1 // ratio -*- C++ -*- 2 3 // Copyright (C) 2008-2024 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 #define __glibcxx_want_ratio 43 #include <bits/version.h> 44 45 namespace std _GLIBCXX_VISIBILITY(default) 46 { 47 _GLIBCXX_BEGIN_NAMESPACE_VERSION 48 49 /** 50 * @defgroup ratio Rational Arithmetic 51 * @ingroup utilities 52 * 53 * Compile time representation of finite rational numbers. 54 * @{ 55 */ 56 57 /// @cond undocumented 58 59 template<intmax_t _Pn> 60 struct __static_sign 61 : integral_constant<intmax_t, (_Pn < 0) ? -1 : 1> 62 { }; 63 64 template<intmax_t _Pn> 65 struct __static_abs 66 : integral_constant<intmax_t, _Pn * __static_sign<_Pn>::value> 67 { }; 68 69 template<intmax_t _Pn, intmax_t _Qn> 70 struct __static_gcd 71 : __static_gcd<_Qn, (_Pn % _Qn)> 72 { }; 73 74 template<intmax_t _Pn> 75 struct __static_gcd<_Pn, 0> 76 : integral_constant<intmax_t, __static_abs<_Pn>::value> 77 { }; 78 79 template<intmax_t _Qn> 80 struct __static_gcd<0, _Qn> 81 : integral_constant<intmax_t, __static_abs<_Qn>::value> 82 { }; 83 84 // Let c = 2^(half # of bits in an intmax_t) 85 // then we find a1, a0, b1, b0 s.t. N = a1*c + a0, M = b1*c + b0 86 // The multiplication of N and M becomes, 87 // N * M = (a1 * b1)c^2 + (a0 * b1 + b0 * a1)c + a0 * b0 88 // Multiplication is safe if each term and the sum of the terms 89 // is representable by intmax_t. 90 template<intmax_t _Pn, intmax_t _Qn> 91 struct __safe_multiply 92 { 93 private: 94 static const uintmax_t __c = uintmax_t(1) << (sizeof(intmax_t) * 4); 95 96 static const uintmax_t __a0 = __static_abs<_Pn>::value % __c; 97 static const uintmax_t __a1 = __static_abs<_Pn>::value / __c; 98 static const uintmax_t __b0 = __static_abs<_Qn>::value % __c; 99 static const uintmax_t __b1 = __static_abs<_Qn>::value / __c; 100 101 static_assert(__a1 == 0 || __b1 == 0, 102 "overflow in multiplication"); 103 static_assert(__a0 * __b1 + __b0 * __a1 < (__c >> 1), 104 "overflow in multiplication"); 105 static_assert(__b0 * __a0 <= __INTMAX_MAX__, 106 "overflow in multiplication"); 107 static_assert((__a0 * __b1 + __b0 * __a1) * __c 108 <= __INTMAX_MAX__ - __b0 * __a0, 109 "overflow in multiplication"); 110 111 public: 112 static const intmax_t value = _Pn * _Qn; 113 }; 114 115 // Some double-precision utilities, where numbers are represented as 116 // __hi*2^(8*sizeof(uintmax_t)) + __lo. 117 template<uintmax_t __hi1, uintmax_t __lo1, uintmax_t __hi2, uintmax_t __lo2> 118 struct __big_less 119 : integral_constant<bool, (__hi1 < __hi2 120 || (__hi1 == __hi2 && __lo1 < __lo2))> 121 { }; 122 123 template<uintmax_t __hi1, uintmax_t __lo1, uintmax_t __hi2, uintmax_t __lo2> 124 struct __big_add 125 { 126 static constexpr uintmax_t __lo = __lo1 + __lo2; 127 static constexpr uintmax_t __hi = (__hi1 + __hi2 + 128 (__lo1 + __lo2 < __lo1)); // carry 129 }; 130 131 // Subtract a number from a bigger one. 132 template<uintmax_t __hi1, uintmax_t __lo1, uintmax_t __hi2, uintmax_t __lo2> 133 struct __big_sub 134 { 135 static_assert(!__big_less<__hi1, __lo1, __hi2, __lo2>::value, 136 "Internal library error"); 137 static constexpr uintmax_t __lo = __lo1 - __lo2; 138 static constexpr uintmax_t __hi = (__hi1 - __hi2 - 139 (__lo1 < __lo2)); // carry 140 }; 141 142 // Same principle as __safe_multiply. 