libstdc++
ratio
Go to the documentation of this file.
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