/* * rational numbers * Copyright (c) 2003 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 * rational numbers * @author Michael Niedermayer <michaelni@gmx.at> */ #include "avassert.h" //#include <math.h> #include <limits.h> #include "common.h" #include "mathematics.h" #include "rational.h" int av_reduce(int *dst_num, int *dst_den, int64_t num, int64_t den, int64_t max){ AVRational a0={0,1}, a1={1,0}; int sign= (num<0) ^ (den<0); int64_t gcd= av_gcd(FFABS(num), FFABS(den)); if(gcd){ num = FFABS(num)/gcd; den = FFABS(den)/gcd; } if(num<=max && den<=max){ a1= (AVRational){num, den}; den=0; } while(den){ uint64_t x = num / den; int64_t next_den= num - den*x; int64_t a2n= x*a1.num + a0.num; int64_t a2d= x*a1.den + a0.den; if(a2n > max || a2d > max){ if(a1.num) x= (max - a0.num) / a1.num; if(a1.den) x= FFMIN(x, (max - a0.den) / a1.den); if (den*(2*x*a1.den + a0.den) > num*a1.den) a1 = (AVRational){x*a1.num + a0.num, x*a1.den + a0.den}; break; } a0= a1; a1= (AVRational){a2n, a2d}; num= den; den= next_den; } av_assert2(av_gcd(a1.num, a1.den) <= 1U); *dst_num = sign ? -a1.num : a1.num; *dst_den = a1.den; return den==0; } AVRational av_mul_q(AVRational b, AVRational c){ av_reduce(&b.num, &b.den, b.num * (int64_t)c.num, b.den * (int64_t)c.den, INT_MAX); return b; } AVRational av_div_q(AVRational b, AVRational c){ return av_mul_q(b, (AVRational){c.den, c.num}); } AVRational av_add_q(AVRational b, AVRational c){ av_reduce(&b.num, &b.den, b.num * (int64_t)c.den + c.num * (int64_t)b.den, b.den * (int64_t)c.den, INT_MAX); return b; } AVRational av_sub_q(AVRational b, AVRational c){ return av_add_q(b, (AVRational){-c.num, c.den}); } AVRational av_d2q(double d, int max){ AVRational a; #define LOG2 0.69314718055994530941723212145817656807550013436025 int exponent; int64_t den; if (isnan(d)) return (AVRational){0,0}; if (isinf(d)) return (AVRational){ d<0 ? -1:1, 0 }; exponent = FFMAX( (int)(log(fabs(d) + 1e-20)/LOG2), 0); den = 1LL << (61 - exponent); av_reduce(&a.num, &a.den, (int64_t)(d * den + 0.5), den, max); return a; } int av_nearer_q(AVRational q, AVRational q1, AVRational q2) { /* n/d is q, a/b is the median between q1 and q2 */ int64_t a = q1.num * (int64_t)q2.den + q2.num * (int64_t)q1.den; int64_t b = 2 * (int64_t)q1.den * q2.den; /* rnd_up(a*d/b) > n => a*d/b > n */ int64_t x_up = av_rescale_rnd(a, q.den, b, AV_ROUND_UP); /* rnd_down(a*d/b) < n => a*d/b < n */ int64_t x_down = av_rescale_rnd(a, q.den, b, AV_ROUND_DOWN); return ((x_up > q.num) - (x_down < q.num)) * av_cmp_q(q2, q1); } int av_find_nearest_q_idx(AVRational q, const AVRational* q_list) { int i, nearest_q_idx = 0; for(i=0; q_list[i].den; i++) if (av_nearer_q(q, q_list[i], q_list[nearest_q_idx]) > 0) nearest_q_idx = i; return nearest_q_idx; } #ifdef TEST main(){ AVRational a,b; for(a.num=-2; a.num<=2; a.num++){ for(a.den=-2; a.den<=2; a.den++){ for(b.num=-2; b.num<=2; b.num++){ for(b.den=-2; b.den<=2; b.den++){ int c= av_cmp_q(a,b); double d= av_q2d(a) == av_q2d(b) ? 0 : (av_q2d(a) - av_q2d(b)); if(d>0) d=1; else if(d<0) d=-1; else if(d != d) d= INT_MIN; if(c!=d) av_log(0, AV_LOG_ERROR, "%d/%d %d/%d, %d %f\n", a.num, a.den, b.num, b.den, c,d); } } } } } #endif