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1 // ratio -*- C++ -*- 2 3 // Copyright (C) 2008-2025 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 #ifdef _GLIBCXX_SYSHDR 34 #pragma GCC system_header 35 #endif 36 37 #if __cplusplus < 201103L 38 # include <bits/c++0x_warning.h> 39 #else 40 41 #include <type_traits> 42 #include <cstdint> // intmax_t, uintmax_t 43 44 #define __glibcxx_want_ratio 45 #include <bits/version.h> 46 47 namespace std _GLIBCXX_VISIBILITY(default) 48 { 49 _GLIBCXX_BEGIN_NAMESPACE_VERSION 50 51 /** 52 * @defgroup ratio Rational Arithmetic 53 * @ingroup utilities 54 * 55 * Compile time representation of finite rational numbers. 56 * @{ 57 */ 58 59 /// @cond undocumented 60 61 template<intmax_t _Pn> 62 struct __static_sign 63 : integral_constant<intmax_t, (_Pn < 0) ? -1 : 1> 64 { }; 65 66 template<intmax_t _Pn> 67 struct __static_abs 68 : integral_constant<intmax_t, _Pn * __static_sign<_Pn>::value> 69 { }; 70 71 template<intmax_t _Pn, intmax_t _Qn> 72 struct __static_gcd 73 : __static_gcd<_Qn, (_Pn % _Qn)> 74 { }; 75 76 template<intmax_t _Pn> 77 struct __static_gcd<_Pn, 0> 78 : integral_constant<intmax_t, __static_abs<_Pn>::value> 79 { }; 80 81 template<intmax_t _Qn> 82 struct __static_gcd<0, _Qn> 83 : integral_constant<intmax_t, __static_abs<_Qn>::value> 84 { }; 85 86 // Let c = 2^(half # of bits in an intmax_t) 87 // then we find a1, a0, b1, b0 s.t. N = a1*c + a0, M = b1*c + b0 88 // The multiplication of N and M becomes, 89 // N * M = (a1 * b1)c^2 + (a0 * b1 + b0 * a1)c + a0 * b0 90 // Multiplication is safe if each term and the sum of the terms 91 // is representable by intmax_t. 92 template<intmax_t _Pn, intmax_t _Qn> 93 struct __safe_multiply 94 { 95 private: 96 static const uintmax_t __c = uintmax_t(1) << (sizeof(intmax_t) * 4); 97 98 static const uintmax_t __a0 = __static_abs<_Pn>::value % __c; 99 static const uintmax_t __a1 = __static_abs<_Pn>::value / __c; 100 static const uintmax_t __b0 = __static_abs<_Qn>::value % __c; 101 static const uintmax_t __b1 = __static_abs<_Qn>::value / __c; 102 103 static_assert(__a1 == 0 || __b1 == 0, 104 "overflow in multiplication"); 105 static_assert(__a0 * __b1 + __b0 * __a1 < (__c >> 1), 106 "overflow in multiplication"); 107 static_assert(__b0 * __a0 <= __INTMAX_MAX__, 108 "overflow in multiplication"); 109 static_assert((__a0 * __b1 + __b0 * __a1) * __c 110 <= __INTMAX_MAX__ - __b0 * __a0, 111 "overflow in multiplication"); 112 113 public: 114 static const intmax_t value = _Pn * _Qn; 115 }; 116 117 // Some double-precision utilities, where numbers are represented as 118 // __hi*2^(8*sizeof(uintmax_t)) + __lo. 119 template<uintmax_t __hi1, uintmax_t __lo1, uintmax_t __hi2, uintmax_t __lo2> 120 struct __big_less 121 : integral_constant<bool, (__hi1 < __hi2 122 || (__hi1 == __hi2 && __lo1 < __lo2))> 123 { }; 124 125 template<uintmax_t __hi1, uintmax_t __lo1, uintmax_t __hi2, uintmax_t __lo2> 126 struct __big_add 127 { 128 static constexpr uintmax_t __lo = __lo1 + __lo2; 129 static constexpr uintmax_t __hi = (__hi1 + __hi2 + 130 (__lo1 + __lo2 < __lo1)); // carry 131 }; 132 133 // Subtract a number from a bigger one. 134 template<uintmax_t __hi1, uintmax_t __lo1, uintmax_t __hi2, uintmax_t __lo2> 135 struct __big_sub 136 { 137 static_assert(!