text: /*
   * 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 */
  