mathematics.h (7975B)
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 = 85 5, ///< Round to nearest and halfway cases away from zero. 86 /** 87 * Flag telling rescaling functions to pass `INT64_MIN`/`MAX` through 88 * unchanged, avoiding special cases for #AV_NOPTS_VALUE. 89 * 90 * Unlike other values of the enumeration AVRounding, this value is a 91 * bitmask that must be used in conjunction with another value of the 92 * enumeration through a bitwise OR, in order to set behavior for normal 93 * cases. 94 * 95 * @code{.c} 96 * av_rescale_rnd(3, 1, 2, AV_ROUND_UP | AV_ROUND_PASS_MINMAX); 97 * // Rescaling 3: 98 * // Calculating 3 * 1 / 2 99 * // 3 / 2 is rounded up to 2 100 * // => 2 101 * 102 * av_rescale_rnd(AV_NOPTS_VALUE, 1, 2, AV_ROUND_UP | AV_ROUND_PASS_MINMAX); 103 * // Rescaling AV_NOPTS_VALUE: 104 * // AV_NOPTS_VALUE == INT64_MIN 105 * // AV_NOPTS_VALUE is passed through 106 * // => AV_NOPTS_VALUE 107 * @endcode 108 */ 109 AV_ROUND_PASS_MINMAX = 8192, 110 }; 111 112 /** 113 * Compute the greatest common divisor of two integer operands. 114 * 115 * @param a Operand 116 * @param b Operand 117 * @return GCD of a and b up to sign; if a >= 0 and b >= 0, return value is >= 118 * 0; if a == 0 and b == 0, returns 0. 119 */ 120 int64_t av_const av_gcd(int64_t a, int64_t b); 121 122 /** 123 * Rescale a 64-bit integer with rounding to nearest. 124 * 125 * The operation is mathematically equivalent to `a * b / c`, but writing that 126 * directly can overflow. 127 * 128 * This function is equivalent to av_rescale_rnd() with #AV_ROUND_NEAR_INF. 129 * 130 * @see av_rescale_rnd(), av_rescale_q(), av_rescale_q_rnd() 131 */ 132 int64_t av_rescale(int64_t a, int64_t b, int64_t c) av_const; 133 134 /** 135 * Rescale a 64-bit integer with specified rounding. 136 * 137 * The operation is mathematically equivalent to `a * b / c`, but writing that 138 * directly can overflow, and does not support different rounding methods. 139 * If the result is not representable then INT64_MIN is returned. 140 * 141 * @see av_rescale(), av_rescale_q(), av_rescale_q_rnd() 142 */ 143 int64_t av_rescale_rnd(int64_t a, int64_t b, int64_t c, 144 enum AVRounding rnd) av_const; 145 146 /** 147 * Rescale a 64-bit integer by 2 rational numbers. 148 * 149 * The operation is mathematically equivalent to `a * bq / cq`. 150 * 151 * This function is equivalent to av_rescale_q_rnd() with #AV_ROUND_NEAR_INF. 152 * 153 * @see av_rescale(), av_rescale_rnd(), av_rescale_q_rnd() 154 */ 155 int64_t av_rescale_q(int64_t a, AVRational bq, AVRational cq) av_const; 156 157 /** 158 * Rescale a 64-bit integer by 2 rational numbers with specified rounding. 159 * 160 * The operation is mathematically equivalent to `a * bq / cq`. 161 * 162 * @see av_rescale(), av_rescale_rnd(), av_rescale_q() 163 */ 164 int64_t av_rescale_q_rnd(int64_t a, AVRational bq, AVRational cq, 165 enum AVRounding rnd) av_const; 166 167 /** 168 * Compare two timestamps each in its own time base. 169 * 170 * @return One of the following values: 171 * - -1 if `ts_a` is before `ts_b` 172 * - 1 if `ts_a` is after `ts_b` 173 * - 0 if they represent the same position 174 * 175 * @warning 176 * The result of the function is undefined if one of the timestamps is outside 177 * the `int64_t` range when represented in the other's timebase. 178 */ 179 int av_compare_ts(int64_t ts_a, AVRational tb_a, int64_t ts_b, AVRational tb_b); 180 181 /** 182 * Compare the remainders of two integer operands divided by a common divisor. 183 * 184 * In other words, compare the least significant `log2(mod)` bits of integers 185 * `a` and `b`. 186 * 187 * @code{.c} 188 * av_compare_mod(0x11, 0x02, 0x10) < 0 // since 0x11 % 0x10 (0x1) < 0x02 % 189 * 0x10 (0x2) av_compare_mod(0x11, 0x02, 0x20) > 0 // since 0x11 % 0x20 (0x11) 190 * > 0x02 % 0x20 (0x02) 191 * @endcode 192 * 193 * @param a Operand 194 * @param b Operand 195 * @param mod Divisor; must be a power of 2 196 * @return 197 * - a negative value if `a % mod < b % mod` 198 * - a positive value if `a % mod > b % mod` 199 * - zero if `a % mod == b % mod` 200 */ 201 int64_t av_compare_mod(uint64_t a, uint64_t b, uint64_t mod); 202 203 /** 204 * Rescale a timestamp while preserving known durations. 205 * 206 * This function is designed to be called per audio packet to scale the input 207 * timestamp to a different time base. Compared to a simple av_rescale_q() 208 * call, this function is robust against possible inconsistent frame durations. 209 * 210 * The `last` parameter is a state variable that must be preserved for all 211 * subsequent calls for the same stream. For the first call, `*last` should be 212 * initialized to #AV_NOPTS_VALUE. 213 * 214 * @param[in] in_tb Input time base 215 * @param[in] in_ts Input timestamp 216 * @param[in] fs_tb Duration time base; typically this is finer-grained 217 * (greater) than `in_tb` and `out_tb` 218 * @param[in] duration Duration till the next call to this function (i.e. 219 * duration of the current packet/frame) 220 * @param[in,out] last Pointer to a timestamp expressed in terms of 221 * `fs_tb`, acting as a state variable 222 * @param[in] out_tb Output timebase 223 * @return Timestamp expressed in terms of `out_tb` 224 * 225 * @note In the context of this function, "duration" is in term of samples, not 226 * seconds. 227 */ 228 int64_t av_rescale_delta(AVRational in_tb, int64_t in_ts, AVRational fs_tb, 229 int duration, int64_t* last, AVRational out_tb); 230 231 /** 232 * Add a value to a timestamp. 233 * 234 * This function guarantees that when the same value is repeatly added that 235 * no accumulation of rounding errors occurs. 236 * 237 * @param[in] ts Input timestamp 238 * @param[in] ts_tb Input timestamp time base 239 * @param[in] inc Value to be added 240 * @param[in] inc_tb Time base of `inc` 241 */ 242 int64_t av_add_stable(AVRational ts_tb, int64_t ts, AVRational inc_tb, 243 int64_t inc); 244 245 /** 246 * @} 247 */ 248 249 #endif /* AVUTIL_MATHEMATICS_H */