libstdc++
ratio
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1 // ratio -*- C++ -*-
2 
3 // Copyright (C) 2008, 2009, 2010, 2011 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 #ifndef __GXX_EXPERIMENTAL_CXX0X__
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 
43 namespace 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 
68  template<intmax_t _Pn, intmax_t _Qn>
69  struct __static_gcd
70  : __static_gcd<_Qn, (_Pn % _Qn)>
71  { };
72 
73  template<intmax_t _Pn>
74  struct __static_gcd<_Pn, 0>
75  : integral_constant<intmax_t, __static_abs<_Pn>::value>
76  { };
77 
78  template<intmax_t _Qn>
79  struct __static_gcd<0, _Qn>
80  : integral_constant<intmax_t, __static_abs<_Qn>::value>
81  { };
82 
83  // Let c = 2^(half # of bits in an intmax_t)
84  // then we find a1, a0, b1, b0 s.t. N = a1*c + a0, M = b1*c + b0
85  // The multiplication of N and M becomes,
86  // N * M = (a1 * b1)c^2 + (a0 * b1 + b0 * a1)c + a0 * b0
87  // Multiplication is safe if each term and the sum of the terms
88  // is representable by intmax_t.
89  template<intmax_t _Pn, intmax_t _Qn>
90  struct __safe_multiply
91  {
92  private:
93  static const uintmax_t __c = uintmax_t(1) << (sizeof(intmax_t) * 4);
94 
95  static const uintmax_t __a0 = __static_abs<_Pn>::value % __c;
96  static const uintmax_t __a1 = __static_abs<_Pn>::value / __c;
97  static const uintmax_t __b0 = __static_abs<_Qn>::value % __c;
98  static const uintmax_t __b1 = __static_abs<_Qn>::value / __c;
99 
100  static_assert(__a1 == 0 || __b1 == 0,
101  "overflow in multiplication");
102  static_assert(__a0 * __b1 + __b0 * __a1 < (__c >> 1),
103  "overflow in multiplication");
104  static_assert(__b0 * __a0 <= __INTMAX_MAX__,
105  "overflow in multiplication");
106  static_assert((__a0 * __b1 + __b0 * __a1) * __c
107  <= __INTMAX_MAX__ - __b0 * __a0,
108  "overflow in multiplication");
109 
110  public:
111  static const intmax_t value = _Pn * _Qn;
112  };
113 
114  // Some double-precision utilities, where numbers are represented as
115  // __hi*2^(8*sizeof(uintmax_t)) + __lo.
116  template<uintmax_t __hi1, uintmax_t __lo1, uintmax_t __hi2, uintmax_t __lo2>
117  struct __big_less
118  : integral_constant<bool, (__hi1 < __hi2
119  || (__hi1 == __hi2 && __lo1 < __lo2))>
120  { };
121 
122  template<uintmax_t __hi1, uintmax_t __lo1, uintmax_t __hi2, uintmax_t __lo2>
123  struct __big_add
124  {
125  static constexpr uintmax_t __lo = __lo1 + __lo2;
126  static constexpr uintmax_t __hi = (__hi1 + __hi2 +
127  (__lo1 + __lo2 < __lo1)); // carry
128  };
129 
130  // Subtract a number from a bigger one.
131  template<uintmax_t __hi1, uintmax_t __lo1, uintmax_t __hi2, uintmax_t __lo2>
132  struct __big_sub
133  {
134  static_assert(!__big_less<__hi1, __lo1, __hi2, __lo2>::value,
135  "Internal library error");
136  static constexpr uintmax_t __lo = __lo1 - __lo2;
137  static constexpr uintmax_t __hi = (__hi1 - __hi2 -
138  (__lo1 < __lo2)); // carry
139  };
140 
141  // Same principle as __safe_multiply.
