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5b9daa7e | 1 | // ratio -*- C++ -*- |
4acedca1 | 2 | |
aa118a03 | 3 | // Copyright (C) 2008-2014 Free Software Foundation, Inc. |
4acedca1 CF |
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 | |
748086b7 | 8 | // Free Software Foundation; either version 3, or (at your option) |
4acedca1 CF |
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 | ||
748086b7 JJ |
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. | |
4acedca1 | 19 | |
748086b7 JJ |
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/>. | |
4acedca1 | 24 | |
f910786b | 25 | /** @file include/ratio |
4acedca1 CF |
26 | * This is a Standard C++ Library header. |
27 | */ | |
28 | ||
29 | #ifndef _GLIBCXX_RATIO | |
30 | #define _GLIBCXX_RATIO 1 | |
31 | ||
32 | #pragma GCC system_header | |
33 | ||
734f5023 | 34 | #if __cplusplus < 201103L |
ab65a4c7 | 35 | # include <bits/c++0x_warning.h> |
4acedca1 CF |
36 | #else |
37 | ||
38 | #include <type_traits> | |
39 | #include <cstdint> | |
40 | ||
41 | #ifdef _GLIBCXX_USE_C99_STDINT_TR1 | |
42 | ||
12ffa228 BK |
43 | namespace std _GLIBCXX_VISIBILITY(default) |
44 | { | |
45 | _GLIBCXX_BEGIN_NAMESPACE_VERSION | |
53dc5044 | 46 | |
5b9daa7e BK |
47 | /** |
48 | * @defgroup ratio Rational Arithmetic | |
49 | * @ingroup utilities | |
50 | * | |
79e2c7b0 | 51 | * Compile time representation of finite rational numbers. |
5b9daa7e BK |
52 | * @{ |
53 | */ | |
54 | ||
4acedca1 CF |
55 | template<intmax_t _Pn> |
56 | struct __static_sign | |
57 | : integral_constant<intmax_t, (_Pn < 0) ? -1 : 1> | |
58 | { }; | |
59 | ||
60 | template<intmax_t _Pn> | |
61 | struct __static_abs | |
62 | : integral_constant<intmax_t, _Pn * __static_sign<_Pn>::value> | |
63 | { }; | |
64 | ||
4acedca1 CF |
65 | template<intmax_t _Pn, intmax_t _Qn> |
66 | struct __static_gcd | |
67 | : __static_gcd<_Qn, (_Pn % _Qn)> | |
68 | { }; | |
69 | ||
70 | template<intmax_t _Pn> | |
71 | struct __static_gcd<_Pn, 0> | |
72 | : integral_constant<intmax_t, __static_abs<_Pn>::value> | |
73 | { }; | |
74 | ||
75 | template<intmax_t _Qn> | |
76 | struct __static_gcd<0, _Qn> | |
77 | : integral_constant<intmax_t, __static_abs<_Qn>::value> | |
78 | { }; | |
79 | ||
80 | // Let c = 2^(half # of bits in an intmax_t) | |
81 | // then we find a1, a0, b1, b0 s.t. N = a1*c + a0, M = b1*c + b0 | |
82 | // The multiplication of N and M becomes, | |
83 | // N * M = (a1 * b1)c^2 + (a0 * b1 + b0 * a1)c + a0 * b0 | |
84 | // Multiplication is safe if each term and the sum of the terms | |
85 | // is representable by intmax_t. | |
86 | template<intmax_t _Pn, intmax_t _Qn> | |
87 | struct __safe_multiply | |
88 | { | |
89 | private: | |
90 | static const uintmax_t __c = uintmax_t(1) << (sizeof(intmax_t) * 4); | |
91 | ||
92 | static const uintmax_t __a0 = __static_abs<_Pn>::value % __c; | |
93 | static const uintmax_t __a1 = __static_abs<_Pn>::value / __c; | |
94 | static const uintmax_t __b0 = __static_abs<_Qn>::value % __c; | |
95 | static const uintmax_t __b1 = __static_abs<_Qn>::value / __c; | |
96 | ||
97 | static_assert(__a1 == 0 || __b1 == 0, | |
91e4938b | 98 | "overflow in multiplication"); |
4acedca1 | 99 | static_assert(__a0 * __b1 + __b0 * __a1 < (__c >> 1), |
