ratio revision 1.1.1.8
1 // ratio -*- C++ -*- 2 3 // Copyright (C) 2008-2020 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 * @ingroup ratio 28 */ 29 30 #ifndef _GLIBCXX_RATIO 31 #define _GLIBCXX_RATIO 1 32 33 #pragma GCC system_header 34 35 #if __cplusplus < 201103L 36 # include <bits/c++0x_warning.h> 37 #else 38 39 #include <type_traits> 40 #include <cstdint> // intmax_t, uintmax_t 41 42 namespace std _GLIBCXX_VISIBILITY(default) 43 { 44 _GLIBCXX_BEGIN_NAMESPACE_VERSION 45 46 /** 47 * @defgroup ratio Rational Arithmetic 48 * @ingroup utilities 49 * 50 * Compile time representation of finite rational numbers. 51 * @{ 52 */ 53 54 /// @cond undocumented 55 56 template<intmax_t _Pn> 57 struct __static_sign 58 : integral_constant<intmax_t, (_Pn < 0) ? -1 : 1> 59 { }; 60 61 template<intmax_t _Pn> 62 struct __static_abs 63 : integral_constant<intmax_t, _Pn * __static_sign<_Pn>::value> 64 { }; 65 66 template<intmax_t _Pn, intmax_t _Qn> 67 struct __static_gcd 68 : __static_gcd<_Qn, (_Pn % _Qn)> 69 { }; 70 71 template<intmax_t _Pn> 72 struct __static_gcd<_Pn, 0> 73 : integral_constant<intmax_t, __static_abs<_Pn>::value> 74 { }; 75 76 template<intmax_t _Qn> 77 struct __static_gcd<0, _Qn> 78 : integral_constant<intmax_t, __static_abs<_Qn>::value> 79 { }; 80 81 // Let c = 2^(half # of bits in an intmax_t) 82 // then we find a1, a0, b1, b0 s.t. N = a1*c + a0, M = b1*c + b0 83 // The multiplication of N and M becomes, 84 // N * M = (a1 * b1)c^2 + (a0 * b1 + b0 * a1)c + a0 * b0 85 // Multiplication is safe if each term and the sum of the terms 86 // is representable by intmax_t. 87 template<intmax_t _Pn, intmax_t _Qn> 88 struct __safe_multiply 89 { 90 private: 91 static const uintmax_t __c = uintmax_t(1) << (sizeof(intmax_t) * 4); 92 93 static const uintmax_t __a0 = __static_abs<_Pn>::value % __c; 94 static const uintmax_t __a1 = __static_abs<_Pn>::value / __c; 95 static const uintmax_t __b0 = __static_abs<_Qn>::value % __c; 96 static const uintmax_t __b1 = __static_abs<_Qn>::value / __c; 97 98 static_assert(__a1 == 0 || __b1 == 0, 99 "overflow in multiplication"); 100 static_assert(__a0 * __b1 + __b0 * __a1 < (__c >> 1), 101 "overflow in multiplication"); 102 static_assert(__b0 * __a0 <= __INTMAX_MAX__, 103 "overflow in multiplication"); 104 static_assert((__a0 * __b1 + __b0 * __a1) * __c 105 <= __INTMAX_MAX__ - __b0 * __a0, 106 "overflow in multiplication"); 107 108 public: 109 static const intmax_t value = _Pn * _Qn; 110 }; 111 112 // Some double-precision utilities, where numbers are represented as 113 // __hi*2^(8*sizeof(uintmax_t)) + __lo. 114 template<uintmax_t __hi1, uintmax_t __lo1, uintmax_t __hi2, uintmax_t __lo2> 115 struct __big_less 116 : integral_constant<bool, (__hi1 < __hi2 117 || (__hi1 == __hi2 && __lo1 < __lo2))> 118 { }; 119 120 template<uintmax_t __hi1, uintmax_t __lo1, uintmax_t __hi2, uintmax_t __lo2> 121 struct __big_add 122 { 123 static constexpr uintmax_t __lo = __lo1 + __lo2; 124 static constexpr uintmax_t __hi = (__hi1 + __hi2 + 125 (__lo1 + __lo2 < __lo1)); // carry 126 }; 127 128 // Subtract a number from a bigger one. 129 template<uintmax_t __hi1, uintmax_t __lo1, uintmax_t __hi2, uintmax_t __lo2> 130 struct __big_sub 131 { 132 static_assert(!