1 | // -*- C++ -*- |
2 | //===---------------------------- ratio -----------------------------------===// |
3 | // |
4 | // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions. |
5 | // See https://llvm.org/LICENSE.txt for license information. |
6 | // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception |
7 | // |
8 | //===----------------------------------------------------------------------===// |
9 | |
10 | #ifndef _LIBCPP_RATIO |
11 | #define _LIBCPP_RATIO |
12 | |
13 | /* |
14 | ratio synopsis |
15 | |
16 | namespace std |
17 | { |
18 | |
19 | template <intmax_t N, intmax_t D = 1> |
20 | class ratio |
21 | { |
22 | public: |
23 | static constexpr intmax_t num; |
24 | static constexpr intmax_t den; |
25 | typedef ratio<num, den> type; |
26 | }; |
27 | |
28 | // ratio arithmetic |
29 | template <class R1, class R2> using ratio_add = ...; |
30 | template <class R1, class R2> using ratio_subtract = ...; |
31 | template <class R1, class R2> using ratio_multiply = ...; |
32 | template <class R1, class R2> using ratio_divide = ...; |
33 | |
34 | // ratio comparison |
35 | template <class R1, class R2> struct ratio_equal; |
36 | template <class R1, class R2> struct ratio_not_equal; |
37 | template <class R1, class R2> struct ratio_less; |
38 | template <class R1, class R2> struct ratio_less_equal; |
39 | template <class R1, class R2> struct ratio_greater; |
40 | template <class R1, class R2> struct ratio_greater_equal; |
41 | |
42 | // convenience SI typedefs |
43 | typedef ratio<1, 1000000000000000000000000> yocto; // not supported |
44 | typedef ratio<1, 1000000000000000000000> zepto; // not supported |
45 | typedef ratio<1, 1000000000000000000> atto; |
46 | typedef ratio<1, 1000000000000000> femto; |
47 | typedef ratio<1, 1000000000000> pico; |
48 | typedef ratio<1, 1000000000> nano; |
49 | typedef ratio<1, 1000000> micro; |
50 | typedef ratio<1, 1000> milli; |
51 | typedef ratio<1, 100> centi; |
52 | typedef ratio<1, 10> deci; |
53 | typedef ratio< 10, 1> deca; |
54 | typedef ratio< 100, 1> hecto; |
55 | typedef ratio< 1000, 1> kilo; |
56 | typedef ratio< 1000000, 1> mega; |
57 | typedef ratio< 1000000000, 1> giga; |
58 | typedef ratio< 1000000000000, 1> tera; |
59 | typedef ratio< 1000000000000000, 1> peta; |
60 | typedef ratio< 1000000000000000000, 1> exa; |
61 | typedef ratio< 1000000000000000000000, 1> zetta; // not supported |
62 | typedef ratio<1000000000000000000000000, 1> yotta; // not supported |
63 | |
64 | // 20.11.5, ratio comparison |
65 | template <class R1, class R2> inline constexpr bool ratio_equal_v |
66 | = ratio_equal<R1, R2>::value; // C++17 |
67 | template <class R1, class R2> inline constexpr bool ratio_not_equal_v |
68 | = ratio_not_equal<R1, R2>::value; // C++17 |
69 | template <class R1, class R2> inline constexpr bool ratio_less_v |
70 | = ratio_less<R1, R2>::value; // C++17 |
71 | template <class R1, class R2> inline constexpr bool ratio_less_equal_v |
72 | = ratio_less_equal<R1, R2>::value; // C++17 |
73 | template <class R1, class R2> inline constexpr bool ratio_greater_v |
74 | = ratio_greater<R1, R2>::value; // C++17 |
