ratio revision 1.1.1.13
1 // ratio -*- C++ -*- 2 3 // Copyright (C) 2008-2022 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 #if ! __cpp_inline_variables 283 template<intmax_t _Num, intmax_t _Den> 284 constexpr intmax_t ratio<_Num, _Den>::num; 285 286 template<intmax_t _Num, intmax_t _Den> 287 constexpr intmax_t ratio<_Num, _Den>::den; 288 #endif 289 290 /// @cond undocumented 291 292 template<typename _Tp> 293 struct __is_ratio 294 : std::false_type 295 { }; 296 297 template<intmax_t _Num, intmax_t _Den> 298 struct __is_ratio<ratio<_Num, _Den>> 299 : std::true_type 300 { }; 301 302 #if __cpp_variable_templates 303 template<typename _Tp> 304 constexpr bool __is_ratio_v = false; 305 template<intmax_t _Num, intmax_t _Den> 306 constexpr bool __is_ratio_v<ratio<_Num, _Den>> = true; 307 #endif 308 309 template<typename _R1, typename _R2> 310 constexpr bool 311 __are_both_ratios() noexcept 312 { 313 #if __cpp_variable_templates && __cpp_if_constexpr 314 if constexpr (__is_ratio_v<_R1>) 315 if constexpr (__is_ratio_v<_R2>) 316 return true; 317 return false; 318 #else 319 return __and_<__is_ratio<_R1>, __is_ratio<_R2>>::value; 320 #endif 321 } 322 323 template<typename _R1, typename _R2> 324 struct __ratio_multiply 325 { 326 static_assert(std::__are_both_ratios<_R1, _R2>(), 327 "both template arguments must be a std::ratio"); 328 329 private: 330 static const intmax_t __gcd1 = 331 __static_gcd<_R1::num, _R2::den>::value; 332 static const intmax_t __gcd2 = 333 __static_gcd<_R2::num, _R1::den>::value; 334 335 public: 336 typedef ratio< 337 __safe_multiply<(_R1::num / __gcd1), 338 (_R2::num / __gcd2)>::value, 339 __safe_multiply<(_R1::den / __gcd2), 340 (_R2::den / __gcd1)>::value> type; 341 342 static constexpr intmax_t num = type::num; 343 static constexpr intmax_t den = type::den; 344 }; 345 346 #if ! __cpp_inline_variables 347 template<typename _R1, typename _R2> 348 constexpr intmax_t __ratio_multiply<_R1, _R2>::num; 349 350 template<typename _R1, typename _R2> 351 constexpr intmax_t __ratio_multiply<_R1, _R2>::den; 352 #endif 353 354 /// @endcond 355 356 /// ratio_multiply 357 template<typename _R1, typename _R2> 358 using ratio_multiply = typename __ratio_multiply<_R1, _R2>::type; 359 360 /// @cond undocumented 361 362 template<typename _R1, typename _R2> 363 struct __ratio_divide 364 { 365 static_assert(_R2::num != 0, "division by 0"); 366 367 typedef typename __ratio_multiply< 368 _R1, 369 ratio<_R2::den, _R2::num>>::type type; 370 371 static constexpr intmax_t num = type::num; 372 static constexpr intmax_t den = type::den; 373 }; 374 375 #if ! __cpp_inline_variables 376 template<typename _R1, typename _R2> 377 constexpr intmax_t __ratio_divide<_R1, _R2>::num; 378 379 template<typename _R1, typename _R2> 380 constexpr intmax_t __ratio_divide<_R1, _R2>::den; 381 #endif 382 383 /// @endcond 384 385 /// ratio_divide 386 template<typename _R1, typename _R2> 387 using ratio_divide = typename __ratio_divide<_R1, _R2>::type; 388 389 /// ratio_equal 390 template<typename _R1, typename _R2> 391 struct ratio_equal 392 : integral_constant<bool, _R1::num == _R2::num && _R1::den == _R2::den> 393 { 394 static_assert(std::__are_both_ratios<_R1, _R2>(), 395 "both template arguments must be a std::ratio"); 396 }; 397 398 /// ratio_not_equal 399 template<typename _R1, typename _R2> 400 struct ratio_not_equal 401 : integral_constant<bool, !ratio_equal<_R1, _R2>::value> 402 { }; 403 404 /// @cond undocumented 405 406 // Both numbers are positive. 