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
av_reduce(int * dst_num,int * dst_den,int64_t num,int64_t den,int64_t max)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 }
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
av_mul_q(AVRational b,AVRational c)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
av_div_q(AVRational b,AVRational c)88 AVRational av_div_q(AVRational b, AVRational c)
89 {
90 return av_mul_q(b, (AVRational) { c.den, c.num });
91 }
92
av_add_q(AVRational b,AVRational c)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
av_sub_q(AVRational b,AVRational c)101 AVRational av_sub_q(AVRational b, AVRational c)
102 {
103 return av_add_q(b, (AVRational) { -c.num, c.den });
104 }
105
av_d2q(double d,int max)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 }
115 if (fabs(d) > INT_MAX + LLN(3)) {
116 return (AVRational) { d < 0 ? -1 : 1, 0 };
117 }
118 exponent = FFMAX( (int)(log(fabs(d) + 1e-20)/LOG2), 0);
119 den = LLN(1) << (61 - exponent);
120 // (int64_t)rint() and llrint() do not work with gcc on ia64 and sparc64
121 av_reduce(&a.num, &a.den, floor(d * den + 0.5), den, max);
122 if ((!a.num || !a.den) && d && max>0 && max<INT_MAX)
123 av_reduce(&a.num, &a.den, floor(d * den + 0.5), den, INT_MAX);
124
125 return a;
126 }
127
av_nearer_q(AVRational q,AVRational q1,AVRational q2)128 int av_nearer_q(AVRational q, AVRational q1, AVRational q2)
129 {
130 /* n/d is q, a/b is the median between q1 and q2 */
131 int64_t a = q1.num * (int64_t)q2.den + q2.num * (int64_t)q1.den;
132 int64_t b = 2 * (int64_t)q1.den * q2.den;
133
134 /* rnd_up(a*d/b) > n => a*d/b > n */
135 int64_t x_up = av_rescale_rnd(a, q.den, b, AV_ROUND_UP);
136
137 /* rnd_down(a*d/b) < n => a*d/b < n */
138 int64_t x_down = av_rescale_rnd(a, q.den, b, AV_ROUND_DOWN);
139
140 return ((x_up > q.num) - (x_down < q.num)) * av_cmp_q(q2, q1);
141 }
142
av_find_nearest_q_idx(AVRational q,const AVRational * q_list)143 int av_find_nearest_q_idx(AVRational q, const AVRational* q_list)
144 {
145 int i, nearest_q_idx = 0;
146 for (i = 0; q_list[i].den; i++)
147 if (av_nearer_q(q, q_list[i], q_list[nearest_q_idx]) > 0)
148 nearest_q_idx = i;
149
150 return nearest_q_idx;
151 }
152
153 #ifdef TEST
main(void)154 int main(void)
155 {
156 AVRational a,b,r;
157 for (a.num = -2; a.num <= 2; a.num++) {
158 for (a.den = -2; a.den <= 2; a.den++) {
159 for (b.num = -2; b.num <= 2; b.num++) {
160 for (b.den = -2; b.den <= 2; b.den++) {
161 int c = av_cmp_q(a,b);
162 double d = av_q2d(a) == av_q2d(b) ?
163 0 : (av_q2d(a) - av_q2d(b));
164 if (d > 0) d = 1;
165 else if (d < 0) d = -1;
166 else if (d != d) d = INT_MIN;
167 if (c != d)
168 av_log(NULL, AV_LOG_ERROR, "%d/%d %d/%d, %d %f\n", a.num,
169 a.den, b.num, b.den, c,d);
170 r = av_sub_q(av_add_q(b,a), b);
171 if(b.den && (r.num*a.den != a.num*r.den || !r.num != !a.num || !r.den != !a.den))
172 av_log(NULL, AV_LOG_ERROR, "%d/%d ", r.num, r.den);
173 }
174 }
175 }
176 }
177
178 for (a.num = 1; a.num <= 10; a.num++) {
179 for (a.den = 1; a.den <= 10; a.den++) {
180 if (av_gcd(a.num, a.den) > 1)
181 continue;
182 for (b.num = 1; b.num <= 10; b.num++) {
183 for (b.den = 1; b.den <= 10; b.den++) {
184 int start;
185 if (av_gcd(b.num, b.den) > 1)
186 continue;
187 if (av_cmp_q(b, a) < 0)
188 continue;
189 for (start = 0; start < 10 ; start++) {
190 int acc= start;
191 int i;
192
193 for (i = 0; i<100; i++) {
194 int exact = start + av_rescale_q(i+1, b, a);
195 acc = av_add_stable(a, acc, b, 1);
196 if (FFABS(acc - exact) > 2) {
197 av_log(NULL, AV_LOG_ERROR, "%d/%d %d/%d, %d %d\n", a.num,
198 a.den, b.num, b.den, acc, exact);
199 return 1;
200 }
201 }
202 }
203 }
204 }
205 }
206 }
207 return 0;
208 }
209 #endif
210