__big_less<__hi1, __lo1, __hi2, __lo2>::value, 138 "Internal library error"); 139 static constexpr uintmax_t __lo = __lo1 - __lo2; 140 static constexpr uintmax_t __hi = (__hi1 - __hi2 - 141 (__lo1 < __lo2)); // carry 142 }; 143 144 // Same principle as __safe_multiply. 145 template<uintmax_t __x, uintmax_t __y> 146 struct __big_mul 147 { 148 private: 149 static constexpr uintmax_t __c = uintmax_t(1) << (sizeof(intmax_t) * 4); 150 static constexpr uintmax_t __x0 = __x % __c; 151 static constexpr uintmax_t __x1 = __x / __c; 152 static constexpr uintmax_t __y0 = __y % __c; 153 static constexpr uintmax_t __y1 = __y / __c; 154 static constexpr uintmax_t __x0y0 = __x0 * __y0; 155 static constexpr uintmax_t __x0y1 = __x0 * __y1; 156 static constexpr uintmax_t __x1y0 = __x1 * __y0; 157 static constexpr uintmax_t __x1y1 = __x1 * __y1; 158 static constexpr uintmax_t __mix = __x0y1 + __x1y0; // possible carry... 159 static constexpr uintmax_t __mix_lo = __mix * __c; 160 static constexpr uintmax_t __mix_hi 161 = __mix / __c + ((__mix < __x0y1) ? __c : 0); // ... added here 162 typedef __big_add<__mix_hi, __mix_lo, __x1y1, __x0y0> _Res; 163 public: 164 static constexpr uintmax_t __hi = _Res::__hi; 165 static constexpr uintmax_t __lo = _Res::__lo; 166 }; 167 168 // Adapted from __udiv_qrnnd_c in longlong.h 169 // This version assumes that the high bit of __d is 1. 170 template<uintmax_t __n1, uintmax_t __n0, uintmax_t __d> 171 struct __big_div_impl 172 { 173 private: 174 static_assert(__d >= (uintmax_t(1) << (sizeof(intmax_t) * 8 - 1)), 175 "Internal library error"); 176 static_assert(__n1 < __d, "Internal library error"); 177 static constexpr uintmax_t __c = uintmax_t(1) << (sizeof(intmax_t) * 4); 178 static constexpr uintmax_t __d1 = __d / __c; 179 static constexpr uintmax_t __d0 = __d % __c; 180 181 static constexpr uintmax_t __q1x = __n1 / __d1; 182 static constexpr uintmax_t __r1x = __n1 % __d1; 183 static constexpr uintmax_t __m = __q1x * __d0; 184 static constexpr uintmax_t __r1y = __r1x * __c + __n0 / __c; 185 static constexpr uintmax_t __r1z = __r1y + __d; 186 static constexpr uintmax_t __r1 187 = ((__r1y < __m) ? ((__r1z >= __d) && (__r1z < __m)) 188 ? (__r1z + __d) : __r1z : __r1y) - __m; 189 static constexpr uintmax_t __q1 190 = __q1x - ((__r1y < __m) 191 ? ((__r1z >= __d) && (__r1z < __m)) ? 2 : 1 : 0); 192 static constexpr uintmax_t __q0x = __r1 / __d1; 193 static constexpr uintmax_t __r0x = __r1 % __d1; 194 static constexpr uintmax_t __n = __q0x * __d0; 195 static constexpr uintmax_t __r0y = __r0x * __c + __n0 % __c; 196 static constexpr uintmax_t __r0z = __r0y + __d; 197 static constexpr uintmax_t __r0 198 = ((__r0y < __n) ? ((__r0z >= __d) && (__r0z < __n)) 199 ? (__r0z + __d) : __r0z : __r0y) - __n; 200 static constexpr uintmax_t __q0 201 = __q0x - ((__r0y < __n) ? ((__r0z >= __d) 202 && (__r0z < __n)) ? 