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_Ef
  40 #define M_Ef           2.7182818284590452354f  /* e */
  41 #endif
  42 #ifndef M_LN2
  43 #define M_LN2          0.69314718055994530942  /* log_e 2 */
  44 #endif
  45 #ifndef M_LN2f
  46 #define M_LN2f         0.69314718055994530942f /* log_e 2 */
  47 #endif
  48 #ifndef M_LN10
  49 #define M_LN10         2.30258509299404568402  /* log_e 10 */
  50 #endif
  51 #ifndef M_LN10f
  52 #define M_LN10f        2.30258509299404568402f /* log_e 10 */
  53 #endif
  54 #ifndef M_LOG2_10
  55 #define M_LOG2_10      3.32192809488736234787  /* log_2 10 */
  56 #endif
  57 #ifndef M_LOG2_10f
  58 #define M_LOG2_10f     3.32192809488736234787f /* log_2 10 */
  59 #endif
  60 #ifndef M_PHI
  61 #define M_PHI          1.61803398874989484820   /* phi / golden ratio */
  62 #endif
  63 #ifndef M_PHIf
  64 #define M_PHIf         1.61803398874989484820f  /* phi / golden ratio */
  65 #endif
  66 #ifndef M_PI
  67 #define M_PI           3.14159265358979323846  /* pi */
  68 #endif
  69 #ifndef M_PIf
  70 #define M_PIf          3.14159265358979323846f /* pi */
  71 #endif
  72 #ifndef M_PI_2
  73 #define M_PI_2         1.57079632679489661923  /* pi/2 */
  74 #endif
  75 #ifndef M_PI_2f
  76 #define M_PI_2f        1.57079632679489661923f /* pi/2 */
  77 #endif
  78 #ifndef M_PI_4
  79 #define M_PI_4         0.78539816339744830962  /* pi/4 */
  80 #endif
  81 #ifndef M_PI_4f
  82 #define M_PI_4f        0.78539816339744830962f /* pi/4 */
  83 #endif
  84 #ifndef M_1_PI
  85 #define M_1_PI         0.31830988618379067154  /* 1/pi */
  86 #endif
  87 #ifndef M_1_PIf
  88 #define M_1_PIf        0.31830988618379067154f /* 1/pi */
  89 #endif
  90 #ifndef M_2_PI
  91 #define M_2_PI         0.63661977236758134308  /* 2/pi */
  92 #endif
  93 #ifndef M_2_PIf
  94 #define M_2_PIf        0.63661977236758134308f /* 2/pi */
  95 #endif
  96 #ifndef M_2_SQRTPI
  97 #define M_2_SQRTPI     1.12837916709551257390  /* 2/sqrt(pi) */
  98 #endif
  99 #ifndef M_2_SQRTPIf
 100 #define M_2_SQRTPIf    1.12837916709551257390f /* 2/sqrt(pi) */
 101 #endif
 102 #ifndef M_SQRT1_2
 103 #define M_SQRT1_2      0.70710678118654752440  /* 1/sqrt(2) */
 104 #endif
 105 #ifndef M_SQRT1_2f
 106 #define M_SQRT1_2f     0.70710678118654752440f /* 1/sqrt(2) */
 107 #endif
 108 #ifndef M_SQRT2
 109 #define M_SQRT2        1.41421356237309504880  /* sqrt(2) */
 110 #endif
 111 #ifndef M_SQRT2f
 112 #define M_SQRT2f       1.41421356237309504880f /* sqrt(2) */
 113 #endif
 114 #ifndef NAN
 115 #define NAN            av_int2float(0x7fc00000)
 116 #endif
 117 #ifndef INFINITY
 118 #define INFINITY       av_int2float(0x7f800000)
 119 #endif
 120
 121 /**
 122  * @addtogroup lavu_math
 123  *
 124  * @{
 125  */
 126
 127 /**
 128  * Rounding methods.