__big_less<__hi1, __lo1, __hi2, __lo2>::value, 133 "Internal library error"); 134 static constexpr uintmax_t __lo = __lo1 - __lo2; 135 static constexpr uintmax_t __hi = (__hi1 - __hi2 - 136 (__lo1 < __lo2)); // carry 137 }; 138 139 // Same principle as __safe_multiply. 140 template<uintmax_t __x, uintmax_t __y> 141 struct __big_mul 142 { 143 private: 144 static constexpr uintmax_t __c = uintmax_t(1) << (sizeof(intmax_t) * 4); 145 static constexpr uintmax_t __x0 = __x % __c; 146 static constexpr uintmax_t __x1 = __x / __c; 147 static constexpr uintmax_t __y0 = __y % __c; 148 static constexpr uintmax_t __y1 = __y / __c; 149 static constexpr uintmax_t __x0y0 = __x0 * __y0; 150 static constexpr uintmax_t __x0y1 = __x0 * __y1; 151 static constexpr uintmax_t __x1y0 = __x1 * __y0; 152 static constexpr uintmax_t __x1y1 = __x1 * __y1; 153 static constexpr uintmax_t __mix = __x0y1 + __x1y0; // possible carry... 154 static constexpr uintmax_t __mix_lo = __mix * __c; 155 static constexpr uintmax_t __mix_hi 156 = __mix / __c + ((__mix < __x0y1) ? __c : 0); // ... added here 157 typedef __big_add<__mix_hi, __mix_lo, __x1y1, __x0y0> _Res; 158 public: 159 static constexpr uintmax_t __hi = _Res::__hi; 160 static constexpr uintmax_t __lo = _Res::__lo; 161 }; 162 163 // Adapted from __udiv_qrnnd_c in longlong.h 164 // This version assumes that the high bit of __d is 1. 165 template<uintmax_t __n1, uintmax_t __n0, uintmax_t __d> 166 struct __big_div_impl 167 { 168 private: 169 static_assert(__d >= (uintmax_t(1) << (sizeof(intmax_t) * 8 - 1)), 170 "Internal library error"); 171 static_assert(__n1 < __d, "Internal library error"); 172 static constexpr uintmax_t __c = uintmax_t(1) << (sizeof(intmax_t) * 4); 173 static constexpr uintmax_t __d1 = __d / __c; 174 static constexpr uintmax_t __d0 = __d % __c; 175 176 static constexpr uintmax_t __q1x = __n1 / __d1; 177 static constexpr uintmax_t __r1x = __n1 % __d1; 178 static constexpr uintmax_t __m = __q1x * __d0; 179 static constexpr uintmax_t __r1y = __r1x * __c + __n0 / __c; 180 static constexpr uintmax_t __r1z = __r1y + __d; 181 static constexpr uintmax_t __r1 182 = ((__r1y < __m) ? ((__r1z >= __d) && (__r1z < __m)) 183 ? (__r1z + __d) : __r1z : __r1y) - __m; 184 static constexpr uintmax_t __q1 185 = __q1x - ((__r1y < __m) 186 ? ((__r1z >= __d) && (__r1z < __m)) ? 2 : 1 : 0); 187 static constexpr uintmax_t __q0x = __r1 / __d1; 188 static constexpr uintmax_t __r0x = __r1 % __d1; 189 static constexpr uintmax_t __n = __q0x * __d0; 190 static constexpr uintmax_t __r0y = __r0x * __c + __n0 % __c; 191 static constexpr uintmax_t __r0z = __r0y + __d; 192 static constexpr uintmax_t __r0 193 = ((__r0y < __n) ? ((__r0z >= __d) && (__r0z < __n)) 194 ? (__r0z + __d) : __r0z : __r0y) - __n; 195 static constexpr uintmax_t __q0 196 = __q0x - ((__r0y < __n) ? ((__r0z >= __d) 197 && (__r0z < __n)) ? 