142  template<uintmax_t __x, uintmax_t __y>
143  struct __big_mul
144  {
145  private:
146  static constexpr uintmax_t __c = uintmax_t(1) << (sizeof(intmax_t) * 4);
147  static constexpr uintmax_t __x0 = __x % __c;
148  static constexpr uintmax_t __x1 = __x / __c;
149  static constexpr uintmax_t __y0 = __y % __c;
150  static constexpr uintmax_t __y1 = __y / __c;
151  static constexpr uintmax_t __x0y0 = __x0 * __y0;
152  static constexpr uintmax_t __x0y1 = __x0 * __y1;
153  static constexpr uintmax_t __x1y0 = __x1 * __y0;
154  static constexpr uintmax_t __x1y1 = __x1 * __y1;
155  static constexpr uintmax_t __mix = __x0y1 + __x1y0; // possible carry...
156  static constexpr uintmax_t __mix_lo = __mix * __c;
157  static constexpr uintmax_t __mix_hi
158  = __mix / __c + ((__mix < __x0y1) ? __c : 0); // ... added here
159  typedef __big_add<__mix_hi, __mix_lo, __x1y1, __x0y0> _Res;
160  public:
161  static constexpr uintmax_t __hi = _Res::__hi;
162  static constexpr uintmax_t __lo = _Res::__lo;
163  };
164 
165  // Adapted from __udiv_qrnnd_c in longlong.h
166  // This version assumes that the high bit of __d is 1.
167  template<uintmax_t __n1, uintmax_t __n0, uintmax_t __d>
168  struct __big_div_impl
169  {
170  private:
171  static_assert(__d >= (uintmax_t(1) << (sizeof(intmax_t) * 8 - 1)),
172  "Internal library error");
173  static_assert(__n1 < __d, "Internal library error");
174  static constexpr uintmax_t __c = uintmax_t(1) << (sizeof(intmax_t) * 4);
175  static constexpr uintmax_t __d1 = __d / __c;
176  static constexpr uintmax_t __d0 = __d % __c;
177 
178  static constexpr uintmax_t __q1x = __n1 / __d1;
179  static constexpr uintmax_t __r1x = __n1 % __d1;
180  static constexpr uintmax_t __m = __q1x * __d0;
181  static constexpr uintmax_t __r1y = __r1x * __c + __n0 / __c;
182  static constexpr uintmax_t __r1z = __r1y + __d;
183  static constexpr uintmax_t __r1
184  = ((__r1y < __m) ? ((__r1z >= __d) && (__r1z < __m))
185  ? (__r1z + __d) : __r1z : __r1y) - __m;
186  static constexpr uintmax_t __q1
187  = __q1x - ((__r1y < __m)
188  ? ((__r1z >= __d) && (__r1z < __m)) ? 2 : 1 : 0);
189  static constexpr uintmax_t __q0x = __r1 / __d1;
190  static constexpr uintmax_t __r0x = __r1 % __d1;
191  static constexpr uintmax_t __n = __q0x * __d0;
192  static constexpr uintmax_t __r0y = __r0x * __c + __n0 % __c;
193  static constexpr uintmax_t __r0z = __r0y + __d;
194  static constexpr uintmax_t __r0
195  = ((__r0y < __n) ? ((__r0z >= __d) && (__r0z < __n))
196  ? (__r0z + __d) : __r0z : __r0y) - __n;
197  static constexpr uintmax_t __q0
198  = __q0x - ((__r0y < __n) ? ((__r0z >= __d)
199  && (__r0z < __n)) ? 2 : 1 : 0);
200 
201  public:
202  static constexpr uintmax_t __quot = __q1 * __c + __q0;
203  static constexpr uintmax_t __rem = __r0;
204 
205  private:
206  typedef __big_mul<__quot, __d> _Prod;
207  typedef __big_add<_Prod::__hi, _Prod::__lo, 0, __rem> _Sum;
208  static_assert(_Sum::__hi == __n1 && _Sum::__lo == __n0,
209  "Internal library error");
210  };
211 
212  template<uintmax_t __n1, uintmax_t __n0, uintmax_t __d>
213  struct __big_div
214  {
215  private:
216  static_assert(__d != 0, "Internal library error");
217  static_assert(sizeof (uintmax_t) == sizeof (unsigned long long),
218  "This library calls __builtin_clzll on uintmax_t, which "