75 | template <class R1, class R2> inline constexpr bool ratio_greater_equal_v |
76 | = ratio_greater_equal<R1, R2>::value; // C++17 |
77 | } |
78 | */ |
79 | |
80 | #include <__config> |
81 | #include <cstdint> |
82 | #include <climits> |
83 | #include <type_traits> |
84 | |
85 | #if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER) |
86 | #pragma GCC system_header |
87 | #endif |
88 | |
89 | _LIBCPP_PUSH_MACROS |
90 | #include <__undef_macros> |
91 | |
92 | |
93 | _LIBCPP_BEGIN_NAMESPACE_STD |
94 | |
95 | // __static_gcd |
96 | |
97 | template <intmax_t _Xp, intmax_t _Yp> |
98 | struct __static_gcd |
99 | { |
100 | static const intmax_t value = __static_gcd<_Yp, _Xp % _Yp>::value; |
101 | }; |
102 | |
103 | template <intmax_t _Xp> |
104 | struct __static_gcd<_Xp, 0> |
105 | { |
106 | static const intmax_t value = _Xp; |
107 | }; |
108 | |
109 | template <> |
110 | struct __static_gcd<0, 0> |
111 | { |
112 | static const intmax_t value = 1; |
113 | }; |
114 | |
115 | // __static_lcm |
116 | |
117 | template <intmax_t _Xp, intmax_t _Yp> |
118 | struct __static_lcm |
119 | { |
120 | static const intmax_t value = _Xp / __static_gcd<_Xp, _Yp>::value * _Yp; |
121 | }; |
122 | |
123 | template <intmax_t _Xp> |
124 | struct __static_abs |
125 | { |
126 | static const intmax_t value = _Xp < 0 ? -_Xp : _Xp; |
127 | }; |
128 | |
129 | template <intmax_t _Xp> |
130 | struct __static_sign |
131 | { |
132 | static const intmax_t value = _Xp == 0 ? 0 : (_Xp < 0 ? -1 : 1); |
133 | }; |
134 | |
135 | template <intmax_t _Xp, intmax_t _Yp, intmax_t = __static_sign<_Yp>::value> |
136 | class __ll_add; |
137 | |
138 | template <intmax_t _Xp, intmax_t _Yp> |
139 | class __ll_add<_Xp, _Yp, 1> |
140 | { |
141 | static const intmax_t min = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)) + 1; |
142 | static const intmax_t max = -min; |
143 | |
144 | static_assert(_Xp <= max - _Yp, "overflow in __ll_add" ); |
145 | public: |
146 | static const intmax_t value = _Xp + _Yp; |
147 | }; |
148 | |
149 | template <intmax_t _Xp, intmax_t _Yp> |
150 | class __ll_add<_Xp, _Yp, 0> |
151 | { |
152 | public: |
153 | static const intmax_t value = _Xp; |
154 | }; |
155 | |
156 | template <intmax_t _Xp, intmax_t _Yp> |
157 | class __ll_add<_Xp, _Yp, -1> |
158 | { |
159 | static const intmax_t min = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)) + 1; |
160 | static const intmax_t max = -min; |
161 | |
162 | static_assert(min - _Yp <= _Xp, "overflow in __ll_add" ); |
163 | public: |
164 | static const intmax_t value = _Xp + _Yp; |
165 | }; |
166 | |
167 | template <intmax_t _Xp, intmax_t _Yp, intmax_t = __static_sign<_Yp>::value> |
168 | class __ll_sub; |
169 | |
170 | template <intmax_t _Xp, intmax_t _Yp> |
171 | class __ll_sub<_Xp, _Yp, 1> |
172 | { |
173 | static const intmax_t min = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)) + 1; |
174 | static const intmax_t max = -min; |
175 | |
176 | static_assert(min + _Yp <= _Xp, "overflow in __ll_sub" ); |
177 | public: |
178 | static const intmax_t value = _Xp - _Yp; |
179 | }; |
180 | |
181 | template <intmax_t _Xp, intmax_t _Yp> |