 129  */
 130 enum AVRounding {
 131     AV_ROUND_ZERO     = 0, ///< Round toward zero.
 132     AV_ROUND_INF      = 1, ///< Round away from zero.
 133     AV_ROUND_DOWN     = 2, ///< Round toward -infinity.
 134     AV_ROUND_UP       = 3, ///< Round toward +infinity.
 135     AV_ROUND_NEAR_INF = 5, ///< Round to nearest and halfway cases away from zero.
 136     /**
 137      * Flag telling rescaling functions to pass `INT64_MIN`/`MAX` through
 138      * unchanged, avoiding special cases for #AV_NOPTS_VALUE.
 139      *
 140      * Unlike other values of the enumeration AVRounding, this value is a
 141      * bitmask that must be used in conjunction with another value of the
 142      * enumeration through a bitwise OR, in order to set behavior for normal
 143      * cases.
 144      *
 145      * @code{.c}
 146      * av_rescale_rnd(3, 1, 2, AV_ROUND_UP | AV_ROUND_PASS_MINMAX);
 147      * // Rescaling 3:
 148      * //     Calculating 3 * 1 / 2
 149      * //     3 / 2 is rounded up to 2
 150      * //     => 2
 151      *
 152      * av_rescale_rnd(AV_NOPTS_VALUE, 1, 2, AV_ROUND_UP | AV_ROUND_PASS_MINMAX);
 153      * // Rescaling AV_NOPTS_VALUE:
 154      * //     AV_NOPTS_VALUE == INT64_MIN
 155      * //     AV_NOPTS_VALUE is passed through
 156      * //     => AV_NOPTS_VALUE
 157      * @endcode
 158      */
 159     AV_ROUND_PASS_MINMAX = 8192,
 160 };
 161
 162 /**
 163  * Compute the greatest common divisor of two integer operands.
 164  *
 165  * @param a Operand
 166  * @param b Operand
 167  * @return GCD of a and b up to sign; if a >= 0 and b >= 0, return value is >= 0;
 168  * if a == 0 and b == 0, returns 0.
 169  */
 170 int64_t av_const av_gcd(int64_t a, int64_t b);
 171
 172 /**
 173  * Rescale a 64-bit integer with rounding to nearest.
 174  *
 175  * The operation is mathematically equivalent to `a * b / c`, but writing that
 176  * directly can overflow.
 177  *
 178  * This function is equivalent to av_rescale_rnd() with #AV_ROUND_NEAR_INF.
 179  *
 180  * @see av_rescale_rnd(), av_rescale_q(), av_rescale_q_rnd()
 181  */
 182 int64_t av_rescale(int64_t a, int64_t b, int64_t c) av_const;
 183
 184 /**
 185  * Rescale a 64-bit integer with specified rounding.
 186  *
 187  * The operation is mathematically equivalent to `a * b / c`, but writing that
 188  * directly can overflow, and does not support different rounding methods.
 189  * If the result is not representable then INT64_MIN is returned.
 190  *
 191  * @see av_rescale(), av_rescale_q(), av_rescale_q_rnd()
 192  */
 193 int64_t av_rescale_rnd(int64_t a, int64_t b, int64_t c, enum AVRounding rnd) av_const;
 194
 195 /**
 196  * Rescale a 64-bit integer by 2 rational numbers.
 197  *
 198  * The operation is mathematically equivalent to `a * bq / cq`.
 199  *
 200  * This function is equivalent to av_rescale_q_rnd() with #AV_ROUND_NEAR_INF.
 201  *
 202  * @see av_rescale(), av_rescale_rnd(), av_rescale_q_rnd()
 203  */
 204 int64_t av_rescale_q(int64_t a, AVRational bq, AVRational cq) av_const;
 205
 206 /**
 207  * Rescale a 64-bit integer by 2 rational numbers with specified rounding.
 208  *
 209  * The operation is mathematically equivalent to `a * bq / cq`.