219  "is unsafe on your platform. Please complain to "
220  "http://gcc.gnu.org/bugzilla/");
221  static constexpr int __shift = __builtin_clzll(__d);
222  static constexpr int __coshift_ = sizeof(uintmax_t) * 8 - __shift;
223  static constexpr int __coshift = (__shift != 0) ? __coshift_ : 0;
224  static constexpr uintmax_t __c1 = uintmax_t(1) << __shift;
225  static constexpr uintmax_t __c2 = uintmax_t(1) << __coshift;
226  static constexpr uintmax_t __new_d = __d * __c1;
227  static constexpr uintmax_t __new_n0 = __n0 * __c1;
228  static constexpr uintmax_t __n1_shifted = (__n1 % __d) * __c1;
229  static constexpr uintmax_t __n0_top = (__shift != 0) ? (__n0 / __c2) : 0;
230  static constexpr uintmax_t __new_n1 = __n1_shifted + __n0_top;
231  typedef __big_div_impl<__new_n1, __new_n0, __new_d> _Res;
232 
233  public:
234  static constexpr uintmax_t __quot_hi = __n1 / __d;
235  static constexpr uintmax_t __quot_lo = _Res::__quot;
236  static constexpr uintmax_t __rem = _Res::__rem / __c1;
237 
238  private:
239  typedef __big_mul<__quot_lo, __d> _P0;
240  typedef __big_mul<__quot_hi, __d> _P1;
241  typedef __big_add<_P0::__hi, _P0::__lo, _P1::__lo, __rem> _Sum;
242  // No overflow.
243  static_assert(_P1::__hi == 0, "Internal library error");
244  static_assert(_Sum::__hi >= _P0::__hi, "Internal library error");
245  // Matches the input data.
246  static_assert(_Sum::__hi == __n1 && _Sum::__lo == __n0,
247  "Internal library error");
248  static_assert(__rem < __d, "Internal library error");
249  };
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  /// ratio_multiply
289  template<typename _R1, typename _R2>
290  struct ratio_multiply
291  {
292  private:
293  static const intmax_t __gcd1 =
294  __static_gcd<_R1::num, _R2::den>::value;
295  static const intmax_t __gcd2 =
296  __static_gcd<_R2::num, _R1::den>::value;
297 
298  public:
299  typedef ratio<
300  __safe_multiply<(_R1::num / __gcd1),
301  (_R2::num / __gcd2)>::value,
302  __safe_multiply<(_R1::den / __gcd2),
303  (_R2::den / __gcd1)>::value> type;
304 
305  static constexpr intmax_t num = type::num;
306  static constexpr intmax_t den = type::den;
307  };
308 
309  template<typename _R1, typename _R2>
310  constexpr intmax_t ratio_multiply<_R1, _R2>::num;
311 
312  template<typename _R1, typename _R2>
313  constexpr intmax_t ratio_multiply<_R1, _R2>::den;
314 
315  /// ratio_divide
316  template<typename _R1, typename _R2>
317  struct ratio_divide
318  {
319  static_assert(_R2::num != 0, "division by 0");
320 
321  typedef typename ratio_multiply<
322  _R1,
323  ratio<_R2::den, _R2::num>>::type type;
324 
325  static constexpr intmax_t num = type::num;
326  static constexpr intmax_t den = type::den;
327  };
328 
329  template<typename _R1, typename _R2>
330  constexpr intmax_t ratio_divide<_R1, _R2>::num;
331 
332  template<typename _R1, typename _R2>
333  constexpr intmax_t ratio_divide<_R1, _R2>::den;
334 
335  /// ratio_equal
336  template<typename _R1, typename _R2>
337  struct ratio_equal
338  : integral_constant<bool, _R1::num == _R2::num && _R1::den == _R2::den>
339  { };
340 
341  /// ratio_not_equal
342  template<typename _R1, typename _R2>
343  struct ratio_not_equal
344  : integral_constant<bool, !ratio_equal<_R1, _R2>::value>
345  { };
346 
347  // Both numbers are positive.
