ratio revision 1.10
1 // ratio -*- C++ -*- 2 3 // Copyright (C) 2008-2019 Free Software Foundation, Inc. 4 // 5 // This file is part of the GNU ISO C++ Library. This library is free 6 // software; you can redistribute it and/or modify it under the 7 // terms of the GNU General Public License as published by the 8 // Free Software Foundation; either version 3, or (at your option) 9 // any later version. 10 11 // This library is distributed in the hope that it will be useful, 12 // but WITHOUT ANY WARRANTY; without even the implied warranty of 13 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 14 // GNU General Public License for more details. 15 16 // Under Section 7 of GPL version 3, you are granted additional 17 // permissions described in the GCC Runtime Library Exception, version 18 // 3.1, as published by the Free Software Foundation. 19 20 // You should have received a copy of the GNU General Public License and 21 // a copy of the GCC Runtime Library Exception along with this program; 22 // see the files COPYING3 and COPYING.RUNTIME respectively. If not, see 23 // <http://www.gnu.org/licenses/>. 24 25 /** @file include/ratio 26 * This is a Standard C++ Library header. 27 */ 28 29 #ifndef _GLIBCXX_RATIO 30 #define _GLIBCXX_RATIO 1 31 32 #pragma GCC system_header 33 34 #if __cplusplus < 201103L 35 # include <bits/c++0x_warning.h> 36 #else 37 38 #include <type_traits> 39 #include <cstdint> // intmax_t, uintmax_t 40 41 namespace std _GLIBCXX_VISIBILITY(default) 42 { 43 _GLIBCXX_BEGIN_NAMESPACE_VERSION 44 45 /** 46 * @defgroup ratio Rational Arithmetic 47 * @ingroup utilities 48 * 49 * Compile time representation of finite rational numbers. 50 * @{ 51 */ 52 53 template<intmax_t _Pn> 54 struct __static_sign 55 : integral_constant<intmax_t, (_Pn < 0) ? -1 : 1> 56 { }; 57 58 template<intmax_t _Pn> 59 struct __static_abs 60 : integral_constant<intmax_t, _Pn * __static_sign<_Pn>::value> 61 { }; 62 63 template<intmax_t _Pn, intmax_t _Qn> 64 struct __static_gcd 65 : __static_gcd<_Qn, (_Pn % _Qn)> 66 { }; 67 68 template<intmax_t _Pn> 69 struct __static_gcd<_Pn, 0> 70 : integral_constant<intmax_t, __static_abs<_Pn>::value> 71 { }; 72 73 template<intmax_t _Qn> 74 struct __static_gcd<0, _Qn> 75 : integral_constant<intmax_t, __static_abs<_Qn>::value> 76 { }; 77 78 // Let c = 2^(half # of bits in an intmax_t) 79 // then we find a1, a0, b1, b0 s.t. N = a1*c + a0, M = b1*c + b0 80 // The multiplication of N and M becomes, 81 // N * M = (a1 * b1)c^2 + (a0 * b1 + b0 * a1)c + a0 * b0 82 // Multiplication is safe if each term and the sum of the terms 83 // is representable by intmax_t. 84 template<intmax_t _Pn, intmax_t _Qn> 85 struct __safe_multiply 86 { 87 private: 88 static const uintmax_t __c = uintmax_t(1) << (sizeof(intmax_t) * 4); 89 90 static const uintmax_t __a0 = __static_abs<_Pn>::value % __c; 91 static const uintmax_t __a1 = __static_abs<_Pn>::value / __c; 92 static const uintmax_t __b0 = __static_abs<_Qn>::value % __c; 93 static const uintmax_t __b1 = __static_abs<_Qn>::value / __c; 94 95 static_assert(__a1 == 0 || __b1 == 0, 96 "overflow in multiplication"); 97 static_assert(__a0 * __b1 + __b0 * __a1 < (__c >> 1), 98 "overflow in multiplication"); 99 static_assert(__b0 * __a0 <= __INTMAX_MAX__, 100 "overflow in