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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 <limits.h> | |
30 | ||
31 | #include "common.h" | |
32 | #include "mathematics.h" | |
33 | #include "rational.h" | |
34 | ||
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 | ||
73 | *dst_num = sign ? -a1.num : a1.num; | |
74 | *dst_den = a1.den; | |
75 | ||
76 | return den == 0; | |
77 | } | |
78 | ||
79 | AVRational av_mul_q(AVRational b, AVRational c) | |
80 | { | |
81 | av_reduce(&b.num, &b.den, | |
82 | b.num * (int64_t) c.num, | |
83 | b.den * (int64_t) c.den, INT_MAX); | |
84 | return b; | |
85 | } | |
86 | ||
87 | AVRational av_div_q(AVRational b, AVRational c) | |
88 | { | |
89 | return av_mul_q(b, (AVRational) { c.den, c.num }); | |
90 | } | |
91 | ||
92 | AVRational av_add_q(AVRational b, AVRational c) { | |
93 | av_reduce(&b.num, &b.den, | |
94 | b.num * (int64_t) c.den + | |
95 | c.num * (int64_t) b.den, | |
96 | b.den * (int64_t) c.den, INT_MAX); | |
97 | return b; | |
98 | } | |
99 | ||
100 | AVRational av_sub_q(AVRational b, AVRational c) | |
101 | { | |
102 | return av_add_q(b, (AVRational) { -c.num, c.den }); | |
103 | } | |
104 | ||
105 | AVRational av_d2q(double d, int max) | |
106 | { | |
107 | AVRational a; | |
108 | #define LOG2 0.69314718055994530941723212145817656807550013436025 | |
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 | exponent = FFMAX( (int)(log(fabs(d) + 1e-20)/LOG2), 0); | |
116 | den = 1LL << (61 - exponent); | |
117 | // (int64_t)rint() and llrint() do not work with gcc on ia64 and sparc64 | |
118 | av_reduce(&a.num, &a.den, floor(d * den + 0.5), den, max); | |
119 | if ((!a.num || !a.den) && d && max>0 && max<INT_MAX) | |
120 | av_reduce(&a.num, &a.den, floor(d * den + 0.5), den, INT_MAX); | |
121 | ||
122 | return a; | |
123 | } | |
124 | ||
125 | int av_nearer_q(AVRational q, AVRational q1, AVRational q2) | |
126 | { | |
127 | /* n/d is q, a/b is the median between q1 and q2 */ | |
128 | int64_t a = q1.num * (int64_t)q2.den + q2.num * (int64_t)q1.den; | |
129 | int64_t b = 2 * (int64_t)q1.den * q2.den; | |
130 | ||
131 | /* rnd_up(a*d/b) > n => a*d/b > n */ | |
132 | int64_t x_up = av_rescale_rnd(a, q.den, b, AV_ROUND_UP); | |
133 | ||
134 | /* rnd_down(a*d/b) < n => a*d/b < n */ | |
135 | int64_t x_down = av_rescale_rnd(a, q.den, b, AV_ROUND_DOWN); | |
136 | ||
137 | return ((x_up > q.num) - (x_down < q.num)) * av_cmp_q(q2, q1); | |
138 | } | |
139 | ||
140 | int av_find_nearest_q_idx(AVRational q, const AVRational* q_list) | |
141 | { | |
142 | int i, nearest_q_idx = 0; | |
143 | for (i = 0; q_list[i].den; i++) | |
144 | if (av_nearer_q(q, q_list[i], q_list[nearest_q_idx]) > 0) | |
145 | nearest_q_idx = i; | |
146 | ||
147 | return nearest_q_idx; | |
148 | } | |
149 | ||
150 | #ifdef TEST | |
151 | int main(void) | |
152 | { | |
153 | AVRational a,b,r; | |
154 | for (a.num = -2; a.num <= 2; a.num++) { | |
155 | for (a.den = -2; a.den <= 2; a.den++) { | |
156 | for (b.num = -2; b.num <= 2; b.num++) { | |
157 | for (b.den = -2; b.den <= 2; b.den++) { | |
158 | int c = av_cmp_q(a,b); | |
159 | double d = av_q2d(a) == av_q2d(b) ? | |
160 | 0 : (av_q2d(a) - av_q2d(b)); | |
161 | if (d > 0) d = 1; | |
162 | else if (d < 0) d = -1; | |
163 | else if (d != d) d = INT_MIN; | |
164 | if (c != d) | |
165 | av_log(NULL, AV_LOG_ERROR, "%d/%d %d/%d, %d %f\n", a.num, | |
166 | a.den, b.num, b.den, c,d); | |
167 | r = av_sub_q(av_add_q(b,a), b); | |
168 | if(b.den && (r.num*a.den != a.num*r.den || !r.num != !a.num || !r.den != !a.den)) | |
169 | av_log(NULL, AV_LOG_ERROR, "%d/%d ", r.num, r.den); | |
170 | } | |
171 | } | |
172 | } | |
173 | } | |
174 | ||
175 | for (a.num = 1; a.num <= 10; a.num++) { | |
176 | for (a.den = 1; a.den <= 10; a.den++) { | |
177 | if (av_gcd(a.num, a.den) > 1) | |
178 | continue; | |
179 | for (b.num = 1; b.num <= 10; b.num++) { | |
180 | for (b.den = 1; b.den <= 10; b.den++) { | |
181 | int start; | |
182 | if (av_gcd(b.num, b.den) > 1) | |
183 | continue; | |
184 | if (av_cmp_q(b, a) < 0) | |
185 | continue; | |
186 | for (start = 0; start < 10 ; start++) { | |
187 | int acc= start; | |
188 | int i; | |
189 | ||
190 | for (i = 0; i<100; i++) { | |
191 | int exact = start + av_rescale_q(i+1, b, a); | |
192 | acc = av_add_stable(a, acc, b, 1); | |
193 | if (FFABS(acc - exact) > 2) { | |
194 | av_log(NULL, AV_LOG_ERROR, "%d/%d %d/%d, %d %d\n", a.num, | |
195 | a.den, b.num, b.den, acc, exact); | |
196 | return 1; | |
197 | } | |
198 | } | |
199 | } | |
200 | } | |
201 | } | |
202 | } | |
203 | } | |
204 | return 0; | |
205 | } | |
206 | #endif |