2 : 1 : 0); 203 204 public: 205 static constexpr uintmax_t __quot = __q1 * __c + __q0; 206 static constexpr uintmax_t __rem = __r0; 207 208 private: 209 typedef __big_mul<__quot, __d> _Prod; 210 typedef __big_add<_Prod::__hi, _Prod::__lo, 0, __rem> _Sum; 211 static_assert(_Sum::__hi == __n1 && _Sum::__lo == __n0, 212 "Internal library error"); 213 }; 214 215 template<uintmax_t __n1, uintmax_t __n0, uintmax_t __d> 216 struct __big_div 217 { 218 private: 219 static_assert(__d != 0, "Internal library error"); 220 static_assert(sizeof (uintmax_t) == sizeof (unsigned long long), 221 "This library calls __builtin_clzll on uintmax_t, which " 222 "is unsafe on your platform. Please complain to " 223 "http://gcc.gnu.org/bugzilla/"); 224 static constexpr int __shift = __builtin_clzll(__d); 225 static constexpr int __coshift_ = sizeof(uintmax_t) * 8 - __shift; 226 static constexpr int __coshift = (__shift != 0) ? __coshift_ : 0; 227 static constexpr uintmax_t __c1 = uintmax_t(1) << __shift; 228 static constexpr uintmax_t __c2 = uintmax_t(1) << __coshift; 229 static constexpr uintmax_t __new_d = __d * __c1; 230 static constexpr uintmax_t __new_n0 = __n0 * __c1; 231 static constexpr uintmax_t __n1_shifted = (__n1 % __d) * __c1; 232 static constexpr uintmax_t __n0_top = (__shift != 0) ? (__n0 / __c2) : 0; 233 static constexpr uintmax_t __new_n1 = __n1_shifted + __n0_top; 234 typedef __big_div_impl<__new_n1, __new_n0, __new_d> _Res; 235 236 public: 237 static constexpr uintmax_t __quot_hi = __n1 / __d; 238 static constexpr uintmax_t __quot_lo = _Res::__quot; 239 static constexpr uintmax_t __rem = _Res::__rem / __c1; 240 241 private: 242 typedef __big_mul<__quot_lo, __d> _P0; 243 typedef __big_mul<__quot_hi, __d> _P1; 244 typedef __big_add<_P0::__hi, _P0::__lo, _P1::__lo, __rem> _Sum; 245 // No overflow. 246 static_assert(_P1::__hi == 0, "Internal library error"); 247 static_assert(_Sum::__hi >= _P0::__hi, "Internal library error"); 248 // Matches the input data. 249 static_assert(_Sum::__hi == __n1 && _Sum::__lo == __n0, 250 "Internal library error"); 251 static_assert(__rem < __d, "Internal library error"); 252 }; 253 254 /// @endcond 255 256 /** 257 * @brief Provides compile-time rational arithmetic. 258 * 259 * This class template represents any finite rational number with a 260 * numerator and denominator representable by compile-time constants of 261 * type intmax_t. The ratio is simplified when instantiated. 262 * 263 * For example: 264 * @code 265 * std::ratio<7,-21>::num == -1; 266 * std::ratio<7,-21>::den == 3; 267 * @endcode 268 * 269 */ 270 template<intmax_t _Num, intmax_t _Den = 1> 271 struct ratio 272 { 273 static_assert(_Den != 0, "denominator cannot be zero"); 274 static_assert(_Num >= -__INTMAX_MAX__ && _Den >= -__INTMAX_MAX__, 275 "out of range"); 276 277 // Note: sign(N) * abs(N) == N 278 static constexpr intmax_t num = 279 _Num * __static_sign<_Den>::value / __static_gcd<_Num, _Den>::value; 280 281 static constexpr intmax_t den = 282 __static_abs<_Den>::value / __static_gcd<_Num, _Den>::value; 283 284 typedef ratio<num, den> type; 285 }; 286 287 #if ! __cpp_inline_variables 288 template<intmax_t _Num, intmax_t _Den> 289 constexpr intmax_t ratio<_Num, _Den>::num; 290 291 template<intmax_t _Num, intmax_t _Den> 292 constexpr intmax_t ratio<_Num, _Den>::den; 293 #endif 294 295 /// @cond undocumented 296 297 template<typename _Tp> 298 struct __is_ratio 299 : std::false_type 300 { }; 301 302 template<intmax_t _Num, intmax_t _Den> 303 struct __is_ratio<ratio<_Num, _Den>> 304 : std::true_type 305 { }; 306 307 #if __cpp_variable_templates 308 template<typename _Tp> 309 constexpr bool __is_ratio_v = false; 310 template<intmax_t _Num, intmax_t _Den> 311 constexpr bool __is_ratio_v<ratio<_Num, _Den>> = true; 312 #endif 313 314 template<typename _R1, typename _R2> 315 constexpr bool 316 __are_both_ratios() noexcept 317 { 318 #if __cpp_variable_templates && __cpp_if_constexpr 319 if constexpr (__is_ratio_v<_R1>) 320 if constexpr (__is_ratio_v<_R2>) 321 return true; 322 return false; 323 #else 324 return __and_<__is_ratio<_R1>, __is_ratio<_R2>>::value; 325 #endif 326 } 327 328 template<typename _R1, typename _R2> 329 struct __ratio_multiply 330 { 331 static_assert(std::__are_both_ratios<_R1, _R2>(), 332 "both template arguments must be a std::ratio"); 333 334 private: 335 static const intmax_t __gcd1 = 336 __static_gcd<_R1::num, _R2::den>::value; 337 static const intmax_t __gcd2 = 338 __static_gcd<_R2::num, _R1::den>::value; 339 340 public: 341 typedef ratio< 342 __safe_multiply<(_R1::num / __gcd1), 343 (_R2::num / __gcd2)>::value, 344 __safe_multiply<(_R1::den / __gcd2), 345 (_R2::den / __gcd1)>::value> type; 346 347 static constexpr intmax_t num = type::num; 348 static constexpr intmax_t den = type::den; 349 }; 350 351 #if ! __cpp_inline_variables 352 template<typename _R1, typename _R2> 353 constexpr intmax_t __ratio_multiply<_R1, _R2>::num; 354 355 template<typename _R1, typename _R2> 356 constexpr intmax_t __ratio_multiply<_R1, _R2>::den; 357 #endif 358 359 /// @endcond 360 361 /// ratio_multiply 362 template<typename _R1, typename _R2> 363 using ratio_multiply = typename __ratio_multiply<_R1, _R2>::type; 364 365 /// @cond undocumented 366 367 template<typename _R1, typename _R2> 368 struct __ratio_divide 369 { 370 static_assert(_R2::num != 0, "division by 0"); 371 372 typedef typename __ratio_multiply< 373 _R1, 374 ratio<_R2::den, _R2::num>>::type type; 375 376 static constexpr intmax_t num = type::num; 377 static constexpr intmax_t den = type::den; 378 }; 379 380 #if ! __cpp_inline_variables 381 template<typename _R1, typename _R2> 382 constexpr intmax_t __ratio_divide<_R1, _R2>::num; 383 384 template<typename _R1, typename _R2> 385 constexpr intmax_t __ratio_divide<_R1, _R2>::den; 386 #endif 387 388 /// @endcond 389 390 /// ratio_divide 391 template<typename _R1, typename _R2> 392 using ratio_divide = typename __ratio_divide<_R1, _R2>::type; 393 394 /// ratio_equal 395 template<typename _R1, typename _R2> 396 struct ratio_equal 397 : integral_constant<bool, _R1::num == _R2::num && _R1::den == _R2::den> 398 { 399 static_assert(std::__are_both_ratios<_R1, _R2>(), 400 "both template arguments must be a std::ratio"); 401 }; 402 403 /// ratio_not_equal 404 template<typename _R1, typename _R2> 405 struct ratio_not_equal 406 : integral_constant<bool, !ratio_equal<_R1, _R2>::value> 407 { }; 408 409 /// @cond undocumented 410 411 // Both numbers are positive. 412 template<typename _R1, typename _R2, 413 typename _Left = __big_mul<_R1::num,_R2::den>, 414 typename _Right = __big_mul<_R2::num,_R1::den> > 415 struct __ratio_less_impl_1 416 : integral_constant<bool, __big_less<_Left::__hi, _Left::__lo, 417 _Right::__hi, _Right::__lo>::value> 418 { }; 419 420 template<typename _R1, typename _R2, 421 bool = (_R1::num == 0 || _R2::num == 0 422 || (__static_sign<_R1::num>::value 423 != __static_sign<_R2::num>::value)), 424 bool = (__static_sign<_R1::num>::value == -1 425 && __static_sign<_R2::num>::value == -1)> 426 struct __ratio_less_impl 427 : __ratio_less_impl_1<_R1, _R2>::type 428 { }; 429 430 template<typename _R1, typename _R2> 431 struct __ratio_less_impl<_R1, _R2, true, false> 432 : integral_constant<bool, _R1::num < _R2::num> 433 { }; 434 435 template<typename _R1, typename _R2> 436 struct __ratio_less_impl<_R1, _R2, false, true> 437 : __ratio_less_impl_1<ratio<-_R2::num, _R2::den>, 438 ratio<-_R1::num, _R1::den> >::type 439 { }; 440 441 /// @endcond 442 443 /// ratio_less 444 template<typename _R1, typename _R2> 445 struct ratio_less 446 : __ratio_less_impl<_R1, _R2>::type 447 { 448 static_assert(std::__are_both_ratios<_R1, _R2>(), 449 "both template arguments must be a std::ratio"); 450 }; 451 452 /// ratio_less_equal 453 template<typename _R1, typename _R2> 454 struct ratio_less_equal 455 : integral_constant<bool, !ratio_less<_R2, _R1>::value> 456 { }; 457 458 /// ratio_greater 459 template<typename _R1, typename _R2> 460 struct ratio_greater 461 : integral_constant<bool, ratio_less<_R2, _R1>::value> 462 { }; 463 464 /// ratio_greater_equal 465 template<typename _R1, typename _R2> 466 struct ratio_greater_equal 467 : integral_constant<bool, !ratio_less<_R1, _R2>::value> 468 { }; 469 470 #if __cplusplus > 201402L 471 template <typename _R1, typename _R2> 472 inline constexpr bool ratio_equal_v = ratio_equal<_R1, _R2>::value; 473 template <typename _R1, typename _R2> 474 inline constexpr bool ratio_not_equal_v = ratio_not_equal<_R1, _R2>::value; 475 template <typename _R1, typename _R2> 476 inline constexpr bool ratio_less_v = ratio_less<_R1, _R2>::value; 477 template <typename _R1, typename _R2> 478 inline constexpr bool ratio_less_equal_v 479 = ratio_less_equal<_R1, _R2>::value; 480 template <typename _R1, typename _R2> 481 inline constexpr bool ratio_greater_v = ratio_greater<_R1, _R2>::value; 482 template <typename _R1, typename _R2> 483 inline constexpr bool ratio_greater_equal_v 