multiplication"); 101 static_assert((__a0 * __b1 + __b0 * __a1) * __c 102 <= __INTMAX_MAX__ - __b0 * __a0, 103 "overflow in multiplication"); 104 105 public: 106 static const intmax_t value = _Pn * _Qn; 107 }; 108 109 // Some double-precision utilities, where numbers are represented as 110 // __hi*2^(8*sizeof(uintmax_t)) + __lo. 111 template<uintmax_t __hi1, uintmax_t __lo1, uintmax_t __hi2, uintmax_t __lo2> 112 struct __big_less 113 : integral_constant<bool, (__hi1 < __hi2 114 || (__hi1 == __hi2 && __lo1 < __lo2))> 115 { }; 116 117 template<uintmax_t __hi1, uintmax_t __lo1, uintmax_t __hi2, uintmax_t __lo2> 118 struct __big_add 119 { 120 static constexpr uintmax_t __lo = __lo1 + __lo2; 121 static constexpr uintmax_t __hi = (__hi1 + __hi2 + 122 (__lo1 + __lo2 < __lo1)); // carry 123 }; 124 125 // Subtract a number from a bigger one. 126 template<uintmax_t __hi1, uintmax_t __lo1, uintmax_t __hi2, uintmax_t __lo2> 127 struct __big_sub 128 { 129 static_assert(!__big_less<__hi1, __lo1, __hi2, __lo2>::value, 130 "Internal library error"); 131 static constexpr uintmax_t __lo = __lo1 - __lo2; 132 static constexpr uintmax_t __hi = (__hi1 - __hi2 - 133 (__lo1 < __lo2)); // carry 134 }; 135 136 // Same principle as __safe_multiply. 137 template<uintmax_t __x, uintmax_t __y> 138 struct __big_mul 139 { 140 private: 141 static constexpr uintmax_t __c = uintmax_t(1) << (sizeof(intmax_t) * 4); 142 static constexpr uintmax_t __x0 = __x % __c; 143 static constexpr uintmax_t __x1 = __x / __c; 144 static constexpr uintmax_t __y0 = __y % __c; 145 static constexpr uintmax_t __y1 = __y / __c; 146 static constexpr uintmax_t __x0y0 = __x0 * __y0; 147 static constexpr uintmax_t __x0y1 = __x0 * __y1; 148 static constexpr uintmax_t __x1y0 = __x1 * __y0; 149 static constexpr uintmax_t __x1y1 = __x1 * __y1; 150 static constexpr uintmax_t __mix = __x0y1 + __x1y0; // possible carry... 151 static constexpr uintmax_t __mix_lo = __mix * __c; 152 static constexpr uintmax_t __mix_hi 153 = __mix / __c + ((__mix < __x0y1) ? __c : 0); // ... added here 154 typedef __big_add<__mix_hi, __mix_lo, __x1y1, __x0y0> _Res; 155 public: 156 static constexpr uintmax_t __hi = _Res::__hi; 157 static constexpr uintmax_t __lo = _Res::__lo; 158 }; 159 160 // Adapted from __udiv_qrnnd_c in longlong.h 161 // This version assumes that the high bit of __d is 1. 162 template<uintmax_t __n1, uintmax_t __n0, uintmax_t __d> 163 struct __big_div_impl 164 { 165 private: 166 static_assert(__d >= (uintmax_t(1) << (sizeof(intmax_t) * 8 - 1)), 167 "Internal library error"); 168 static_assert(__n1 < __d, "Internal library error"); 169 static constexpr uintmax_t __c = uintmax_t(1) << (sizeof(intmax_t) * 4); 170 static constexpr uintmax_t __d1 = __d / __c; 171 static constexpr uintmax_t __d0 = __d % __c; 172 173 static constexpr uintmax_t __q1x = __n1 / __d1; 174 static constexpr uintmax_t __r1x = __n1 % __d1; 175 static constexpr uintmax_t __m = __q1x * __d0; 176 static constexpr uintmax_t __r1y = __r1x * __c + __n0 / __c; 177 static constexpr uintmax_t __r1z = __r1y + __d; 178 static constexpr uintmax_t __r1 179 = ((__r1y < __m) ? ((__r1z >= __d) && (__r1z < __m)) 180 ? (__r1z + __d) : __r1z : __r1y) - __m; 181 static constexpr uintmax_t __q1 182 = __q1x - ((__r1y < __m) 183 ? ((__r1z >= __d) && (__r1z < __m)) ? 