/* * Copyright (c) 2005-2012 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 * miscellaneous math routines and tables */ #include <stdint.h> #include <limits.h> #include "mathematics.h" #include "libavutil/intmath.h" #include "libavutil/common.h" #include "avassert.h" #include "version.h" /* Stein's binary GCD algorithm: * https://en.wikipedia.org/wiki/Binary_GCD_algorithm */ int64_t av_gcd(int64_t a, int64_t b) { int za, zb, k; int64_t u, v; if (a == 0) return b; if (b == 0) return a; za = ff_ctzll(a); zb = ff_ctzll(b); k = FFMIN(za, zb); u = llabs(a >> za); v = llabs(b >> zb); while (u != v) { if (u > v) FFSWAP(int64_t, v, u); v -= u; v >>= ff_ctzll(v); } return (uint64_t)u << k; } int64_t av_rescale_rnd(int64_t a, int64_t b, int64_t c, enum AVRounding rnd) { int64_t r = 0; av_assert2(c > 0); av_assert2(b >=0); av_assert2((unsigned)(rnd&~AV_ROUND_PASS_MINMAX)<=5 && (rnd&~AV_ROUND_PASS_MINMAX)!=4); if (c <= 0 || b < 0 || !((unsigned)(rnd&~AV_ROUND_PASS_MINMAX)<=5 && (rnd&~AV_ROUND_PASS_MINMAX)!=4)) return INT64_MIN; if (rnd & AV_ROUND_PASS_MINMAX) { if (a == INT64_MIN || a == INT64_MAX) return a; rnd -= AV_ROUND_PASS_MINMAX; } if (a < 0) return -(uint64_t)av_rescale_rnd(-FFMAX(a, -INT64_MAX), 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 { int64_t ad = a / c; int64_t a2 = (a % c * b + r) / c; if (ad >= INT32_MAX && b && ad > (INT64_MAX - a2) / b) return INT64_MIN; return ad * b + a2; } } 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--) { a1 += a1 + ((a0 >> i) & 1); t1 += t1; if (c <= a1) { a1 -= c; t1++; } } if (t1 > INT64_MAX) return INT64_MIN; return t1; #else /* reference code doing (a*b + r) / c, requires libavutil/integer.h */ 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_rnd(int64_t a, AVRational bq, AVRational cq, enum AVRounding rnd) { 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, rnd); } int64_t av_rescale_q(int64_t a, AVRational bq, AVRational cq) { return av_rescale_q_rnd(a, bq, cq, AV_ROUND_NEAR_INF); } int av_compare_ts(int64_t ts_a, AVRational tb_a, int64_t ts_b, AVRational tb_b) { int64_t a = tb_a.num * (int64_t)tb_b.den; int64_t b = tb_b.num * (int64_t)tb_a.den; if ((FFABS(ts_a)|a|FFABS(ts_b)|b) <= INT_MAX) return (ts_a*a > ts_b*b) - (ts_a*a < ts_b*b); if (av_rescale_rnd(ts_a, a, b, AV_ROUND_DOWN) < ts_b) return -1; if (av_rescale_rnd(ts_b, b, a, AV_ROUND_DOWN) < ts_a) return 1; return 0; } int64_t av_compare_mod(uint64_t a, uint64_t b, uint64_t mod) { int64_t c = (a - b) & (mod - 1); if (c > (mod >> 1)) c -= mod; return c; } int64_t av_rescale_delta(AVRational in_tb, int64_t in_ts, AVRational fs_tb, int duration, int64_t *last, AVRational out_tb){ int64_t a, b, this; av_assert0(in_ts != AV_NOPTS_VALUE); av_assert0(duration >= 0); if (*last == AV_NOPTS_VALUE || !duration || in_tb.num*(int64_t)out_tb.den <= out_tb.num*(int64_t)in_tb.den) { simple_round: *last = av_rescale_q(in_ts, in_tb, fs_tb) + duration; return av_rescale_q(in_ts, in_tb, out_tb); } a = av_rescale_q_rnd(2*in_ts-1, in_tb, fs_tb, AV_ROUND_DOWN) >>1; b = (av_rescale_q_rnd(2*in_ts+1, in_tb, fs_tb, AV_ROUND_UP )+1)>>1; if (*last < 2*a - b || *last > 2*b - a) goto simple_round; this = av_clip64(*last, a, b); *last = this + duration; return av_rescale_q(this, fs_tb, out_tb); } int64_t av_add_stable(AVRational ts_tb, int64_t ts, AVRational inc_tb, int64_t inc) { int64_t m, d; if (inc != 1) inc_tb = av_mul_q(inc_tb, (AVRational) {inc, 1}); m = inc_tb.num * (int64_t)ts_tb.den; d = inc_tb.den * (int64_t)ts_tb.num; if (m % d == 0) return ts + m / d; if (m < d) return ts; { int64_t old = av_rescale_q(ts, ts_tb, inc_tb); int64_t old_ts = av_rescale_q(old, inc_tb, ts_tb); return av_rescale_q(old + 1, inc_tb, ts_tb) + (ts - old_ts); } }