FFmpeg
 All Data Structures Namespaces Files Functions Variables Typedefs Enumerations Enumerator Macros Groups Pages
rational.c
Go to the documentation of this file.
1 /*
2  * rational numbers
3  * Copyright (c) 2003 Michael Niedermayer <michaelni@gmx.at>
4  *
5  * This file is part of FFmpeg.
6  *
7  * FFmpeg is free software; you can redistribute it and/or
8  * modify it under the terms of the GNU Lesser General Public
9  * License as published by the Free Software Foundation; either
10  * version 2.1 of the License, or (at your option) any later version.
11  *
12  * FFmpeg is distributed in the hope that it will be useful,
13  * but WITHOUT ANY WARRANTY; without even the implied warranty of
14  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
15  * Lesser General Public License for more details.
16  *
17  * You should have received a copy of the GNU Lesser General Public
18  * License along with FFmpeg; if not, write to the Free Software
19  * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
20  */
21 
22 /**
23  * @file
24  * rational numbers
25  * @author Michael Niedermayer <michaelni@gmx.at>
26  */
27 
28 #include "avassert.h"
29 #include <limits.h>
30 
31 #include "common.h"
32 #include "mathematics.h"
33 #include "rational.h"
34 
35 int av_reduce(int *dst_num, int *dst_den,
36  int64_t num, int64_t den, int64_t max)
37 {
38  AVRational a0 = { 0, 1 }, a1 = { 1, 0 };
39  int sign = (num < 0) ^ (den < 0);
40  int64_t gcd = av_gcd(FFABS(num), FFABS(den));
41 
42  if (gcd) {
43  num = FFABS(num) / gcd;
44  den = FFABS(den) / gcd;
45  }
46  if (num <= max && den <= max) {
47  a1 = (AVRational) { num, den };
48  den = 0;
49  }
50 
51  while (den) {
52  uint64_t x = num / den;
53  int64_t next_den = num - den * x;
54  int64_t a2n = x * a1.num + a0.num;
55  int64_t a2d = x * a1.den + a0.den;
56 
57  if (a2n > max || a2d > max) {
58  if (a1.num) x = (max - a0.num) / a1.num;
59  if (a1.den) x = FFMIN(x, (max - a0.den) / a1.den);
60 
61  if (den * (2 * x * a1.den + a0.den) > num * a1.den)
62  a1 = (AVRational) { x * a1.num + a0.num, x * a1.den + a0.den };
63  break;
64  }
65 
66  a0 = a1;
67  a1 = (AVRational) { a2n, a2d };
68  num = den;
69  den = next_den;
70  }
71  av_assert2(av_gcd(a1.num, a1.den) <= 1U);
72  av_assert2(a1.num <= max && a1.den <= max);
73 
74  *dst_num = sign ? -a1.num : a1.num;
75  *dst_den = a1.den;
76 
77  return den == 0;
78 }
79 
80 AVRational av_mul_q(AVRational b, AVRational c)
81 {
82  av_reduce(&b.num, &b.den,
83  b.num * (int64_t) c.num,
84  b.den * (int64_t) c.den, INT_MAX);
85  return b;
86 }
87 
88 AVRational av_div_q(AVRational b, AVRational c)
89 {
90  return av_mul_q(b, (AVRational) { c.den, c.num });
91 }
92 
93 AVRational av_add_q(AVRational b, AVRational c) {
94  av_reduce(&b.num, &b.den,
95  b.num * (int64_t) c.den +
96  c.num * (int64_t) b.den,
97  b.den * (int64_t) c.den, INT_MAX);
98  return b;
99 }
100 
101 AVRational av_sub_q(AVRational b, AVRational c)
102 {
103  return av_add_q(b, (AVRational) { -c.num, c.den });
104 }
105 
106 AVRational av_d2q(double d, int max)
107 {
