ratio revision 262801 
1// -*- C++ -*-
2//===---------------------------- ratio -----------------------------------===//
3//
4//                     The LLVM Compiler Infrastructure
5//
6// This file is dual licensed under the MIT and the University of Illinois Open
7// Source Licenses. See LICENSE.TXT for details.
8//
9//===----------------------------------------------------------------------===//
10
11#ifndef _LIBCPP_RATIO
12#define _LIBCPP_RATIO
13
14/*
15    ratio synopsis
16
17namespace std
18{
19
20template <intmax_t N, intmax_t D = 1>
21class ratio
22{
23public:
24    static const intmax_t num;
25    static const intmax_t den;
26    typedef ratio<num, den> type;
27};
28
29// ratio arithmetic
30template <class R1, class R2> using ratio_add = ...;
31template <class R1, class R2> using ratio_subtract = ...;
32template <class R1, class R2> using ratio_multiply = ...;
33template <class R1, class R2> using ratio_divide = ...;
34
35// ratio comparison
36template <class R1, class R2> struct ratio_equal;
37template <class R1, class R2> struct ratio_not_equal;
38template <class R1, class R2> struct ratio_less;
39template <class R1, class R2> struct ratio_less_equal;
40template <class R1, class R2> struct ratio_greater;
41template <class R1, class R2> struct ratio_greater_equal;
42
43// convenience SI typedefs
44typedef ratio<1, 1000000000000000000000000> yocto;  // not supported
45typedef ratio<1,    1000000000000000000000> zepto;  // not supported
46typedef ratio<1,       1000000000000000000> atto;
47typedef ratio<1,          1000000000000000> femto;
48typedef ratio<1,             1000000000000> pico;
49typedef ratio<1,                1000000000> nano;
50typedef ratio<1,                   1000000> micro;
51typedef ratio<1,                      1000> milli;
52typedef ratio<1,                       100> centi;
53typedef ratio<1,                        10> deci;
54typedef ratio<                       10, 1> deca;
55typedef ratio<                      100, 1> hecto;
56typedef ratio<                     1000, 1> kilo;
57typedef ratio<                  1000000, 1> mega;
58typedef ratio<               1000000000, 1> giga;
59typedef ratio<            1000000000000, 1> tera;
60typedef ratio<         1000000000000000, 1> peta;
61typedef ratio<      1000000000000000000, 1> exa;
62typedef ratio<   1000000000000000000000, 1> zetta;  // not supported
63typedef ratio<1000000000000000000000000, 1> yotta;  // not supported
64
65}
66*/
67
68#include <__config>
69#include <cstdint>
70#include <climits>
71#include <type_traits>
72
73#include <__undef_min_max>
74
75#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
76#pragma GCC system_header
77#endif
78
79_LIBCPP_BEGIN_NAMESPACE_STD
80
81// __static_gcd
82
83template <intmax_t _Xp, intmax_t _Yp>
84struct __static_gcd
85{
86    static const intmax_t value = __static_gcd<_Yp, _Xp % _Yp>::value;
87};
88
89template <intmax_t _Xp>
90struct __static_gcd<_Xp, 0>
91{
92    static const intmax_t value = _Xp;
93};
94
95template <>
96struct __static_gcd<0, 0>
97{
98    static const intmax_t value = 1;
99};
100
101// __static_lcm
102
103template <intmax_t _Xp, intmax_t _Yp>
104struct __static_lcm
105{
106    static const intmax_t value = _Xp / __static_gcd<_Xp, _Yp>::value * _Yp;
107};
108
109template <intmax_t _Xp>
110struct __static_abs
111{
112    static const intmax_t value = _Xp < 0 ? -_Xp : _Xp;
113};
114
115template <intmax_t _Xp>
116struct __static_sign
117{
118    static const intmax_t value = _Xp == 0 ? 0 : (_Xp < 0 ? -1 : 1);
119};
120
121template <intmax_t _Xp, intmax_t _Yp, intmax_t = __static_sign<_Yp>::value>
122class __ll_add;
123
124template <intmax_t _Xp, intmax_t _Yp>
125class __ll_add<_Xp, _Yp, 1>
126{
127    static const intmax_t min = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)) + 1;
128    static const intmax_t max = -min;
129
130    static_assert(_Xp <= max - _Yp, "overflow in __ll_add");
131public:
132    static const intmax_t value = _Xp + _Yp;