182 | class __ll_sub<_Xp, _Yp, 0> |
183 | { |
184 | public: |
185 | static const intmax_t value = _Xp; |
186 | }; |
187 | |
188 | template <intmax_t _Xp, intmax_t _Yp> |
189 | class __ll_sub<_Xp, _Yp, -1> |
190 | { |
191 | static const intmax_t min = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)) + 1; |
192 | static const intmax_t max = -min; |
193 | |
194 | static_assert(_Xp <= max + _Yp, "overflow in __ll_sub" ); |
195 | public: |
196 | static const intmax_t value = _Xp - _Yp; |
197 | }; |
198 | |
199 | template <intmax_t _Xp, intmax_t _Yp> |
200 | class __ll_mul |
201 | { |
202 | static const intmax_t nan = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)); |
203 | static const intmax_t min = nan + 1; |
204 | static const intmax_t max = -min; |
205 | static const intmax_t __a_x = __static_abs<_Xp>::value; |
206 | static const intmax_t __a_y = __static_abs<_Yp>::value; |
207 | |
208 | static_assert(_Xp != nan && _Yp != nan && __a_x <= max / __a_y, "overflow in __ll_mul" ); |
209 | public: |
210 | static const intmax_t value = _Xp * _Yp; |
211 | }; |
212 | |
213 | template <intmax_t _Yp> |
214 | class __ll_mul<0, _Yp> |
215 | { |
216 | public: |
217 | static const intmax_t value = 0; |
218 | }; |
219 | |
220 | template <intmax_t _Xp> |
221 | class __ll_mul<_Xp, 0> |
222 | { |
223 | public: |
224 | static const intmax_t value = 0; |
225 | }; |
226 | |
227 | template <> |
228 | class __ll_mul<0, 0> |
229 | { |
230 | public: |
231 | static const intmax_t value = 0; |
232 | }; |
233 | |
234 | // Not actually used but left here in case needed in future maintenance |
235 | template <intmax_t _Xp, intmax_t _Yp> |
236 | class __ll_div |
237 | { |
238 | static const intmax_t nan = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)); |
239 | static const intmax_t min = nan + 1; |
240 | static const intmax_t max = -min; |
241 | |
242 | static_assert(_Xp != nan && _Yp != nan && _Yp != 0, "overflow in __ll_div" ); |
243 | public: |
244 | static const intmax_t value = _Xp / _Yp; |
245 | }; |
246 | |
247 | template <intmax_t _Num, intmax_t _Den = 1> |
248 | class _LIBCPP_TEMPLATE_VIS ratio |
249 | { |
250 | static_assert(__static_abs<_Num>::value >= 0, "ratio numerator is out of range" ); |
251 | static_assert(_Den != 0, "ratio divide by 0" ); |
252 | static_assert(__static_abs<_Den>::value > 0, "ratio denominator is out of range" ); |
253 | static _LIBCPP_CONSTEXPR const intmax_t __na = __static_abs<_Num>::value; |
254 | static _LIBCPP_CONSTEXPR const intmax_t __da = __static_abs<_Den>::value; |
255 | static _LIBCPP_CONSTEXPR const intmax_t __s = __static_sign<_Num>::value * __static_sign<_Den>::value; |
256 | static _LIBCPP_CONSTEXPR const intmax_t __gcd = __static_gcd<__na, __da>::value; |
257 | public: |
258 | static _LIBCPP_CONSTEXPR const intmax_t num = __s * __na / __gcd; |
259 | static _LIBCPP_CONSTEXPR const intmax_t den = __da / __gcd; |
260 | |
261 | typedef ratio<num, den> type; |
262 | }; |
263 | |
264 | template <intmax_t _Num, intmax_t _Den> |
265 | _LIBCPP_CONSTEXPR const intmax_t ratio<_Num, _Den>::num; |
266 | |
267 | template <intmax_t _Num, intmax_t _Den> |
