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rational.c
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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 <math.h>
30 #include <limits.h>
31 
32 #include "common.h"
33 #include "mathematics.h"
34 #include "rational.h"
35 
36 int av_reduce(int *dst_num, int *dst_den,
37  int64_t num, int64_t den, int64_t max)
38 {
39  AVRational a0 = { 0, 1 }, a1 = { 1, 0 };
40  int sign = (num < 0) ^ (den < 0);
41  int64_t gcd = av_gcd(FFABS(num), FFABS(den));
42 
43  if (gcd) {
44  num = FFABS(num) / gcd;
45  den = FFABS(den) / gcd;
46  }
47  if (num <= max && den <= max) {
48  a1 = (AVRational) { num, den };
49  den = 0;
50  }
51 
52  while (den) {
53  uint64_t x = num / den;
54  int64_t next_den = num - den * x;
55  int64_t a2n = x * a1.num + a0.num;
56  int64_t a2d = x * a1.den + a0.den;
57 
58  if (a2n > max || a2d > max) {
59  if (a1.num) x = (max - a0.num) / a1.num;
60  if (a1.den) x = FFMIN(x, (max - a0.den) / a1.den);
61 
62  if (den * (2 * x * a1.den + a0.den) > num * a1.den)
63  a1 = (AVRational) { x * a1.num + a0.num, x * a1.den + a0.den };
64  break;
65  }
66 
67  a0 = a1;
68  a1 = (AVRational) { a2n, a2d };
69  num = den;
70  den = next_den;
71  }
72  av_assert2(av_gcd(a1.num, a1.den) <= 1U);
73 
74  *dst_num = sign ? -a1.num : a1.num;
75  *dst_den = a1.den;
76 
77  return den == 0;
78 }
79 
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 
89 {
90  return av_mul_q(b, (AVRational) { c.den, c.num });
91 }
92 
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 
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 (isinf(d))
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  av_reduce(&a.num, &a.den, (int64_t)(d * den + 0.5), den, max);
119 
120  return a;
121 }
122 
124 {
125  /* n/d is q, a/b is the median between q1 and q2 */
126  int64_t a = q1.num * (int64_t)q2.den + q2.num * (int64_t)q1.den;
127  int64_t b = 2 * (int64_t)q1.den * q2.den;
128 
129  /* rnd_up(a*d/b) > n => a*d/b > n */
130  int64_t x_up = av_rescale_rnd(a, q.den, b, AV_ROUND_UP);
131 
132  /* rnd_down(a*d/b) < n => a*d/b < n */
133  int64_t x_down = av_rescale_rnd(a, q.den, b, AV_ROUND_DOWN);
134 
135  return ((x_up > q.num) - (x_down < q.num)) * av_cmp_q(q2, q1);
136 }
137 
139 {
140  int i, nearest_q_idx = 0;
141  for (i = 0; q_list[i].den; i++)
142  if (av_nearer_q(q, q_list[i], q_list[nearest_q_idx]) > 0)
143  nearest_q_idx = i;
144 
145  return nearest_q_idx;
146 }
147 
148 #ifdef TEST
149 int main(void)
150 {
151  AVRational a,b,r;
152  for (a.num = -2; a.num <= 2; a.num++) {
153  for (a.den = -2; a.den <= 2; a.den++) {
154  for (b.num = -2; b.num <= 2; b.num++) {
155  for (b.den = -2; b.den <= 2; b.den++) {
156  int c = av_cmp_q(a,b);
157  double d = av_q2d(a) == av_q2d(b) ?
158  0 : (av_q2d(a) - av_q2d(b));
159  if (d > 0) d = 1;
160  else if (d < 0) d = -1;
161  else if (d != d) d = INT_MIN;
162  if (c != d)
163  av_log(NULL, AV_LOG_ERROR, "%d/%d %d/%d, %d %f\n", a.num,
164  a.den, b.num, b.den, c,d);
165  r = av_sub_q(av_add_q(b,a), b);
166  if(b.den && (r.num*a.den != a.num*r.den || !r.num != !a.num || !r.den != !a.den))
167  av_log(NULL, AV_LOG_ERROR, "%d/%d ", r.num, r.den);
168  }
169  }
170  }
171  }
172  return 0;
173 }
174 #endif