp, 0> 435{ 436 static const bool value = false; 437}; 438 439template <class _R1, class _R2, bool _Odd, intmax_t _Qp, intmax_t _M2> 440struct __ratio_less1<_R1, _R2, _Odd, _Qp, 0, _Qp, _M2> 441{ 442 static const bool value = !_Odd; 443}; 444 445template <class _R1, class _R2, bool _Odd, intmax_t _Qp, intmax_t _M1> 446struct __ratio_less1<_R1, _R2, _Odd, _Qp, _M1, _Qp, 0> 447{ 448 static const bool value = _Odd; 449}; 450 451template <class _R1, class _R2, bool _Odd, intmax_t _Qp, intmax_t _M1, 452 intmax_t _M2> 453struct __ratio_less1<_R1, _R2, _Odd, _Qp, _M1, _Qp, _M2> 454{ 455 static const bool value = __ratio_less1<ratio<_R1::den, _M1>, 456 ratio<_R2::den, _M2>, !_Odd>::value; 457}; 458 459template <class _R1, class _R2, intmax_t _S1 = __static_sign<_R1::num>::value, 460 intmax_t _S2 = __static_sign<_R2::num>::value> 461struct __ratio_less 462{ 463 static const bool value = _S1 < _S2; 464}; 465 466template <class _R1, class _R2> 467struct __ratio_less<_R1, _R2, 1LL, 1LL> 468{ 469 static const bool value = __ratio_less1<_R1, _R2>::value; 470}; 471 472template <class _R1, class _R2> 473struct __ratio_less<_R1, _R2, -1LL, -1LL> 474{ 475 static const bool value = __ratio_less1<ratio<-_R2::num, _R2::den>, ratio<-_R1::num, _R1::den> >::value; 476}; 477 478template <class _R1, class _R2> 479struct _LIBCPP_TEMPLATE_VIS ratio_less 480 : public _LIBCPP_BOOL_CONSTANT((__ratio_less<_R1, _R2>::value)) {}; 481 482template <class _R1, class _R2> 483struct _LIBCPP_TEMPLATE_VIS ratio_less_equal 484 : public _LIBCPP_BOOL_CONSTANT((!ratio_less<_R2, _R1>::value)) {}; 485 486template <class _R1, class _R2> 487struct _LIBCPP_TEMPLATE_VIS ratio_greater 488 : public _LIBCPP_BOOL_CONSTANT((ratio_less<_R2, _R1>::value)) {}; 489 490template <class _R1, class _R2> 491struct _LIBCPP_TEMPLATE_VIS ratio_greater_equal 492 : public _LIBCPP_BOOL_CONSTANT((!ratio_less<_R1, _R2>::value)) {}; 493 494template <class _R1, class _R2> 495struct __ratio_gcd 496{ 497 typedef ratio<__static_gcd<_R1::num, _R2::num>::value, 498 __static_lcm<_R1::den, _R2::den>::value> type; 499}; 500 501#if _LIBCPP_STD_VER > 14 && !defined(_LIBCPP_HAS_NO_VARIABLE_TEMPLATES) 502template <class _R1, class _R2> _LIBCPP_CONSTEXPR bool ratio_equal_v 503 = ratio_equal<_R1, _R2>::value; 504 505template <class _R1, class _R2> _LIBCPP_CONSTEXPR bool ratio_not_equal_v 506 = ratio_not_equal<_R1, _R2>::value; 507 508template <class _R1, class _R2> _LIBCPP_CONSTEXPR bool ratio_less_v 509 = ratio_less<_R1, _R2>::value; 510 511template <class _R1, class _R2> _LIBCPP_CONSTEXPR bool ratio_less_equal_v 512 = ratio_less_equal<_R1, _R2>::value; 513 514template <class _R1, class _R2> _LIBCPP_CONSTEXPR bool ratio_greater_v 515 = ratio_greater<_R1, _R2>::value; 516 517template <class _R1, class _R2> _LIBCPP_CONSTEXPR bool ratio_greater_equal_v 518 = ratio_greater_equal<_R1, _R2>::value; 519#endif 520 521_LIBCPP_END_NAMESPACE_STD 522 523#endif // _LIBCPP_RATIO 524