/*

  * 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 <math.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 (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

 int main(void)
 {

     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);

                 }
             }
         }
     }

     return 0;

 }
 #endif