2 : 1 : 0); 198 199 public: 200 static constexpr uintmax_t __quot = __q1 * __c + __q0; 201 static constexpr uintmax_t __rem = __r0; 202 203 private: 204 typedef __big_mul<__quot, __d> _Prod; 205 typedef __big_add<_Prod::__hi, _Prod::__lo, 0, __rem> _Sum; 206 static_assert(_Sum::__hi == __n1 && _Sum::__lo == __n0, 207 "Internal library error"); 208 }; 209 210 template<uintmax_t __n1, uintmax_t __n0, uintmax_t __d> 211 struct __big_div 212 { 213 private: 214 static_assert(__d != 0, "Internal library error"); 215 static_assert(sizeof (uintmax_t) == sizeof (unsigned long long), 216 "This library calls __builtin_clzll on uintmax_t, which " 217 "is unsafe on your platform. Please complain to " 218 "http://gcc.gnu.org/bugzilla/"); 219 static constexpr int __shift = __builtin_clzll(__d); 220 static constexpr int __coshift_ = sizeof(uintmax_t) * 8 - __shift; 221 static constexpr int __coshift = (__shift != 0) ? __coshift_ : 0; 222 static constexpr uintmax_t __c1 = uintmax_t(1) << __shift; 223 static constexpr uintmax_t __c2 = uintmax_t(1) << __coshift; 224 static constexpr uintmax_t __new_d = __d * __c1; 225 static constexpr uintmax_t __new_n0 = __n0 * __c1; 226 static constexpr uintmax_t __n1_shifted = (__n1 % __d) * __c1; 227 static constexpr uintmax_t __n0_top = (__shift != 0) ? (__n0 / __c2) : 0; 228 static constexpr uintmax_t __new_n1 = __n1_shifted + __n0_top; 229 typedef __big_div_impl<__new_n1, __new_n0, __new_d> _Res; 230 231 public: 232 static constexpr uintmax_t __quot_hi = __n1 / __d; 233 static constexpr uintmax_t __quot_lo = _Res::__quot; 234 static constexpr uintmax_t __rem = _Res::__rem / __c1; 235 236 private: 237 typedef __big_mul<__quot_lo, __d> _P0; 238 typedef __big_mul<__quot_hi, __d> _P1; 239 typedef __big_add<_P0::__hi, _P0::__lo, _P1::__lo, __rem> _Sum; 240 // No overflow. 241 static_assert(_P1::__hi == 0, "Internal library error"); 242 static_assert(_Sum::__hi >= _P0::__hi, "Internal library error"); 243 // Matches the input data. 244 static_assert(_Sum::__hi == __n1 && _Sum::__lo == __n0, 245 "Internal library error"); 246 static_assert(__rem < __d, "Internal library error"); 247 }; 248 249 /// @endcond 250 251 /** 252 * @brief Provides compile-time rational arithmetic. 253 * 254 * This class template represents any finite rational number with a 255 * numerator and denominator representable by compile-time constants of 256 * type intmax_t. The ratio is simplified when instantiated. 257 * 258 * For example: 259 * @code 260 * std::ratio<7,-21>::num == -1; 261 * std::ratio<7,-21>::den == 3; 262 * @endcode 263 * 264 */ 265 template<intmax_t _Num, intmax_t _Den = 1> 266 struct ratio 267 { 268 static_assert(_Den != 0, "denominator cannot be zero"); 269 static_assert(_Num >= -__INTMAX_MAX__ && _Den >= -__INTMAX_MAX__, 270 "out of range"); 271 272 // Note: sign(N) * abs(N) == N 273 static constexpr intmax_t num = 274 _Num * __static_sign<_Den>::value / __static_gcd<_Num, _Den>::value; 275 276 static constexpr intmax_t den = 277 __static_abs<_Den>::value / __static_gcd<_Num, _Den>::value; 278 279 typedef ratio<num, den> type; 280 }; 281 282 template<intmax_t _Num, intmax_t _Den> 283 constexpr intmax_t ratio<_Num, _Den>::num; 284 285 template<intmax_t _Num, intmax_t _Den> 286 constexpr intmax_t ratio<_Num, _Den>::den; 287 288 /// @cond undocumented 289 290 template<typename _R1, typename _R2> 291 struct __ratio_multiply 292 { 293 private: 294 static const intmax_t __gcd1 = 295 __static_gcd<_R1::num, _R2::den>::value; 296 static const intmax_t __gcd2 = 297 __static_gcd<_R2::num, _R1::den>::value; 298 299 public: 300 typedef ratio< 301 __safe_multiply<(_R1::num / __gcd1), 302 (_R2::num / __gcd2)>::value, 303 __safe_multiply<(_R1::den / __gcd2), 304 (_R2::den / __gcd1)>::value> type; 305 306 static constexpr intmax_t num = type::num; 307 static constexpr intmax_t den = type::den; 308 }; 309 310 template<typename _R1, typename _R2> 311 constexpr intmax_t __ratio_multiply<_R1, _R2>::num; 312 313 template<typename _R1, typename _R2> 314 constexpr intmax_t __ratio_multiply<_R1, _R2>::den; 315 316 /// @endcond 317 318 /// ratio_multiply 319 template<typename _R1, typename _R2> 320 using ratio_multiply = typename __ratio_multiply<_R1, _R2>::type; 321 322 /// @cond undocumented 323 324 template<typename _R1, typename _R2> 325 struct __ratio_divide 326 { 327 static_assert(_R2::num != 0, "division by 0"); 328 329 typedef typename __ratio_multiply< 330 _R1, 331 ratio<_R2::den, _R2::num>>::type type; 332 333 static constexpr intmax_t num = type::num; 334 static constexpr intmax_t den = type::den; 335 }; 336 337 template<typename _R1, typename _R2> 338 constexpr intmax_t __ratio_divide<_R1, _R2>::num; 339 340 template<typename _R1, typename _R2> 341 constexpr intmax_t __ratio_divide<_R1, _R2>::den; 342 343 /// @endcond 344 345 /// ratio_divide 346 template<typename _R1, typename _R2> 347 using ratio_divide = typename __ratio_divide<_R1, _R2>::type; 348 349 /// ratio_equal 350 template<typename _R1, typename _R2> 351 struct ratio_equal 352 : integral_constant<bool, _R1::num == _R2::num && _R1::den == _R2::den> 353 { }; 354 355 /// ratio_not_equal 356 template<typename _R1, typename _R2> 357 struct ratio_not_equal 358 : integral_constant<bool, !ratio_equal<_R1, _R2>::value> 359 { }; 360 361 /// @cond undocumented 362 363 // Both numbers are positive. 364 template<typename _R1, typename _R2, 365 typename _Left = __big_mul<_R1::num,_R2::den>, 366 typename _Right = __big_mul<_R2::num,_R1::den> > 367 struct __ratio_less_impl_1 368 : integral_constant<bool, __big_less<_Left::__hi, _Left::__lo, 369 _Right::__hi, _Right::__lo>::value> 370 { }; 371 372 template<typename _R1, typename _R2, 373 bool = (_R1::num == 0 || _R2::num == 0 374 || (__static_sign<_R1::num>::value 375 != __static_sign<_R2::num>::value)), 376 bool = (__static_sign<_R1::num>::value == -1 377 && __static_sign<_R2::num>::value == -1)> 378 struct __ratio_less_impl 379 : __ratio_less_impl_1<_R1, _R2>::type 380 { }; 381 382 template<typename _R1, typename _R2> 383 struct __ratio_less_impl<_R1, _R2, true, false> 384 : integral_constant<bool, _R1::num < _R2::num> 385 { }; 386 387 template<typename _R1, typename _R2> 388 struct __ratio_less_impl<_R1, _R2, false, true> 389 : __ratio_less_impl_1<ratio<-_R2::num, _R2::den>, 390 ratio<-_R1::num, _R1::den> >::type 391 { }; 392 393 /// @endcond 394 395 /// ratio_less 396 template<typename _R1, typename _R2> 397 struct ratio_less 398 : __ratio_less_impl<_R1, _R2>::type 399 { }; 400 401 /// ratio_less_equal 402 template<typename _R1, typename _R2> 403 struct ratio_less_equal 404 : integral_constant<bool, !ratio_less<_R2, _R1>::value> 405 { }; 406 407 /// ratio_greater 408 template<typename _R1, typename _R2> 409 struct ratio_greater 410 : integral_constant<bool, ratio_less<_R2, _R1>::value> 411 { }; 412 413 /// ratio_greater_equal 414 template<typename _R1, typename _R2> 415 struct ratio_greater_equal 416 : integral_constant<bool, !ratio_less<_R1, _R2>::value> 417 { }; 418 419 #if __cplusplus > 201402L 420 template <typename _R1, typename _R2> 421 inline constexpr bool ratio_equal_v = ratio_equal<_R1, _R2>::value; 422 template <typename _R1, typename _R2> 423 inline constexpr bool ratio_not_equal_v = ratio_not_equal<_R1, _R2>::value; 424 template <typename _R1, typename _R2> 425 inline constexpr bool ratio_less_v = ratio_less<_R1, _R2>::value; 426 template <typename _R1, typename _R2> 427 inline constexpr bool ratio_less_equal_v = 428 ratio_less_equal<_R1, _R2>::value; 429 template <typename _R1, typename _R2> 430 inline constexpr bool ratio_greater_v = ratio_greater<_R1, _R2>::value; 431 template <typename _R1, typename _R2> 432 inline constexpr bool ratio_greater_equal_v 433 = ratio_greater_equal<_R1, _R2>::value; 434 #endif // C++17 435 436 /// @cond undocumented 437 438 template<typename _R1, typename _R2, 439 bool = (_R1::num >= 0), 440 bool = (_R2::num >= 0), 441 bool = ratio_less<ratio<__static_abs<_R1::num>::value, _R1::den>, 442 ratio<__static_abs<_R2::num>::value, _R2::den> >::value> 443 struct __ratio_add_impl 444 { 445 private: 446 typedef typename __ratio_add_impl< 447 ratio<-_R1::num, _R1::den>, 448 ratio<-_R2::num, _R2::den> >::type __t; 449 public: 450 typedef ratio<-__t::num, __t::den> type; 451 }; 452 453 // True addition of nonnegative numbers. 454 template<typename _R1, typename _R2, bool __b> 455 struct __ratio_add_impl<_R1, _R2, true, true, __b> 456 { 457 private: 458 static constexpr uintmax_t __g = __static_gcd<_R1::den, _R2::den>::value; 459 static constexpr uintmax_t __d2 = _R2::den / __g; 460 typedef __big_mul<_R1::den, __d2> __d; 461 typedef __big_mul<_R1::num, _R2::den / __g> __x; 462 typedef __big_mul<_R2::num, _R1::den / __g> __y; 463 typedef __big_add<__x::__hi, __x::__lo, __y::__hi, __y::__lo> __n; 464 static_assert(__n::__hi >= __x::__hi, "Internal library error"); 465 typedef __big_div<__n::__hi, __n::__lo, __g> __ng; 466 static constexpr uintmax_t __g2 = __static_gcd<__ng::__rem, __g>::value; 467 typedef __big_div<__n::__hi, __n::__lo, __g2> __n_final; 468 static_assert(__n_final::__rem == 0, "Internal library error"); 469 static_assert(__n_final::__quot_hi == 0 && 470 __n_final::__quot_lo <= __INTMAX_MAX__, "overflow in addition"); 471 typedef __big_mul<_R1::den / __g2, __d2> __d_final; 472 static_assert(__d_final::__hi == 0 && 473 __d_final::__lo <= __INTMAX_MAX__, "overflow in addition"); 474 public: 475 typedef ratio<__n_final::__quot_lo, __d_final::__lo> type; 476 }; 477 478 template<typename _R1, typename _R2> 479 struct __ratio_add_impl<_R1, _R2, false, true, true> 480 : __ratio_add_impl<_R2, _R1> 481 { }; 482 483 // True subtraction of nonnegative numbers yielding a nonnegative result. 