143 template<uintmax_t __x, uintmax_t __y> 144 struct __big_mul 145 { 146 private: 147 static constexpr uintmax_t __c = uintmax_t(1) << (sizeof(intmax_t) * 4); 148 static constexpr uintmax_t __x0 = __x % __c; 149 static constexpr uintmax_t __x1 = __x / __c; 150 static constexpr uintmax_t __y0 = __y % __c; 151 static constexpr uintmax_t __y1 = __y / __c; 152 static constexpr uintmax_t __x0y0 = __x0 * __y0; 153 static constexpr uintmax_t __x0y1 = __x0 * __y1; 154 static constexpr uintmax_t __x1y0 = __x1 * __y0; 155 static constexpr uintmax_t __x1y1 = __x1 * __y1; 156 static constexpr uintmax_t __mix = __x0y1 + __x1y0; // possible carry... 157 static constexpr uintmax_t __mix_lo = __mix * __c; 158 static constexpr uintmax_t __mix_hi 159 = __mix / __c + ((__mix < __x0y1) ? __c : 0); // ... added here 160 typedef __big_add<__mix_hi, __mix_lo, __x1y1, __x0y0> _Res; 161 public: 162 static constexpr uintmax_t __hi = _Res::__hi; 163 static constexpr uintmax_t __lo = _Res::__lo; 164 }; 165 166 // Adapted from __udiv_qrnnd_c in longlong.h 167 // This version assumes that the high bit of __d is 1. 168 template<uintmax_t __n1, uintmax_t __n0, uintmax_t __d> 169 struct __big_div_impl 170 { 171 private: 172 static_assert(__d >= (uintmax_t(1) << (sizeof(intmax_t) * 8 - 1)), 173 "Internal library error"); 174 static_assert(__n1 < __d, "Internal library error"); 175 static constexpr uintmax_t __c = uintmax_t(1) << (sizeof(intmax_t) * 4); 176 static constexpr uintmax_t __d1 = __d / __c; 177 static constexpr uintmax_t __d0 = __d % __c; 178 179 static constexpr uintmax_t __q1x = __n1 / __d1; 180 static constexpr uintmax_t __r1x = __n1 % __d1; 181 static constexpr uintmax_t __m = __q1x * __d0; 182 static constexpr uintmax_t __r1y = __r1x * __c + __n0 / __c; 183 static constexpr uintmax_t __r1z = __r1y + __d; 184 static constexpr uintmax_t __r1 185 = ((__r1y < __m) ? ((__r1z >= __d) && (__r1z < __m)) 186 ? (__r1z + __d) : __r1z : __r1y) - __m; 187 static constexpr uintmax_t __q1 188 = __q1x - ((__r1y < __m) 189 ? ((__r1z >= __d) && (__r1z < __m)) ? 2 : 1 : 0); 190 static constexpr uintmax_t __q0x = __r1 / __d1; 191 static constexpr uintmax_t __r0x = __r1 % __d1; 192 static constexpr uintmax_t __n = __q0x * __d0; 193 static constexpr uintmax_t __r0y = __r0x * __c + __n0 % __c; 194 static constexpr uintmax_t __r0z = __r0y + __d; 195 static constexpr uintmax_t __r0 196 = ((__r0y < __n) ? ((__r0z >= __d) && (__r0z < __n)) 197 ? (__r0z + __d) : __r0z : __r0y) - __n; 198 static constexpr uintmax_t __q0 199 = __q0x - ((__r0y < __n) ? ((__r0z >= __d) 200 && (__r0z < __n)) ? 2 : 1 : 0); 201 202 public: 203 static constexpr uintmax_t __quot = __q1 * __c + __q0; 204 static constexpr uintmax_t __rem = __r0; 205 206 private: 207 typedef __big_mul<__quot, __d> _Prod; 208 typedef __big_add<_Prod::__hi, _Prod::__lo, 0, __rem> _Sum; 209 static_assert(_Sum::__hi == __n1 && _Sum::__lo == __n0, 210 "Internal library error"); 211 }; 212 213 template<uintmax_t __n1, uintmax_t __n0, uintmax_t __d> 214 struct __big_div 215 { 216 private: 217 static_assert(__d != 0, "Internal library error"); 218 static_assert(sizeof (uintmax_t) == sizeof (unsigned long long), 219 "This library calls __builtin_clzll on uintmax_t, which " 220 "is unsafe on your platform. Please complain to " 221 "http://gcc.gnu.org/bugzilla/"); 222 static constexpr int __shift = __builtin_clzll(__d); 223 static constexpr int __coshift_ = sizeof(uintmax_t) * 8 - __shift; 224 static constexpr int __coshift = (__shift != 0) ? __coshift_ : 0; 225 static constexpr uintmax_t __c1 = uintmax_t(1) << __shift; 226 static constexpr uintmax_t __c2 = uintmax_t(1) << __coshift; 227 static constexpr uintmax_t __new_d = __d * __c1; 228 static constexpr uintmax_t __new_n0 = __n0 * __c1; 229 static constexpr uintmax_t __n1_shifted = (__n1 % __d) * __c1; 230 static constexpr uintmax_t __n0_top = (__shift != 0) ? (__n0 / __c2) : 0; 231 static constexpr uintmax_t __new_n1 = __n1_shifted + __n0_top; 232 typedef __big_div_impl<__new_n1, __new_n0, __new_d> _Res; 233 234 public: 235 static constexpr uintmax_t __quot_hi = __n1 / __d; 236 static constexpr uintmax_t __quot_lo = _Res::__quot; 237 static constexpr uintmax_t __rem = _Res::__rem / __c1; 238 239 private: 240 typedef __big_mul<__quot_lo, __d> _P0; 241 typedef __big_mul<__quot_hi, __d> _P1; 242 typedef __big_add<_P0::__hi, _P0::__lo, _P1::__lo, __rem> _Sum; 243 // No overflow. 244 static_assert(_P1::__hi == 0, "Internal library error"); 245 static_assert(_Sum::__hi >= _P0::__hi, "Internal library error"); 246 // Matches the input data. 247 static_assert(_Sum::__hi == __n1 && _Sum::__lo == __n0, 248 "Internal library error"); 249 static_assert(__rem < __d, "Internal library error"); 250 }; 251 252 /// @endcond 253 254 /** 255 * @brief Provides compile-time rational arithmetic. 256 * 257 * This class template represents any finite rational number with a 258 * numerator and denominator representable by compile-time constants of 259 * type intmax_t. The ratio is simplified when instantiated. 260 * 261 * For example: 262 * @code 263 * std::ratio<7,-21>::num == -1; 264 * std::ratio<7,-21>::den == 3; 265 * @endcode 266 * 267 */ 268 template<intmax_t _Num, intmax_t _Den = 1> 269 struct ratio 270 { 271 static_assert(_Den != 0, "denominator cannot be zero"); 272 static_assert(_Num >= -__INTMAX_MAX__ && _Den >= -__INTMAX_MAX__, 273 "out of range"); 274 275 // Note: sign(N) * abs(N) == N 276 static constexpr intmax_t num = 277 _Num * __static_sign<_Den>::value / __static_gcd<_Num, _Den>::value; 278 279 static constexpr intmax_t den = 280 __static_abs<_Den>::value / __static_gcd<_Num, _Den>::value; 281 282 typedef ratio<num, den> type; 283 }; 284 285 #if ! __cpp_inline_variables 286 template<intmax_t _Num, intmax_t _Den> 287 constexpr intmax_t ratio<_Num, _Den>::num; 288 289 template<intmax_t _Num, intmax_t _Den> 290 constexpr intmax_t ratio<_Num, _Den>::den; 291 #endif 292 293 /// @cond undocumented 294 295 template<typename _Tp> 296 struct __is_ratio 297 : std::false_type 298 { }; 299 300 template<intmax_t _Num, intmax_t _Den> 301 struct __is_ratio<ratio<_Num, _Den>> 302 : std::true_type 303 { }; 304 305 #if __cpp_variable_templates 306 template<typename _Tp> 307 constexpr bool __is_ratio_v = false; 308 template<intmax_t _Num, intmax_t _Den> 309 constexpr bool __is_ratio_v<ratio<_Num, _Den>> = true; 310 #endif 311 312 template<typename _R1, typename _R2> 313 constexpr bool 314 __are_both_ratios() noexcept 315 { 316 #if __cpp_variable_templates && __cpp_if_constexpr 317 if constexpr (__is_ratio_v<_R1>) 318 if constexpr (__is_ratio_v<_R2>) 319 return true; 320 return false; 321 #else 322 return __and_<__is_ratio<_R1>, __is_ratio<_R2>>::value; 323 #endif 324 } 325 326 template<typename _R1, typename _R2> 327 struct __ratio_multiply 328 { 329 static_assert(std::__are_both_ratios<_R1, _R2>(), 330 "both template arguments must be a std::ratio"); 331 332 private: 333 static const intmax_t __gcd1 = 334 __static_gcd<_R1::num, _R2::den>::value; 335 static const intmax_t __gcd2 = 336 __static_gcd<_R2::num, _R1::den>::value; 337 338 public: 339 typedef ratio< 340 __safe_multiply<(_R1::num / __gcd1), 341 (_R2::num / __gcd2)>::value, 342 __safe_multiply<(_R1::den / __gcd2), 343 (_R2::den / __gcd1)>::value> type; 344 345 static constexpr intmax_t num = type::num; 346 static constexpr intmax_t den = type::den; 347 }; 348 349 #if ! __cpp_inline_variables 350 template<typename _R1, typename _R2> 351 constexpr intmax_t __ratio_multiply<_R1, _R2>::num; 352 353 template<typename _R1, typename _R2> 354 constexpr intmax_t __ratio_multiply<_R1, _R2>::den; 355 #endif 356 357 /// @endcond 358 359 /// ratio_multiply 360 template<typename _R1, typename _R2> 361 using ratio_multiply = typename __ratio_multiply<_R1, _R2>::type; 362 363 /// @cond undocumented 364 365 template<typename _R1, typename _R2> 366 struct __ratio_divide 367 { 368 static_assert(_R2::num != 0, "division by 0"); 369 370 typedef typename __ratio_multiply< 371 _R1, 372 ratio<_R2::den, _R2::num>>::type type; 373 374 static constexpr intmax_t num = type::num; 375 static constexpr intmax_t den = type::den; 376 }; 377 378 #if ! __cpp_inline_variables 379 template<typename _R1, typename _R2> 380 constexpr intmax_t __ratio_divide<_R1, _R2>::num; 381 382 template<typename _R1, typename _R2> 383 constexpr intmax_t __ratio_divide<_R1, _R2>::den; 384 #endif 385 386 /// @endcond 387 388 /// ratio_divide 389 template<typename _R1, typename _R2> 390 using ratio_divide = typename __ratio_divide<_R1, _R2>::type; 391 392 /// ratio_equal 393 template<typename _R1, typename _R2> 394 struct ratio_equal 395 : integral_constant<bool, _R1::num == _R2::num && _R1::den == _R2::den> 396 { 397 static_assert(std::__are_both_ratios<_R1, _R2>(), 398 "both template arguments must be a std::ratio"); 399 }; 400 401 /// ratio_not_equal 402 template<typename _R1, typename _R2> 403 struct ratio_not_equal 404 : integral_constant<bool, !ratio_equal<_R1, _R2>::value> 405 { }; 406 407 /// @cond undocumented 408 409 // Both numbers are positive. 410 template<typename _R1, typename _R2, 411 typename _Left = __big_mul<_R1::num,_R2::den>, 412 typename _Right = __big_mul<_R2::num,_R1::den> > 413 struct __ratio_less_impl_1 414 : integral_constant<bool, __big_less<_Left::__hi, _Left::__lo, 415 _Right::__hi, _Right::__lo>::value> 416 { }; 417 418 template<typename _R1, typename _R2, 419 bool = (_R1::num == 0 || _R2::num == 0 420 || (__static_sign<_R1::num>::value 421 != __static_sign<_R2::num>::value)), 422 bool = (__static_sign<_R1::num>::value == -1 423 && __static_sign<_R2::num>::value == -1)> 424 struct __ratio_less_impl 425 : __ratio_less_impl_1<_R1, _R2>::type 426 { }; 427 428 template<typename _R1, typename _R2> 429 struct __ratio_less_impl<_R1, _R2, true, false> 430 : integral_constant<bool, _R1::num < _R2::num> 431 { }; 432 433 template<typename _R1, typename _R2> 434 struct __ratio_less_impl<_R1, _R2, false, true> 435 : __ratio_less_impl_1<ratio<-_R2::num, _R2::den>, 436 ratio<-_R1::num, _R1::den> >::type 437 { }; 438 439 /// @endcond 440 441 /// ratio_less 442 template<typename _R1, typename _R2> 443 struct ratio_less 444 : __ratio_less_impl<_R1, _R2>::type 445 { 446 static_assert(std::__are_both_ratios<_R1, _R2>(), 447 "both template arguments must be a std::ratio"); 448 }; 449 450 /// ratio_less_equal 451 template<typename _R1, typename _R2> 452 struct ratio_less_equal 453 : integral_constant<bool, !ratio_less<_R2, _R1>::value> 454 { }; 455 456 /// ratio_greater 457 template<typename _R1, typename _R2> 458 struct ratio_greater 459 : integral_constant<bool, ratio_less<_R2, _R1>::value> 460 { }; 