source: Daodan/MSYS2/mingw32/include/c++/11.2.0/ratio@ 1181

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1// ratio -*- C++ -*-
2
3// Copyright (C) 2008-2021 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
42namespace 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 template<intmax_t _Num, intmax_t _Den>
283 constexpr intmax_t ratio<_Num, _Den>::num;
284
285 template<intmax_t _Num, intmax_t _Den>
286 constexpr intmax_t ratio<_Num, _Den>::den;
287
288 /// @cond undocumented
289
290 template<typename _R1, typename _R2>
291 struct __ratio_multiply
292 {
293 private:
294 static const intmax_t __gcd1 =
295 __static_gcd<_R1::num, _R2::den>::value;
296 static const intmax_t __gcd2 =
297 __static_gcd<_R2::num, _R1::den>::value;
298
299 public:
300 typedef ratio<
301 __safe_multiply<(_R1::num / __gcd1),
302 (_R2::num / __gcd2)>::value,
303 __safe_multiply<(_R1::den / __gcd2),
304 (_R2::den / __gcd1)>::value> type;
305
306 static constexpr intmax_t num = type::num;
307 static constexpr intmax_t den = type::den;
308 };
309
310 template<typename _R1, typename _R2>
311 constexpr intmax_t __ratio_multiply<_R1, _R2>::num;
312
313 template<typename _R1, typename _R2>
314 constexpr intmax_t __ratio_multiply<_R1, _R2>::den;
315
316 /// @endcond
317
318 /// ratio_multiply
319 template<typename _R1, typename _R2>
320 using ratio_multiply = typename __ratio_multiply<_R1, _R2>::type;
321
322 /// @cond undocumented
323
324 template<typename _R1, typename _R2>
325 struct __ratio_divide
326 {
327 static_assert(_R2::num != 0, "division by 0");
328
329 typedef typename __ratio_multiply<
330 _R1,
331 ratio<_R2::den, _R2::num>>::type type;
332
333 static constexpr intmax_t num = type::num;
334 static constexpr intmax_t den = type::den;
335 };
336
337 template<typename _R1, typename _R2>
338 constexpr intmax_t __ratio_divide<_R1, _R2>::num;
339
340 template<typename _R1, typename _R2>
341 constexpr intmax_t __ratio_divide<_R1, _R2>::den;
342
343 /// @endcond
344
345 /// ratio_divide
346 template<typename _R1, typename _R2>
347 using ratio_divide = typename __ratio_divide<_R1, _R2>::type;
348
349 /// ratio_equal
350 template<typename _R1, typename _R2>
351 struct ratio_equal
352 : integral_constant<bool, _R1::num == _R2::num && _R1::den == _R2::den>
353 { };
354
355 /// ratio_not_equal
356 template<typename _R1, typename _R2>
357 struct ratio_not_equal
358 : integral_constant<bool, !ratio_equal<_R1, _R2>::value>
359 { };
360
361 /// @cond undocumented
362
363 // Both numbers are positive.