484 template<typename _R1, typename _R2> 485 struct __ratio_add_impl<_R1, _R2, true, false, false> 486 { 487 private: 488 static constexpr uintmax_t __g = __static_gcd<_R1::den, _R2::den>::value; 489 static constexpr uintmax_t __d2 = _R2::den / __g; 490 typedef __big_mul<_R1::den, __d2> __d; 491 typedef __big_mul<_R1::num, _R2::den / __g> __x; 492 typedef __big_mul<-_R2::num, _R1::den / __g> __y; 493 typedef __big_sub<__x::__hi, __x::__lo, __y::__hi, __y::__lo> __n; 494 typedef __big_div<__n::__hi, __n::__lo, __g> __ng; 495 static constexpr uintmax_t __g2 = __static_gcd<__ng::__rem, __g>::value; 496 typedef __big_div<__n::__hi, __n::__lo, __g2> __n_final; 497 static_assert(__n_final::__rem == 0, "Internal library error"); 498 static_assert(__n_final::__quot_hi == 0 && 499 __n_final::__quot_lo <= __INTMAX_MAX__, "overflow in addition"); 500 typedef __big_mul<_R1::den / __g2, __d2> __d_final; 501 static_assert(__d_final::__hi == 0 && 502 __d_final::__lo <= __INTMAX_MAX__, "overflow in addition"); 503 public: 504 typedef ratio<__n_final::__quot_lo, __d_final::__lo> type; 505 }; 506 507 template<typename _R1, typename _R2> 508 struct __ratio_add 509 { 510 typedef typename __ratio_add_impl<_R1, _R2>::type type; 511 static constexpr intmax_t num = type::num; 512 static constexpr intmax_t den = type::den; 513 }; 514 515 template<typename _R1, typename _R2> 516 constexpr intmax_t __ratio_add<_R1, _R2>::num; 517 518 template<typename _R1, typename _R2> 519 constexpr intmax_t __ratio_add<_R1, _R2>::den; 520 521 /// @endcond 522 523 /// ratio_add 524 template<typename _R1, typename _R2> 525 using ratio_add = typename __ratio_add<_R1, _R2>::type; 526 527 /// @cond undocumented 528 529 template<typename _R1, typename _R2> 530 struct __ratio_subtract 531 { 532 typedef typename __ratio_add< 533 _R1, 534 ratio<-_R2::num, _R2::den>>::type type; 535 536 static constexpr intmax_t num = type::num; 537 static constexpr intmax_t den = type::den; 538 }; 539 540 template<typename _R1, typename _R2> 541 constexpr intmax_t __ratio_subtract<_R1, _R2>::num; 542 543 template<typename _R1, typename _R2> 544 constexpr intmax_t __ratio_subtract<_R1, _R2>::den; 545 546 /// @endcond 547 548 /// ratio_subtract 549 template<typename _R1, typename _R2> 550 using ratio_subtract = typename __ratio_subtract<_R1, _R2>::type; 551 552 553 typedef ratio<1, 1000000000000000000> atto; 554 typedef ratio<1, 1000000000000000> femto; 555 typedef ratio<1, 1000000000000> pico; 556 typedef ratio<1, 1000000000> nano; 557 typedef ratio<1, 1000000> micro; 558 typedef ratio<1, 1000> milli; 559 typedef ratio<1, 100> centi; 560 typedef ratio<1, 10> deci; 561 typedef ratio< 10, 1> deca; 562 typedef ratio< 100, 1> hecto; 563 typedef ratio< 1000, 1> kilo; 564 typedef ratio< 1000000, 1> mega; 565 typedef ratio< 1000000000, 1> giga; 566 typedef ratio< 1000000000000, 1> tera; 567 typedef ratio< 1000000000000000, 1> peta; 568 typedef ratio< 1000000000000000000, 1> exa; 569 570 /// @} group ratio 571 _GLIBCXX_END_NAMESPACE_VERSION 572 } // namespace 573 574 #endif // C++11 575 576 #endif //_GLIBCXX_RATIO 577
Indexes created Thu Sep 10 00:26:39 UTC 2026