mathematics.c

/*
 * Copyright (c) 2005 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 mathematics.c
 * Miscellaneous math routines and tables.
 */

#include "common.h"
#include "mathematics.h"

const uint8_t ff_sqrt_tab[128]={
        0, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5,
        5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
        8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
        9, 9, 9, 9,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11
};

const uint8_t ff_log2_tab[256]={
        0,0,1,1,2,2,2,2,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,
        5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,
        6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,
        6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,
        7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,
        7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,
        7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,
        7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7
};

int64_t ff_gcd(int64_t a, int64_t b){
    if(b) return ff_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;
    assert(c > 0);
    assert(b >=0);
    assert(rnd >=0 && rnd<=5 && rnd!=4);

    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(int64_t a, AVRational bq, AVRational cq){
    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, AV_ROUND_NEAR_INF);
}
#if 0
#include "integer.h"
#undef printf
main(void){
    int64_t a,b,c,d,e;

    for(a=7; a<(1LL<<62); a+=a/3+1){
        for(b=3; b<(1LL<<62); b+=b/4+1){
            for(c=9; c<(1LL<<62); c+=(c*2)/5+3){
                int64_t r= c/2;
                AVInteger ai;
                ai= av_mul_i(av_int2i(a), av_int2i(b));
                ai= av_add_i(ai, av_int2i(r));

                d= av_i2int(av_div_i(ai, av_int2i(c)));

                e= av_rescale(a,b,c);

                if((double)a * (double)b / (double)c > (1LL<<63))
                    continue;

                if(d!=e) printf("%"PRId64"*%"PRId64"/%"PRId64"= %"PRId64"=%"PRId64"\n", a, b, c, d, e);
            }
        }
    }
}
#endif