/*

  * Copyright (c) 2005-2012 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

  * miscellaneous math routines and tables

  */
 

 #include <stdint.h>
 #include <limits.h>

 #include "mathematics.h"

 #include "libavutil/intmath.h"

 #include "libavutil/common.h"

 #include "avassert.h"

 #include "version.h"

 /* Stein's binary GCD algorithm:
  * https://en.wikipedia.org/wiki/Binary_GCD_algorithm */
 int64_t av_gcd(int64_t a, int64_t b) {
     int za, zb, k;
     int64_t u, v;
     if (a == 0)
         return b;
     if (b == 0)

         return a;

     za = ff_ctzll(a);
     zb = ff_ctzll(b);
     k  = FFMIN(za, zb);
     u = llabs(a >> za);
     v = llabs(b >> zb);
     while (u != v) {
         if (u > v)
             FFSWAP(int64_t, v, u);
         v -= u;
         v >>= ff_ctzll(v);
     }

     return (uint64_t)u << k;

 }
 

 int64_t av_rescale_rnd(int64_t a, int64_t b, int64_t c, enum AVRounding rnd)
 {
     int64_t r = 0;

     av_assert2(c > 0);
     av_assert2(b >=0);

     av_assert2((unsigned)(rnd&~AV_ROUND_PASS_MINMAX)<=5 && (rnd&~AV_ROUND_PASS_MINMAX)!=4);
 

     if (c <= 0 || b < 0 || !((unsigned)(rnd&~AV_ROUND_PASS_MINMAX)<=5 && (rnd&~AV_ROUND_PASS_MINMAX)!=4))

         return INT64_MIN;

     if (rnd & AV_ROUND_PASS_MINMAX) {
         if (a == INT64_MIN || a == INT64_MAX)
             return a;
         rnd -= AV_ROUND_PASS_MINMAX;
     }

     if (a < 0)

         return -(uint64_t)av_rescale_rnd(-FFMAX(a, -INT64_MAX), b, c, rnd ^ ((rnd >> 1) & 1));

     if (rnd == AV_ROUND_NEAR_INF)
         r = c / 2;
     else if (rnd & 1)
         r = c - 1;

     if (b <= INT_MAX && c <= INT_MAX) {
         if (a <= INT_MAX)
             return (a * b + r) / c;

         else {
             int64_t ad = a / c;
             int64_t a2 = (a % c * b + r) / c;

             if (ad >= INT32_MAX && b && ad > (INT64_MAX - a2) / b)

                 return INT64_MIN;
             return ad * b + a2;
         }

     } else {

 #if 1

         uint64_t a0  = a & 0xFFFFFFFF;
         uint64_t a1  = a >> 32;
         uint64_t b0  = b & 0xFFFFFFFF;
         uint64_t b1  = b >> 32;
         uint64_t t1  = a0 * b1 + a1 * b0;
         uint64_t t1a = t1 << 32;

         int i;
 

         a0  = a0 * b0 + t1a;
         a1  = a1 * b1 + (t1 >> 32) + (a0 < t1a);

         a0 += r;

         a1 += a0 < r;

         for (i = 63; i >= 0; i--) {
             a1 += a1 + ((a0 >> i) & 1);
             t1 += t1;
             if (c <= a1) {

                 a1 -= c;
                 t1++;
             }
         }

         if (t1 > INT64_MAX)
             return INT64_MIN;

         return t1;
     }
 #else
         AVInteger ai;

         ai = av_mul_i(av_int2i(a), av_int2i(b));
         ai = av_add_i(ai, av_int2i(r));

         return av_i2int(av_div_i(ai, av_int2i(c)));
     }
 #endif

 }
 

 int64_t av_rescale(int64_t a, int64_t b, int64_t c)
 {

     return av_rescale_rnd(a, b, c, AV_ROUND_NEAR_INF);
 }
 

 int64_t av_rescale_q_rnd(int64_t a, AVRational bq, AVRational cq,
                          enum AVRounding rnd)
 {

     int64_t b = bq.num * (int64_t)cq.den;
     int64_t c = cq.num * (int64_t)bq.den;

     return av_rescale_rnd(a, b, c, rnd);
 }
 
 int64_t av_rescale_q(int64_t a, AVRational bq, AVRational cq)
 {
     return av_rescale_q_rnd(a, bq, cq, AV_ROUND_NEAR_INF);

 }

 int av_compare_ts(int64_t ts_a, AVRational tb_a, int64_t ts_b, AVRational tb_b)
 {
     int64_t a = tb_a.num * (int64_t)tb_b.den;
     int64_t b = tb_b.num * (int64_t)tb_a.den;

     if ((FFABS(ts_a)|a|FFABS(ts_b)|b) <= INT_MAX)

         return (ts_a*a > ts_b*b) - (ts_a*a < ts_b*b);

     if (av_rescale_rnd(ts_a, a, b, AV_ROUND_DOWN) < ts_b)
         return -1;
     if (av_rescale_rnd(ts_b, b, a, AV_ROUND_DOWN) < ts_a)
         return 1;

     return 0;
 }
 

 int64_t av_compare_mod(uint64_t a, uint64_t b, uint64_t mod)
 {
     int64_t c = (a - b) & (mod - 1);
     if (c > (mod >> 1))
         c -= mod;

     return c;
 }

 
 int64_t av_rescale_delta(AVRational in_tb, int64_t in_ts,  AVRational fs_tb, int duration, int64_t *last, AVRational out_tb){
     int64_t a, b, this;
 
     av_assert0(in_ts != AV_NOPTS_VALUE);
     av_assert0(duration >= 0);
 
     if (*last == AV_NOPTS_VALUE || !duration || in_tb.num*(int64_t)out_tb.den <= out_tb.num*(int64_t)in_tb.den) {
 simple_round:
         *last = av_rescale_q(in_ts, in_tb, fs_tb) + duration;
         return av_rescale_q(in_ts, in_tb, out_tb);
     }
 
     a =  av_rescale_q_rnd(2*in_ts-1, in_tb, fs_tb, AV_ROUND_DOWN)   >>1;
     b = (av_rescale_q_rnd(2*in_ts+1, in_tb, fs_tb, AV_ROUND_UP  )+1)>>1;
     if (*last < 2*a - b || *last > 2*b - a)
         goto simple_round;
 
     this = av_clip64(*last, a, b);
     *last = this + duration;
 
     return av_rescale_q(this, fs_tb, out_tb);
 }

 
 int64_t av_add_stable(AVRational ts_tb, int64_t ts, AVRational inc_tb, int64_t inc)
 {

     int64_t m, d;
 

     if (inc != 1)
         inc_tb = av_mul_q(inc_tb, (AVRational) {inc, 1});

     m = inc_tb.num * (int64_t)ts_tb.den;
     d = inc_tb.den * (int64_t)ts_tb.num;
 
     if (m % d == 0)
         return ts + m / d;

     if (m < d)

         return ts;

 
     {

         int64_t old = av_rescale_q(ts, ts_tb, inc_tb);
         int64_t old_ts = av_rescale_q(old, inc_tb, ts_tb);
         return av_rescale_q(old + 1, inc_tb, ts_tb) + (ts - old_ts);

     }
 }