PeerStreamer

/*

 * 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 libavutil/mathematics.c

 * miscellaneous math routines and tables

 */

#include <assert.h>

#include "avutil.h"

#include "common.h"

#include "mathematics.h"

const uint8_t ff_sqrt_tab[256]={

  0, 16, 23, 28, 32, 36, 40, 43, 46, 48, 51, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 77, 79, 80, 82, 84, 85, 87, 88, 90,

 91, 92, 94, 95, 96, 98, 99,100,102,103,104,105,107,108,109,110,111,112,114,115,116,117,118,119,120,121,122,123,124,125,126,127,

128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,144,145,146,147,148,149,150,151,151,152,153,154,155,156,156,

157,158,159,160,160,161,162,163,164,164,165,166,167,168,168,169,170,171,171,172,173,174,174,175,176,176,177,178,179,179,180,181,

182,182,183,184,184,185,186,186,187,188,188,189,190,190,191,192,192,193,194,194,195,196,196,197,198,198,199,200,200,201,202,202,

203,204,204,205,205,206,207,207,208,208,209,210,210,211,212,212,213,213,214,215,215,216,216,217,218,218,219,219,220,220,221,222,

222,223,223,224,224,225,226,226,227,227,228,228,229,230,230,231,231,232,232,233,233,234,235,235,236,236,237,237,238,238,239,239,

240,240,241,242,242,243,243,244,244,245,245,246,246,247,247,248,248,249,249,250,250,251,251,252,252,253,253,254,254,255,255,255

};

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

};

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,

};

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;

    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);

}

#ifdef TEST

#include "integer.h"

#undef printf

int 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);

            }

        }

    }

    return 0;

}

#endif