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75918016ab
0th order modified bessel function of the first kind are used in multiple places, lets avoid having 3+ different implementations I picked this one as its accurate and quite fast, it can be replaced if a better one is found Signed-off-by: Michael Niedermayer <michael@niedermayer.cc>
320 lines
9.8 KiB
C
320 lines
9.8 KiB
C
/*
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* Copyright (c) 2005-2012 Michael Niedermayer <michaelni@gmx.at>
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*
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* This file is part of FFmpeg.
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*
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* FFmpeg is free software; you can redistribute it and/or
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* modify it under the terms of the GNU Lesser General Public
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* License as published by the Free Software Foundation; either
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* version 2.1 of the License, or (at your option) any later version.
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*
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* FFmpeg is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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* Lesser General Public License for more details.
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*
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* You should have received a copy of the GNU Lesser General Public
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* License along with FFmpeg; if not, write to the Free Software
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* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
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*/
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/**
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* @file
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* miscellaneous math routines and tables
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*/
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#include <stdint.h>
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#include <limits.h>
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#include "avutil.h"
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#include "mathematics.h"
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#include "libavutil/intmath.h"
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#include "libavutil/common.h"
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#include "avassert.h"
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/* Stein's binary GCD algorithm:
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* https://en.wikipedia.org/wiki/Binary_GCD_algorithm */
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int64_t av_gcd(int64_t a, int64_t b) {
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int za, zb, k;
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int64_t u, v;
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if (a == 0)
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return b;
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if (b == 0)
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return a;
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za = ff_ctzll(a);
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zb = ff_ctzll(b);
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k = FFMIN(za, zb);
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u = llabs(a >> za);
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v = llabs(b >> zb);
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while (u != v) {
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if (u > v)
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FFSWAP(int64_t, v, u);
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v -= u;
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v >>= ff_ctzll(v);
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}
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return (uint64_t)u << k;
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}
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int64_t av_rescale_rnd(int64_t a, int64_t b, int64_t c, enum AVRounding rnd)
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{
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int64_t r = 0;
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av_assert2(c > 0);
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av_assert2(b >=0);
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av_assert2((unsigned)(rnd&~AV_ROUND_PASS_MINMAX)<=5 && (rnd&~AV_ROUND_PASS_MINMAX)!=4);
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if (c <= 0 || b < 0 || !((unsigned)(rnd&~AV_ROUND_PASS_MINMAX)<=5 && (rnd&~AV_ROUND_PASS_MINMAX)!=4))
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return INT64_MIN;
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if (rnd & AV_ROUND_PASS_MINMAX) {
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if (a == INT64_MIN || a == INT64_MAX)
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return a;
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rnd -= AV_ROUND_PASS_MINMAX;
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}
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if (a < 0)
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return -(uint64_t)av_rescale_rnd(-FFMAX(a, -INT64_MAX), b, c, rnd ^ ((rnd >> 1) & 1));
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if (rnd == AV_ROUND_NEAR_INF)
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r = c / 2;
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else if (rnd & 1)
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r = c - 1;
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if (b <= INT_MAX && c <= INT_MAX) {
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if (a <= INT_MAX)
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return (a * b + r) / c;
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else {
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int64_t ad = a / c;
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int64_t a2 = (a % c * b + r) / c;
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if (ad >= INT32_MAX && b && ad > (INT64_MAX - a2) / b)
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return INT64_MIN;
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return ad * b + a2;
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}
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} else {
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#if 1
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uint64_t a0 = a & 0xFFFFFFFF;
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uint64_t a1 = a >> 32;
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uint64_t b0 = b & 0xFFFFFFFF;
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uint64_t b1 = b >> 32;
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uint64_t t1 = a0 * b1 + a1 * b0;
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uint64_t t1a = t1 << 32;
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int i;
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a0 = a0 * b0 + t1a;
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a1 = a1 * b1 + (t1 >> 32) + (a0 < t1a);
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a0 += r;
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a1 += a0 < r;
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for (i = 63; i >= 0; i--) {
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a1 += a1 + ((a0 >> i) & 1);
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t1 += t1;
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if (c <= a1) {
