PeerStreamer

/*

 * arbitrary precision integers

 * Copyright (c) 2004 Michael Niedermayer <michaelni@gmx.at>

 *

 * This library 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 of the License, or (at your option) any later version.

 *

 * This library 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 this library; if not, write to the Free Software

 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA

 *

 */

/**

 * @file integer.c

 * arbitrary precision integers.

 * @author Michael Niedermayer <michaelni@gmx.at>

 */

#include "common.h"

#include "integer.h"

AVInteger av_add_i(AVInteger a, AVInteger b){

    int i, carry=0;

    for(i=0; i<AV_INTEGER_SIZE; i++){

        carry= (carry>>16) + a.v[i] + b.v[i];

        a.v[i]= carry;

    }

    return a;

}

AVInteger av_sub_i(AVInteger a, AVInteger b){

    int i, carry=0;

    for(i=0; i<AV_INTEGER_SIZE; i++){

        carry= (carry>>16) + a.v[i] - b.v[i];

        a.v[i]= carry;

    }

    return a;

}

/**

 * returns the rounded down value of the logarithm of base 2 of the given AVInteger.

 * this is simply the index of the most significant bit which is 1. Or 0 of all bits are 0

 */

int av_log2_i(AVInteger a){

    int i;

    for(i=AV_INTEGER_SIZE-1; i>=0; i--){

        if(a.v[i])

            return av_log2_16bit(a.v[i]) + 16*i;

    }

    return -1;

}

AVInteger av_mul_i(AVInteger a, AVInteger b){

    AVInteger out;

    int i, j;

    int na= (av_log2_i(a)+16) >> 4;

    int nb= (av_log2_i(b)+16) >> 4;

    memset(&out, 0, sizeof(out));

    for(i=0; i<na; i++){

        unsigned int carry=0;

        if(a.v[i])

            for(j=i; j<AV_INTEGER_SIZE && j-i<=nb; j++){

                carry= (carry>>16) + out.v[j] + a.v[i]*b.v[j-i];

                out.v[j]= carry;

            }

    }

    return out;

}

/**

 * returns 0 if a==b, 1 if a>b and -1 if a<b.

 */

int av_cmp_i(AVInteger a, AVInteger b){

    int i;

    int v= (int16_t)a.v[AV_INTEGER_SIZE-1] - (int16_t)b.v[AV_INTEGER_SIZE-1];

    if(v) return (v>>16)|1;

    for(i=AV_INTEGER_SIZE-2; i>=0; i--){

        int v= a.v[i] - b.v[i];

        if(v) return (v>>16)|1;

    }

    return 0;

}

/**

 * bitwise shift.

 * @param s the number of bits by which the value should be shifted right, may be negative for shifting left

 */

AVInteger av_shr_i(AVInteger a, int s){

    AVInteger out;

    int i;

    for(i=0; i<AV_INTEGER_SIZE; i++){

        int index= i + (s>>4);

        unsigned int v=0;

        if(index+1<AV_INTEGER_SIZE && index+1>=0) v = a.v[index+1]<<16;

        if(index  <AV_INTEGER_SIZE && index  >=0) v+= a.v[index  ];

        out.v[i]= v >> (s&15);

    }

    return out;

}

/**

 * returns a % b.

 * @param quot a/b will be stored here

 */

AVInteger av_mod_i(AVInteger *quot, AVInteger a, AVInteger b){

    int i= av_log2_i(a) - av_log2_i(b);

    AVInteger quot_temp;

    if(!quot) quot = &quot_temp;

    assert((int16_t)a[AV_INTEGER_SIZE-1] >= 0 && (int16_t)b[AV_INTEGER_SIZE-1] >= 0);

    assert(av_log2(b)>=0);

    if(i > 0)

        b= av_shr_i(b, -i);

    memset(quot, 0, sizeof(AVInteger));

    while(i-- >= 0){

        *quot= av_shr_i(*quot, -1);

        if(av_cmp_i(a, b) >= 0){

            a= av_sub_i(a, b);

            quot->v[0] += 1;

        }

        b= av_shr_i(b, 1);

    }

    return a;

}

/**

 * returns a/b.

 */

AVInteger av_div_i(AVInteger a, AVInteger b){

    AVInteger quot;

    av_mod_i(&quot, a, b);

    return quot;

}

/**

 * converts the given int64_t to an AVInteger.

 */

AVInteger av_int2i(int64_t a){

    AVInteger out;

    int i;

    for(i=0; i<AV_INTEGER_SIZE; i++){

        out.v[i]= a;

        a>>=16;

    }

    return out;

}

/**

 * converts the given AVInteger to an int64_t.

 * if the AVInteger is too large to fit into an int64_t,

 * then only the least significant 64bit will be used

 */

int64_t av_i2int(AVInteger a){

    int i;

    int64_t out=(int8_t)a.v[AV_INTEGER_SIZE-1];

    for(i= AV_INTEGER_SIZE-2; i>=0; i--){

        out = (out<<16) + a.v[i];

    }

    return out;

}

#if 0

#undef NDEBUG

#include <assert.h>

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

};

main(){

    int64_t a,b;

    for(a=7; a<256*256*256; a+=13215){

        for(b=3; b<256*256*256; b+=27118){

            AVInteger ai= av_int2i(a);

            AVInteger bi= av_int2i(b);

            assert(av_i2int(ai) == a);

            assert(av_i2int(bi) == b);

            assert(av_i2int(av_add_i(ai,bi)) == a+b);

            assert(av_i2int(av_sub_i(ai,bi)) == a-b);

            assert(av_i2int(av_mul_i(ai,bi)) == a*b);

            assert(av_i2int(av_shr_i(ai, 9)) == a>>9);

            assert(av_i2int(av_shr_i(ai,-9)) == a<<9);

            assert(av_i2int(av_shr_i(ai, 17)) == a>>17);

            assert(av_i2int(av_shr_i(ai,-17)) == a<<17);

            assert(av_log2_i(ai) == av_log2(a));

            assert(av_i2int(av_div_i(ai,bi)) == a/b);

        }

    }

}

#endif