91e4938b | 100 | "overflow in multiplication"); |
ea31932d | 101 | static_assert(__b0 * __a0 <= __INTMAX_MAX__, |
91e4938b MG |
102 | "overflow in multiplication"); |
103 | static_assert((__a0 * __b1 + __b0 * __a1) * __c | |
104 | <= __INTMAX_MAX__ - __b0 * __a0, | |
105 | "overflow in multiplication"); | |
4acedca1 CF |
106 | |
107 | public: | |
108 | static const intmax_t value = _Pn * _Qn; | |
109 | }; | |
110 | ||
91e4938b MG |
111 | // Some double-precision utilities, where numbers are represented as |
112 | // __hi*2^(8*sizeof(uintmax_t)) + __lo. | |
113 | template<uintmax_t __hi1, uintmax_t __lo1, uintmax_t __hi2, uintmax_t __lo2> | |
114 | struct __big_less | |
115 | : integral_constant<bool, (__hi1 < __hi2 | |
116 | || (__hi1 == __hi2 && __lo1 < __lo2))> | |
4acedca1 CF |
117 | { }; |
118 | ||
91e4938b MG |
119 | template<uintmax_t __hi1, uintmax_t __lo1, uintmax_t __hi2, uintmax_t __lo2> |
120 | struct __big_add | |
121 | { | |
122 | static constexpr uintmax_t __lo = __lo1 + __lo2; | |
123 | static constexpr uintmax_t __hi = (__hi1 + __hi2 + | |
124 | (__lo1 + __lo2 < __lo1)); // carry | |
125 | }; | |
4acedca1 | 126 | |
91e4938b MG |
127 | // Subtract a number from a bigger one. |
128 | template<uintmax_t __hi1, uintmax_t __lo1, uintmax_t __hi2, uintmax_t __lo2> | |
129 | struct __big_sub | |
130 | { | |
131 | static_assert(!__big_less<__hi1, __lo1, __hi2, __lo2>::value, | |
132 | "Internal library error"); | |
133 | static constexpr uintmax_t __lo = __lo1 - __lo2; | |
134 | static constexpr uintmax_t __hi = (__hi1 - __hi2 - | |
135 | (__lo1 < __lo2)); // carry | |
136 | }; | |
4acedca1 | 137 | |
91e4938b MG |
138 | // Same principle as __safe_multiply. |
139 | template<uintmax_t __x, uintmax_t __y> | |
140 | struct __big_mul | |
141 | { | |
142 | private: | |
143 | static constexpr uintmax_t __c = uintmax_t(1) << (sizeof(intmax_t) * 4); | |
144 | static constexpr uintmax_t __x0 = __x % __c; | |
145 | static constexpr uintmax_t __x1 = __x / __c; | |
146 | static constexpr uintmax_t __y0 = __y % __c; | |
147 | static constexpr uintmax_t __y1 = __y / __c; | |
148 | static constexpr uintmax_t __x0y0 = __x0 * __y0; | |
149 | static constexpr uintmax_t __x0y1 = __x0 * __y1; | |
150 | static constexpr uintmax_t __x1y0 = __x1 * __y0; | |
151 | static constexpr uintmax_t __x1y1 = __x1 * __y1; | |
152 | static constexpr uintmax_t __mix = __x0y1 + __x1y0; // possible carry... | |
153 | static constexpr uintmax_t __mix_lo = __mix * __c; | |
154 | static constexpr uintmax_t __mix_hi | |
155 | = __mix / __c + ((__mix < __x0y1) ? __c : 0); // ... added here | |
156 | typedef __big_add<__mix_hi, __mix_lo, __x1y1, __x0y0> _Res; | |
157 | public: | |
158 | static constexpr uintmax_t __hi = _Res::__hi; | |
159 | static constexpr uintmax_t __lo = _Res::__lo; | |
160 | }; | |
161 | ||
162 | // Adapted from __udiv_qrnnd_c in longlong.h | |
163 | // This version assumes that the high bit of __d is 1. | |
164 | template<uintmax_t __n1, uintmax_t __n0, uintmax_t __d> | |
165 | struct __big_div_impl | |
166 | { | |
167 | private: | |
168 | static_assert(__d >= (uintmax_t(1) << (sizeof(intmax_t) * 8 - 1)), | |
169 | "Internal library error"); | |
170 | static_assert(__n1 < __d, "Internal library error"); | |
