1// ratio -*- C++ -*-
2
3// Copyright (C) 2008-2016 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 */
28
29#ifndef _GLIBCXX_RATIO
30#define _GLIBCXX_RATIO 1
31
32#pragma GCC system_header
33
34#if __cplusplus < 201103L
35# include <bits/c++0x_warning.h>
36#else
37
38#include <type_traits>
39#include <cstdint>
40
41#ifdef _GLIBCXX_USE_C99_STDINT_TR1
42
43namespace std _GLIBCXX_VISIBILITY(default)
44{
45_GLIBCXX_BEGIN_NAMESPACE_VERSION
46
47  /**
48   * @defgroup ratio Rational Arithmetic
49   * @ingroup utilities
50   *
51   * Compile time representation of finite rational numbers.
52   * @{
53   */
54
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
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,
98		    "overflow in multiplication");
99      static_assert(__a0 * __b1 + __b0 * __a1 < (__c >> 1),
100		    "overflow in multiplication");
101      static_assert(__b0 * __a0 <= __INTMAX_MAX__,
102		    "overflow in multiplication");
103      static_assert((__a0 * __b1 + __b0 * __a1) * __c
104		    <= __INTMAX_MAX__ -  __b0 * __a0,
105		    "overflow in multiplication");
106
107    public:
108      static const intmax_t value = _Pn * _Qn;
109    };
110
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))>
117    { };
118
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    };
126
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    };
137
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
211    {
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;
234
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");
246    };
247
248  /**
249   *  @brief Provides compile-time rational arithmetic.
250   *
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  */
262  template<intmax_t _Num, intmax_t _Den = 1>
263    struct ratio
264    {
265      static_assert(_Den != 0, "denominator cannot be zero");
266      static_assert(_Num >= -__INTMAX_MAX__ && _Den >= -__INTMAX_MAX__,
267		    "out of range");
268
269      // Note: sign(N) * abs(N) == N
270      static constexpr intmax_t num =
271        _Num * __static_sign<_Den>::value / __static_gcd<_Num, _Den>::value;
272
273      static constexpr intmax_t den =
274        __static_abs<_Den>::value / __static_gcd<_Num, _Den>::value;
275
276      typedef ratio<num, den> type;
277    };
278
279  template<intmax_t _Num, intmax_t _Den>
280    constexpr intmax_t ratio<_Num, _Den>::num;
281
282  template<intmax_t _Num, intmax_t _Den>
283    constexpr intmax_t ratio<_Num, _Den>::den;
284
285  template<typename _R1, typename _R2>
286    struct __ratio_multiply
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;
300
301      static constexpr intmax_t num = type::num;
302      static constexpr intmax_t den = type::den;
303    };
304
305  template<typename _R1, typename _R2>
306    constexpr intmax_t __ratio_multiply<_R1, _R2>::num;
307
308  template<typename _R1, typename _R2>
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;
314
315  template<typename _R1, typename _R2>
316    struct __ratio_divide
317    {
318      static_assert(_R2::num != 0, "division by 0");
319
320      typedef typename __ratio_multiply<
321        _R1,
322        ratio<_R2::den, _R2::num>>::type type;
323
324      static constexpr intmax_t num = type::num;
325      static constexpr intmax_t den = type::den;
326    };
327
328  template<typename _R1, typename _R2>
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;
333
334  /// ratio_divide
335  template<typename _R1, typename _R2>
336    using ratio_divide = typename __ratio_divide<_R1, _R2>::type;
337
338  /// ratio_equal
339  template<typename _R1, typename _R2>
340    struct ratio_equal
341    : integral_constant<bool, _R1::num == _R2::num && _R1::den == _R2::den>
342    { };
343
344  /// ratio_not_equal
345  template<typename _R1, typename _R2>
346    struct ratio_not_equal
347    : integral_constant<bool, !ratio_equal<_R1, _R2>::value>
348    { };
349
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> >
354    struct __ratio_less_impl_1
355    : integral_constant<bool, __big_less<_Left::__hi, _Left::__lo,
356           _Right::__hi, _Right::__lo>::value>
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
366    : __ratio_less_impl_1<_R1, _R2>::type
367    { };
368
369  template<typename _R1, typename _R2>
370    struct __ratio_less_impl<_R1, _R2, true, false>
371    : integral_constant<bool, _R1::num < _R2::num>
372    { };
373
374  template<typename _R1, typename _R2>
375    struct __ratio_less_impl<_R1, _R2, false, true>
376    : __ratio_less_impl_1<ratio<-_R2::num, _R2::den>,
377           ratio<-_R1::num, _R1::den> >::type
378    { };
379
380  /// ratio_less
381  template<typename _R1, typename _R2>
382    struct ratio_less
383    : __ratio_less_impl<_R1, _R2>::type
384    { };
385
386  /// ratio_less_equal
387  template<typename _R1, typename _R2>
388    struct ratio_less_equal
389    : integral_constant<bool, !ratio_less<_R2, _R1>::value>
390    { };
391
392  /// ratio_greater
393  template<typename _R1, typename _R2>
394    struct ratio_greater
395    : integral_constant<bool, ratio_less<_R2, _R1>::value>
396    { };
397
398  /// ratio_greater_equal
399  template<typename _R1, typename _R2>
400    struct ratio_greater_equal
401    : integral_constant<bool, !ratio_less<_R1, _R2>::value>
402    { };
403
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
473  template<typename _R1, typename _R2>
474    struct __ratio_add
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>
482    constexpr intmax_t __ratio_add<_R1, _R2>::num;
483
484  template<typename _R1, typename _R2>
485    constexpr intmax_t __ratio_add<_R1, _R2>::den;
486
487  /// ratio_add
488  template<typename _R1, typename _R2>
489    using ratio_add = typename __ratio_add<_R1, _R2>::type;
490
491  template<typename _R1, typename _R2>
492    struct __ratio_subtract
493    {
494      typedef typename __ratio_add<
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>
503    constexpr intmax_t __ratio_subtract<_R1, _R2>::num;
504
505  template<typename _R1, typename _R2>
506    constexpr intmax_t __ratio_subtract<_R1, _R2>::den;
507
508  /// ratio_subtract
509  template<typename _R1, typename _R2>
510    using ratio_subtract = typename __ratio_subtract<_R1, _R2>::type;
511
512
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;
529
530  // @} group ratio
531_GLIBCXX_END_NAMESPACE_VERSION
532} // namespace
533
534#endif //_GLIBCXX_USE_C99_STDINT_TR1
535
536#endif // C++11
537
538#endif //_GLIBCXX_RATIO
539