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a1 -= c;
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t1++;
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}
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}
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if (t1 > INT64_MAX)
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return INT64_MIN;
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return t1;
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#else
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/* reference code doing (a*b + r) / c, requires libavutil/integer.h */
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AVInteger ai;
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ai = av_mul_i(av_int2i(a), av_int2i(b));
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ai = av_add_i(ai, av_int2i(r));
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return av_i2int(av_div_i(ai, av_int2i(c)));
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#endif
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}
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}
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int64_t av_rescale(int64_t a, int64_t b, int64_t c)
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{
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return av_rescale_rnd(a, b, c, AV_ROUND_NEAR_INF);
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}
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int64_t av_rescale_q_rnd(int64_t a, AVRational bq, AVRational cq,
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enum AVRounding rnd)
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{
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int64_t b = bq.num * (int64_t)cq.den;
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int64_t c = cq.num * (int64_t)bq.den;
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return av_rescale_rnd(a, b, c, rnd);
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}
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int64_t av_rescale_q(int64_t a, AVRational bq, AVRational cq)
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{
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return av_rescale_q_rnd(a, bq, cq, AV_ROUND_NEAR_INF);
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}
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int av_compare_ts(int64_t ts_a, AVRational tb_a, int64_t ts_b, AVRational tb_b)
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{
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int64_t a = tb_a.num * (int64_t)tb_b.den;
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int64_t b = tb_b.num * (int64_t)tb_a.den;
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if ((FFABS64U(ts_a)|a|FFABS64U(ts_b)|b) <= INT_MAX)
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return (ts_a*a > ts_b*b) - (ts_a*a < ts_b*b);
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if (av_rescale_rnd(ts_a, a, b, AV_ROUND_DOWN) < ts_b)
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return -1;
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if (av_rescale_rnd(ts_b, b, a, AV_ROUND_DOWN) < ts_a)
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return 1;
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return 0;
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}
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int64_t av_compare_mod(uint64_t a, uint64_t b, uint64_t mod)
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{
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int64_t c = (a - b) & (mod - 1);
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if (c > (mod >> 1))
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c -= mod;
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return c;
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}
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int64_t av_rescale_delta(AVRational in_tb, int64_t in_ts, AVRational fs_tb, int duration, int64_t *last, AVRational out_tb){
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int64_t a, b, this;
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av_assert0(in_ts != AV_NOPTS_VALUE);
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av_assert0(duration >= 0);
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if (*last == AV_NOPTS_VALUE || !duration || in_tb.num*(int64_t)out_tb.den <= out_tb.num*(int64_t)in_tb.den) {
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simple_round:
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*last = av_rescale_q(in_ts, in_tb, fs_tb) + duration;
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return av_rescale_q(in_ts, in_tb, out_tb);
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}
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a = av_rescale_q_rnd(2*in_ts-1, in_tb, fs_tb, AV_ROUND_DOWN) >>1;
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b = (av_rescale_q_rnd(2*in_ts+1, in_tb, fs_tb, AV_ROUND_UP )+1)>>1;
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if (*last < 2*a - b || *last > 2*b - a)
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goto simple_round;
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this = av_clip64(*last, a, b);
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*last = this + duration;
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return av_rescale_q(this, fs_tb, out_tb);
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}
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int64_t av_add_stable(AVRational ts_tb, int64_t ts, AVRational inc_tb, int64_t inc)
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{
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int64_t m, d;
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if (inc != 1)
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inc_tb = av_mul_q(inc_tb, (AVRational) {inc, 1});
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m = inc_tb.num * (int64_t)ts_tb.den;
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d = inc_tb.den * (int64_t)ts_tb.num;
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if (m % d == 0 && ts <= INT64_MAX - m / d)
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return ts + m / d;
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if (m < d)
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return ts;
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{
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int64_t old = av_rescale_q(ts, ts_tb, inc_tb);
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int64_t old_ts = av_rescale_q(old, inc_tb, ts_tb);
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if (old == INT64_MAX || old == AV_NOPTS_VALUE || old_ts == AV_NOPTS_VALUE)
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return ts;
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return av_sat_add64(av_rescale_q(old + 1, inc_tb, ts_tb), ts - old_ts);
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}
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}
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static inline double eval_poly(const double *coeff, int size, double x) {
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double sum = coeff[size-1];
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int i;
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for (i = size-2; i >= 0; --i) {
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sum *= x;
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sum += coeff[i];
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}
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return sum;
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}
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/**
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* 0th order modified bessel function of the first kind.
