libstdc++: ratio Source File

libstdc++

ratio
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1// ratio -*- C++ -*-
2
3// Copyright (C) 2008-2026 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
47namespace 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
type_traits
cstdint
c++0x_warning.h
version.h
std
ISO C++ entities toplevel namespace is std.
std::integral_constant
integral_constant
Definition type_traits:96