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rational.c (5332B)

---

/*
* 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 << (62 - 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);

   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));
}

AVRational av_gcd_q(AVRational a, AVRational b, int max_den, AVRational def)
{
   int64_t gcd, lcm;

   gcd = av_gcd(a.den, b.den);
   lcm = (a.den / gcd) * b.den;
   return lcm < max_den ? av_make_q(av_gcd(a.num, b.num), lcm) : def;
}