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* arbitrary precision integers
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* Copyright (c) 2004 Michael Niedermayer <michaelni@gmx.at>
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* This file is part of FFmpeg.
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* FFmpeg 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 2.1 of the License, or (at your option) any later version.
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* FFmpeg 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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* You should have received a copy of the GNU Lesser General Public
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* License along with FFmpeg; 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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* arbitrary precision integers.
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* @author Michael Niedermayer <michaelni@gmx.at>
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AVInteger av_add_i(AVInteger a, AVInteger b){
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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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AVInteger av_sub_i(AVInteger a, AVInteger b){
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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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* 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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int av_log2_i(AVInteger a){
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for(i=AV_INTEGER_SIZE-1; i>=0; i--){
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return av_log2_16bit(a.v[i]) + 16*i;
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AVInteger av_mul_i(AVInteger a, AVInteger b){
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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(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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* returns 0 if a==b, 1 if a>b and -1 if a<b.
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int av_cmp_i(AVInteger a, AVInteger b){
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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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* @param s the number of bits by which the value should be shifted right, may be negative for shifting left
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AVInteger av_shr_i(AVInteger a, int s){
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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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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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* @param quot a/b will be stored here
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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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if(!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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memset(quot, 0, sizeof(AVInteger));
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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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AVInteger av_div_i(AVInteger a, AVInteger b){
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av_mod_i(", a, b);
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* converts the given int64_t to an AVInteger.
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AVInteger av_int2i(int64_t a){
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for(i=0; i<AV_INTEGER_SIZE; i++){
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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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int64_t av_i2int(AVInteger a){
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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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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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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);