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 <assert.h>
29//#include <math.h>
30#include <limits.h>
31
32#include "common.h"
33#include "mathematics.h"
34#include "rational.h"
35
36int 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    assert(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
78AVRational 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
83AVRational av_div_q(AVRational b, AVRational c){
84    return av_mul_q(b, (AVRational){c.den, c.num});
85}
86
87AVRational 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
92AVRational av_sub_q(AVRational b, AVRational c){
93    return av_add_q(b, (AVRational){-c.num, c.den});
94}
95
96AVRational av_d2q(double d, int max){
97    AVRational a;
98#define LOG2  0.69314718055994530941723212145817656807550013436025
99    int exponent= FFMAX( (int)(log(fabs(d) + 1e-20)/LOG2), 0);
100    int64_t den= 1LL << (61 - exponent);
101    if (isnan(d))
102        return (AVRational){0,0};
103    av_reduce(&a.num, &a.den, (int64_t)(d * den + 0.5), den, max);
104
105    return a;
106}
107
108int av_nearer_q(AVRational q, AVRational q1, AVRational q2)
109{
110    /* n/d is q, a/b is the median between q1 and q2 */
111    int64_t a = q1.num * (int64_t)q2.den + q2.num * (int64_t)q1.den;
112    int64_t b = 2 * (int64_t)q1.den * q2.den;
113
114    /* rnd_up(a*d/b) > n => a*d/b > n */
115    int64_t x_up = av_rescale_rnd(a, q.den, b, AV_ROUND_UP);
116
117    /* rnd_down(a*d/b) < n => a*d/b < n */
118    int64_t x_down = av_rescale_rnd(a, q.den, b, AV_ROUND_DOWN);
119
120    return ((x_up > q.num) - (x_down < q.num)) * av_cmp_q(q2, q1);
121}
122
123int av_find_nearest_q_idx(AVRational q, const AVRational* q_list)
124{
125    int i, nearest_q_idx = 0;
126    for(i=0; q_list[i].den; i++)
127        if (av_nearer_q(q, q_list[i], q_list[nearest_q_idx]) > 0)
128            nearest_q_idx = i;
129
130    return nearest_q_idx;
131}
132