484 = ratio_greater_equal<_R1, _R2>::value; 485 #endif // C++17 486 487 /// @cond undocumented 488 489 template<typename _R1, typename _R2, 490 bool = (_R1::num >= 0), 491 bool = (_R2::num >= 0), 492 bool = ratio_less<ratio<__static_abs<_R1::num>::value, _R1::den>, 493 ratio<__static_abs<_R2::num>::value, _R2::den> >::value> 494 struct __ratio_add_impl 495 { 496 private: 497 typedef typename __ratio_add_impl< 498 ratio<-_R1::num, _R1::den>, 499 ratio<-_R2::num, _R2::den> >::type __t; 500 public: 501 typedef ratio<-__t::num, __t::den> type; 502 }; 503 504 // True addition of nonnegative numbers. 505 template<typename _R1, typename _R2, bool __b> 506 struct __ratio_add_impl<_R1, _R2, true, true, __b> 507 { 508 private: 509 static constexpr uintmax_t __g = __static_gcd<_R1::den, _R2::den>::value; 510 static constexpr uintmax_t __d2 = _R2::den / __g; 511 typedef __big_mul<_R1::den, __d2> __d; 512 typedef __big_mul<_R1::num, _R2::den / __g> __x; 513 typedef __big_mul<_R2::num, _R1::den / __g> __y; 514 typedef __big_add<__x::__hi, __x::__lo, __y::__hi, __y::__lo> __n; 515 static_assert(__n::__hi >= __x::__hi, "Internal library error"); 516 typedef __big_div<__n::__hi, __n::__lo, __g> __ng; 517 static constexpr uintmax_t __g2 = __static_gcd<__ng::__rem, __g>::value; 518 typedef __big_div<__n::__hi, __n::__lo, __g2> __n_final; 519 static_assert(__n_final::__rem == 0, "Internal library error"); 520 static_assert(__n_final::__quot_hi == 0 && 521 __n_final::__quot_lo <= __INTMAX_MAX__, "overflow in addition"); 522 typedef __big_mul<_R1::den / __g2, __d2> __d_final; 523 static_assert(__d_final::__hi == 0 && 524 __d_final::__lo <= __INTMAX_MAX__, "overflow in addition"); 525 public: 526 typedef ratio<__n_final::__quot_lo, __d_final::__lo> type; 527 }; 528 529 template<typename _R1, typename _R2> 530 struct __ratio_add_impl<_R1, _R2, false, true, true> 531 : __ratio_add_impl<_R2, _R1> 532 { }; 533 534 // True subtraction of nonnegative numbers yielding a nonnegative result. 535 template<typename _R1, typename _R2> 536 struct __ratio_add_impl<_R1, _R2, true, false, false> 537 { 538 private: 539 static constexpr uintmax_t __g = __static_gcd<_R1::den, _R2::den>::value; 540 static constexpr uintmax_t __d2 = _R2::den / __g; 541 typedef __big_mul<_R1::den, __d2> __d; 542 typedef __big_mul<_R1::num, _R2::den / __g> __x; 543 typedef __big_mul<-_R2::num, _R1::den / __g> __y; 544 typedef __big_sub<__x::__hi, __x::__lo, __y::__hi, __y::__lo> __n; 545 typedef __big_div<__n::__hi, __n::__lo, __g> __ng; 546 static constexpr uintmax_t __g2 = __static_gcd<__ng::__rem, __g>::value; 547 typedef __big_div<__n::__hi, __n::__lo, __g2> __n_final; 548 static_assert(__n_final::__rem == 0, "Internal library error"); 549 static_assert(__n_final::__quot_hi == 0 && 550 __n_final::__quot_lo <= __INTMAX_MAX__, "overflow in addition"); 551 typedef __big_mul<_R1::den / __g2, __d2> __d_final; 552 static_assert(__d_final::__hi == 0 && 553 __d_final::__lo <= __INTMAX_MAX__, "overflow in addition"); 554 