364 template<typename _R1, typename _R2,
365 typename _Left = __big_mul<_R1::num,_R2::den>,
366 typename _Right = __big_mul<_R2::num,_R1::den> >
367 struct __ratio_less_impl_1
368 : integral_constant<bool, __big_less<_Left::__hi, _Left::__lo,
369 _Right::__hi, _Right::__lo>::value>
370 { };
371
372 template<typename _R1, typename _R2,
373 bool = (_R1::num == 0 || _R2::num == 0
374 || (__static_sign<_R1::num>::value
375 != __static_sign<_R2::num>::value)),
376 bool = (__static_sign<_R1::num>::value == -1
377 && __static_sign<_R2::num>::value == -1)>
378 struct __ratio_less_impl
379 : __ratio_less_impl_1<_R1, _R2>::type
380 { };
381
382 template<typename _R1, typename _R2>
383 struct __ratio_less_impl<_R1, _R2, true, false>
384 : integral_constant<bool, _R1::num < _R2::num>
385 { };
386
387 template<typename _R1, typename _R2>
388 struct __ratio_less_impl<_R1, _R2, false, true>
389 : __ratio_less_impl_1<ratio<-_R2::num, _R2::den>,
390 ratio<-_R1::num, _R1::den> >::type
391 { };
392
393 /// @endcond
394
395 /// ratio_less
396 template<typename _R1, typename _R2>
397 struct ratio_less
398 : __ratio_less_impl<_R1, _R2>::type
399 { };
400
401 /// ratio_less_equal
402 template<typename _R1, typename _R2>
403 struct ratio_less_equal
404 : integral_constant<bool, !ratio_less<_R2, _R1>::value>
405 { };
406
407 /// ratio_greater
408 template<typename _R1, typename _R2>
409 struct ratio_greater
410 : integral_constant<bool, ratio_less<_R2, _R1>::value>
411 { };
412
413 /// ratio_greater_equal
414 template<typename _R1, typename _R2>
415 struct ratio_greater_equal
416 : integral_constant<bool, !ratio_less<_R1, _R2>::value>
417 { };
418
419#if __cplusplus > 201402L
420 template <typename _R1, typename _R2>
421 inline constexpr bool ratio_equal_v = ratio_equal<_R1, _R2>::value;
422 template <typename _R1, typename _R2>
423 inline constexpr bool ratio_not_equal_v = ratio_not_equal<_R1, _R2>::value;
424 template <typename _R1, typename _R2>
425 inline constexpr bool ratio_less_v = ratio_less<_R1, _R2>::value;
426 template <typename _R1, typename _R2>
427 inline constexpr bool ratio_less_equal_v =
428 ratio_less_equal<_R1, _R2>::value;
429 template <typename _R1, typename _R2>
430 inline constexpr bool ratio_greater_v = ratio_greater<_R1, _R2>::value;
431 template <typename _R1, typename _R2>
432 inline constexpr bool ratio_greater_equal_v
433 = ratio_greater_equal<_R1, _R2>::value;
434#endif // C++17
435
436 /// @cond undocumented
437
438 template<typename _R1, typename _R2,
439 bool = (_R1::num >= 0),
440 bool = (_R2::num >= 0),
441 bool = ratio_less<ratio<__static_abs<_R1::num>::value, _R1::den>,
442 ratio<__static_abs<_R2::num>::value, _R2::den> >::value>
443 struct __ratio_add_impl
444 {
445 private:
446 typedef typename __ratio_add_impl<
447 ratio<-_R1::num, _R1::den>,
448 ratio<-_R2::num, _R2::den> >::type __t;
449 public:
450 typedef ratio<-__t::num, __t::den> type;
451 };
452
453 // True addition of nonnegative numbers.
454 template<typename _R1, typename _R2, bool __b>
455 struct __ratio_add_impl<_R1, _R2, true, true, __b>
456 {
457 private:
458 static constexpr uintmax_t __g = __static_gcd<_R1::den, _R2::den>::value;
459 static constexpr uintmax_t __d2 = _R2::den / __g;
460 typedef __big_mul<_R1::den, __d2> __d;
461 typedef __big_mul<_R1::num, _R2::den / __g> __x;
462 typedef __big_mul<_R2::num, _R1::den / __g> __y;
463 typedef __big_add<__x::__hi, __x::__lo, __y::__hi, __y::__lo> __n;
464 static_assert(__n::__hi >= __x::__hi, "Internal library error");
465 typedef __big_div<__n::__hi, __n::__lo, __g> __ng;
466 static constexpr uintmax_t __g2 = __static_gcd<__ng::__rem, __g>::value;
467 typedef __big_div<__n::__hi, __n::__lo, __g2> __n_final;
468 static_assert(__n_final::__rem == 0, "Internal library error");
469 static_assert(__n_final::__quot_hi == 0 &&
470 __n_final::__quot_lo <= __INTMAX_MAX__, "overflow in addition");
471 typedef __big_mul<_R1::den / __g2, __d2> __d_final;
472 static_assert(__d_final::__hi == 0 &&
473 __d_final::__lo <= __INTMAX_MAX__, "overflow in addition");
474 public:
475 typedef ratio<__n_final::__quot_lo, __d_final::__lo> type;
476 };
477
478 template<typename _R1, typename _R2>
479 struct __ratio_add_impl<_R1, _R2, false, true, true>
480 : __ratio_add_impl<_R2, _R1>
481 { };
482
483 // True subtraction of nonnegative numbers yielding a nonnegative result.
