libstdc++
ratio
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1 // ratio -*- C++ -*-
2 
3 // Copyright (C) 2008, 2009 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 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 <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
44 {
45  /**
46  * @defgroup ratio Rational Arithmetic
47  * @ingroup utilities
48  *
49  * Compile time representation of fininte rational numbers.
50  * @{
51  */
52 
53  template<intmax_t _Pn>
54  struct __static_sign
55  : integral_constant<intmax_t, (_Pn < 0) ? -1 : 1>
56  { };
57 
58  template<intmax_t _Pn>
59  struct __static_abs
60  : integral_constant<intmax_t, _Pn * __static_sign<_Pn>::value>
61  { };
62 
63  template<intmax_t _Pn, intmax_t _Qn>
64  struct __static_gcd;
65 
66  template<intmax_t _Pn, intmax_t _Qn>
67  struct __static_gcd
68  : __static_gcd<_Qn, (_Pn % _Qn)>
69  { };
70 
71  template<intmax_t _Pn>
72  struct __static_gcd<_Pn, 0>
73  : integral_constant<intmax_t, __static_abs<_Pn>::value>
74  { };
75 
76  template<intmax_t _Qn>
77  struct __static_gcd<0, _Qn>
78  : integral_constant<intmax_t, __static_abs<_Qn>::value>
79  { };
80 
81  // Let c = 2^(half # of bits in an intmax_t)
82  // then we find a1, a0, b1, b0 s.t. N = a1*c + a0, M = b1*c + b0
83  // The multiplication of N and M becomes,
84  // N * M = (a1 * b1)c^2 + (a0 * b1 + b0 * a1)c + a0 * b0
85  // Multiplication is safe if each term and the sum of the terms
86  // is representable by intmax_t.
87  template<intmax_t _Pn, intmax_t _Qn>
88  struct __safe_multiply
89  {
90  private:
91  static const uintmax_t __c = uintmax_t(1) << (sizeof(intmax_t) * 4);
92 
93  static const uintmax_t __a0 = __static_abs<_Pn>::value % __c;
94  static const uintmax_t __a1 = __static_abs<_Pn>::value / __c;
95  static const uintmax_t __b0 = __static_abs<_Qn>::value % __c;
96  static const uintmax_t __b1 = __static_abs<_Qn>::value / __c;
97 
98  static_assert(__a1 == 0 || __b1 == 0,
99  "overflow in multiplication");
100  static_assert(__a0 * __b1 + __b0 * __a1 < (__c >> 1),
101  "overflow in multiplication");
102  static_assert(__b0 * __a0 <= __INTMAX_MAX__,
103  "overflow in multiplication");
104  static_assert((__a0 * __b1 + __b0 * __a1) * __c <=
105  __INTMAX_MAX__ - __b0 * __a0, "overflow in multiplication");
106 
107  public:
108  static const intmax_t value = _Pn * _Qn;
109  };
110 
111  // Helpers for __safe_add
112  template<intmax_t _Pn, intmax_t _Qn, bool>
113  struct __add_overflow_check_impl
114  : integral_constant<bool, (_Pn <= __INTMAX_MAX__ - _Qn)>
115  { };
116 
117  template<intmax_t _Pn, intmax_t _Qn>
118  struct __add_overflow_check_impl<_Pn, _Qn, false>
119  : integral_constant<bool, (_Pn >= -__INTMAX_MAX__ - _Qn)>
120  { };
121 
122  template<intmax_t _Pn, intmax_t _Qn>
123  struct __add_overflow_check
124  : __add_overflow_check_impl<_Pn, _Qn, (_Qn >= 0)>
125  { };
126 
127  template<intmax_t _Pn, intmax_t _Qn>
128  struct __safe_add
129  {
130  static_assert(__add_overflow_check<_Pn, _Qn>::value != 0,
131  "overflow in addition");
132 
133  static const intmax_t value = _Pn + _Qn;
134  };
135 
136  /**
137  * @brief Provides compile-time rational arithmetic.
138  *
139  * This class template represents any finite rational number with a
140  * numerator and denominator representable by compile-time constants of
141  * type intmax_t. The ratio is simplified when instantiated.