268 | _LIBCPP_CONSTEXPR const intmax_t ratio<_Num, _Den>::den; |
269 | |
270 | template <class _Tp> struct __is_ratio : false_type {}; |
271 | template <intmax_t _Num, intmax_t _Den> struct __is_ratio<ratio<_Num, _Den> > : true_type {}; |
272 | |
273 | typedef ratio<1LL, 1000000000000000000LL> atto; |
274 | typedef ratio<1LL, 1000000000000000LL> femto; |
275 | typedef ratio<1LL, 1000000000000LL> pico; |
276 | typedef ratio<1LL, 1000000000LL> nano; |
277 | typedef ratio<1LL, 1000000LL> micro; |
278 | typedef ratio<1LL, 1000LL> milli; |
279 | typedef ratio<1LL, 100LL> centi; |
280 | typedef ratio<1LL, 10LL> deci; |
281 | typedef ratio< 10LL, 1LL> deca; |
282 | typedef ratio< 100LL, 1LL> hecto; |
283 | typedef ratio< 1000LL, 1LL> kilo; |
284 | typedef ratio< 1000000LL, 1LL> mega; |
285 | typedef ratio< 1000000000LL, 1LL> giga; |
286 | typedef ratio< 1000000000000LL, 1LL> tera; |
287 | typedef ratio< 1000000000000000LL, 1LL> peta; |
288 | typedef ratio<1000000000000000000LL, 1LL> exa; |
289 | |
290 | template <class _R1, class _R2> |
291 | struct __ratio_multiply |
292 | { |
293 | private: |
294 | static const intmax_t __gcd_n1_d2 = __static_gcd<_R1::num, _R2::den>::value; |
295 | static const intmax_t __gcd_d1_n2 = __static_gcd<_R1::den, _R2::num>::value; |
296 | public: |
297 | typedef typename ratio |
298 | < |
299 | __ll_mul<_R1::num / __gcd_n1_d2, _R2::num / __gcd_d1_n2>::value, |
300 | __ll_mul<_R2::den / __gcd_n1_d2, _R1::den / __gcd_d1_n2>::value |
301 | >::type type; |
302 | }; |
303 | |
304 | #ifndef _LIBCPP_CXX03_LANG |
305 | |
306 | template <class _R1, class _R2> using ratio_multiply |
307 | = typename __ratio_multiply<_R1, _R2>::type; |
308 | |
309 | #else // _LIBCPP_CXX03_LANG |
310 | |
311 | template <class _R1, class _R2> |
312 | struct _LIBCPP_TEMPLATE_VIS ratio_multiply |
313 | : public __ratio_multiply<_R1, _R2>::type {}; |
314 | |
315 | #endif // _LIBCPP_CXX03_LANG |
316 | |
317 | template <class _R1, class _R2> |
318 | struct __ratio_divide |
319 | { |
320 | private: |
321 | static const intmax_t __gcd_n1_n2 = __static_gcd<_R1::num, _R2::num>::value; |
322 | static const intmax_t __gcd_d1_d2 = __static_gcd<_R1::den, _R2::den>::value; |
323 | public: |
324 | typedef typename ratio |
325 | < |
326 | __ll_mul<_R1::num / __gcd_n1_n2, _R2::den / __gcd_d1_d2>::value, |
327 | __ll_mul<_R2::num / __gcd_n1_n2, _R1::den / __gcd_d1_d2>::value |
328 | >::type type; |
329 | }; |
330 | |
331 | #ifndef _LIBCPP_CXX03_LANG |
332 | |
333 | template <class _R1, class _R2> using ratio_divide |
334 | = typename __ratio_divide<_R1, _R2>::type; |
335 | |
336 | #else // _LIBCPP_CXX03_LANG |
337 | |
338 | template <class _R1, class _R2> |
339 | struct _LIBCPP_TEMPLATE_VIS ratio_divide |
340 | : public __ratio_divide<_R1, _R2>::type {}; |
341 | |
342 | #endif // _LIBCPP_CXX03_LANG |
343 | |
344 | template <class _R1, class _R2> |
345 | struct __ratio_add |
346 | { |
347 | private: |
348 | static const intmax_t __gcd_n1_n2 = __static_gcd<_R1::num, _R2::num>::value; |
349 | static const intmax_t __gcd_d1_d2 = __static_gcd<_R1::den, _R2::den>::value; |
350 | public: |
