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third_party_ffmpeg/libavutil/rational.c
Ganesh Ajjanagadde 7dabc78ce1 lavu/rational: add more info regarding floor(x+0.5) usage 
Add some more verbose info regarding why the imprecise and slow floor(x+0.5) hack
is used; helpful for future maintenance.

Reviewed-by: Michael Niedermayer <michael@niedermayer.cc>
Signed-off-by: Ganesh Ajjanagadde <gajjanag@gmail.com>
2016-02-29 19:26:55 -05:00

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/*
* 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);
av_assert2(a1.num <= max && a1.den <= max);
*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;
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 };
frexp(d, &exponent);
exponent = FFMAX(exponent-1, 0);
den = 1LL << (61 - exponent);
// (int64_t)rint() and llrint() do not work with gcc on ia64 and sparc64,
// see Ticket2713 for affected gcc/glibc versions
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;
}
uint32_t av_q2intfloat(AVRational q) {
int64_t n;
int shift;
int sign = 0;
if (q.den < 0) {
q.den *= -1;
q.num *= -1;
}
if (q.num < 0) {
q.num *= -1;
sign = 1;
}
if (!q.num && !q.den) return 0xFFC00000;
if (!q.num) return 0;
if (!q.den) return 0x7F800000 | (q.num & 0x80000000);
shift = 23 + av_log2(q.den) - av_log2(q.num);
if (shift >= 0) n = av_rescale(q.num, 1LL<<shift, q.den);
else n = av_rescale(q.num, 1, ((int64_t)q.den) << -shift);
shift -= n >= (1<<24);
shift += n < (1<<23);
if (shift >= 0) n = av_rescale(q.num, 1LL<<shift, q.den);
else n = av_rescale(q.num, 1, ((int64_t)q.den) << -shift);
av_assert1(n < (1<<24));
av_assert1(n >= (1<<23));
return sign<<31 | (150-shift)<<23 | (n - (1<<23));
}
#ifdef TEST
#include "integer.h"
int main(void)
{
AVRational a,b,r;
int i,j,k;
static const int64_t numlist[] = {
INT64_MIN, INT64_MIN+1, INT64_MAX, INT32_MIN, INT32_MAX, 1,0,-1,
123456789, INT32_MAX-1, INT32_MAX+1LL, UINT32_MAX-1, UINT32_MAX, UINT32_MAX+1LL
};
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);
}
}
}
}
for (i = 0; i < FF_ARRAY_ELEMS(numlist); i++) {
int64_t a = numlist[i];
for (j = 0; j < FF_ARRAY_ELEMS(numlist); j++) {
int64_t b = numlist[j];
if (b<=0)
continue;
for (k = 0; k < FF_ARRAY_ELEMS(numlist); k++) {
int64_t c = numlist[k];
int64_t res;
AVInteger ai;
if (c<=0)
continue;
res = av_rescale_rnd(a,b,c, AV_ROUND_ZERO);
ai = av_mul_i(av_int2i(a), av_int2i(b));
ai = av_div_i(ai, av_int2i(c));
if (av_cmp_i(ai, av_int2i(INT64_MAX)) > 0 && res == INT64_MIN)
continue;
if (av_cmp_i(ai, av_int2i(INT64_MIN)) < 0 && res == INT64_MIN)
continue;
if (av_cmp_i(ai, av_int2i(res)) == 0)
continue;
// Special exception for INT64_MIN, remove this in case INT64_MIN is handled without off by 1 error
if (av_cmp_i(ai, av_int2i(res-1)) == 0 && a == INT64_MIN)
continue;
av_log(NULL, AV_LOG_ERROR, "%"PRId64" * %"PRId64" / %"PRId64" = %"PRId64" or %"PRId64"\n", a,b,c, res, av_i2int(ai));
}
}
}
for (a.num = 1; a.num <= 10; a.num++) {
for (a.den = 1; a.den <= 10; a.den++) {
if (av_gcd(a.num, a.den) > 1)
continue;
for (b.num = 1; b.num <= 10; b.num++) {
for (b.den = 1; b.den <= 10; b.den++) {
int start;
if (av_gcd(b.num, b.den) > 1)
continue;
if (av_cmp_q(b, a) < 0)
continue;
for (start = 0; start < 10 ; start++) {
int acc= start;
int i;
for (i = 0; i<100; i++) {
int exact = start + av_rescale_q(i+1, b, a);
acc = av_add_stable(a, acc, b, 1);
if (FFABS(acc - exact) > 2) {
av_log(NULL, AV_LOG_ERROR, "%d/%d %d/%d, %d %d\n", a.num,
a.den, b.num, b.den, acc, exact);
return 1;
}
}
}
}
}
}
}
for (a.den = 1; a.den < 0x100000000U/3; a.den*=3) {
for (a.num = -1; a.num < (1<<27); a.num += 1 + a.num/100) {
float f = av_int2float(av_q2intfloat(a));
float f2 = av_q2d(a);
if (fabs(f - f2) > fabs(f)/5000000) {
av_log(NULL, AV_LOG_ERROR, "%d/%d %f %f\n", a.num,
a.den, f, f2);
return 1;
}
}
}
return 0;
}
#endif
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