348  template<typename _R1, typename _R2,
349  typename _Left = __big_mul<_R1::num,_R2::den>,
350  typename _Right = __big_mul<_R2::num,_R1::den> >
351  struct __ratio_less_impl_1
352  : integral_constant<bool, __big_less<_Left::__hi, _Left::__lo,
353  _Right::__hi, _Right::__lo>::value>
354  { };
355 
356  template<typename _R1, typename _R2,
357  bool = (_R1::num == 0 || _R2::num == 0
358  || (__static_sign<_R1::num>::value
359  != __static_sign<_R2::num>::value)),
360  bool = (__static_sign<_R1::num>::value == -1
361  && __static_sign<_R2::num>::value == -1)>
362  struct __ratio_less_impl
363  : __ratio_less_impl_1<_R1, _R2>::type
364  { };
365 
366  template<typename _R1, typename _R2>
367  struct __ratio_less_impl<_R1, _R2, true, false>
368  : integral_constant<bool, _R1::num < _R2::num>
369  { };
370 
371  template<typename _R1, typename _R2>
372  struct __ratio_less_impl<_R1, _R2, false, true>
373  : __ratio_less_impl_1<ratio<-_R2::num, _R2::den>,
374  ratio<-_R1::num, _R1::den> >::type
375  { };
376 
377  /// ratio_less
378  template<typename _R1, typename _R2>
379  struct ratio_less
380  : __ratio_less_impl<_R1, _R2>::type
381  { };
382 
383  /// ratio_less_equal
384  template<typename _R1, typename _R2>
385  struct ratio_less_equal
386  : integral_constant<bool, !ratio_less<_R2, _R1>::value>
387  { };
388 
389  /// ratio_greater
390  template<typename _R1, typename _R2>
391  struct ratio_greater
392  : integral_constant<bool, ratio_less<_R2, _R1>::value>
393  { };
394 
395  /// ratio_greater_equal
396  template<typename _R1, typename _R2>
397  struct ratio_greater_equal
398  : integral_constant<bool, !ratio_less<_R1, _R2>::value>
399  { };
400 
401  template<typename _R1, typename _R2,
402  bool = (_R1::num >= 0),
403  bool = (_R2::num >= 0),
404  bool = ratio_less<ratio<__static_abs<_R1::num>::value, _R1::den>,
405  ratio<__static_abs<_R2::num>::value, _R2::den> >::value>
406  struct __ratio_add_impl
407  {
408  private:
409  typedef typename __ratio_add_impl<
410  ratio<-_R1::num, _R1::den>,
411  ratio<-_R2::num, _R2::den> >::type __t;
412  public:
413  typedef ratio<-__t::num, __t::den> type;
414  };
415 
416  // True addition of nonnegative numbers.
417  template<typename _R1, typename _R2, bool __b>
418  struct __ratio_add_impl<_R1, _R2, true, true, __b>
419  {
420  private:
421  static constexpr uintmax_t __g = __static_gcd<_R1::den, _R2::den>::value;
422  static constexpr uintmax_t __d2 = _R2::den / __g;
423  typedef __big_mul<_R1::den, __d2> __d;
424  typedef __big_mul<_R1::num, _R2::den / __g> __x;
425  typedef __big_mul<_R2::num, _R1::den / __g> __y;
426  typedef __big_add<__x::__hi, __x::__lo, __y::__hi, __y::__lo> __n;
427  static_assert(__n::__hi >= __x::__hi, "Internal library error");
428  typedef __big_div<__n::__hi, __n::__lo, __g> __ng;
429  static constexpr uintmax_t __g2 = __static_gcd<__ng::__rem, __g>::value;
430  typedef __big_div<__n::__hi, __n::__lo, __g2> __n_final;
431  static_assert(__n_final::__rem == 0, "Internal library error");
432  static_assert(__n_final::__quot_hi == 0 &&
433  __n_final::__quot_lo <= __INTMAX_MAX__, "overflow in addition");
434  typedef __big_mul<_R1::den / __g2, __d2> __d_final;
435  static_assert(__d_final::__hi == 0 &&
436  __d_final::__lo <= __INTMAX_MAX__, "overflow in addition");
437  public:
438  typedef ratio<__n_final::__quot_lo, __d_final::__lo> type;
439  };
440 
441  template<typename _R1, typename _R2>
442  struct __ratio_add_impl<_R1, _R2, false, true, true>
443  : __ratio_add_impl<_R2, _R1>
444  { };
445 
446  // True subtraction of nonnegative numbers yielding a nonnegative result.