2 : 1 : 0); 184 static constexpr uintmax_t __q0x = __r1 / __d1; 185 static constexpr uintmax_t __r0x = __r1 % __d1; 186 static constexpr uintmax_t __n = __q0x * __d0; 187 static constexpr uintmax_t __r0y = __r0x * __c + __n0 % __c; 188 static constexpr uintmax_t __r0z = __r0y + __d; 189 static constexpr uintmax_t __r0 190 = ((__r0y < __n) ? ((__r0z >= __d) && (__r0z < __n)) 191 ? (__r0z + __d) : __r0z : __r0y) - __n; 192 static constexpr uintmax_t __q0 193 = __q0x - ((__r0y < __n) ? ((__r0z >= __d) 194 && (__r0z < __n)) ? 2 : 1 : 0); 195 196 public: 197 static constexpr uintmax_t __quot = __q1 * __c + __q0; 198 static constexpr uintmax_t __rem = __r0; 199 200 private: 201 typedef __big_mul<__quot, __d> _Prod; 202 typedef __big_add<_Prod::__hi, _Prod::__lo, 0, __rem> _Sum; 203 static_assert(_Sum::__hi == __n1 && _Sum::__lo == __n0, 204 "Internal library error"); 205 }; 206 207 template<uintmax_t __n1, uintmax_t __n0, uintmax_t __d> 208 struct __big_div 209 { 210 private: 211 static_assert(__d != 0, "Internal library error"); 212 static_assert(sizeof (uintmax_t) == sizeof (unsigned long long), 213 "This library calls __builtin_clzll on uintmax_t, which " 214 "is unsafe on your platform. Please complain to " 215 "http://gcc.gnu.org/bugzilla/"); 216 static constexpr int __shift = __builtin_clzll(__d); 217 static constexpr int __coshift_ = sizeof(uintmax_t) * 8 - __shift; 218 static constexpr int __coshift = (__shift != 0) ? __coshift_ : 0; 219 static constexpr uintmax_t __c1 = uintmax_t(1) << __shift; 220 static constexpr uintmax_t __c2 = uintmax_t(1) << __coshift; 221 static constexpr uintmax_t __new_d = __d * __c1; 222 static constexpr uintmax_t __new_n0 = __n0 * __c1; 223 static constexpr uintmax_t __n1_shifted = (__n1 % __d) * __c1; 224 static constexpr uintmax_t __n0_top = (__shift != 0) ? (__n0 / __c2) : 0; 225 static constexpr uintmax_t __new_n1 = __n1_shifted + __n0_top; 226 typedef __big_div_impl<__new_n1, __new_n0, __new_d> _Res; 227 228 public: 229 static constexpr uintmax_t __quot_hi = __n1 / __d; 230 static constexpr uintmax_t __quot_lo = _Res::__quot; 231 static constexpr uintmax_t __rem = _Res::__rem / __c1; 232 233 private: 234 typedef __big_mul<__quot_lo, __d> _P0; 235 typedef __big_mul<__quot_hi, __d> _P1; 236 typedef __big_add<_P0::__hi, _P0::__lo, _P1::__lo, __rem> _Sum; 237 // No overflow. 238 static_assert(_P1::__hi == 0, "Internal library error"); 239 static_assert(_Sum::__hi >= _P0::__hi, "Internal library error"); 240 // Matches the input data. 241 static_assert(_Sum::__hi == __n1 && _Sum::__lo == __n0, 242 "Internal library error"); 243 static_assert(__rem < __d, "Internal library error"); 244 }; 245 246 /** 247 * @brief Provides compile-time rational arithmetic. 248 * 249 * This class template represents any finite rational number with a 250 * numerator and denominator representable by compile-time constants of 251 * type intmax_t. The ratio is simplified when instantiated. 