public: 555 typedef ratio<__n_final::__quot_lo, __d_final::__lo> type; 556 }; 557 558 template<typename _R1, typename _R2> 559 struct __ratio_add 560 { 561 static_assert(std::__are_both_ratios<_R1, _R2>(), 562 "both template arguments must be a std::ratio"); 563 564 typedef typename __ratio_add_impl<_R1, _R2>::type type; 565 static constexpr intmax_t num = type::num; 566 static constexpr intmax_t den = type::den; 567 }; 568 569 #if ! __cpp_inline_variables 570 template<typename _R1, typename _R2> 571 constexpr intmax_t __ratio_add<_R1, _R2>::num; 572 573 template<typename _R1, typename _R2> 574 constexpr intmax_t __ratio_add<_R1, _R2>::den; 575 #endif 576 577 /// @endcond 578 579 /// ratio_add 580 template<typename _R1, typename _R2> 581 using ratio_add = typename __ratio_add<_R1, _R2>::type; 582 583 /// @cond undocumented 584 585 template<typename _R1, typename _R2> 586 struct __ratio_subtract 587 { 588 typedef typename __ratio_add< 589 _R1, 590 ratio<-_R2::num, _R2::den>>::type type; 591 592 static constexpr intmax_t num = type::num; 593 static constexpr intmax_t den = type::den; 594 }; 595 596 #if ! __cpp_inline_variables 597 template<typename _R1, typename _R2> 598 constexpr intmax_t __ratio_subtract<_R1, _R2>::num; 599 600 template<typename _R1, typename _R2> 601 constexpr intmax_t __ratio_subtract<_R1, _R2>::den; 602 #endif 603 604 /// @endcond 605 606 /// ratio_subtract 607 template<typename _R1, typename _R2> 608 using ratio_subtract = typename __ratio_subtract<_R1, _R2>::type; 609 610 #if __INTMAX_WIDTH__ >= 96 611 # if __cpp_lib_ratio >= 202306L 612 # if __INTMAX_WIDTH__ >= 128 613 using quecto = ratio< 1, 1000000000000000000000000000000>; 614 # endif 615 using ronto = ratio< 1, 1000000000000000000000000000>; 616 # endif 617 using yocto = ratio< 1, 1000000000000000000000000>; 618 using zepto = ratio< 1, 1000000000000000000000>; 619 #endif 620 using atto = ratio< 1, 1000000000000000000>; 621 using femto = ratio< 1, 1000000000000000>; 622 using pico = ratio< 1, 1000000000000>; 623 using nano = ratio< 1, 1000000000>; 624 using micro = ratio< 1, 1000000>; 625 using milli = ratio< 1, 1000>; 626 using centi = ratio< 1, 100>; 627 using deci = ratio< 1, 10>; 628 using deca = ratio< 10, 1>; 629 using hecto = ratio< 100, 1>; 630 using kilo = ratio< 1000, 1>; 631 using mega = ratio< 1000000, 1>; 632 using giga = ratio< 1000000000, 1>; 633 using tera = ratio< 1000000000000, 1>; 634 using peta = ratio< 1000000000000000, 1>; 635 using exa = ratio< 1000000000000000000, 1>; 636 #if __INTMAX_WIDTH__ >= 96 637 using zetta = ratio< 1000000000000000000000, 1>; 638 using yotta = ratio<1000000000000000000000000, 1>; 639 # if __cpp_lib_ratio >= 202306L 640 using ronna = ratio<1000000000000000000000000000, 1>; 641 # if __INTMAX_WIDTH__ >= 128 642 using quetta = ratio<1000000000000000000000000000000, 1>; 643 # endif 644 # endif 645 #endif 646 647 /// @} group ratio 648 _GLIBCXX_END_NAMESPACE_VERSION 649 } // namespace 650 651 #endif // C++11 652 653 #endif //_GLIBCXX_RATIO
