/*

  * 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
  * @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 */