407 template<typename _R1, typename _R2, 408 typename _Left = __big_mul<_R1::num,_R2::den>, 409 typename _Right = __big_mul<_R2::num,_R1::den> > 410 struct __ratio_less_impl_1 411 : integral_constant<bool, __big_less<_Left::__hi, _Left::__lo, 412 _Right::__hi, _Right::__lo>::value> 413 { }; 414 415 template<typename _R1, typename _R2, 416 bool = (_R1::num == 0 || _R2::num == 0 417 || (__static_sign<_R1::num>::value 418 != __static_sign<_R2::num>::value)), 419 bool = (__static_sign<_R1::num>::value == -1 420 && __static_sign<_R2::num>::value == -1)> 421 struct __ratio_less_impl 422 : __ratio_less_impl_1<_R1, _R2>::type 423 { }; 424 425 template<typename _R1, typename _R2> 426 struct __ratio_less_impl<_R1, _R2, true, false> 427 : integral_constant<bool, _R1::num < _R2::num> 428 { }; 429 430 template<typename _R1, typename _R2> 431 struct __ratio_less_impl<_R1, _R2, false, true> 432 : __ratio_less_impl_1<ratio<-_R2::num, _R2::den>, 433 ratio<-_R1::num, _R1::den> >::type 434 { }; 435 436 /// @endcond 437 438 /// ratio_less 439 template<typename _R1, typename _R2> 440 struct ratio_less 441 : __ratio_less_impl<_R1, _R2>::type 442 { 443 static_assert(std::__are_both_ratios<_R1, _R2>(), 444 "both template arguments must be a std::ratio"); 445 }; 446 447 /// ratio_less_equal 448 template<typename _R1, typename _R2> 449 struct ratio_less_equal 450 : integral_constant<bool, !ratio_less<_R2, _R1>::value> 451 { }; 452 453 /// ratio_greater 454 template<typename _R1, typename _R2> 455 struct ratio_greater 456 : integral_constant<bool, ratio_less<_R2, _R1>::value> 457 { }; 458 459 /// ratio_greater_equal 460 template<typename _R1, typename _R2> 461 struct ratio_greater_equal 462 : integral_constant<bool, !ratio_less<_R1, _R2>::value> 463 { }; 464 465 #if __cplusplus > 201402L 466 template <typename _R1, typename _R2> 467 inline constexpr bool ratio_equal_v = ratio_equal<_R1, _R2>::value; 468 template <typename _R1, typename _R2> 469 inline constexpr bool ratio_not_equal_v = ratio_not_equal<_R1, _R2>::value; 470 template <typename _R1, typename _R2> 471 inline constexpr bool ratio_less_v = ratio_less<_R1, _R2>::value; 472 template <typename _R1, typename _R2> 473 inline constexpr bool ratio_less_equal_v 474 = ratio_less_equal<_R1, _R2>::value; 475 template <typename _R1, typename _R2> 476 inline constexpr bool ratio_greater_v = ratio_greater<_R1, _R2>::value; 477 template <typename _R1, typename _R2> 478 inline constexpr bool ratio_greater_equal_v 479 = ratio_greater_equal<_R1, _R2>::value; 480 #endif // C++17 481 482 /// @cond undocumented 483 484 template<typename _R1, typename _R2, 485 bool = (_R1::num >= 0), 486 bool = (_R2::num >= 0), 487 bool = ratio_less<ratio<__static_abs<_R1::num>::value, _R1::den>, 488 ratio<__static_abs<_R2::num>::value, _R2::den> >::value> 489 struct __ratio_add_impl 490 { 491 private: 492 typedef typename __ratio_add_impl< 493 ratio<-_R1::num, _R1::den>, 494 ratio<-_R2::num, _R2::den> >::type __t; 495 public: 496 typedef ratio<-__t::num, __t::den> type; 497 }; 498 499 // True addition of nonnegative numbers. 500 template<typename _R1, typename _R2, bool __b> 501 struct __ratio_add_impl<_R1, _R2, true, true, __b> 502 { 503 private: 504 static constexpr uintmax_t __g = __static_gcd<_R1::den, _R2::den>::value; 505 static constexpr uintmax_t __d2 = _R2::den / __g; 506 typedef __big_mul<_R1::den, __d2> __d; 507 typedef __big_mul<_R1::num, _R2::den / __g> __x; 508 typedef __big_mul<_R2::num, _R1::den / __g> __y; 509 typedef __big_add<__x::__hi, __x::__lo, __y::__hi, __y::__lo> __n; 510 static_assert(__n::__hi >= __x::__hi, "Internal library error"); 511 typedef __big_div<__n::__hi, __n::__lo, __g> __ng; 512 static constexpr uintmax_t __g2 = __static_gcd<__ng::__rem, __g>::value; 513 typedef __big_div<__n::__hi, __n::__lo, __g2> __n_final; 514 static_assert(__n_final::__rem == 0, "Internal library error"); 515 static_assert(__n_final::__quot_hi == 0 && 516 __n_final::__quot_lo <= __INTMAX_MAX__, "overflow in addition"); 517 typedef __big_mul<_R1::den / __g2, __d2> __d_final; 518 static_assert(__d_final::__hi == 0 && 519 __d_final::__lo <= __INTMAX_MAX__, "overflow in addition"); 520 public: 521 typedef ratio<__n_final::__quot_lo, __d_final::__lo> type; 522 }; 523 524 template<typename _R1, typename _R2> 525 struct __ratio_add_impl<_R1, _R2, false, true, true> 526 : __ratio_add_impl<_R2, _R1> 527 { }; 528 529 // True subtraction of nonnegative numbers yielding a nonnegative result. 