mathematics.h (9565B)
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 */