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1 29adde83 Michael Niedermayer
/*
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 * arbitrary precision integers
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 * Copyright (c) 2004 Michael Niedermayer <michaelni@gmx.at>
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 *
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 * This library is free software; you can redistribute it and/or
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 * modify it under the terms of the GNU Lesser General Public
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 * License as published by the Free Software Foundation; either
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 * version 2 of the License, or (at your option) any later version.
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 *
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 * This library is distributed in the hope that it will be useful,
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 * but WITHOUT ANY WARRANTY; without even the implied warranty of
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 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
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 * Lesser General Public License for more details.
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 *
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 * You should have received a copy of the GNU Lesser General Public
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 * License along with this library; if not, write to the Free Software
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 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
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 *
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 */
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/**
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 * @file integer.c
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 * arbitrary precision integers.
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 * @author Michael Niedermayer <michaelni@gmx.at>
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 */
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#include "common.h"
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#include "integer.h"
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AVInteger av_add_i(AVInteger a, AVInteger b){
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    int i, carry=0;
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    for(i=0; i<AV_INTEGER_SIZE; i++){
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        carry= (carry>>16) + a.v[i] + b.v[i];
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        a.v[i]= carry;
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    }
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    return a;
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}
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AVInteger av_sub_i(AVInteger a, AVInteger b){
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    int i, carry=0;
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    for(i=0; i<AV_INTEGER_SIZE; i++){
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        carry= (carry>>16) + a.v[i] - b.v[i];
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        a.v[i]= carry;
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    }
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    return a;
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}
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/**
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 * returns the rounded down value of the logarithm of base 2 of the given AVInteger.
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 * this is simply the index of the most significant bit which is 1. Or 0 of all bits are 0
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 */
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int av_log2_i(AVInteger a){
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    int i;
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    for(i=AV_INTEGER_SIZE-1; i>=0; i--){
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        if(a.v[i])
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            return av_log2_16bit(a.v[i]) + 16*i;
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    }
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    return -1;
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}
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AVInteger av_mul_i(AVInteger a, AVInteger b){
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    AVInteger out;
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    int i, j;
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    int na= (av_log2_i(a)+16) >> 4;
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    int nb= (av_log2_i(b)+16) >> 4;
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    memset(&out, 0, sizeof(out));
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    for(i=0; i<na; i++){
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        unsigned int carry=0;
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        if(a.v[i])
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            for(j=i; j<AV_INTEGER_SIZE && j-i<=nb; j++){
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                carry= (carry>>16) + out.v[j] + a.v[i]*b.v[j-i];
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                out.v[j]= carry;
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            }
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    }
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    return out;
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}
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/**
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 * returns 0 if a==b, 1 if a>b and -1 if a<b.
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 */
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int av_cmp_i(AVInteger a, AVInteger b){
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    int i;
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    int v= (int16_t)a.v[AV_INTEGER_SIZE-1] - (int16_t)b.v[AV_INTEGER_SIZE-1];
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    if(v) return (v>>16)|1;
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    for(i=AV_INTEGER_SIZE-2; i>=0; i--){
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        int v= a.v[i] - b.v[i];
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        if(v) return (v>>16)|1;
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    }
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    return 0;
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}
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/**
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 * bitwise shift.
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 * @param s the number of bits by which the value should be shifted right, may be negative for shifting left
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 */
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AVInteger av_shr_i(AVInteger a, int s){
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    AVInteger out;
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    int i;
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    for(i=0; i<AV_INTEGER_SIZE; i++){
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        int index= i + (s>>4);
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        unsigned int v=0;
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        if(index+1<AV_INTEGER_SIZE && index+1>=0) v = a.v[index+1]<<16;
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        if(index  <AV_INTEGER_SIZE && index  >=0) v+= a.v[index  ];
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        out.v[i]= v >> (s&15);
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    }
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    return out;
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}
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/**
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 * returns a % b.
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 * @param quot a/b will be stored here
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 */
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AVInteger av_mod_i(AVInteger *quot, AVInteger a, AVInteger b){
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    int i= av_log2_i(a) - av_log2_i(b);
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    AVInteger quot_temp;
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    if(!quot) quot = &quot_temp;
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    assert((int16_t)a[AV_INTEGER_SIZE-1] >= 0 && (int16_t)b[AV_INTEGER_SIZE-1] >= 0);
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    assert(av_log2(b)>=0);
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    if(i > 0)
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        b= av_shr_i(b, -i);
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    memset(quot, 0, sizeof(AVInteger));
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    while(i-- >= 0){
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        *quot= av_shr_i(*quot, -1);
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        if(av_cmp_i(a, b) >= 0){
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            a= av_sub_i(a, b);
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            quot->v[0] += 1;
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        }
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        b= av_shr_i(b, 1);
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    }
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    return a;
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}
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/**
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 * returns a/b.
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 */
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AVInteger av_div_i(AVInteger a, AVInteger b){
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    AVInteger quot;
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    av_mod_i(&quot, a, b);
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    return quot;
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}
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/**
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 * converts the given int64_t to an AVInteger.
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 */
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AVInteger av_int2i(int64_t a){
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    AVInteger out;
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    int i;
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    for(i=0; i<AV_INTEGER_SIZE; i++){
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        out.v[i]= a;
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        a>>=16;
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    }
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    return out;
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}
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/**
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 * converts the given AVInteger to an int64_t.
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 * if the AVInteger is too large to fit into an int64_t,
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 * then only the least significant 64bit will be used
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 */
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int64_t av_i2int(AVInteger a){
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    int i;
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    int64_t out=(int8_t)a.v[AV_INTEGER_SIZE-1];
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    for(i= AV_INTEGER_SIZE-2; i>=0; i--){
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        out = (out<<16) + a.v[i];
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    }
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    return out;
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}
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#if 0
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#undef NDEBUG
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#include <assert.h>
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const uint8_t ff_log2_tab[256]={
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        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,
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        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,
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        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,
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        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,
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        7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,
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        7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,
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        7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,
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        7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7
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};
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main(){
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    int64_t a,b;
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    for(a=7; a<256*256*256; a+=13215){
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        for(b=3; b<256*256*256; b+=27118){
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            AVInteger ai= av_int2i(a);
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            AVInteger bi= av_int2i(b);
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            assert(av_i2int(ai) == a);
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            assert(av_i2int(bi) == b);
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            assert(av_i2int(av_add_i(ai,bi)) == a+b);
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            assert(av_i2int(av_sub_i(ai,bi)) == a-b);
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            assert(av_i2int(av_mul_i(ai,bi)) == a*b);
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            assert(av_i2int(av_shr_i(ai, 9)) == a>>9);
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            assert(av_i2int(av_shr_i(ai,-9)) == a<<9);
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            assert(av_i2int(av_shr_i(ai, 17)) == a>>17);
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            assert(av_i2int(av_shr_i(ai,-17)) == a<<17);
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            assert(av_log2_i(ai) == av_log2(a));
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            assert(av_i2int(av_div_i(ai,bi)) == a/b);
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        }
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    }
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}
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#endif