 210  *
 211  * @see av_rescale(), av_rescale_rnd(), av_rescale_q()
 212  */
 213 int64_t av_rescale_q_rnd(int64_t a, AVRational bq, AVRational cq,
 214                          enum AVRounding rnd) av_const;
 215
 216 /**
 217  * Compare two timestamps each in its own time base.
 218  *
 219  * @return One of the following values:
 220  *         - -1 if `ts_a` is before `ts_b`
 221  *         - 1 if `ts_a` is after `ts_b`
 222  *         - 0 if they represent the same position
 223  *
 224  * @warning
 225  * The result of the function is undefined if one of the timestamps is outside
 226  * the `int64_t` range when represented in the other's timebase.
 227  */
 228 int av_compare_ts(int64_t ts_a, AVRational tb_a, int64_t ts_b, AVRational tb_b);
 229
 230 /**
 231  * Compare the remainders of two integer operands divided by a common divisor.
 232  *
 233  * In other words, compare the least significant `log2(mod)` bits of integers
 234  * `a` and `b`.
 235  *
 236  * @code{.c}
 237  * av_compare_mod(0x11, 0x02, 0x10) < 0 // since 0x11 % 0x10  (0x1) < 0x02 % 0x10  (0x2)
 238  * av_compare_mod(0x11, 0x02, 0x20) > 0 // since 0x11 % 0x20 (0x11) > 0x02 % 0x20 (0x02)
 239  * @endcode
 240  *
 241  * @param a Operand
 242  * @param b Operand
 243  * @param mod Divisor; must be a power of 2
 244  * @return
 245  *         - a negative value if `a % mod < b % mod`
 246  *         - a positive value if `a % mod > b % mod`
 247  *         - zero             if `a % mod == b % mod`
 248  */
 249 int64_t av_compare_mod(uint64_t a, uint64_t b, uint64_t mod);
 250
 251 /**
 252  * Rescale a timestamp while preserving known durations.
 253  *
 254  * This function is designed to be called per audio packet to scale the input
 255  * timestamp to a different time base. Compared to a simple av_rescale_q()
 256  * call, this function is robust against possible inconsistent frame durations.
 257  *
 258  * The `last` parameter is a state variable that must be preserved for all
 259  * subsequent calls for the same stream. For the first call, `*last` should be
 260  * initialized to #AV_NOPTS_VALUE.
 261  *
 262  * @param[in]     in_tb    Input time base
 263  * @param[in]     in_ts    Input timestamp
 264  * @param[in]     fs_tb    Duration time base; typically this is finer-grained
 265  *                         (greater) than `in_tb` and `out_tb`
 266  * @param[in]     duration Duration till the next call to this function (i.e.
 267  *                         duration of the current packet/frame)
 268  * @param[in,out] last     Pointer to a timestamp expressed in terms of
 269  *                         `fs_tb`, acting as a state variable
 270  * @param[in]     out_tb   Output timebase
 271  * @return        Timestamp expressed in terms of `out_tb`
 272  *
 273  * @note In the context of this function, "duration" is in term of samples, not
 274  *       seconds.
 275  */
 276 int64_t av_rescale_delta(AVRational in_tb, int64_t in_ts,  AVRational fs_tb, int duration, int64_t *last, AVRational out_tb);
 277
 278 /**
 279  * Add a value to a timestamp.
 280  *
 281  * This function guarantees that when the same value is repeatedly added that
 282  * no accumulation of rounding errors occurs.
 283  *
 284  * @param[in] ts     Input timestamp
 285  * @param[in] ts_tb  Input timestamp time base
 286  * @param[in] inc    Value to be added
 287  * @param[in] inc_tb Time base of `inc`
 288  */
 289 int64_t av_add_stable(AVRational ts_tb, int64_t ts, AVRational inc_tb, int64_t inc);
 290
 291 /**
 292  * 0th order modified bessel function of the first kind.
 293  */
 294 double av_bessel_i0(double x);
 295
 296 /**
 297  * @}
 298  */
 299
 300 #endif /* AVUTIL_MATHEMATICS_H */