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* Algorithm taken from the Boost project, source:
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* https://searchcode.com/codesearch/view/14918379/
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* Use, modification and distribution are subject to the
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* Boost Software License, Version 1.0 (see notice below).
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* Boost Software License - Version 1.0 - August 17th, 2003
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Permission is hereby granted, free of charge, to any person or organization
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obtaining a copy of the software and accompanying documentation covered by
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this license (the "Software") to use, reproduce, display, distribute,
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execute, and transmit the Software, and to prepare derivative works of the
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Software, and to permit third-parties to whom the Software is furnished to
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do so, all subject to the following:
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The copyright notices in the Software and this entire statement, including
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the above license grant, this restriction and the following disclaimer,
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must be included in all copies of the Software, in whole or in part, and
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all derivative works of the Software, unless such copies or derivative
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works are solely in the form of machine-executable object code generated by
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a source language processor.
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THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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FITNESS FOR A PARTICULAR PURPOSE, TITLE AND NON-INFRINGEMENT. IN NO EVENT
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SHALL THE COPYRIGHT HOLDERS OR ANYONE DISTRIBUTING THE SOFTWARE BE LIABLE
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FOR ANY DAMAGES OR OTHER LIABILITY, WHETHER IN CONTRACT, TORT OR OTHERWISE,
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ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
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DEALINGS IN THE SOFTWARE.
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*/
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double av_bessel_i0(double x) {
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// Modified Bessel function of the first kind of order zero
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// minimax rational approximations on intervals, see
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// Blair and Edwards, Chalk River Report AECL-4928, 1974
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static const double p1[] = {
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-2.2335582639474375249e+15,
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-5.5050369673018427753e+14,
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-3.2940087627407749166e+13,
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-8.4925101247114157499e+11,
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-1.1912746104985237192e+10,
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-1.0313066708737980747e+08,
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-5.9545626019847898221e+05,
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-2.4125195876041896775e+03,
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-7.0935347449210549190e+00,
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-1.5453977791786851041e-02,
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-2.5172644670688975051e-05,
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-3.0517226450451067446e-08,
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-2.6843448573468483278e-11,
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-1.5982226675653184646e-14,
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-5.2487866627945699800e-18,
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};
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static const double q1[] = {
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-2.2335582639474375245e+15,
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7.8858692566751002988e+12,
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-1.2207067397808979846e+10,
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1.0377081058062166144e+07,
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-4.8527560179962773045e+03,
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1.0,
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};
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static const double p2[] = {
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-2.2210262233306573296e-04,
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1.3067392038106924055e-02,
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-4.4700805721174453923e-01,
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5.5674518371240761397e+00,
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-2.3517945679239481621e+01,
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3.1611322818701131207e+01,
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-9.6090021968656180000e+00,
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};
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static const double q2[] = {
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-5.5194330231005480228e-04,
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3.2547697594819615062e-02,
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-1.1151759188741312645e+00,
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1.3982595353892851542e+01,
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-6.0228002066743340583e+01,
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8.5539563258012929600e+01,
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-3.1446690275135491500e+01,
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1.0,
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};
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double y, r, factor;
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if (x == 0)
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return 1.0;
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x = fabs(x);
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if (x <= 15) {
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y = x * x;
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return eval_poly(p1, FF_ARRAY_ELEMS(p1), y) / eval_poly(q1, FF_ARRAY_ELEMS(q1), y);
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}
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else {
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y = 1 / x - 1.0 / 15;
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r = eval_poly(p2, FF_ARRAY_ELEMS(p2), y) / eval_poly(q2, FF_ARRAY_ELEMS(q2), y);
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factor = exp(x) / sqrt(x);
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return factor * r;
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}
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}
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