171 | static constexpr uintmax_t __c = uintmax_t(1) << (sizeof(intmax_t) * 4); | |
172 | static constexpr uintmax_t __d1 = __d / __c; | |
173 | static constexpr uintmax_t __d0 = __d % __c; | |
174 | ||
175 | static constexpr uintmax_t __q1x = __n1 / __d1; | |
176 | static constexpr uintmax_t __r1x = __n1 % __d1; | |
177 | static constexpr uintmax_t __m = __q1x * __d0; | |
178 | static constexpr uintmax_t __r1y = __r1x * __c + __n0 / __c; | |
179 | static constexpr uintmax_t __r1z = __r1y + __d; | |
180 | static constexpr uintmax_t __r1 | |
181 | = ((__r1y < __m) ? ((__r1z >= __d) && (__r1z < __m)) | |
182 | ? (__r1z + __d) : __r1z : __r1y) - __m; | |
183 | static constexpr uintmax_t __q1 | |
184 | = __q1x - ((__r1y < __m) | |
185 | ? ((__r1z >= __d) && (__r1z < __m)) ? 2 : 1 : 0); | |
186 | static constexpr uintmax_t __q0x = __r1 / __d1; | |
187 | static constexpr uintmax_t __r0x = __r1 % __d1; | |
188 | static constexpr uintmax_t __n = __q0x * __d0; | |
189 | static constexpr uintmax_t __r0y = __r0x * __c + __n0 % __c; | |
190 | static constexpr uintmax_t __r0z = __r0y + __d; | |
191 | static constexpr uintmax_t __r0 | |
192 | = ((__r0y < __n) ? ((__r0z >= __d) && (__r0z < __n)) | |
193 | ? (__r0z + __d) : __r0z : __r0y) - __n; | |
194 | static constexpr uintmax_t __q0 | |
195 | = __q0x - ((__r0y < __n) ? ((__r0z >= __d) | |
196 | && (__r0z < __n)) ? 2 : 1 : 0); | |
197 | ||
198 | public: | |
199 | static constexpr uintmax_t __quot = __q1 * __c + __q0; | |
200 | static constexpr uintmax_t __rem = __r0; | |
201 | ||
202 | private: | |
203 | typedef __big_mul<__quot, __d> _Prod; | |
204 | typedef __big_add<_Prod::__hi, _Prod::__lo, 0, __rem> _Sum; | |
205 | static_assert(_Sum::__hi == __n1 && _Sum::__lo == __n0, | |
206 | "Internal library error"); | |
207 | }; | |
208 | ||
209 | template<uintmax_t __n1, uintmax_t __n0, uintmax_t __d> | |
210 | struct __big_div | |
4acedca1 | 211 | { |
91e4938b MG |
212 | private: |
213 | static_assert(__d != 0, "Internal library error"); | |
214 | static_assert(sizeof (uintmax_t) == sizeof (unsigned long long), | |
215 | "This library calls __builtin_clzll on uintmax_t, which " | |
216 | "is unsafe on your platform. Please complain to " | |
217 | "http://gcc.gnu.org/bugzilla/"); | |
218 | static constexpr int __shift = __builtin_clzll(__d); | |
219 | static constexpr int __coshift_ = sizeof(uintmax_t) * 8 - __shift; | |
220 | static constexpr int __coshift = (__shift != 0) ? __coshift_ : 0; | |
221 | static constexpr uintmax_t __c1 = uintmax_t(1) << __shift; | |
222 | static constexpr uintmax_t __c2 = uintmax_t(1) << __coshift; | |
223 | static constexpr uintmax_t __new_d = __d * __c1; | |
224 | static constexpr uintmax_t __new_n0 = __n0 * __c1; | |
225 | static constexpr uintmax_t __n1_shifted = (__n1 % __d) * __c1; | |
226 | static constexpr uintmax_t __n0_top = (__shift != 0) ? (__n0 / __c2) : 0; | |
227 | static constexpr uintmax_t __new_n1 = __n1_shifted + __n0_top; | |
228 | typedef __big_div_impl<__new_n1, __new_n0, __new_d> _Res; | |
229 | ||
230 | public: | |
231 | static constexpr uintmax_t __quot_hi = __n1 / __d; | |
232 | static constexpr uintmax_t __quot_lo = _Res::__quot; | |
233 | static constexpr uintmax_t __rem = _Res::__rem / __c1; | |