461 462 /// ratio_greater_equal 463 template<typename _R1, typename _R2> 464 struct ratio_greater_equal 465 : integral_constant<bool, !ratio_less<_R1, _R2>::value> 466 { }; 467 468 #if __cplusplus > 201402L 469 template <typename _R1, typename _R2> 470 inline constexpr bool ratio_equal_v = ratio_equal<_R1, _R2>::value; 471 template <typename _R1, typename _R2> 472 inline constexpr bool ratio_not_equal_v = ratio_not_equal<_R1, _R2>::value; 473 template <typename _R1, typename _R2> 474 inline constexpr bool ratio_less_v = ratio_less<_R1, _R2>::value; 475 template <typename _R1, typename _R2> 476 inline constexpr bool ratio_less_equal_v 477 = ratio_less_equal<_R1, _R2>::value; 478 template <typename _R1, typename _R2> 479 inline constexpr bool ratio_greater_v = ratio_greater<_R1, _R2>::value; 480 template <typename _R1, typename _R2> 481 inline constexpr bool ratio_greater_equal_v 482 = ratio_greater_equal<_R1, _R2>::value; 483 #endif // C++17 484 485 /// @cond undocumented 486 487 template<typename _R1, typename _R2, 488 bool = (_R1::num >= 0), 489 bool = (_R2::num >= 0), 490 bool = ratio_less<ratio<__static_abs<_R1::num>::value, _R1::den>, 491 ratio<__static_abs<_R2::num>::value, _R2::den> >::value> 492 struct __ratio_add_impl 493 { 494 private: 495 typedef typename __ratio_add_impl< 496 ratio<-_R1::num, _R1::den>, 497 ratio<-_R2::num, _R2::den> >::type __t; 498 public: 499 typedef ratio<-__t::num, __t::den> type; 500 }; 501 502 // True addition of nonnegative numbers. 503 template<typename _R1, typename _R2, bool __b> 504 struct __ratio_add_impl<_R1, _R2, true, true, __b> 505 { 506 private: 507 static constexpr uintmax_t __g = __static_gcd<_R1::den, _R2::den>::value; 508 static constexpr uintmax_t __d2 = _R2::den / __g; 509 typedef __big_mul<_R1::den, __d2> __d; 510 typedef __big_mul<_R1::num, _R2::den / __g> __x; 511 typedef __big_mul<_R2::num, _R1::den / __g> __y; 512 typedef __big_add<__x::__hi, __x::__lo, __y::__hi, __y::__lo> __n; 513 static_assert(__n::__hi >= __x::__hi, "Internal library error"); 514 typedef __big_div<__n::__hi, __n::__lo, __g> __ng; 515 static constexpr uintmax_t __g2 = __static_gcd<__ng::__rem, __g>::value; 516 typedef __big_div<__n::__hi, __n::__lo, __g2> __n_final; 517 static_assert(__n_final::__rem == 0, "Internal library error"); 518 static_assert(__n_final::__quot_hi == 0 && 519 __n_final::__quot_lo <= __INTMAX_MAX__, "overflow in addition"); 520 typedef __big_mul<_R1::den / __g2, __d2> __d_final; 521 static_assert(__d_final::__hi == 0 && 522 __d_final::__lo <= __INTMAX_MAX__, "overflow in addition"); 523 public: 524 typedef ratio<__n_final::__quot_lo, __d_final::__lo> type; 525 }; 526 527 template<typename _R1, typename _R2> 528 struct __ratio_add_impl<_R1, _R2, false, true, true> 529 : __ratio_add_impl<_R2, _R1> 530 { }; 531 532 // True subtraction of nonnegative numbers yielding a nonnegative result. 533 template<typename _R1, typename _R2> 534 struct __ratio_add_impl<_R1, _R2, true, false, false> 535 { 536 private: 537 static constexpr uintmax_t __g = __static_gcd<_R1::den, _R2::den>::value; 538 static constexpr uintmax_t __d2 = _R2::den / __g; 539 typedef __big_mul<_R1::den, __d2> __d; 540 typedef __big_mul<_R1::num, _R2::den / __g> __x; 541 typedef __big_mul<-_R2::num, _R1::den / __g> __y; 542 typedef __big_sub<__x::__hi, __x::__lo, __y::__hi, __y::__lo> __n; 543 typedef __big_div<__n::__hi, __n::__lo, __g> __ng; 544 static constexpr uintmax_t __g2 = __static_gcd<__ng::__rem, __g>::value; 