libavutil/mathematics.h

   1 /*
   2  * copyright (c) 2005-2012 Michael Niedermayer <michaelni@gmx.at>
   3  *
   4  * This file is part of FFmpeg.
   5  *
   6  * FFmpeg is free software; you can redistribute it and/or
   7  * modify it under the terms of the GNU Lesser General Public
   8  * License as published by the Free Software Foundation; either
   9  * version 2.1 of the License, or (at your option) any later version.
  10  *
  11  * FFmpeg is distributed in the hope that it will be useful,
  12  * but WITHOUT ANY WARRANTY; without even the implied warranty of
  13  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  14  * Lesser General Public License for more details.
  15  *
  16  * You should have received a copy of the GNU Lesser General Public
  17  * License along with FFmpeg; if not, write to the Free Software
  18  * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
  19  */
  20
  21 /**
  22  * @file
  23  * @addtogroup lavu_math
  24  * Mathematical utilities for working with timestamp and time base.
  25  */
  26
  27 #ifndef AVUTIL_MATHEMATICS_H
  28 #define AVUTIL_MATHEMATICS_H
  29
  30 #include <stdint.h>
  31 #include <math.h>
  32 #include "attributes.h"
  33 #include "rational.h"
  34 #include "intfloat.h"
  35
  36 #ifndef M_E
  37 #define M_E            2.7182818284590452354   /* e */
  38 #endif
  39 #ifndef M_LN2
  40 #define M_LN2          0.69314718055994530942  /* log_e 2 */
  41 #endif
  42 #ifndef M_LN10
  43 #define M_LN10         2.30258509299404568402  /* log_e 10 */
  44 #endif
  45 #ifndef M_LOG2_10
  46 #define M_LOG2_10      3.32192809488736234787  /* log_2 10 */
  47 #endif
  48 #ifndef M_PHI
  49 #define M_PHI          1.61803398874989484820   /* phi / golden ratio */
  50 #endif
  51 #ifndef M_PI
  52 #define M_PI           3.14159265358979323846  /* pi */
  53 #endif
  54 #ifndef M_PI_2
  55 #define M_PI_2         1.57079632679489661923  /* pi/2 */
  56 #endif
  57 #ifndef M_SQRT1_2
  58 #define M_SQRT1_2      0.70710678118654752440  /* 1/sqrt(2) */
  59 #endif
  60 #ifndef M_SQRT2
  61 #define M_SQRT2        1.41421356237309504880  /* sqrt(2) */
  62 #endif
  63 #ifndef NAN
  64 #define NAN            av_int2float(0x7fc00000)
  65 #endif
  66 #ifndef INFINITY
  67 #define INFINITY       av_int2float(0x7f800000)
  68 #endif
  69
  70 /**
  71  * @addtogroup lavu_math
  72  *
  73  * @{
  74  */
  75
  76 /**
  77  * Rounding methods.
  78  */
  79 enum AVRounding {
  80     AV_ROUND_ZERO     = 0, ///< Round toward zero.
  81     AV_ROUND_INF      = 1, ///< Round away from zero.
  82     AV_ROUND_DOWN     = 2, ///< Round toward -infinity.
  83     AV_ROUND_UP       = 3, ///< Round toward +infinity.
  84     AV_ROUND_NEAR_INF = 5, ///< Round to nearest and halfway cases away from zero.
  85     /**
  86      * Flag telling rescaling functions to pass `INT64_MIN`/`MAX` through
  87      * unchanged, avoiding special cases for #AV_NOPTS_VALUE.
  88      *
  89      * Unlike other values of the enumeration AVRounding, this value is a
  90      * bitmask that must be used in conjunction with another value of the
  91      * enumeration through a bitwise OR, in order to set behavior for normal
  92      * cases.
  93      *
  94      * @code{.c}
  95      * av_rescale_rnd(3, 1, 2, AV_ROUND_UP | AV_ROUND_PASS_MINMAX);
  96      * // Rescaling 3:
  97      * //     Calculating 3 * 1 / 2
  98      * //     3 / 2 is rounded up to 2
  99      * //     => 2
 100      *
 101      * av_rescale_rnd(AV_NOPTS_VALUE, 1, 2, AV_ROUND_UP | AV_ROUND_PASS_MINMAX);
 102      * // Rescaling AV_NOPTS_VALUE:
 103      * //     AV_NOPTS_VALUE == INT64_MIN
 104      * //     AV_NOPTS_VALUE is passed through
 105      * //     => AV_NOPTS_VALUE
 106      * @endcode
 107      */
 108     AV_ROUND_PASS_MINMAX = 8192,
 109 };
 110
 111 /**
 112  * Compute the greatest common divisor of two integer operands.
 113  *
 114  * @param a,b Operands
 115  * @return GCD of a and b up to sign; if a >= 0 and b >= 0, return value is >= 0;
 116  * if a == 0 and b == 0, returns 0.
 117  */
 118 int64_t av_const av_gcd(int64_t a, int64_t b);
 119
 120 /**
 121  * Rescale a 64-bit integer with rounding to nearest.
 122  *
 123  * The operation is mathematically equivalent to `a * b / c`, but writing that
 124  * directly can overflow.
 125  *
 126  * This function is equivalent to av_rescale_rnd() with #AV_ROUND_NEAR_INF.