4acedca1 | 234 | |
91e4938b MG |
235 | private: |
236 | typedef __big_mul<__quot_lo, __d> _P0; | |
237 | typedef __big_mul<__quot_hi, __d> _P1; | |
238 | typedef __big_add<_P0::__hi, _P0::__lo, _P1::__lo, __rem> _Sum; | |
239 | // No overflow. | |
240 | static_assert(_P1::__hi == 0, "Internal library error"); | |
241 | static_assert(_Sum::__hi >= _P0::__hi, "Internal library error"); | |
242 | // Matches the input data. | |
243 | static_assert(_Sum::__hi == __n1 && _Sum::__lo == __n0, | |
244 | "Internal library error"); | |
245 | static_assert(__rem < __d, "Internal library error"); | |
4acedca1 CF |
246 | }; |
247 | ||
ea31932d PC |
248 | /** |
249 | * @brief Provides compile-time rational arithmetic. | |
5b9daa7e | 250 | * |
ea31932d PC |
251 | * This class template represents any finite rational number with a |
252 | * numerator and denominator representable by compile-time constants of | |
253 | * type intmax_t. The ratio is simplified when instantiated. | |
254 | * | |
255 | * For example: | |
256 | * @code | |
257 | * std::ratio<7,-21>::num == -1; | |
258 | * std::ratio<7,-21>::den == 3; | |
259 | * @endcode | |
260 | * | |
261 | */ | |
4acedca1 CF |
262 | template<intmax_t _Num, intmax_t _Den = 1> |
263 | struct ratio | |
264 | { | |
265 | static_assert(_Den != 0, "denominator cannot be zero"); | |
ea31932d PC |
266 | static_assert(_Num >= -__INTMAX_MAX__ && _Den >= -__INTMAX_MAX__, |
267 | "out of range"); | |
268 | ||
4acedca1 | 269 | // Note: sign(N) * abs(N) == N |
94a86be0 | 270 | static constexpr intmax_t num = |
4acedca1 CF |
271 | _Num * __static_sign<_Den>::value / __static_gcd<_Num, _Den>::value; |
272 | ||
94a86be0 | 273 | static constexpr intmax_t den = |
4acedca1 | 274 | __static_abs<_Den>::value / __static_gcd<_Num, _Den>::value; |
e1d4e035 PC |
275 | |
276 | typedef ratio<num, den> type; | |
4acedca1 CF |
277 | }; |
278 | ||
279 | template<intmax_t _Num, intmax_t _Den> | |
94a86be0 | 280 | constexpr intmax_t ratio<_Num, _Den>::num; |
4acedca1 CF |
281 | |
282 | template<intmax_t _Num, intmax_t _Den> | |
94a86be0 | 283 | constexpr intmax_t ratio<_Num, _Den>::den; |
4acedca1 | 284 | |
4acedca1 | 285 | template<typename _R1, typename _R2> |
c128d203 | 286 | struct __ratio_multiply |
4acedca1 CF |
287 | { |
288 | private: | |
289 | static const intmax_t __gcd1 = | |
290 | __static_gcd<_R1::num, _R2::den>::value; | |
291 | static const intmax_t __gcd2 = | |
292 | __static_gcd<_R2::num, _R1::den>::value; | |
293 | ||
294 | public: | |
295 | typedef ratio< | |
296 | __safe_multiply<(_R1::num / __gcd1), | |
297 | (_R2::num / __gcd2)>::value, | |
298 | __safe_multiply<(_R1::den / __gcd2), | |
299 | (_R2::den / __gcd1)>::value> type; | |
e1d4e035 | 300 | |
76d0be83 PC |
301 | static constexpr intmax_t num = type::num; |
302 | static constexpr intmax_t den = type::den; | |
4acedca1 CF |
303 | }; |
304 | ||
e1d4e035 | 305 | template<typename _R1, typename _R2> |
c128d203 | 306 | constexpr intmax_t __ratio_multiply<_R1, _R2>::num; |
e1d4e035 PC |
307 | |
308 | template<typename _R1, typename _R2> | |
c128d203 PC |
309 | constexpr intmax_t __ratio_multiply<_R1, _R2>::den; |
310 | ||
311 | /// ratio_multiply | |
312 | template<typename _R1, typename _R2> | |