252 * 253 * For example: 254 * @code 255 * std::ratio<7,-21>::num == -1; 256 * std::ratio<7,-21>::den == 3; 257 * @endcode 258 * 259 */ 260 template<intmax_t _Num, intmax_t _Den = 1> 261 struct ratio 262 { 263 static_assert(_Den != 0, "denominator cannot be zero"); 264 static_assert(_Num >= -__INTMAX_MAX__ && _Den >= -__INTMAX_MAX__, 265 "out of range"); 266 267 // Note: sign(N) * abs(N) == N 268 static constexpr intmax_t num = 269 _Num * __static_sign<_Den>::value / __static_gcd<_Num, _Den>::value; 270 271 static constexpr intmax_t den = 272 __static_abs<_Den>::value / __static_gcd<_Num, _Den>::value; 273 274 typedef ratio<num, den> type; 275 }; 276 277 template<intmax_t _Num, intmax_t _Den> 278 constexpr intmax_t ratio<_Num, _Den>::num; 279 280 template<intmax_t _Num, intmax_t _Den> 281 constexpr intmax_t ratio<_Num, _Den>::den; 282 283 template<typename _R1, typename _R2> 284 struct __ratio_multiply 285 { 286 private: 287 static const intmax_t __gcd1 = 288 __static_gcd<_R1::num, _R2::den>::value; 289 static const intmax_t __gcd2 = 290 __static_gcd<_R2::num, _R1::den>::value; 291 292 public: 293 typedef ratio< 294 __safe_multiply<(_R1::num / __gcd1), 295 (_R2::num / __gcd2)>::value, 296 __safe_multiply<(_R1::den / __gcd2), 297 (_R2::den / __gcd1)>::value> type; 298 299 static constexpr intmax_t num = type::num; 300 static constexpr intmax_t den = type::den; 301 }; 302 303 template<typename _R1, typename _R2> 304 constexpr intmax_t __ratio_multiply<_R1, _R2>::num; 305 306 template<typename _R1, typename _R2> 307 constexpr intmax_t __ratio_multiply<_R1, _R2>::den; 308 309 /// ratio_multiply 310 template<typename _R1, typename _R2> 311 using ratio_multiply = typename __ratio_multiply<_R1, _R2>::type; 312 313 template<typename _R1, typename _R2> 314 struct __ratio_divide 315 { 316 static_assert(_R2::num != 0, "division by 0"); 317 318 typedef typename __ratio_multiply< 319 _R1, 320 ratio<_R2::den, _R2::num>>::type type; 321 322 static constexpr intmax_t num = type::num; 323 static constexpr intmax_t den = type::den; 324 }; 325 326 template<typename _R1, typename _R2> 327 constexpr intmax_t __ratio_divide<_R1, _R2>::num; 328 329 template<typename _R1, typename _R2> 330 constexpr intmax_t __ratio_divide<_R1, _R2>::den; 331 332 /// ratio_divide 333 template<typename _R1, typename _R2> 334 using ratio_divide = typename __ratio_divide<_R1, _R2>::type; 335 336 /// ratio_equal 337 template<typename _R1, typename _R2> 338 struct ratio_equal 339 : integral_constant<bool, _R1::num == _R2::num && _R1::den == _R2::den> 340 { }; 341 342 /// ratio_not_equal 343 template<typename _R1, typename _R2> 344 struct ratio_not_equal 345 : integral_constant<bool, !ratio_equal<_R1, _R2>::value> 346 { }; 347 348 // Both numbers are positive. 349 template<typename _R1, typename _R2, 350 typename _Left = __big_mul<_R1::num,_R2::den>, 351 typename _Right = __big_mul<_R2::num,_R1::den> > 352 struct __ratio_less_impl_1 353 : integral_constant<bool, __big_less<_Left::__hi, _Left::__lo, 354 _Right::__hi, _Right::__lo>::value> 355 { }; 356 357 template<typename _R1, typename _R2, 358 bool = (_R1::num == 0 || _R2::num == 0 359 || (__static_sign<_R1::num>::value 360 != __static_sign<_R2::num>::value)), 361 bool = (__static_sign<_R1::num>::value == -1 362 && __static_sign<_R2::num>::value == -1)> 363 struct __ratio_less_impl 364 : __ratio_less_impl_1<_R1, _R2>::type 365 { }; 366 367 template<typename _R1, typename _R2> 368 struct __ratio_less_impl<_R1, _R2, true, false> 369 : integral_constant<bool, _R1::num < _R2::num> 370 { }; 371 372 template<typename _R1, typename _R2> 373 struct __ratio_less_impl<_R1, _R2, false, true> 374 : __ratio_less_impl_1<ratio<-_R2::num, _R2::den>, 375 ratio<-_R1::num, _R1::den> >::type 376 { }; 377 378 /// ratio_less 379 template<typename _R1, typename _R2> 380 struct ratio_less 381 : __ratio_less_impl<_R1, _R2>::type 382 { }; 383 384 /// ratio_less_equal 385 template<typename _R1, typename _R2> 386 struct ratio_less_equal 387 : integral_constant<bool, !ratio_less<_R2, _R1>::value> 388 { }; 389 390 /// ratio_greater 391 template<typename _R1, typename _R2> 392 struct ratio_greater 393 : integral_constant<bool, ratio_less<_R2, _R1>::value> 394 { }; 395 396 /// ratio_greater_equal 397 template<typename _R1, typename _R2> 398 struct ratio_greater_equal 399 : integral_constant<bool, !ratio_less<_R1, _R2>::value> 400 { }; 401 402 #if __cplusplus > 201402L 403 template <typename _R1, typename _R2> 404 inline constexpr bool ratio_equal_v = ratio_equal<_R1, _R2>::value; 405 template <typename _R1, typename _R2> 406 inline constexpr bool ratio_not_equal_v = ratio_not_equal<_R1, _R2>::value; 407 template <typename _R1, typename _R2> 408 inline constexpr bool ratio_less_v = ratio_less<_R1, _R2>::value; 409 template <typename _R1, typename _R2> 410 inline constexpr bool ratio_less_equal_v = 411 ratio_less_equal<_R1, _R2>::value; 412 template <typename _R1, typename _R2> 413 inline constexpr bool ratio_greater_v = ratio_greater<_R1, _R2>::value; 414 template <typename _R1, typename _R2> 415 inline constexpr bool ratio_greater_equal_v 416 = ratio_greater_equal<_R1, _R2>::value; 417 #endif // C++17 418 419 template<typename _R1, typename _R2, 420 bool = (_R1::num >= 0), 421 bool = (_R2::num >= 0), 422 bool = ratio_less<ratio<__static_abs<_R1::num>::value, _R1::den>, 423 ratio<__static_abs<_R2::num>::value, _R2::den> >::value> 424 struct __ratio_add_impl 425 { 426 private: 427 typedef typename __ratio_add_impl< 428 ratio<-_R1::num, _R1::den>, 429 ratio<-_R2::num, _R2::den> >::type __t; 430 public: 431 typedef ratio<-__t::num, __t::den> type; 432 }; 433 434 // True addition of nonnegative numbers. 435 template<typename _R1, typename _R2, bool __b> 436 struct __ratio_add_impl<_R1, _R2, true, true, __b> 437 { 438 private: 439 static constexpr uintmax_t __g = __static_gcd<_R1::den, _R2::den>::value; 440 static constexpr uintmax_t __d2 = _R2::den / __g; 441 typedef __big_mul<_R1::den, __d2> __d; 442 typedef __big_mul<_R1::num, _R2::den / __g> __x; 443 typedef __big_mul<_R2::num, _R1::den / __g> __y; 444 typedef __big_add<__x::__hi, __x::__lo, __y::__hi, __y::__lo> __n; 445 static_assert(__n::__hi >= __x::__hi, "Internal library error"); 446 typedef __big_div<__n::__hi, __n::__lo, __g> __ng; 447 static constexpr uintmax_t __g2 = __static_gcd<__ng::__rem, __g>::value; 448 typedef __big_div<__n::__hi, __n::__lo, __g2> __n_final; 449 static_assert(__n_final::__rem == 0, "Internal library error"); 450 static_assert(__n_final::__quot_hi == 0 && 451 __n_final::__quot_lo <= __INTMAX_MAX__, "overflow in addition"); 452 typedef __big_mul<_R1::den / __g2, __d2> __d_final; 453 static_assert(__d_final::__hi == 0 && 454 __d_final::__lo <= __INTMAX_MAX__, "overflow in addition"); 455 public: 456 typedef ratio<__n_final::__quot_lo, __d_final::__lo> type; 457 }; 458 459 template<typename _R1, typename _R2> 460 struct __ratio_add_impl<_R1, _R2, false, true, true> 461 : __ratio_add_impl<_R2, _R1> 462 { }; 463 464 // True subtraction of nonnegative numbers yielding a nonnegative result. 