 127  *
 128  * @see av_rescale_rnd(), av_rescale_q(), av_rescale_q_rnd()
 129  */
 130 int64_t av_rescale(int64_t a, int64_t b, int64_t c) av_const;
 131
 132 /**
 133  * Rescale a 64-bit integer with specified rounding.
 134  *
 135  * The operation is mathematically equivalent to `a * b / c`, but writing that
 136  * directly can overflow, and does not support different rounding methods.
 137  * If the result is not representable then INT64_MIN is returned.
 138  *
 139  * @see av_rescale(), av_rescale_q(), av_rescale_q_rnd()
 140  */
 141 int64_t av_rescale_rnd(int64_t a, int64_t b, int64_t c, enum AVRounding rnd) av_const;
 142
 143 /**
 144  * Rescale a 64-bit integer by 2 rational numbers.
 145  *
 146  * The operation is mathematically equivalent to `a * bq / cq`.
 147  *
 148  * This function is equivalent to av_rescale_q_rnd() with #AV_ROUND_NEAR_INF.
 149  *
 150  * @see av_rescale(), av_rescale_rnd(), av_rescale_q_rnd()
 151  */
 152 int64_t av_rescale_q(int64_t a, AVRational bq, AVRational cq) av_const;
 153
 154 /**
 155  * Rescale a 64-bit integer by 2 rational numbers with specified rounding.
 156  *
 157  * The operation is mathematically equivalent to `a * bq / cq`.
 158  *
 159  * @see av_rescale(), av_rescale_rnd(), av_rescale_q()
 160  */
 161 int64_t av_rescale_q_rnd(int64_t a, AVRational bq, AVRational cq,
 162                          enum AVRounding rnd) av_const;
 163
 164 /**
 165  * Compare two timestamps each in its own time base.
 166  *
 167  * @return One of the following values:
 168  *         - -1 if `ts_a` is before `ts_b`
 169  *         - 1 if `ts_a` is after `ts_b`
 170  *         - 0 if they represent the same position
 171  *
 172  * @warning
 173  * The result of the function is undefined if one of the timestamps is outside
 174  * the `int64_t` range when represented in the other's timebase.
 175  */
 176 int av_compare_ts(int64_t ts_a, AVRational tb_a, int64_t ts_b, AVRational tb_b);
 177
 178 /**
 179  * Compare the remainders of two integer operands divided by a common divisor.
 180  *
 181  * In other words, compare the least significant `log2(mod)` bits of integers
 182  * `a` and `b`.
 183  *
 184  * @code{.c}
 185  * av_compare_mod(0x11, 0x02, 0x10) < 0 // since 0x11 % 0x10  (0x1) < 0x02 % 0x10  (0x2)
 186  * av_compare_mod(0x11, 0x02, 0x20) > 0 // since 0x11 % 0x20 (0x11) > 0x02 % 0x20 (0x02)
 187  * @endcode
 188  *
 189  * @param a,b Operands
 190  * @param mod Divisor; must be a power of 2
 191  * @return
 192  *         - a negative value if `a % mod < b % mod`
 193  *         - a positive value if `a % mod > b % mod`
 194  *         - zero             if `a % mod == b % mod`
 195  */
 196 int64_t av_compare_mod(uint64_t a, uint64_t b, uint64_t mod);
 197
 198 /**
 199  * Rescale a timestamp while preserving known durations.
 200  *
 201  * This function is designed to be called per audio packet to scale the input
 202  * timestamp to a different time base. Compared to a simple av_rescale_q()
 203  * call, this function is robust against possible inconsistent frame durations.
 204  *
 205  * The `last` parameter is a state variable that must be preserved for all
 206  * subsequent calls for the same stream. For the first call, `*last` should be
 207  * initialized to #AV_NOPTS_VALUE.
 208  *
 209  * @param[in]     in_tb    Input time base
 210  * @param[in]     in_ts    Input timestamp
 211  * @param[in]     fs_tb    Duration time base; typically this is finer-grained
 212  *                         (greater) than `in_tb` and `out_tb`
 213  * @param[in]     duration Duration till the next call to this function (i.e.
 214  *                         duration of the current packet/frame)
 215  * @param[in,out] last     Pointer to a timestamp expressed in terms of
 216  *                         `fs_tb`, acting as a state variable
 217  * @param[in]     out_tb   Output timebase
 218  * @return        Timestamp expressed in terms of `out_tb`
 219  *
 220  * @note In the context of this function, "duration" is in term of samples, not
 221  *       seconds.
 222  */
 223 int64_t av_rescale_delta(AVRational in_tb, int64_t in_ts,  AVRational fs_tb, int duration, int64_t *last, AVRational out_tb);
 224
 225 /**
 226  * Add a value to a timestamp.
 227  *
 228  * This function guarantees that when the same value is repeatly added that
 229  * no accumulation of rounding errors occurs.
 230  *
 231  * @param[in] ts     Input timestamp
 232  * @param[in] ts_tb  Input timestamp time base
 233  * @param[in] inc    Value to be added
 234  * @param[in] inc_tb Time base of `inc`
 235  */
 236 int64_t av_add_stable(AVRational ts_tb, int64_t ts, AVRational inc_tb, int64_t inc);
 237
 238
 239 /**
 240  * @}
 241  */
 242
 243 #endif /* AVUTIL_MATHEMATICS_H */