313 | using ratio_multiply = typename __ratio_multiply<_R1, _R2>::type; | |
e1d4e035 | 314 | |
4acedca1 | 315 | template<typename _R1, typename _R2> |
c128d203 | 316 | struct __ratio_divide |
4acedca1 CF |
317 | { |
318 | static_assert(_R2::num != 0, "division by 0"); | |
319 | ||
c128d203 | 320 | typedef typename __ratio_multiply< |
4acedca1 CF |
321 | _R1, |
322 | ratio<_R2::den, _R2::num>>::type type; | |
e1d4e035 | 323 | |
76d0be83 PC |
324 | static constexpr intmax_t num = type::num; |
325 | static constexpr intmax_t den = type::den; | |
4acedca1 CF |
326 | }; |
327 | ||
e1d4e035 | 328 | template<typename _R1, typename _R2> |
c128d203 PC |
329 | constexpr intmax_t __ratio_divide<_R1, _R2>::num; |
330 | ||
331 | template<typename _R1, typename _R2> | |
332 | constexpr intmax_t __ratio_divide<_R1, _R2>::den; | |
e1d4e035 | 333 | |
c128d203 | 334 | /// ratio_divide |
e1d4e035 | 335 | template<typename _R1, typename _R2> |
c128d203 | 336 | using ratio_divide = typename __ratio_divide<_R1, _R2>::type; |
e1d4e035 | 337 | |
ad68e9fc | 338 | /// ratio_equal |
4acedca1 CF |
339 | template<typename _R1, typename _R2> |
340 | struct ratio_equal | |
341 | : integral_constant<bool, _R1::num == _R2::num && _R1::den == _R2::den> | |
342 | { }; | |
343 | ||
ad68e9fc | 344 | /// ratio_not_equal |
4acedca1 CF |
345 | template<typename _R1, typename _R2> |
346 | struct ratio_not_equal | |
347 | : integral_constant<bool, !ratio_equal<_R1, _R2>::value> | |
348 | { }; | |
cd6b4a4b | 349 | |
91e4938b MG |
350 | // Both numbers are positive. |
351 | template<typename _R1, typename _R2, | |
352 | typename _Left = __big_mul<_R1::num,_R2::den>, | |
353 | typename _Right = __big_mul<_R2::num,_R1::den> > | |
cd6b4a4b | 354 | struct __ratio_less_impl_1 |
91e4938b MG |
355 | : integral_constant<bool, __big_less<_Left::__hi, _Left::__lo, |
356 | _Right::__hi, _Right::__lo>::value> | |
cd6b4a4b PC |
357 | { }; |
358 | ||
359 | template<typename _R1, typename _R2, | |
360 | bool = (_R1::num == 0 || _R2::num == 0 | |
361 | || (__static_sign<_R1::num>::value | |
362 | != __static_sign<_R2::num>::value)), | |
363 | bool = (__static_sign<_R1::num>::value == -1 | |
364 | && __static_sign<_R2::num>::value == -1)> | |
365 | struct __ratio_less_impl | |
d154f927 | 366 | : __ratio_less_impl_1<_R1, _R2>::type |
cd6b4a4b PC |
367 | { }; |
368 | ||
4acedca1 | 369 | template<typename _R1, typename _R2> |
cd6b4a4b PC |
370 | struct __ratio_less_impl<_R1, _R2, true, false> |
371 | : integral_constant<bool, _R1::num < _R2::num> | |
ea31932d PC |
372 | { }; |
373 | ||
ea31932d | 374 | template<typename _R1, typename _R2> |
cd6b4a4b | 375 | struct __ratio_less_impl<_R1, _R2, false, true> |
d154f927 PC |
376 | : __ratio_less_impl_1<ratio<-_R2::num, _R2::den>, |
377 | ratio<-_R1::num, _R1::den> >::type | |
ea31932d PC |
378 | { }; |
379 | ||
ad68e9fc | 380 | /// ratio_less |
ea31932d PC |
381 | template<typename _R1, typename _R2> |
382 | struct ratio_less | |
383 | : __ratio_less_impl<_R1, _R2>::type | |
4acedca1 CF |
384 | { }; |
385 | ||
ad68e9fc | 386 | /// ratio_less_equal |
4acedca1 CF |
387 | template<typename _R1, typename _R2> |
388 | struct ratio_less_equal | |
389 | : integral_constant<bool, !ratio_less<_R2, _R1>::value> | |
390 | { }; | |
