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/*
* Copyright (c) 2005 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 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
#undef printf
main(){
int64_t a,b,c,d,e;
for(a=7; a<(1LL<<60); a=(a*3)+1){
for(b=3; b<(1LL<<60); b=(b*5)/4+1){
for(c=9; c<(1LL<<60); c=(c*7)/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("%Ld*%Ld/%Ld= %Ld=%Ld\n", a, b, c, d, e);
}
}
}
}
#endif
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