/*

  * 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));
 }