ac5111b896a5d97998dabdaccae3ba6f5897191f
[libav.git] / libavutil / rational.c
1 /*
2 * rational numbers
3 * Copyright (c) 2003 Michael Niedermayer <michaelni@gmx.at>
4 *
5 * This file is part of Libav.
6 *
7 * Libav 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 * Libav 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 Libav; 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, int64_t num, int64_t den, int64_t max){
37 AVRational a0={0,1}, a1={1,0};
38 int sign= (num<0) ^ (den<0);
39 int64_t gcd= av_gcd(FFABS(num), FFABS(den));
40
41 if(gcd){
42 num = FFABS(num)/gcd;
43 den = FFABS(den)/gcd;
44 }
45 if(num<=max && den<=max){
46 a1= (AVRational){num, den};
47 den=0;
48 }
49
50 while(den){
51 uint64_t x = num / den;
52 int64_t next_den= num - den*x;
53 int64_t a2n= x*a1.num + a0.num;
54 int64_t a2d= x*a1.den + a0.den;
55
56 if(a2n > max || a2d > max){
57 if(a1.num) x= (max - a0.num) / a1.num;
58 if(a1.den) x= FFMIN(x, (max - a0.den) / a1.den);
59
60 if (den*(2*x*a1.den + a0.den) > num*a1.den)
61 a1 = (AVRational){x*a1.num + a0.num, x*a1.den + a0.den};
62 break;
63 }
64
65 a0= a1;
66 a1= (AVRational){a2n, a2d};
67 num= den;
68 den= next_den;
69 }
70 av_assert2(av_gcd(a1.num, a1.den) <= 1U);
71
72 *dst_num = sign ? -a1.num : a1.num;
73 *dst_den = a1.den;
74
75 return den==0;
76 }
77
78 AVRational av_mul_q(AVRational b, AVRational c){
79 av_reduce(&b.num, &b.den, b.num * (int64_t)c.num, b.den * (int64_t)c.den, INT_MAX);
80 return b;
81 }
82
83 AVRational av_div_q(AVRational b, AVRational c){
84 return av_mul_q(b, (AVRational){c.den, c.num});
85 }
86
87 AVRational av_add_q(AVRational b, AVRational c){
88 av_reduce(&b.num, &b.den, b.num * (int64_t)c.den + c.num * (int64_t)b.den, b.den * (int64_t)c.den, INT_MAX);
89 return b;
90 }
91
92 AVRational av_sub_q(AVRational b, AVRational c){
93 return av_add_q(b, (AVRational){-c.num, c.den});
94 }
95
96 AVRational av_d2q(double d, int max){
97 AVRational a;
98 #define LOG2 0.69314718055994530941723212145817656807550013436025
99 int exponent;
100 int64_t den;
101 if (isnan(d))
102 return (AVRational){0,0};
103 if (isinf(d))
104 return (AVRational){ d<0 ? -1:1, 0 };
105 exponent = FFMAX( (int)(log(fabs(d) + 1e-20)/LOG2), 0);
106 den = 1LL << (61 - exponent);
107 av_reduce(&a.num, &a.den, (int64_t)(d * den + 0.5), den, max);
108
109 return a;
110 }
111
112 int av_nearer_q(AVRational q, AVRational q1, AVRational q2)
113 {
114 /* n/d is q, a/b is the median between q1 and q2 */
115 int64_t a = q1.num * (int64_t)q2.den + q2.num * (int64_t)q1.den;
116 int64_t b = 2 * (int64_t)q1.den * q2.den;
117
118 /* rnd_up(a*d/b) > n => a*d/b > n */
119 int64_t x_up = av_rescale_rnd(a, q.den, b, AV_ROUND_UP);
120
121 /* rnd_down(a*d/b) < n => a*d/b < n */
122 int64_t x_down = av_rescale_rnd(a, q.den, b, AV_ROUND_DOWN);
123
124 return ((x_up > q.num) - (x_down < q.num)) * av_cmp_q(q2, q1);
125 }
126
127 int av_find_nearest_q_idx(AVRational q, const AVRational* q_list)
128 {
129 int i, nearest_q_idx = 0;
130 for(i=0; q_list[i].den; i++)
131 if (av_nearer_q(q, q_list[i], q_list[nearest_q_idx]) > 0)
132 nearest_q_idx = i;
133
134 return nearest_q_idx;
135 }
136
137 #ifdef TEST
138 int main(void)
139 {
140 AVRational a,b;
141 for(a.num=-2; a.num<=2; a.num++){
142 for(a.den=-2; a.den<=2; a.den++){
143 for(b.num=-2; b.num<=2; b.num++){
144 for(b.den=-2; b.den<=2; b.den++){
145 int c= av_cmp_q(a,b);
146 double d= av_q2d(a) == av_q2d(b) ? 0 : (av_q2d(a) - av_q2d(b));
147 if(d>0) d=1;
148 else if(d<0) d=-1;
149 else if(d != d) d= INT_MIN;
150 if(c!=d) av_log(0, AV_LOG_ERROR, "%d/%d %d/%d, %d %f\n", a.num, a.den, b.num, b.den, c,d);
151 }
152 }
153 }
154 }
155 return 0;
156 }
157 #endif