/*
- * Rational numbers
+ * rational numbers
* Copyright (c) 2003 Michael Niedermayer <michaelni@gmx.at>
*
- * This library is free software; you can redistribute it and/or
+ * 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 of the License, or (at your option) any later version.
+ * version 2.1 of the License, or (at your option) any later version.
*
- * This library is distributed in the hope that it will be useful,
+ * 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 this library; if not, write to the Free Software
+ * 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.c
- * Rational numbers
+ * @file
+ * rational numbers
* @author Michael Niedermayer <michaelni@gmx.at>
*/
+#include "avassert.h"
//#include <math.h>
#include <limits.h>
#include "mathematics.h"
#include "rational.h"
-int av_reduce(int *dst_nom, int *dst_den, int64_t nom, int64_t den, int64_t max){
+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= (nom<0) ^ (den<0);
- int64_t gcd= ff_gcd(ABS(nom), ABS(den));
+ int sign= (num<0) ^ (den<0);
+ int64_t gcd= av_gcd(FFABS(num), FFABS(den));
- nom = ABS(nom)/gcd;
- den = ABS(den)/gcd;
- if(nom<=max && den<=max){
- a1= (AVRational){nom, den};
+ if(gcd){
+ num = FFABS(num)/gcd;
+ den = FFABS(den)/gcd;
+ }
+ if(num<=max && den<=max){
+ a1= (AVRational){num, den};
den=0;
}
while(den){
- int64_t x = nom / den;
- int64_t next_den= nom - den*x;
+ 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) break;
+ 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};
- nom= den;
+ num= den;
den= next_den;
}
- assert(ff_gcd(a1.num, a1.den) == 1);
+ av_assert2(av_gcd(a1.num, a1.den) <= 1U);
- *dst_nom = sign ? -a1.num : a1.num;
+ *dst_num = sign ? -a1.num : a1.num;
*dst_den = a1.den;
return den==0;
}
-/**
- * returns b*c.
- */
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;
}
-/**
- * returns b/c.
- */
AVRational av_div_q(AVRational b, AVRational c){
return av_mul_q(b, (AVRational){c.den, c.num});
}
-/**
- * returns b+c.
- */
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;
}
-/**
- * returns b-c.
- */
AVRational av_sub_q(AVRational b, AVRational c){
return av_add_q(b, (AVRational){-c.num, c.den});
}
-/**
- * Converts a double precission floating point number to a AVRational.
- * @param max the maximum allowed numerator and denominator
- */
AVRational av_d2q(double d, int max){
AVRational a;
#define LOG2 0.69314718055994530941723212145817656807550013436025
- int exponent= FFMAX( (int)(log(fabs(d) + 1e-20)/LOG2), 0);
- int64_t den= 1LL << (61 - exponent);
+ int exponent;
+ int64_t den;
+ if (isnan(d))
+ return (AVRational){0,0};
+ if (isinf(d))
+ return (AVRational){ d<0 ? -1:1, 0 };
+ exponent = FFMAX( (int)(log(fabs(d) + 1e-20)/LOG2), 0);
+ den = 1LL << (61 - exponent);
av_reduce(&a.num, &a.den, (int64_t)(d * den + 0.5), den, 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
+main(){
+ AVRational a,b;
+ 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(0, AV_LOG_ERROR, "%d/%d %d/%d, %d %f\n", a.num, a.den, b.num, b.den, c,d);
+ }
+ }
+ }
+ }
+}
+#endif