351 | typedef typename ratio_multiply |
352 | < |
353 | ratio<__gcd_n1_n2, _R1::den / __gcd_d1_d2>, |
354 | ratio |
355 | < |
356 | __ll_add |
357 | < |
358 | __ll_mul<_R1::num / __gcd_n1_n2, _R2::den / __gcd_d1_d2>::value, |
359 | __ll_mul<_R2::num / __gcd_n1_n2, _R1::den / __gcd_d1_d2>::value |
360 | >::value, |
361 | _R2::den |
362 | > |
363 | >::type type; |
364 | }; |
365 | |
366 | #ifndef _LIBCPP_CXX03_LANG |
367 | |
368 | template <class _R1, class _R2> using ratio_add |
369 | = typename __ratio_add<_R1, _R2>::type; |
370 | |
371 | #else // _LIBCPP_CXX03_LANG |
372 | |
373 | template <class _R1, class _R2> |
374 | struct _LIBCPP_TEMPLATE_VIS ratio_add |
375 | : public __ratio_add<_R1, _R2>::type {}; |
376 | |
377 | #endif // _LIBCPP_CXX03_LANG |
378 | |
379 | template <class _R1, class _R2> |
380 | struct __ratio_subtract |
381 | { |
382 | private: |
383 | static const intmax_t __gcd_n1_n2 = __static_gcd<_R1::num, _R2::num>::value; |
384 | static const intmax_t __gcd_d1_d2 = __static_gcd<_R1::den, _R2::den>::value; |
385 | public: |
386 | typedef typename ratio_multiply |
387 | < |
388 | ratio<__gcd_n1_n2, _R1::den / __gcd_d1_d2>, |
389 | ratio |
390 | < |
391 | __ll_sub |
392 | < |
393 | __ll_mul<_R1::num / __gcd_n1_n2, _R2::den / __gcd_d1_d2>::value, |
394 | __ll_mul<_R2::num / __gcd_n1_n2, _R1::den / __gcd_d1_d2>::value |
395 | >::value, |
396 | _R2::den |
397 | > |
398 | >::type type; |
399 | }; |
400 | |
401 | #ifndef _LIBCPP_CXX03_LANG |
402 | |
403 | template <class _R1, class _R2> using ratio_subtract |
404 | = typename __ratio_subtract<_R1, _R2>::type; |
405 | |
406 | #else // _LIBCPP_CXX03_LANG |
407 | |
408 | template <class _R1, class _R2> |
409 | struct _LIBCPP_TEMPLATE_VIS ratio_subtract |
410 | : public __ratio_subtract<_R1, _R2>::type {}; |
411 | |
412 | #endif // _LIBCPP_CXX03_LANG |
413 | |
414 | // ratio_equal |
415 | |
416 | template <class _R1, class _R2> |
417 | struct _LIBCPP_TEMPLATE_VIS ratio_equal |
418 | : public _LIBCPP_BOOL_CONSTANT((_R1::num == _R2::num && _R1::den == _R2::den)) {}; |
419 | |
420 | template <class _R1, class _R2> |
421 | struct _LIBCPP_TEMPLATE_VIS ratio_not_equal |
422 | : public _LIBCPP_BOOL_CONSTANT((!ratio_equal<_R1, _R2>::value)) {}; |
423 | |
424 | // ratio_less |
425 | |
426 | template <class _R1, class _R2, bool _Odd = false, |
427 | intmax_t _Q1 = _R1::num / _R1::den, intmax_t _M1 = _R1::num % _R1::den, |
428 | intmax_t _Q2 = _R2::num / _R2::den, intmax_t _M2 = _R2::num % _R2::den> |
429 | struct __ratio_less1 |
430 | { |
431 | static const bool value = _Odd ? _Q2 < _Q1 : _Q1 < _Q2; |
432 | }; |
433 | |
434 | template <class _R1, class _R2, bool _Odd, intmax_t _Qp> |
435 | struct __ratio_less1<_R1, _R2, _Odd, _Qp, 0, _Qp, 0> |
436 | { |
437 | static const bool value = false; |
438 | }; |
439 | |
440 | template <class _R1, class _R2, bool _Odd, intmax_t _Qp, intmax_t _M2> |
441 | struct __ratio_less1<_R1, _R2, _Odd, _Qp, 0, _Qp, _M2> |
442 | { |
443 | static const bool value = !_Odd; |
444 | }; |
445 | |
446 | template <class _R1, class _R2, bool _Odd, intmax_t _Qp, intmax_t _M1> |
447 | struct __ratio_less1<_R1, _R2, _Odd, _Qp, _M1, _Qp, 0> |