545 typedef __big_div<__n::__hi, __n::__lo, __g2> __n_final; 546 static_assert(__n_final::__rem == 0, "Internal library error"); 547 static_assert(__n_final::__quot_hi == 0 && 548 __n_final::__quot_lo <= __INTMAX_MAX__, "overflow in addition"); 549 typedef __big_mul<_R1::den / __g2, __d2> __d_final; 550 static_assert(__d_final::__hi == 0 && 551 __d_final::__lo <= __INTMAX_MAX__, "overflow in addition"); 552 public: 553 typedef ratio<__n_final::__quot_lo, __d_final::__lo> type; 554 }; 555 556 template<typename _R1, typename _R2> 557 struct __ratio_add 558 { 559 static_assert(std::__are_both_ratios<_R1, _R2>(), 560 "both template arguments must be a std::ratio"); 561 562 typedef typename __ratio_add_impl<_R1, _R2>::type type; 563 static constexpr intmax_t num = type::num; 564 static constexpr intmax_t den = type::den; 565 }; 566 567 #if ! __cpp_inline_variables 568 template<typename _R1, typename _R2> 569 constexpr intmax_t __ratio_add<_R1, _R2>::num; 570 571 template<typename _R1, typename _R2> 572 constexpr intmax_t __ratio_add<_R1, _R2>::den; 573 #endif 574 575 /// @endcond 576 577 /// ratio_add 578 template<typename _R1, typename _R2> 579 using ratio_add = typename __ratio_add<_R1, _R2>::type; 580 581 /// @cond undocumented 582 583 template<typename _R1, typename _R2> 584 struct __ratio_subtract 585 { 586 typedef typename __ratio_add< 587 _R1, 588 ratio<-_R2::num, _R2::den>>::type type; 589 590 static constexpr intmax_t num = type::num; 591 static constexpr intmax_t den = type::den; 592 }; 593 594 #if ! __cpp_inline_variables 595 template<typename _R1, typename _R2> 596 constexpr intmax_t __ratio_subtract<_R1, _R2>::num; 597 598 template<typename _R1, typename _R2> 599 constexpr intmax_t __ratio_subtract<_R1, _R2>::den; 600 #endif 601 602 /// @endcond 603 604 /// ratio_subtract 605 template<typename _R1, typename _R2> 606 using ratio_subtract = typename __ratio_subtract<_R1, _R2>::type; 607 608 #if __INTMAX_WIDTH__ >= 96 609 # if __cpp_lib_ratio >= 202306L 610 # if __INTMAX_WIDTH__ >= 128 611 using quecto = ratio< 1, 1000000000000000000000000000000>; 612 # endif 613 using ronto = ratio< 1, 1000000000000000000000000000>; 614 # endif 615 using yocto = ratio< 1, 1000000000000000000000000>; 616 using zepto = ratio< 1, 1000000000000000000000>; 617 #endif 618 using atto = ratio< 1, 1000000000000000000>; 619 using femto = ratio< 1, 1000000000000000>; 620 using pico = ratio< 1, 1000000000000>; 621 using nano = ratio< 1, 1000000000>; 622 using micro = ratio< 1, 1000000>; 623 using milli = ratio< 1, 1000>; 624 using centi = ratio< 1, 100>; 625 using deci = ratio< 1, 10>; 626 using deca = ratio< 10, 1>; 627 using hecto = ratio< 100, 1>; 628 using kilo = ratio< 1000, 1>; 629 using mega = ratio< 1000000, 1>; 630 using giga = ratio< 1000000000, 1>; 631 using tera = ratio< 1000000000000, 1>; 632 using peta = ratio< 1000000000000000, 1>; 633 using exa = ratio< 1000000000000000000, 1>; 634 #if __INTMAX_WIDTH__ >= 96 635 using zetta = ratio< 1000000000000000000000, 1>; 636 using yotta = ratio<1000000000000000000000000, 1>; 637 # if __cpp_lib_ratio >= 202306L 638 using ronna = ratio<1000000000000000000000000000, 1>; 639 # if __INTMAX_WIDTH__ >= 128 640 using quetta = ratio<1000000000000000000000000000000, 1>; 641 # endif 642 # endif 643 #endif 644 645 /// @} group ratio 646 _GLIBCXX_END_NAMESPACE_VERSION 647 } // namespace 648 649 #endif // C++11 650 651 #endif //_GLIBCXX_RATIO 652
Indexes created Fri Apr 24 00:22:58 UTC 2026