530 template<typename _R1, typename _R2> 531 struct __ratio_add_impl<_R1, _R2, true, false, false> 532 { 533 private: 534 static constexpr uintmax_t __g = __static_gcd<_R1::den, _R2::den>::value; 535 static constexpr uintmax_t __d2 = _R2::den / __g; 536 typedef __big_mul<_R1::den, __d2> __d; 537 typedef __big_mul<_R1::num, _R2::den / __g> __x; 538 typedef __big_mul<-_R2::num, _R1::den / __g> __y; 539 typedef __big_sub<__x::__hi, __x::__lo, __y::__hi, __y::__lo> __n; 540 typedef __big_div<__n::__hi, __n::__lo, __g> __ng; 541 static constexpr uintmax_t __g2 = __static_gcd<__ng::__rem, __g>::value; 542 typedef __big_div<__n::__hi, __n::__lo, __g2> __n_final; 543 static_assert(__n_final::__rem == 0, "Internal library error"); 544 static_assert(__n_final::__quot_hi == 0 && 545 __n_final::__quot_lo <= __INTMAX_MAX__, "overflow in addition"); 546 typedef __big_mul<_R1::den / __g2, __d2> __d_final; 547 static_assert(__d_final::__hi == 0 && 548 __d_final::__lo <= __INTMAX_MAX__, "overflow in addition"); 549 public: 550 typedef ratio<__n_final::__quot_lo, __d_final::__lo> type; 551 }; 552 553 template<typename _R1, typename _R2> 554 struct __ratio_add 555 { 556 static_assert(std::__are_both_ratios<_R1, _R2>(), 557 "both template arguments must be a std::ratio"); 558 559 typedef typename __ratio_add_impl<_R1, _R2>::type type; 560 static constexpr intmax_t num = type::num; 561 static constexpr intmax_t den = type::den; 562 }; 563 564 #if ! __cpp_inline_variables 565 template<typename _R1, typename _R2> 566 constexpr intmax_t __ratio_add<_R1, _R2>::num; 567 568 template<typename _R1, typename _R2> 569 constexpr intmax_t __ratio_add<_R1, _R2>::den; 570 #endif 571 572 /// @endcond 573 574 /// ratio_add 575 template<typename _R1, typename _R2> 576 using ratio_add = typename __ratio_add<_R1, _R2>::type; 577 578 /// @cond undocumented 579 580 template<typename _R1, typename _R2> 581 struct __ratio_subtract 582 { 583 typedef typename __ratio_add< 584 _R1, 585 ratio<-_R2::num, _R2::den>>::type type; 586 587 static constexpr intmax_t num = type::num; 588 static constexpr intmax_t den = type::den; 589 }; 590 591 #if ! __cpp_inline_variables 592 template<typename _R1, typename _R2> 593 constexpr intmax_t __ratio_subtract<_R1, _R2>::num; 594 595 template<typename _R1, typename _R2> 596 constexpr intmax_t __ratio_subtract<_R1, _R2>::den; 597 #endif 598 599 /// @endcond 600 601 /// ratio_subtract 602 template<typename _R1, typename _R2> 603 using ratio_subtract = typename __ratio_subtract<_R1, _R2>::type; 604 605 606 typedef ratio<1, 1000000000000000000> atto; 607 typedef ratio<1, 1000000000000000> femto; 608 typedef ratio<1, 1000000000000> pico; 609 typedef ratio<1, 1000000000> nano; 610 typedef ratio<1, 1000000> micro; 611 typedef ratio<1, 1000> milli; 612 typedef ratio<1, 100> centi; 613 typedef ratio<1, 10> deci; 614 typedef ratio< 10, 1> deca; 615 typedef ratio< 100, 1> hecto; 616 typedef ratio< 1000, 1> kilo; 617 typedef ratio< 1000000, 1> mega; 618 typedef ratio< 1000000000, 1> giga; 619 typedef ratio< 1000000000000, 1> tera; 620 typedef ratio< 1000000000000000, 1> peta; 621 typedef ratio< 1000000000000000000, 1> exa; 622 623 /// @} group ratio 624 _GLIBCXX_END_NAMESPACE_VERSION 625 } // namespace 626 627 #endif // C++11 628 629 #endif //_GLIBCXX_RATIO 630
Indexes created Thu Apr 30 00:23:01 UTC 2026