FFmpeg中有关时间戳的函数

/**
 * @file
 * @addtogroup lavu_math
 * Mathematical utilities for working with timestamp and time base.
 */


#ifndef AVUTIL_MATHEMATICS_H
#define AVUTIL_MATHEMATICS_H


#include <stdint.h>
#include <math.h>
#include "attributes.h"
#include "rational.h"
#include "intfloat.h"


#ifndef M_E
#define M_E            2.7182818284590452354   /* e */
#endif
#ifndef M_LN2
#define M_LN2          0.69314718055994530942  /* log_e 2 */
#endif
#ifndef M_LN10
#define M_LN10         2.30258509299404568402  /* log_e 10 */
#endif
#ifndef M_LOG2_10
#define M_LOG2_10      3.32192809488736234787  /* log_2 10 */
#endif
#ifndef M_PHI
#define M_PHI          1.61803398874989484820   /* phi / golden ratio */
#endif
#ifndef M_PI
#define M_PI           3.14159265358979323846  /* pi */
#endif
#ifndef M_PI_2
#define M_PI_2         1.57079632679489661923  /* pi/2 */
#endif
#ifndef M_SQRT1_2
#define M_SQRT1_2      0.70710678118654752440  /* 1/sqrt(2) */
#endif
#ifndef M_SQRT2
#define M_SQRT2        1.41421356237309504880  /* sqrt(2) */
#endif
#ifndef NAN
#define NAN            av_int2float(0x7fc00000)
#endif
#ifndef INFINITY
#define INFINITY       av_int2float(0x7f800000)
#endif


/**
 * @addtogroup lavu_math
 *
 * @{
 */


/**
 * Rounding methods.
 */
enum AVRounding {
    AV_ROUND_ZERO     = 0, ///< Round toward zero.
    AV_ROUND_INF      = 1, ///< Round away from zero.
    AV_ROUND_DOWN     = 2, ///< Round toward -infinity.
    AV_ROUND_UP       = 3, ///< Round toward +infinity.
    AV_ROUND_NEAR_INF = 5, ///< Round to nearest and halfway cases away from zero.
    /**
     * Flag telling rescaling functions to pass `INT64_MIN`/`MAX` through
     * unchanged, avoiding special cases for #AV_NOPTS_VALUE.
     *
     * Unlike other values of the enumeration AVRounding, this value is a
     * bitmask that must be used in conjunction with another value of the
     * enumeration through a bitwise OR, in order to set behavior for normal
     * cases.
     *
     * @code{.c}
     * av_rescale_rnd(3, 1, 2, AV_ROUND_UP | AV_ROUND_PASS_MINMAX);
     * // Rescaling 3:
     * //     Calculating 3 * 1 / 2
     * //     3 / 2 is rounded up to 2
     * //     => 2
     *
     * av_rescale_rnd(AV_NOPTS_VALUE, 1, 2, AV_ROUND_UP | AV_ROUND_PASS_MINMAX);
     * // Rescaling AV_NOPTS_VALUE:
     * //     AV_NOPTS_VALUE == INT64_MIN
     * //     AV_NOPTS_VALUE is passed through
     * //     => AV_NOPTS_VALUE
     * @endcode
     */
    AV_ROUND_PASS_MINMAX = 8192,
};


/**
 * Compute the greatest common divisor of two integer operands.
 *
 * @param a,b Operands
 * @return GCD of a and b up to sign; if a >= 0 and b >= 0, return value is >= 0;
 * if a == 0 and b == 0, returns 0.
 */
int64_t av_const av_gcd(int64_t a, int64_t b);


/**
 * Rescale a 64-bit integer with rounding to nearest.
 *
 * The operation is mathematically equivalent to `a * b / c`, but writing that
 * directly can overflow.
 *
 * This function is equivalent to av_rescale_rnd() with #AV_ROUND_NEAR_INF.
 *
 * @see av_rescale_rnd(), av_rescale_q(), av_rescale_q_rnd()
 */
int64_t av_rescale(int64_t a, int64_t b, int64_t c) av_const;


/**
 * Rescale a 64-bit integer with specified rounding.
 *
 * The operation is mathematically equivalent to `a * b / c`, but writing that
 * directly can overflow, and does not support different rounding methods.
 *
 * @see av_rescale(), av_rescale_q(), av_rescale_q_rnd()
 */
int64_t av_rescale_rnd(int64_t a, int64_t b, int64_t c, enum AVRounding rnd) av_const;