391 | ||
ad68e9fc | 392 | /// ratio_greater |
4acedca1 CF |
393 | template<typename _R1, typename _R2> |
394 | struct ratio_greater | |
395 | : integral_constant<bool, ratio_less<_R2, _R1>::value> | |
396 | { }; | |
397 | ||
ad68e9fc | 398 | /// ratio_greater_equal |
4acedca1 CF |
399 | template<typename _R1, typename _R2> |
400 | struct ratio_greater_equal | |
401 | : integral_constant<bool, !ratio_less<_R1, _R2>::value> | |
402 | { }; | |
403 | ||
91e4938b MG |
404 | template<typename _R1, typename _R2, |
405 | bool = (_R1::num >= 0), | |
406 | bool = (_R2::num >= 0), | |
407 | bool = ratio_less<ratio<__static_abs<_R1::num>::value, _R1::den>, | |
408 | ratio<__static_abs<_R2::num>::value, _R2::den> >::value> | |
409 | struct __ratio_add_impl | |
410 | { | |
411 | private: | |
412 | typedef typename __ratio_add_impl< | |
413 | ratio<-_R1::num, _R1::den>, | |
414 | ratio<-_R2::num, _R2::den> >::type __t; | |
415 | public: | |
416 | typedef ratio<-__t::num, __t::den> type; | |
417 | }; | |
418 | ||
419 | // True addition of nonnegative numbers. | |
420 | template<typename _R1, typename _R2, bool __b> | |
421 | struct __ratio_add_impl<_R1, _R2, true, true, __b> | |
422 | { | |
423 | private: | |
424 | static constexpr uintmax_t __g = __static_gcd<_R1::den, _R2::den>::value; | |
425 | static constexpr uintmax_t __d2 = _R2::den / __g; | |
426 | typedef __big_mul<_R1::den, __d2> __d; | |
427 | typedef __big_mul<_R1::num, _R2::den / __g> __x; | |
428 | typedef __big_mul<_R2::num, _R1::den / __g> __y; | |
429 | typedef __big_add<__x::__hi, __x::__lo, __y::__hi, __y::__lo> __n; | |
430 | static_assert(__n::__hi >= __x::__hi, "Internal library error"); | |
431 | typedef __big_div<__n::__hi, __n::__lo, __g> __ng; | |
432 | static constexpr uintmax_t __g2 = __static_gcd<__ng::__rem, __g>::value; | |
433 | typedef __big_div<__n::__hi, __n::__lo, __g2> __n_final; | |
434 | static_assert(__n_final::__rem == 0, "Internal library error"); | |
435 | static_assert(__n_final::__quot_hi == 0 && | |
436 | __n_final::__quot_lo <= __INTMAX_MAX__, "overflow in addition"); | |
437 | typedef __big_mul<_R1::den / __g2, __d2> __d_final; | |
438 | static_assert(__d_final::__hi == 0 && | |
439 | __d_final::__lo <= __INTMAX_MAX__, "overflow in addition"); | |
440 | public: | |
441 | typedef ratio<__n_final::__quot_lo, __d_final::__lo> type; | |
442 | }; | |
443 | ||
444 | template<typename _R1, typename _R2> | |
445 | struct __ratio_add_impl<_R1, _R2, false, true, true> | |
446 | : __ratio_add_impl<_R2, _R1> | |
447 | { }; | |
448 | ||
449 | // True subtraction of nonnegative numbers yielding a nonnegative result. | |
450 | template<typename _R1, typename _R2> | |
451 | struct __ratio_add_impl<_R1, _R2, true, false, false> | |
452 | { | |
453 | private: | |
454 | static constexpr uintmax_t __g = __static_gcd<_R1::den, _R2::den>::value; | |
455 | static constexpr uintmax_t __d2 = _R2::den / __g; | |
456 | typedef __big_mul<_R1::den, __d2> __d; | |
457 | typedef __big_mul<_R1::num, _R2::den / __g> __x; | |
458 | typedef __big_mul<-_R2::num, _R1::den / __g> __y; | |
459 | typedef __big_sub<__x::__hi, __x::__lo, __y::__hi, __y::__lo> __n; | |
460 | typedef __big_div<__n::__hi, __n::__lo, __g> __ng; | |
