mathematics.c

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/*
 * 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/common.h"
#include "avassert.h"
#include "version.h"

#if FF_API_AV_REVERSE
const uint8_t av_reverse[256]={
0x00,0x80,0x40,0xC0,0x20,0xA0,0x60,0xE0,0x10,0x90,0x50,0xD0,0x30,0xB0,0x70,0xF0,
0x08,0x88,0x48,0xC8,0x28,0xA8,0x68,0xE8,0x18,0x98,0x58,0xD8,0x38,0xB8,0x78,0xF8,
0x04,0x84,0x44,0xC4,0x24,0xA4,0x64,0xE4,0x14,0x94,0x54,0xD4,0x34,0xB4,0x74,0xF4,
0x0C,0x8C,0x4C,0xCC,0x2C,0xAC,0x6C,0xEC,0x1C,0x9C,0x5C,0xDC,0x3C,0xBC,0x7C,0xFC,
0x02,0x82,0x42,0xC2,0x22,0xA2,0x62,0xE2,0x12,0x92,0x52,0xD2,0x32,0xB2,0x72,0xF2,
0x0A,0x8A,0x4A,0xCA,0x2A,0xAA,0x6A,0xEA,0x1A,0x9A,0x5A,0xDA,0x3A,0xBA,0x7A,0xFA,
0x06,0x86,0x46,0xC6,0x26,0xA6,0x66,0xE6,0x16,0x96,0x56,0xD6,0x36,0xB6,0x76,0xF6,
0x0E,0x8E,0x4E,0xCE,0x2E,0xAE,0x6E,0xEE,0x1E,0x9E,0x5E,0xDE,0x3E,0xBE,0x7E,0xFE,
0x01,0x81,0x41,0xC1,0x21,0xA1,0x61,0xE1,0x11,0x91,0x51,0xD1,0x31,0xB1,0x71,0xF1,
0x09,0x89,0x49,0xC9,0x29,0xA9,0x69,0xE9,0x19,0x99,0x59,0xD9,0x39,0xB9,0x79,0xF9,
0x05,0x85,0x45,0xC5,0x25,0xA5,0x65,0xE5,0x15,0x95,0x55,0xD5,0x35,0xB5,0x75,0xF5,
0x0D,0x8D,0x4D,0xCD,0x2D,0xAD,0x6D,0xED,0x1D,0x9D,0x5D,0xDD,0x3D,0xBD,0x7D,0xFD,
0x03,0x83,0x43,0xC3,0x23,0xA3,0x63,0xE3,0x13,0x93,0x53,0xD3,0x33,0xB3,0x73,0xF3,
0x0B,0x8B,0x4B,0xCB,0x2B,0xAB,0x6B,0xEB,0x1B,0x9B,0x5B,0xDB,0x3B,0xBB,0x7B,0xFB,
0x07,0x87,0x47,0xC7,0x27,0xA7,0x67,0xE7,0x17,0x97,0x57,0xD7,0x37,0xB7,0x77,0xF7,
0x0F,0x8F,0x4F,0xCF,0x2F,0xAF,0x6F,0xEF,0x1F,0x9F,0x5F,0xDF,0x3F,0xBF,0x7F,0xFF,
};
#endif

int64_t av_gcd(int64_t a, int64_t b){
    if(b) return av_gcd(b, a%b);
    else  return a;
}

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

    if(a<0 && a != INT64_MIN) return -av_rescale_rnd(-a, 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
            return a/c*b + (a%c*b + r)/c;
    }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--){
//            int o= a1 & 0x8000000000000000ULL;
            a1+= a1 + ((a0>>i)&1);
            t1+=t1;
            if(/*o || */c <= a1){
                a1 -= c;
                t1++;
            }
        }
        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);
}