/* * 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("%"PRId64"*%"PRId64"/%"PRId64"= %"PRId64"=%"PRId64"\n", a, b, c, d, e); } } } } #endif