| 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 |