133};
134
135template <intmax_t _Xp, intmax_t _Yp>
136class __ll_add<_Xp, _Yp, 0>
137{
138public:
139    static const intmax_t value = _Xp;
140};
141
142template <intmax_t _Xp, intmax_t _Yp>
143class __ll_add<_Xp, _Yp, -1>
144{
145    static const intmax_t min = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)) + 1;
146    static const intmax_t max = -min;
147
148    static_assert(min - _Yp <= _Xp, "overflow in __ll_add");
149public:
150    static const intmax_t value = _Xp + _Yp;
151};
152
153template <intmax_t _Xp, intmax_t _Yp, intmax_t = __static_sign<_Yp>::value>
154class __ll_sub;
155
156template <intmax_t _Xp, intmax_t _Yp>
157class __ll_sub<_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_sub");
163public:
164    static const intmax_t value = _Xp - _Yp;
165};
166
167template <intmax_t _Xp, intmax_t _Yp>
168class __ll_sub<_Xp, _Yp, 0>
169{
170public:
171    static const intmax_t value = _Xp;
172};
173
174template <intmax_t _Xp, intmax_t _Yp>
175class __ll_sub<_Xp, _Yp, -1>
176{
177    static const intmax_t min = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)) + 1;
178    static const intmax_t max = -min;
179
180    static_assert(_Xp <= max + _Yp, "overflow in __ll_sub");
181public:
182    static const intmax_t value = _Xp - _Yp;
183};
184
185template <intmax_t _Xp, intmax_t _Yp>
186class __ll_mul
187{
188    static const intmax_t nan = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1));
189    static const intmax_t min = nan + 1;
190    static const intmax_t max = -min;
191    static const intmax_t __a_x = __static_abs<_Xp>::value;
192    static const intmax_t __a_y = __static_abs<_Yp>::value;
193
194    static_assert(_Xp != nan && _Yp != nan && __a_x <= max / __a_y, "overflow in __ll_mul");
195public:
196    static const intmax_t value = _Xp * _Yp;
197};
198
199template <intmax_t _Yp>
200class __ll_mul<0, _Yp>
201{
202public:
203    static const intmax_t value = 0;
204};
205
206template <intmax_t _Xp>
207class __ll_mul<_Xp, 0>
208{
209public:
210    static const intmax_t value = 0;
211};
212
213template <>
214class __ll_mul<0, 0>
215{
216public:
217    static const intmax_t value = 0;
218};
219
220// Not actually used but left here in case needed in future maintenance
221template <intmax_t _Xp, intmax_t _Yp>
222class __ll_div
223{
224    static const intmax_t nan = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1));
225    static const intmax_t min = nan + 1;
226    static const intmax_t max = -min;
227
228    static_assert(_Xp != nan && _Yp != nan && _Yp != 0, "overflow in __ll_div");
229public:
230    static const intmax_t value = _Xp / _Yp;
231};
232
233template <intmax_t _Num, intmax_t _Den = 1>
234class _LIBCPP_TYPE_VIS_ONLY ratio
235{
236    static_assert(__static_abs<_Num>::value >= 0, "ratio numerator is out of range");
237    static_assert(_Den != 0, "ratio divide by 0");
238    static_assert(__static_abs<_Den>::value >  0, "ratio denominator is out of range");
239    static const intmax_t __na = __static_abs<_Num>::value;
240    static const intmax_t __da = __static_abs<_Den>::value;
241    static const intmax_t __s = __static_sign<_Num>::value * __static_sign<_Den>::value;
242    static const intmax_t __gcd = __static_gcd<__na, __da>::value;
243public:
244    static const intmax_t num = __s * __na / __gcd;
245    static const intmax_t den = __da / __gcd;
246
247    typedef ratio<num, den> type;
248};
249
250template <intmax_t _Num, intmax_t _Den> const intmax_t ratio<_Num, _Den>::num;
251template <intmax_t _Num, intmax_t _Den> const intmax_t ratio<_Num, _Den>::den;
252
253template <class _Tp>                    struct __is_ratio                     : false_type {};
254template <intmax_t _Num, intmax_t _Den> struct __is_ratio<ratio<_Num, _Den> > : true_type  {};
255
256typedef ratio<1LL, 1000000000000000000LL> atto;
257typedef ratio<1LL,    1000000000000000LL> femto;
258typedef ratio<1LL,       1000000000000LL> pico;
259typedef ratio<1LL,          1000000000LL> nano;
