mathematics.h (7945B)
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 * 138 * @see av_rescale(), av_rescale_q(), av_rescale_q_rnd() 139 */ 140 int64_t av_rescale_rnd(int64_t a, int64_t b, int64_t c, enum AVRounding rnd) av_const; 141 142 /** 143 * Rescale a 64-bit integer by 2 rational numbers. 144 * 145 * The operation is mathematically equivalent to `a * bq / cq`. 146 * 147 * This function is equivalent to av_rescale_q_rnd() with #AV_ROUND_NEAR_INF. 148 * 149 * @see av_rescale(), av_rescale_rnd(), av_rescale_q_rnd() 150 */ 151 int64_t av_rescale_q(int64_t a, AVRational bq, AVRational cq) av_const; 152 153 /** 154 * Rescale a 64-bit integer by 2 rational numbers with specified rounding. 155 * 156 * The operation is mathematically equivalent to `a * bq / cq`. 157 * 158 * @see av_rescale(), av_rescale_rnd(), av_rescale_q() 159 */ 160 int64_t av_rescale_q_rnd(int64_t a, AVRational bq, AVRational cq, 161 enum AVRounding rnd) av_const; 162 163 /** 164 * Compare two timestamps each in its own time base. 165 * 166 * @return One of the following values: 167 * - -1 if `ts_a` is before `ts_b` 168 * - 1 if `ts_a` is after `ts_b` 169 * - 0 if they represent the same position 170 * 171 * @warning 172 * The result of the function is undefined if one of the timestamps is outside 173 * the `int64_t` range when represented in the other's timebase. 174 */ 175 int av_compare_ts(int64_t ts_a, AVRational tb_a, int64_t ts_b, AVRational tb_b); 176 177 /** 178 * Compare the remainders of two integer operands divided by a common divisor. 179 * 180 * In other words, compare the least significant `log2(mod)` bits of integers 181 * `a` and `b`. 182 * 183 * @code{.c} 184 * av_compare_mod(0x11, 0x02, 0x10) < 0 // since 0x11 % 0x10 (0x1) < 0x02 % 0x10 (0x2) 185 * av_compare_mod(0x11, 0x02, 0x20) > 0 // since 0x11 % 0x20 (0x11) > 0x02 % 0x20 (0x02) 186 * @endcode 187 * 188 * @param a,b Operands 189 * @param mod Divisor; must be a power of 2 190 * @return 191 * - a negative value if `a % mod < b % mod` 192 * - a positive value if `a % mod > b % mod` 193 * - zero if `a % mod == b % mod` 194 */ 195 int64_t av_compare_mod(uint64_t a, uint64_t b, uint64_t mod); 196 197 /** 198 * Rescale a timestamp while preserving known durations. 199 * 200 * This function is designed to be called per audio packet to scale the input 201 * timestamp to a different time base. Compared to a simple av_rescale_q() 202 * call, this function is robust against possible inconsistent frame durations. 203 * 204 * The `last` parameter is a state variable that must be preserved for all 205 * subsequent calls for the same stream. For the first call, `*last` should be 206 * initialized to #AV_NOPTS_VALUE. 207 * 208 * @param[in] in_tb Input time base 209 * @param[in] in_ts Input timestamp 210 * @param[in] fs_tb Duration time base; typically this is finer-grained 211 * (greater) than `in_tb` and `out_tb` 212 * @param[in] duration Duration till the next call to this function (i.e. 213 * duration of the current packet/frame) 214 * @param[in,out] last Pointer to a timestamp expressed in terms of 215 * `fs_tb`, acting as a state variable 216 * @param[in] out_tb Output timebase 217 * @return Timestamp expressed in terms of `out_tb` 218 * 219 * @note In the context of this function, "duration" is in term of samples, not 220 * seconds. 221 */ 222 int64_t av_rescale_delta(AVRational in_tb, int64_t in_ts, AVRational fs_tb, int duration, int64_t *last, AVRational out_tb); 223 224 /** 225 * Add a value to a timestamp. 226 * 227 * This function guarantees that when the same value is repeatly added that 228 * no accumulation of rounding errors occurs. 229 * 230 * @param[in] ts Input timestamp 231 * @param[in] ts_tb Input timestamp time base 232 * @param[in] inc Value to be added 233 * @param[in] inc_tb Time base of `inc` 234 */ 235 int64_t av_add_stable(AVRational ts_tb, int64_t ts, AVRational inc_tb, int64_t inc); 236 237 238 /** 239 * @} 240 */ 241 242 #endif /* AVUTIL_MATHEMATICS_H */