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 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
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 int exponent;
110 int64_t den;
111 if (isnan(d))
112 return (AVRational) { 0,0 };
113 if (fabs(d) > INT_MAX + 3LL)
114 return (AVRational) { d < 0 ? -1 : 1, 0 };
115 frexp(d, &exponent);
116 exponent = FFMAX(exponent-1, 0);
117 den = 1LL << (61 - exponent);
118 // (int64_t)rint() and llrint() do not work with gcc on ia64 and sparc64,
119 // see Ticket2713 for affected gcc/glibc versions
120 av_reduce(&a.num, &a.den, floor(d * den + 0.5), den, max);
121 if ((!a.num || !a.den) && d && max>0 && max<INT_MAX)
122 av_reduce(&a.num, &a.den, floor(d * den + 0.5), den, INT_MAX);
123
124 return a;
125 }
126
av_nearer_q(AVRational q,AVRational q1,AVRational q2)127 int av_nearer_q(AVRational q, AVRational q1, AVRational q2)
128 {
129 /* n/d is q, a/b is the median between q1 and q2 */
130 int64_t a = q1.num * (int64_t)q2.den + q2.num * (int64_t)q1.den;
131 int64_t b = 2 * (int64_t)q1.den * q2.den;
132
133 /* rnd_up(a*d/b) > n => a*d/b > n */
134 int64_t x_up = av_rescale_rnd(a, q.den, b, AV_ROUND_UP);
135
136 /* rnd_down(a*d/b) < n => a*d/b < n */
137 int64_t x_down = av_rescale_rnd(a, q.den, b, AV_ROUND_DOWN);
138
139 return ((x_up > q.num) - (x_down < q.num)) * av_cmp_q(q2, q1);
140 }
141
av_find_nearest_q_idx(AVRational q,const AVRational * q_list)142 int av_find_nearest_q_idx(AVRational q, const AVRational* q_list)
143 {
144 int i, nearest_q_idx = 0;
145 for (i = 0; q_list[i].den; i++)
146 if (av_nearer_q(q, q_list[i], q_list[nearest_q_idx]) > 0)
147 nearest_q_idx = i;
148
149 return nearest_q_idx;
150 }
151
av_q2intfloat(AVRational q)152 uint32_t av_q2intfloat(AVRational q) {
153 int64_t n;
154 int shift;
155 int sign = 0;
156
157 if (q.den < 0) {
158 q.den *= -1;
159 q.num *= -1;
160 }
161 if (q.num < 0) {
162 q.num *= -1;
163 sign = 1;
164 }
165
166 if (!q.num && !q.den) return 0xFFC00000;
167 if (!q.num) return 0;
168 if (!q.den) return 0x7F800000 | (q.num & 0x80000000);
169
170 shift = 23 + av_log2(q.den) - av_log2(q.num);
171 if (shift >= 0) n = av_rescale(q.num, 1LL<<shift, q.den);
172 else n = av_rescale(q.num, 1, ((int64_t)q.den) << -shift);
173
174 shift -= n >= (1<<24);
175 shift += n < (1<<23);
176
177 if (shift >= 0) n = av_rescale(q.num, 1LL<<shift, q.den);
178 else n = av_rescale(q.num, 1, ((int64_t)q.den) << -shift);
179
180 av_assert1(n < (1<<24));
181 av_assert1(n >= (1<<23));
182
183 return sign<<31 | (150-shift)<<23 | (n - (1<<23));
184 }
185
av_gcd_q(AVRational a,AVRational b,int max_den,AVRational def)186 AVRational av_gcd_q(AVRational a, AVRational b, int max_den, AVRational def)
187 {
188 int64_t gcd, lcm;
189
190 gcd = av_gcd(a.den, b.den);
191 lcm = (a.den / gcd) * b.den;
192 return lcm < max_den ? av_make_q(av_gcd(a.num, b.num), lcm) : def;
193 }
194