484 template<typename _R1, typename _R2>
485 struct __ratio_add_impl<_R1, _R2, true, false, false>
486 {
487 private:
488 static constexpr uintmax_t __g = __static_gcd<_R1::den, _R2::den>::value;
489 static constexpr uintmax_t __d2 = _R2::den / __g;
490 typedef __big_mul<_R1::den, __d2> __d;
491 typedef __big_mul<_R1::num, _R2::den / __g> __x;
492 typedef __big_mul<-_R2::num, _R1::den / __g> __y;
493 typedef __big_sub<__x::__hi, __x::__lo, __y::__hi, __y::__lo> __n;
494 typedef __big_div<__n::__hi, __n::__lo, __g> __ng;
495 static constexpr uintmax_t __g2 = __static_gcd<__ng::__rem, __g>::value;
496 typedef __big_div<__n::__hi, __n::__lo, __g2> __n_final;
497 static_assert(__n_final::__rem == 0, "Internal library error");
498 static_assert(__n_final::__quot_hi == 0 &&
499 __n_final::__quot_lo <= __INTMAX_MAX__, "overflow in addition");
500 typedef __big_mul<_R1::den / __g2, __d2> __d_final;
501 static_assert(__d_final::__hi == 0 &&
502 __d_final::__lo <= __INTMAX_MAX__, "overflow in addition");
503 public:
504 typedef ratio<__n_final::__quot_lo, __d_final::__lo> type;
505 };
506
507 template<typename _R1, typename _R2>
508 struct __ratio_add
509 {
510 typedef typename __ratio_add_impl<_R1, _R2>::type type;
511 static constexpr intmax_t num = type::num;
512 static constexpr intmax_t den = type::den;
513 };
514
515 template<typename _R1, typename _R2>
516 constexpr intmax_t __ratio_add<_R1, _R2>::num;
517
518 template<typename _R1, typename _R2>
519 constexpr intmax_t __ratio_add<_R1, _R2>::den;
520
521 /// @endcond
522
523 /// ratio_add
524 template<typename _R1, typename _R2>
525 using ratio_add = typename __ratio_add<_R1, _R2>::type;
526
527 /// @cond undocumented
528
529 template<typename _R1, typename _R2>
530 struct __ratio_subtract
531 {
532 typedef typename __ratio_add<
533 _R1,
534 ratio<-_R2::num, _R2::den>>::type type;
535
536 static constexpr intmax_t num = type::num;
537 static constexpr intmax_t den = type::den;
538 };
539
540 template<typename _R1, typename _R2>
541 constexpr intmax_t __ratio_subtract<_R1, _R2>::num;
542
543 template<typename _R1, typename _R2>
544 constexpr intmax_t __ratio_subtract<_R1, _R2>::den;
545
546 /// @endcond
547
548 /// ratio_subtract
549 template<typename _R1, typename _R2>
550 using ratio_subtract = typename __ratio_subtract<_R1, _R2>::type;
551
552
553 typedef ratio<1, 1000000000000000000> atto;
554 typedef ratio<1, 1000000000000000> femto;
555 typedef ratio<1, 1000000000000> pico;
556 typedef ratio<1, 1000000000> nano;
557 typedef ratio<1, 1000000> micro;
558 typedef ratio<1, 1000> milli;
559 typedef ratio<1, 100> centi;
560 typedef ratio<1, 10> deci;
561 typedef ratio< 10, 1> deca;
562 typedef ratio< 100, 1> hecto;
563 typedef ratio< 1000, 1> kilo;
564 typedef ratio< 1000000, 1> mega;
565 typedef ratio< 1000000000, 1> giga;
566 typedef ratio< 1000000000000, 1> tera;
567 typedef ratio< 1000000000000000, 1> peta;
568 typedef ratio< 1000000000000000000, 1> exa;
569
570 /// @} group ratio
571_GLIBCXX_END_NAMESPACE_VERSION
572} // namespace
573
574#endif // C++11
575
576#endif //_GLIBCXX_RATIO
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