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- /*
- * 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 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
- #include "integer.h"
- #undef printf
- main(){
- 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("%Ld*%Ld/%Ld= %Ld=%Ld\n", a, b, c, d, e);
- }
- }
- }
- }
- #endif
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