0,0 → 1,176 |
/* |
* rational numbers |
* Copyright (c) 2003 Michael Niedermayer <michaelni@gmx.at> |
* |
* This file is part of FFmpeg. |
* |
* FFmpeg is free software; you can redistribute it and/or |
* modify it under the terms of the GNU Lesser General Public |
* License as published by the Free Software Foundation; either |
* version 2.1 of the License, or (at your option) any later version. |
* |
* FFmpeg is distributed in the hope that it will be useful, |
* but WITHOUT ANY WARRANTY; without even the implied warranty of |
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
* Lesser General Public License for more details. |
* |
* You should have received a copy of the GNU Lesser General Public |
* License along with FFmpeg; if not, write to the Free Software |
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA |
*/ |
|
/** |
* @file |
* rational numbers |
* @author Michael Niedermayer <michaelni@gmx.at> |
*/ |
|
#include "avassert.h" |
#include <limits.h> |
|
#include "common.h" |
#include "mathematics.h" |
#include "rational.h" |
|
int av_reduce(int *dst_num, int *dst_den, |
int64_t num, int64_t den, int64_t max) |
{ |
AVRational a0 = { 0, 1 }, a1 = { 1, 0 }; |
int sign = (num < 0) ^ (den < 0); |
int64_t gcd = av_gcd(FFABS(num), FFABS(den)); |
|
if (gcd) { |
num = FFABS(num) / gcd; |
den = FFABS(den) / gcd; |
} |
if (num <= max && den <= max) { |
a1 = (AVRational) { num, den }; |
den = 0; |
} |
|
while (den) { |
uint64_t x = num / den; |
int64_t next_den = num - den * x; |
int64_t a2n = x * a1.num + a0.num; |
int64_t a2d = x * a1.den + a0.den; |
|
if (a2n > max || a2d > max) { |
if (a1.num) x = (max - a0.num) / a1.num; |
if (a1.den) x = FFMIN(x, (max - a0.den) / a1.den); |
|
if (den * (2 * x * a1.den + a0.den) > num * a1.den) |
a1 = (AVRational) { x * a1.num + a0.num, x * a1.den + a0.den }; |
break; |
} |
|
a0 = a1; |
a1 = (AVRational) { a2n, a2d }; |
num = den; |
den = next_den; |
} |
av_assert2(av_gcd(a1.num, a1.den) <= 1U); |
|
*dst_num = sign ? -a1.num : a1.num; |
*dst_den = a1.den; |
|
return den == 0; |
} |
|
AVRational av_mul_q(AVRational b, AVRational c) |
{ |
av_reduce(&b.num, &b.den, |
b.num * (int64_t) c.num, |
b.den * (int64_t) c.den, INT_MAX); |
return b; |
} |
|
AVRational av_div_q(AVRational b, AVRational c) |
{ |
return av_mul_q(b, (AVRational) { c.den, c.num }); |
} |
|
AVRational av_add_q(AVRational b, AVRational c) { |
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); |
return b; |
} |
|
AVRational av_sub_q(AVRational b, AVRational c) |
{ |
return av_add_q(b, (AVRational) { -c.num, c.den }); |
} |
|
AVRational av_d2q(double d, int max) |
{ |
AVRational a; |
#define LOG2 0.69314718055994530941723212145817656807550013436025 |
int exponent; |
int64_t den; |
if (isnan(d)) |
return (AVRational) { 0,0 }; |
if (fabs(d) > INT_MAX + 3LL) |
return (AVRational) { d < 0 ? -1 : 1, 0 }; |
exponent = FFMAX( (int)(log(fabs(d) + 1e-20)/LOG2), 0); |
den = 1LL << (61 - exponent); |
// (int64_t)rint() and llrint() do not work with gcc on ia64 and sparc64 |
av_reduce(&a.num, &a.den, floor(d * den + 0.5), den, max); |
if ((!a.num || !a.den) && d && max>0 && max<INT_MAX) |
av_reduce(&a.num, &a.den, floor(d * den + 0.5), den, INT_MAX); |
|
return a; |
} |
|
int av_nearer_q(AVRational q, AVRational q1, AVRational q2) |
{ |
/* n/d is q, a/b is the median between q1 and q2 */ |
int64_t a = q1.num * (int64_t)q2.den + q2.num * (int64_t)q1.den; |
int64_t b = 2 * (int64_t)q1.den * q2.den; |
|
/* rnd_up(a*d/b) > n => a*d/b > n */ |
int64_t x_up = av_rescale_rnd(a, q.den, b, AV_ROUND_UP); |
|
/* rnd_down(a*d/b) < n => a*d/b < n */ |
int64_t x_down = av_rescale_rnd(a, q.den, b, AV_ROUND_DOWN); |
|
return ((x_up > q.num) - (x_down < q.num)) * av_cmp_q(q2, q1); |
} |
|
int av_find_nearest_q_idx(AVRational q, const AVRational* q_list) |
{ |
int i, nearest_q_idx = 0; |
for (i = 0; q_list[i].den; i++) |
if (av_nearer_q(q, q_list[i], q_list[nearest_q_idx]) > 0) |
nearest_q_idx = i; |
|
return nearest_q_idx; |
} |
|
#ifdef TEST |
int main(void) |
{ |
AVRational a,b,r; |
for (a.num = -2; a.num <= 2; a.num++) { |
for (a.den = -2; a.den <= 2; a.den++) { |
for (b.num = -2; b.num <= 2; b.num++) { |
for (b.den = -2; b.den <= 2; b.den++) { |
int c = av_cmp_q(a,b); |
double d = av_q2d(a) == av_q2d(b) ? |
0 : (av_q2d(a) - av_q2d(b)); |
if (d > 0) d = 1; |
else if (d < 0) d = -1; |
else if (d != d) d = INT_MIN; |
if (c != d) |
av_log(NULL, AV_LOG_ERROR, "%d/%d %d/%d, %d %f\n", a.num, |
a.den, b.num, b.den, c,d); |
r = av_sub_q(av_add_q(b,a), b); |
if(b.den && (r.num*a.den != a.num*r.den || !r.num != !a.num || !r.den != !a.den)) |
av_log(NULL, AV_LOG_ERROR, "%d/%d ", r.num, r.den); |
} |
} |
} |
} |
return 0; |
} |
#endif |