447  template<typename _R1, typename _R2>
448  struct __ratio_add_impl<_R1, _R2, true, false, false>
449  {
450  private:
451  static constexpr uintmax_t __g = __static_gcd<_R1::den, _R2::den>::value;
452  static constexpr uintmax_t __d2 = _R2::den / __g;
453  typedef __big_mul<_R1::den, __d2> __d;
454  typedef __big_mul<_R1::num, _R2::den / __g> __x;
455  typedef __big_mul<-_R2::num, _R1::den / __g> __y;
456  typedef __big_sub<__x::__hi, __x::__lo, __y::__hi, __y::__lo> __n;
457  typedef __big_div<__n::__hi, __n::__lo, __g> __ng;
458  static constexpr uintmax_t __g2 = __static_gcd<__ng::__rem, __g>::value;
459  typedef __big_div<__n::__hi, __n::__lo, __g2> __n_final;
460  static_assert(__n_final::__rem == 0, "Internal library error");
461  static_assert(__n_final::__quot_hi == 0 &&
462  __n_final::__quot_lo <= __INTMAX_MAX__, "overflow in addition");
463  typedef __big_mul<_R1::den / __g2, __d2> __d_final;
464  static_assert(__d_final::__hi == 0 &&
465  __d_final::__lo <= __INTMAX_MAX__, "overflow in addition");
466  public:
467  typedef ratio<__n_final::__quot_lo, __d_final::__lo> type;
468  };
469 
470  /// ratio_add
471  template<typename _R1, typename _R2>
472  struct ratio_add
473  {
474  typedef typename __ratio_add_impl<_R1, _R2>::type type;
475  static constexpr intmax_t num = type::num;
476  static constexpr intmax_t den = type::den;
477  };
478 
479  template<typename _R1, typename _R2>
480  constexpr intmax_t ratio_add<_R1, _R2>::num;
481 
482  template<typename _R1, typename _R2>
483  constexpr intmax_t ratio_add<_R1, _R2>::den;
484 
485  /// ratio_subtract
486  template<typename _R1, typename _R2>
487  struct ratio_subtract
488  {
489  typedef typename ratio_add<
490  _R1,
491  ratio<-_R2::num, _R2::den>>::type type;
492 
493  static constexpr intmax_t num = type::num;
494  static constexpr intmax_t den = type::den;
495  };
496 
497  template<typename _R1, typename _R2>
498  constexpr intmax_t ratio_subtract<_R1, _R2>::num;
499 
500  template<typename _R1, typename _R2>
501  constexpr intmax_t ratio_subtract<_R1, _R2>::den;
502 
503 
504 
505  typedef ratio<1, 1000000000000000000> atto;
506  typedef ratio<1, 1000000000000000> femto;
507  typedef ratio<1, 1000000000000> pico;
508  typedef ratio<1, 1000000000> nano;
509  typedef ratio<1, 1000000> micro;
510  typedef ratio<1, 1000> milli;
511  typedef ratio<1, 100> centi;
512  typedef ratio<1, 10> deci;
513  typedef ratio< 10, 1> deca;
514  typedef ratio< 100, 1> hecto;
515  typedef ratio< 1000, 1> kilo;
516  typedef ratio< 1000000, 1> mega;
517  typedef ratio< 1000000000, 1> giga;
518  typedef ratio< 1000000000000, 1> tera;
519  typedef ratio< 1000000000000000, 1> peta;
520  typedef ratio< 1000000000000000000, 1> exa;
521 
522  // @} group ratio
523 _GLIBCXX_END_NAMESPACE_VERSION
524 } // namespace
525 
526 #endif //_GLIBCXX_USE_C99_STDINT_TR1
527 
528 #endif //__GXX_EXPERIMENTAL_CXX0X__
529 
530 #endif //_GLIBCXX_RATIO