448 | { |
449 | static const bool value = _Odd; |
450 | }; |
451 | |
452 | template <class _R1, class _R2, bool _Odd, intmax_t _Qp, intmax_t _M1, |
453 | intmax_t _M2> |
454 | struct __ratio_less1<_R1, _R2, _Odd, _Qp, _M1, _Qp, _M2> |
455 | { |
456 | static const bool value = __ratio_less1<ratio<_R1::den, _M1>, |
457 | ratio<_R2::den, _M2>, !_Odd>::value; |
458 | }; |
459 | |
460 | template <class _R1, class _R2, intmax_t _S1 = __static_sign<_R1::num>::value, |
461 | intmax_t _S2 = __static_sign<_R2::num>::value> |
462 | struct __ratio_less |
463 | { |
464 | static const bool value = _S1 < _S2; |
465 | }; |
466 | |
467 | template <class _R1, class _R2> |
468 | struct __ratio_less<_R1, _R2, 1LL, 1LL> |
469 | { |
470 | static const bool value = __ratio_less1<_R1, _R2>::value; |
471 | }; |
472 | |
473 | template <class _R1, class _R2> |
474 | struct __ratio_less<_R1, _R2, -1LL, -1LL> |
475 | { |
476 | static const bool value = __ratio_less1<ratio<-_R2::num, _R2::den>, ratio<-_R1::num, _R1::den> >::value; |
477 | }; |
478 | |
479 | template <class _R1, class _R2> |
480 | struct _LIBCPP_TEMPLATE_VIS ratio_less |
481 | : public _LIBCPP_BOOL_CONSTANT((__ratio_less<_R1, _R2>::value)) {}; |
482 | |
483 | template <class _R1, class _R2> |
484 | struct _LIBCPP_TEMPLATE_VIS ratio_less_equal |
485 | : public _LIBCPP_BOOL_CONSTANT((!ratio_less<_R2, _R1>::value)) {}; |
486 | |
487 | template <class _R1, class _R2> |
488 | struct _LIBCPP_TEMPLATE_VIS ratio_greater |
489 | : public _LIBCPP_BOOL_CONSTANT((ratio_less<_R2, _R1>::value)) {}; |
490 | |
491 | template <class _R1, class _R2> |
492 | struct _LIBCPP_TEMPLATE_VIS ratio_greater_equal |
493 | : public _LIBCPP_BOOL_CONSTANT((!ratio_less<_R1, _R2>::value)) {}; |
494 | |
495 | template <class _R1, class _R2> |
496 | struct __ratio_gcd |
497 | { |
498 | typedef ratio<__static_gcd<_R1::num, _R2::num>::value, |
499 | __static_lcm<_R1::den, _R2::den>::value> type; |
500 | }; |
501 | |
502 | #if _LIBCPP_STD_VER > 14 && !defined(_LIBCPP_HAS_NO_VARIABLE_TEMPLATES) |
503 | template <class _R1, class _R2> |
504 | _LIBCPP_INLINE_VAR _LIBCPP_CONSTEXPR bool ratio_equal_v |
505 | = ratio_equal<_R1, _R2>::value; |
506 | |
507 | template <class _R1, class _R2> |
508 | _LIBCPP_INLINE_VAR _LIBCPP_CONSTEXPR bool ratio_not_equal_v |
509 | = ratio_not_equal<_R1, _R2>::value; |
510 | |
511 | template <class _R1, class _R2> |
512 | _LIBCPP_INLINE_VAR _LIBCPP_CONSTEXPR bool ratio_less_v |
513 | = ratio_less<_R1, _R2>::value; |
514 | |
515 | template <class _R1, class _R2> |
516 | _LIBCPP_INLINE_VAR _LIBCPP_CONSTEXPR bool ratio_less_equal_v |
517 | = ratio_less_equal<_R1, _R2>::value; |
518 | |
519 | template <class _R1, class _R2> |
520 | _LIBCPP_INLINE_VAR _LIBCPP_CONSTEXPR bool ratio_greater_v |
521 | = ratio_greater<_R1, _R2>::value; |
522 | |
523 | template <class _R1, class _R2> |
524 | _LIBCPP_INLINE_VAR _LIBCPP_CONSTEXPR bool ratio_greater_equal_v |
525 | = ratio_greater_equal<_R1, _R2>::value; |
526 | #endif |
527 | |
528 | _LIBCPP_END_NAMESPACE_STD |
529 | |
530 | _LIBCPP_POP_MACROS |
531 | |
532 | #endif // _LIBCPP_RATIO |
533 | |