461 | static constexpr uintmax_t __g2 = __static_gcd<__ng::__rem, __g>::value; | |
462 | typedef __big_div<__n::__hi, __n::__lo, __g2> __n_final; | |
463 | static_assert(__n_final::__rem == 0, "Internal library error"); | |
464 | static_assert(__n_final::__quot_hi == 0 && | |
465 | __n_final::__quot_lo <= __INTMAX_MAX__, "overflow in addition"); | |
466 | typedef __big_mul<_R1::den / __g2, __d2> __d_final; | |
467 | static_assert(__d_final::__hi == 0 && | |
468 | __d_final::__lo <= __INTMAX_MAX__, "overflow in addition"); | |
469 | public: | |
470 | typedef ratio<__n_final::__quot_lo, __d_final::__lo> type; | |
471 | }; | |
472 | ||
91e4938b | 473 | template<typename _R1, typename _R2> |
c128d203 | 474 | struct __ratio_add |
91e4938b MG |
475 | { |
476 | typedef typename __ratio_add_impl<_R1, _R2>::type type; | |
477 | static constexpr intmax_t num = type::num; | |
478 | static constexpr intmax_t den = type::den; | |
479 | }; | |
480 | ||
481 | template<typename _R1, typename _R2> | |
c128d203 | 482 | constexpr intmax_t __ratio_add<_R1, _R2>::num; |
91e4938b MG |
483 | |
484 | template<typename _R1, typename _R2> | |
c128d203 | 485 | constexpr intmax_t __ratio_add<_R1, _R2>::den; |
91e4938b | 486 | |
c128d203 | 487 | /// ratio_add |
91e4938b | 488 | template<typename _R1, typename _R2> |
c128d203 PC |
489 | using ratio_add = typename __ratio_add<_R1, _R2>::type; |
490 | ||
491 | template<typename _R1, typename _R2> | |
492 | struct __ratio_subtract | |
91e4938b | 493 | { |
c128d203 | 494 | typedef typename __ratio_add< |
91e4938b MG |
495 | _R1, |
496 | ratio<-_R2::num, _R2::den>>::type type; | |
497 | ||
498 | static constexpr intmax_t num = type::num; | |
499 | static constexpr intmax_t den = type::den; | |
500 | }; | |
501 | ||
502 | template<typename _R1, typename _R2> | |
c128d203 | 503 | constexpr intmax_t __ratio_subtract<_R1, _R2>::num; |
91e4938b MG |
504 | |
505 | template<typename _R1, typename _R2> | |
c128d203 | 506 | constexpr intmax_t __ratio_subtract<_R1, _R2>::den; |
91e4938b | 507 | |
c128d203 PC |
508 | /// ratio_subtract |
509 | template<typename _R1, typename _R2> | |
510 | using ratio_subtract = typename __ratio_subtract<_R1, _R2>::type; | |
91e4938b MG |
511 | |
512 | ||
4acedca1 CF |
513 | typedef ratio<1, 1000000000000000000> atto; |
514 | typedef ratio<1, 1000000000000000> femto; | |
515 | typedef ratio<1, 1000000000000> pico; | |
516 | typedef ratio<1, 1000000000> nano; | |
517 | typedef ratio<1, 1000000> micro; | |
518 | typedef ratio<1, 1000> milli; | |
519 | typedef ratio<1, 100> centi; | |
520 | typedef ratio<1, 10> deci; | |
521 | typedef ratio< 10, 1> deca; | |
522 | typedef ratio< 100, 1> hecto; | |
523 | typedef ratio< 1000, 1> kilo; | |
524 | typedef ratio< 1000000, 1> mega; | |
525 | typedef ratio< 1000000000, 1> giga; | |
526 | typedef ratio< 1000000000000, 1> tera; | |
527 | typedef ratio< 1000000000000000, 1> peta; | |
528 | typedef ratio< 1000000000000000000, 1> exa; | |
5b9daa7e BK |
529 | |
530 | // @} group ratio | |
12ffa228 BK |
531 | _GLIBCXX_END_NAMESPACE_VERSION |
532 | } // namespace | |
4acedca1 CF |
533 | |
534 | #endif //_GLIBCXX_USE_C99_STDINT_TR1 | |
535 | ||
734f5023 | 536 | #endif // C++11 |
4acedca1 CF |
537 | |
538 | #endif //_GLIBCXX_RATIO |