/**
 * Rescale a 64-bit integer by 2 rational numbers.
 *
 * The operation is mathematically equivalent to `a * bq / cq`.
 *
 * This function is equivalent to av_rescale_q_rnd() with #AV_ROUND_NEAR_INF.
 *
 * @see av_rescale(), av_rescale_rnd(), av_rescale_q_rnd()
 */
int64_t av_rescale_q(int64_t a, AVRational bq, AVRational cq) av_const;


/**
 * Rescale a 64-bit integer by 2 rational numbers with specified rounding.
 *
 * The operation is mathematically equivalent to `a * bq / cq`.
 *
 * @see av_rescale(), av_rescale_rnd(), av_rescale_q()
 */
int64_t av_rescale_q_rnd(int64_t a, AVRational bq, AVRational cq,
                         enum AVRounding rnd) av_const;


/**
 * Compare two timestamps each in its own time base.
 *
 * @return One of the following values:
 *         - -1 if `ts_a` is before `ts_b`
 *         - 1 if `ts_a` is after `ts_b`
 *         - 0 if they represent the same position
 *
 * @warning
 * The result of the function is undefined if one of the timestamps is outside
 * the `int64_t` range when represented in the other's timebase.
 */
int av_compare_ts(int64_t ts_a, AVRational tb_a, int64_t ts_b, AVRational tb_b);


/**
 * Compare the remainders of two integer operands divided by a common divisor.
 *
 * In other words, compare the least significant `log2(mod)` bits of integers
 * `a` and `b`.
 *
 * @code{.c}
 * av_compare_mod(0x11, 0x02, 0x10) < 0 // since 0x11 % 0x10  (0x1) < 0x02 % 0x10  (0x2)
 * av_compare_mod(0x11, 0x02, 0x20) > 0 // since 0x11 % 0x20 (0x11) > 0x02 % 0x20 (0x02)
 * @endcode
 *
 * @param a,b Operands
 * @param mod Divisor; must be a power of 2
 * @return
 *         - a negative value if `a % mod < b % mod`
 *         - a positive value if `a % mod > b % mod`
 *         - zero             if `a % mod == b % mod`
 */
int64_t av_compare_mod(uint64_t a, uint64_t b, uint64_t mod);


/**
 * Rescale a timestamp while preserving known durations.
 *
 * This function is designed to be called per audio packet to scale the input
 * timestamp to a different time base. Compared to a simple av_rescale_q()
 * call, this function is robust against possible inconsistent frame durations.
 *
 * The `last` parameter is a state variable that must be preserved for all
 * subsequent calls for the same stream. For the first call, `*last` should be
 * initialized to #AV_NOPTS_VALUE.
 *
 * @param[in]     in_tb    Input time base
 * @param[in]     in_ts    Input timestamp
 * @param[in]     fs_tb    Duration time base; typically this is finer-grained
 *                         (greater) than `in_tb` and `out_tb`
 * @param[in]     duration Duration till the next call to this function (i.e.
 *                         duration of the current packet/frame)
 * @param[in,out] last     Pointer to a timestamp expressed in terms of
 *                         `fs_tb`, acting as a state variable
 * @param[in]     out_tb   Output timebase
 * @return        Timestamp expressed in terms of `out_tb`
 *
 * @note In the context of this function, "duration" is in term of samples, not
 *       seconds.
 */
int64_t av_rescale_delta(AVRational in_tb, int64_t in_ts,  AVRational fs_tb, int duration, int64_t *last, AVRational out_tb);


/**
 * Add a value to a timestamp.
 *
 * This function guarantees that when the same value is repeatly added that
 * no accumulation of rounding errors occurs.
 *
 * @param[in] ts     Input timestamp
 * @param[in] ts_tb  Input timestamp time base
 * @param[in] inc    Value to be added
 * @param[in] inc_tb Time base of `inc`
 */
int64_t av_add_stable(AVRational ts_tb, int64_t ts, AVRational inc_tb, int64_t inc);




/**
 * @}
 */


#endif /* AVUTIL_MATHEMATICS_H */







/*
 * 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
        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);
    }
}