465 template<typename _R1, typename _R2> 466 struct __ratio_add_impl<_R1, _R2, true, false, false> 467 { 468 private: 469 static constexpr uintmax_t __g = __static_gcd<_R1::den, _R2::den>::value; 470 static constexpr uintmax_t __d2 = _R2::den / __g; 471 typedef __big_mul<_R1::den, __d2> __d; 472 typedef __big_mul<_R1::num, _R2::den / __g> __x; 473 typedef __big_mul<-_R2::num, _R1::den / __g> __y; 474 typedef __big_sub<__x::__hi, __x::__lo, __y::__hi, __y::__lo> __n; 475 typedef __big_div<__n::__hi, __n::__lo, __g> __ng; 476 static constexpr uintmax_t __g2 = __static_gcd<__ng::__rem, __g>::value; 477 typedef __big_div<__n::__hi, __n::__lo, __g2> __n_final; 478 static_assert(__n_final::__rem == 0, "Internal library error"); 479 static_assert(__n_final::__quot_hi == 0 && 480 __n_final::__quot_lo <= __INTMAX_MAX__, "overflow in addition"); 481 typedef __big_mul<_R1::den / __g2, __d2> __d_final; 482 static_assert(__d_final::__hi == 0 && 483 __d_final::__lo <= __INTMAX_MAX__, "overflow in addition"); 484 public: 485 typedef ratio<__n_final::__quot_lo, __d_final::__lo> type; 486 }; 487 488 template<typename _R1, typename _R2> 489 struct __ratio_add 490 { 491 typedef typename __ratio_add_impl<_R1, _R2>::type type; 492 static constexpr intmax_t num = type::num; 493 static constexpr intmax_t den = type::den; 494 }; 495 496 template<typename _R1, typename _R2> 497 constexpr intmax_t __ratio_add<_R1, _R2>::num; 498 499 template<typename _R1, typename _R2> 500 constexpr intmax_t __ratio_add<_R1, _R2>::den; 501 502 /// ratio_add 503 template<typename _R1, typename _R2> 504 using ratio_add = typename __ratio_add<_R1, _R2>::type; 505 506 template<typename _R1, typename _R2> 507 struct __ratio_subtract 508 { 509 typedef typename __ratio_add< 510 _R1, 511 ratio<-_R2::num, _R2::den>>::type type; 512 513 static constexpr intmax_t num = type::num; 514 static constexpr intmax_t den = type::den; 515 }; 516 517 template<typename _R1, typename _R2> 518 constexpr intmax_t __ratio_subtract<_R1, _R2>::num; 519 520 template<typename _R1, typename _R2> 521 constexpr intmax_t __ratio_subtract<_R1, _R2>::den; 522 523 /// ratio_subtract 524 template<typename _R1, typename _R2> 525 using ratio_subtract = typename __ratio_subtract<_R1, _R2>::type; 526 527 528 typedef ratio<1, 1000000000000000000> atto; 529 typedef ratio<1, 1000000000000000> femto; 530 typedef ratio<1, 1000000000000> pico; 531 typedef ratio<1, 1000000000> nano; 532 typedef ratio<1, 1000000> micro; 533 typedef ratio<1, 1000> milli; 534 typedef ratio<1, 100> centi; 535 typedef ratio<1, 10> deci; 536 typedef ratio< 10, 1> deca; 537 typedef ratio< 100, 1> hecto; 538 typedef ratio< 1000, 1> kilo; 539 typedef ratio< 1000000, 1> mega; 540 typedef ratio< 1000000000, 1> giga; 541 typedef ratio< 1000000000000, 1> tera; 542 typedef ratio< 1000000000000000, 1> peta; 543 typedef ratio< 1000000000000000000, 1> exa; 544 545 // @} group ratio 546 _GLIBCXX_END_NAMESPACE_VERSION 547 } // namespace 548 549 #endif // C++11 550 551 #endif //_GLIBCXX_RATIO 552
Indexes created Thu Sep 10 00:26:39 UTC 2026