260typedef ratio<1LL,             1000000LL> micro;
261typedef ratio<1LL,                1000LL> milli;
262typedef ratio<1LL,                 100LL> centi;
263typedef ratio<1LL,                  10LL> deci;
264typedef ratio<                 10LL, 1LL> deca;
265typedef ratio<                100LL, 1LL> hecto;
266typedef ratio<               1000LL, 1LL> kilo;
267typedef ratio<            1000000LL, 1LL> mega;
268typedef ratio<         1000000000LL, 1LL> giga;
269typedef ratio<      1000000000000LL, 1LL> tera;
270typedef ratio<   1000000000000000LL, 1LL> peta;
271typedef ratio<1000000000000000000LL, 1LL> exa;
272
273template <class _R1, class _R2>
274struct __ratio_multiply
275{
276private:
277    static const intmax_t __gcd_n1_d2 = __static_gcd<_R1::num, _R2::den>::value;
278    static const intmax_t __gcd_d1_n2 = __static_gcd<_R1::den, _R2::num>::value;
279public:
280    typedef typename ratio
281        <
282            __ll_mul<_R1::num / __gcd_n1_d2, _R2::num / __gcd_d1_n2>::value,
283            __ll_mul<_R2::den / __gcd_n1_d2, _R1::den / __gcd_d1_n2>::value
284        >::type type;
285};
286
287#ifndef _LIBCPP_HAS_NO_TEMPLATE_ALIASES
288
289template <class _R1, class _R2> using ratio_multiply
290                                    = typename __ratio_multiply<_R1, _R2>::type;
291
292#else  // _LIBCPP_HAS_NO_TEMPLATE_ALIASES
293
294template <class _R1, class _R2>
295struct _LIBCPP_TYPE_VIS_ONLY ratio_multiply
296    : public __ratio_multiply<_R1, _R2>::type {};
297
298#endif  // _LIBCPP_HAS_NO_TEMPLATE_ALIASES
299
300template <class _R1, class _R2>
301struct __ratio_divide
302{
303private:
304    static const intmax_t __gcd_n1_n2 = __static_gcd<_R1::num, _R2::num>::value;
305    static const intmax_t __gcd_d1_d2 = __static_gcd<_R1::den, _R2::den>::value;
306public:
307    typedef typename ratio
308        <
309            __ll_mul<_R1::num / __gcd_n1_n2, _R2::den / __gcd_d1_d2>::value,
310            __ll_mul<_R2::num / __gcd_n1_n2, _R1::den / __gcd_d1_d2>::value
311        >::type type;
312};
313
314#ifndef _LIBCPP_HAS_NO_TEMPLATE_ALIASES
315
316template <class _R1, class _R2> using ratio_divide
317                                      = typename __ratio_divide<_R1, _R2>::type;
318
319#else  // _LIBCPP_HAS_NO_TEMPLATE_ALIASES
320
321template <class _R1, class _R2>
322struct _LIBCPP_TYPE_VIS_ONLY ratio_divide
323    : public __ratio_divide<_R1, _R2>::type {};
324
325#endif  // _LIBCPP_HAS_NO_TEMPLATE_ALIASES
326
327template <class _R1, class _R2>
328struct __ratio_add
329{
330private:
331    static const intmax_t __gcd_n1_n2 = __static_gcd<_R1::num, _R2::num>::value;
332    static const intmax_t __gcd_d1_d2 = __static_gcd<_R1::den, _R2::den>::value;
333public:
334    typedef typename ratio_multiply
335        <
336            ratio<__gcd_n1_n2, _R1::den / __gcd_d1_d2>,
337            ratio
338            <
339                __ll_add
340                <
341                    __ll_mul<_R1::num / __gcd_n1_n2, _R2::den / __gcd_d1_d2>::value,
342                    __ll_mul<_R2::num / __gcd_n1_n2, _R1::den / __gcd_d1_d2>::value
343                >::value,
344                _R2::den
345            >
346        >::type type;
347};
348
349#ifndef _LIBCPP_HAS_NO_TEMPLATE_ALIASES
350
351template <class _R1, class _R2> using ratio_add
352                                         = typename __ratio_add<_R1, _R2>::type;
353
354#else  // _LIBCPP_HAS_NO_TEMPLATE_ALIASES
355
356template <class _R1, class _R2>
357struct _LIBCPP_TYPE_VIS_ONLY ratio_add
358    : public __ratio_add<_R1, _R2>::type {};
359
360#endif  // _LIBCPP_HAS_NO_TEMPLATE_ALIASES
361
362template <class _R1, class _R2>
363struct __ratio_subtract
364{
365private:
366    static const intmax_t __gcd_n1_n2 = __static_gcd<_R1::num, _R2::num>::value;
367    static const intmax_t __gcd_d1_d2 = __static_gcd<_R1::den, _R2::den>::value;
368public:
369    typedef typename ratio_multiply
370        <
371            ratio<__gcd_n1_n2, _R1::den / __gcd_d1_d2>,