142  *
143  * For example:
144  * @code
145  * std::ratio<7,-21>::num == -1;
146  * std::ratio<7,-21>::den == 3;
147  * @endcode
148  *
149  */
150  template<intmax_t _Num, intmax_t _Den = 1>
151  struct ratio
152  {
153  static_assert(_Den != 0, "denominator cannot be zero");
154  static_assert(_Num >= -__INTMAX_MAX__ && _Den >= -__INTMAX_MAX__,
155  "out of range");
156 
157  // Note: sign(N) * abs(N) == N
158  static const intmax_t num =
159  _Num * __static_sign<_Den>::value / __static_gcd<_Num, _Den>::value;
160 
161  static const intmax_t den =
162  __static_abs<_Den>::value / __static_gcd<_Num, _Den>::value;
163  };
164 
165  template<intmax_t _Num, intmax_t _Den>
166  const intmax_t ratio<_Num, _Den>::num;
167 
168  template<intmax_t _Num, intmax_t _Den>
169  const intmax_t ratio<_Num, _Den>::den;
170 
171  /// ratio_add
172  template<typename _R1, typename _R2>
173  struct ratio_add
174  {
175  private:
176  static const intmax_t __gcd =
177  __static_gcd<_R1::den, _R2::den>::value;
178 
179  public:
180  typedef ratio<
181  __safe_add<
182  __safe_multiply<_R1::num, (_R2::den / __gcd)>::value,
183  __safe_multiply<_R2::num, (_R1::den / __gcd)>::value>::value,
184  __safe_multiply<_R1::den, (_R2::den / __gcd)>::value> type;
185  };
186 
187  /// ratio_subtract
188  template<typename _R1, typename _R2>
189  struct ratio_subtract
190  {
191  typedef typename ratio_add<
192  _R1,
193  ratio<-_R2::num, _R2::den>>::type type;
194  };
195 
196  /// ratio_multiply
197  template<typename _R1, typename _R2>
198  struct ratio_multiply
199  {
200  private:
201  static const intmax_t __gcd1 =
202  __static_gcd<_R1::num, _R2::den>::value;
203  static const intmax_t __gcd2 =
204  __static_gcd<_R2::num, _R1::den>::value;
205 
206  public:
207  typedef ratio<
208  __safe_multiply<(_R1::num / __gcd1),
209  (_R2::num / __gcd2)>::value,
210  __safe_multiply<(_R1::den / __gcd2),
211  (_R2::den / __gcd1)>::value> type;
212  };
213 
214  /// ratio_divide
215  template<typename _R1, typename _R2>
216  struct ratio_divide
217  {
218  static_assert(_R2::num != 0, "division by 0");
219 
220  typedef typename ratio_multiply<
221  _R1,
222  ratio<_R2::den, _R2::num>>::type type;
223  };
224 
225  /// ratio_equal
226  template<typename _R1, typename _R2>
227  struct ratio_equal
228  : integral_constant<bool, _R1::num == _R2::num && _R1::den == _R2::den>
229  { };
230 
231  /// ratio_not_equal
232  template<typename _R1, typename _R2>
233  struct ratio_not_equal
234  : integral_constant<bool, !ratio_equal<_R1, _R2>::value>
235  { };
236 
237  template<typename _R1, typename _R2>
238  struct __ratio_less_simple_impl
239  : integral_constant<bool,
240  (__safe_multiply<_R1::num, _R2::den>::value
241  < __safe_multiply<_R2::num, _R1::den>::value)>
242  { };
243 
244  // If the denominators are equal or the signs differ, we can just compare
245  // numerators, otherwise fallback to the simple cross-multiply method.
246  template<typename _R1, typename _R2>
247  struct __ratio_less_impl
248  : conditional<(_R1::den == _R2::den
249  || (__static_sign<_R1::num>::value
250  != __static_sign<_R2::num>::value)),
251  integral_constant<bool, (_R1::num < _R2::num)>,
252  __ratio_less_simple_impl<_R1, _R2>>::type
253  { };
254 
255  /// ratio_less
256  template<typename _R1, typename _R2>
257  struct ratio_less
258  : __ratio_less_impl<_R1, _R2>::type
259  { };
260 
261  /// ratio_less_equal
262  template<typename _R1, typename _R2>
263  struct ratio_less_equal
264  : integral_constant<bool, !ratio_less<_R2, _R1>::value>
265  { };
266 
267  /// ratio_greater
268  template<typename _R1, typename _R2>
269  struct ratio_greater
270  : integral_constant<bool, ratio_less<_R2, _R1>::value>
271  { };
272 
273  /// ratio_greater_equal
274  template<typename _R1, typename _R2>
275  struct ratio_greater_equal
276  : integral_constant<bool, !ratio_less<_R1, _R2>::value>
277  { };
278 
279  typedef ratio<1, 1000000000000000000> atto;
280  typedef ratio<1, 1000000000000000> femto;
281  typedef ratio<1, 1000000000000> pico;
282  typedef ratio<1, 1000000000> nano;
283  typedef ratio<1, 1000000> micro;
284  typedef ratio<1, 1000> milli;
285  typedef ratio<1, 100> centi;
286  typedef ratio<1, 10> deci;
287  typedef ratio< 10, 1> deca;
288  typedef ratio< 100, 1> hecto;
289  typedef ratio< 1000, 1> kilo;
290  typedef ratio< 1000000, 1> mega;
291  typedef ratio< 1000000000, 1> giga;
292  typedef ratio< 1000000000000, 1> tera;
293  typedef ratio< 1000000000000000, 1> peta;
294  typedef ratio< 1000000000000000000, 1> exa;
295 
296  // @} group ratio
297 }
298 
299 #endif //_GLIBCXX_USE_C99_STDINT_TR1
300 
301 #endif //__GXX_EXPERIMENTAL_CXX0X__
302 
303 #endif //_GLIBCXX_RATIO