108  AVRational a;
109 #define LOG2 0.69314718055994530941723212145817656807550013436025
110  int exponent;
111  int64_t den;
112  if (isnan(d))
113  return (AVRational) { 0,0 };
114  if (fabs(d) > INT_MAX + 3LL)
115  return (AVRational) { d < 0 ? -1 : 1, 0 };
116  exponent = FFMAX( (int)(log(fabs(d) + 1e-20)/LOG2), 0);
117  den = 1LL << (61 - exponent);
118  // (int64_t)rint() and llrint() do not work with gcc on ia64 and sparc64
119  av_reduce(&a.num, &a.den, floor(d * den + 0.5), den, max);
120  if ((!a.num || !a.den) && d && max>0 && max<INT_MAX)
121  av_reduce(&a.num, &a.den, floor(d * den + 0.5), den, INT_MAX);
122 
123  return a;
124 }
125 
126 int av_nearer_q(AVRational q, AVRational q1, AVRational q2)
127 {
128  /* n/d is q, a/b is the median between q1 and q2 */
129  int64_t a = q1.num * (int64_t)q2.den + q2.num * (int64_t)q1.den;
130  int64_t b = 2 * (int64_t)q1.den * q2.den;
131 
132  /* rnd_up(a*d/b) > n => a*d/b > n */
133  int64_t x_up = av_rescale_rnd(a, q.den, b, AV_ROUND_UP);
134 
135  /* rnd_down(a*d/b) < n => a*d/b < n */
136  int64_t x_down = av_rescale_rnd(a, q.den, b, AV_ROUND_DOWN);
137 
138  return ((x_up > q.num) - (x_down < q.num)) * av_cmp_q(q2, q1);
139 }
140 
141 int av_find_nearest_q_idx(AVRational q, const AVRational* q_list)
142 {
143  int i, nearest_q_idx = 0;
144  for (i = 0; q_list[i].den; i++)
145  if (av_nearer_q(q, q_list[i], q_list[nearest_q_idx]) > 0)
146  nearest_q_idx = i;
147 
148  return nearest_q_idx;
149 }
150 
151 #ifdef TEST
152 int main(void)
153 {
154  AVRational a,b,r;
155  for (a.num = -2; a.num <= 2; a.num++) {
156  for (a.den = -2; a.den <= 2; a.den++) {
157  for (b.num = -2; b.num <= 2; b.num++) {
158  for (b.den = -2; b.den <= 2; b.den++) {
159  int c = av_cmp_q(a,b);
160  double d = av_q2d(a) == av_q2d(b) ?
161  0 : (av_q2d(a) - av_q2d(b));
162  if (d > 0) d = 1;
163  else if (d < 0) d = -1;
164  else if (d != d) d = INT_MIN;
165  if (c != d)
166  av_log(NULL, AV_LOG_ERROR, "%d/%d %d/%d, %d %f\n", a.num,
167  a.den, b.num, b.den, c,d);
168  r = av_sub_q(av_add_q(b,a), b);
169  if(b.den && (r.num*a.den != a.num*r.den || !r.num != !a.num || !r.den != !a.den))
170  av_log(NULL, AV_LOG_ERROR, "%d/%d ", r.num, r.den);
171  }
172  }
173  }
174  }
175 
176  for (a.num = 1; a.num <= 10; a.num++) {
177  for (a.den = 1; a.den <= 10; a.den++) {
178  if (av_gcd(a.num, a.den) > 1)
179  continue;
180  for (b.num = 1; b.num <= 10; b.num++) {
181  for (b.den = 1; b.den <= 10; b.den++) {
182  int start;
183  if (av_gcd(b.num, b.den) > 1)
184  continue;
185  if (av_cmp_q(b, a) < 0)
186  continue;
187  for (start = 0; start < 10 ; start++) {
188  int acc= start;
189  int i;
190 
191  for (i = 0; i<100; i++) {
192  int exact = start + av_rescale_q(i+1, b, a);
193  acc = av_add_stable(a, acc, b, 1);
194  if (FFABS(acc - exact) > 2) {
195  av_log(NULL, AV_LOG_ERROR, "%d/%d %d/%d, %d %d\n", a.num,
196  a.den, b.num, b.den, acc, exact);
197  return 1;
198  }
199  }
200  }
201  }
202  }
203  }
204  }
205  return 0;
206 }
207 #endif
Generated on Sun Mar 8 2015 02:35:14 for FFmpeg by   doxygen 1.8.2