372            ratio
373            <
374                __ll_sub
375                <
376                    __ll_mul<_R1::num / __gcd_n1_n2, _R2::den / __gcd_d1_d2>::value,
377                    __ll_mul<_R2::num / __gcd_n1_n2, _R1::den / __gcd_d1_d2>::value
378                >::value,
379                _R2::den
380            >
381        >::type type;
382};
383
384#ifndef _LIBCPP_HAS_NO_TEMPLATE_ALIASES
385
386template <class _R1, class _R2> using ratio_subtract
387                                    = typename __ratio_subtract<_R1, _R2>::type;
388
389#else  // _LIBCPP_HAS_NO_TEMPLATE_ALIASES
390
391template <class _R1, class _R2>
392struct _LIBCPP_TYPE_VIS_ONLY ratio_subtract
393    : public __ratio_subtract<_R1, _R2>::type {};
394
395#endif  // _LIBCPP_HAS_NO_TEMPLATE_ALIASES
396
397// ratio_equal
398
399template <class _R1, class _R2>
400struct _LIBCPP_TYPE_VIS_ONLY ratio_equal
401    : public integral_constant<bool, _R1::num == _R2::num && _R1::den == _R2::den> {};
402
403template <class _R1, class _R2>
404struct _LIBCPP_TYPE_VIS_ONLY ratio_not_equal
405    : public integral_constant<bool, !ratio_equal<_R1, _R2>::value> {};
406
407// ratio_less
408
409template <class _R1, class _R2, bool _Odd = false,
410          intmax_t _Q1 = _R1::num / _R1::den, intmax_t _M1 = _R1::num % _R1::den,
411          intmax_t _Q2 = _R2::num / _R2::den, intmax_t _M2 = _R2::num % _R2::den>
412struct __ratio_less1
413{
414    static const bool value = _Odd ? _Q2 < _Q1 : _Q1 < _Q2;
415};
416
417template <class _R1, class _R2, bool _Odd, intmax_t _Qp>
418struct __ratio_less1<_R1, _R2, _Odd, _Qp, 0, _Qp, 0>
419{
420    static const bool value = false;
421};
422
423template <class _R1, class _R2, bool _Odd, intmax_t _Qp, intmax_t _M2>
424struct __ratio_less1<_R1, _R2, _Odd, _Qp, 0, _Qp, _M2>
425{
426    static const bool value = !_Odd;
427};
428
429template <class _R1, class _R2, bool _Odd, intmax_t _Qp, intmax_t _M1>
430struct __ratio_less1<_R1, _R2, _Odd, _Qp, _M1, _Qp, 0>
431{
432    static const bool value = _Odd;
433};
434
435template <class _R1, class _R2, bool _Odd, intmax_t _Qp, intmax_t _M1,
436                                                        intmax_t _M2>
437struct __ratio_less1<_R1, _R2, _Odd, _Qp, _M1, _Qp, _M2>
438{
439    static const bool value = __ratio_less1<ratio<_R1::den, _M1>,
440                                            ratio<_R2::den, _M2>, !_Odd>::value;
441};
442
443template <class _R1, class _R2, intmax_t _S1 = __static_sign<_R1::num>::value,
444                                intmax_t _S2 = __static_sign<_R2::num>::value>
445struct __ratio_less
446{
447    static const bool value = _S1 < _S2;
448};
449
450template <class _R1, class _R2>
451struct __ratio_less<_R1, _R2, 1LL, 1LL>
452{
453    static const bool value = __ratio_less1<_R1, _R2>::value;
454};
455
456template <class _R1, class _R2>
457struct __ratio_less<_R1, _R2, -1LL, -1LL>
458{
459    static const bool value = __ratio_less1<ratio<-_R2::num, _R2::den>, ratio<-_R1::num, _R1::den> >::value;
460};
461
462template <class _R1, class _R2>
463struct _LIBCPP_TYPE_VIS_ONLY ratio_less
464    : public integral_constant<bool, __ratio_less<_R1, _R2>::value> {};
465
466template <class _R1, class _R2>
467struct _LIBCPP_TYPE_VIS_ONLY ratio_less_equal
468    : public integral_constant<bool, !ratio_less<_R2, _R1>::value> {};
469
470template <class _R1, class _R2>
471struct _LIBCPP_TYPE_VIS_ONLY ratio_greater
472    : public integral_constant<bool, ratio_less<_R2, _R1>::value> {};
473
474template <class _R1, class _R2>
475struct _LIBCPP_TYPE_VIS_ONLY ratio_greater_equal
476    : public integral_constant<bool, !ratio_less<_R1, _R2>::value> {};
477
478template <class _R1, class _R2>
479struct __ratio_gcd
480{
481    typedef ratio<__static_gcd<_R1::num, _R2::num>::value,
482                  __static_lcm<_R1::den, _R2::den>::value> type;
483};
484
485_LIBCPP_END_NAMESPACE_STD
486
487#endif  // _LIBCPP_RATIO
488