mathematics.h (9407B)
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 = 136 5, ///< Round to nearest and halfway cases away from zero. 137 /** 138 * Flag telling rescaling functions to pass `INT64_MIN`/`MAX` through 139 * unchanged, avoiding special cases for #AV_NOPTS_VALUE. 140 * 141 * Unlike other values of the enumeration AVRounding, this value is a 142 * bitmask that must be used in conjunction with another value of the 143 * enumeration through a bitwise OR, in order to set behavior for normal 144 * cases. 145 * 146 * @code{.c} 147 * av_rescale_rnd(3, 1, 2, AV_ROUND_UP | AV_ROUND_PASS_MINMAX); 148 * // Rescaling 3: 149 * // Calculating 3 * 1 / 2 150 * // 3 / 2 is rounded up to 2 151 * // => 2 152 * 153 * av_rescale_rnd(AV_NOPTS_VALUE, 1, 2, AV_ROUND_UP | AV_ROUND_PASS_MINMAX); 154 * // Rescaling AV_NOPTS_VALUE: 155 * // AV_NOPTS_VALUE == INT64_MIN 156 * // AV_NOPTS_VALUE is passed through 157 * // => AV_NOPTS_VALUE 158 * @endcode 159 */ 160 AV_ROUND_PASS_MINMAX = 8192, 161 }; 162 163 /** 164 * Compute the greatest common divisor of two integer operands. 165 * 166 * @param a Operand 167 * @param b Operand 168 * @return GCD of a and b up to sign; if a >= 0 and b >= 0, return value is >= 169 * 0; if a == 0 and b == 0, returns 0. 170 */ 171 int64_t av_const av_gcd(int64_t a, int64_t b); 172 173 /** 174 * Rescale a 64-bit integer with rounding to nearest. 175 * 176 * The operation is mathematically equivalent to `a * b / c`, but writing that 177 * directly can overflow. 178 * 179 * This function is equivalent to av_rescale_rnd() with #AV_ROUND_NEAR_INF. 180 * 181 * @see av_rescale_rnd(), av_rescale_q(), av_rescale_q_rnd() 182 */ 183 int64_t av_rescale(int64_t a, int64_t b, int64_t c) av_const; 184 185 /** 186 * Rescale a 64-bit integer with specified rounding. 187 * 188 * The operation is mathematically equivalent to `a * b / c`, but writing that 189 * directly can overflow, and does not support different rounding methods. 190 * If the result is not representable then INT64_MIN is returned. 191 * 192 * @see av_rescale(), av_rescale_q(), av_rescale_q_rnd() 193 */ 194 int64_t av_rescale_rnd(int64_t a, int64_t b, int64_t c, 195 enum AVRounding rnd) av_const; 196 197 /** 198 * Rescale a 64-bit integer by 2 rational numbers. 199 * 200 * The operation is mathematically equivalent to `a * bq / cq`. 201 * 202 * This function is equivalent to av_rescale_q_rnd() with #AV_ROUND_NEAR_INF. 203 * 204 * @see av_rescale(), av_rescale_rnd(), av_rescale_q_rnd() 205 */ 206 int64_t av_rescale_q(int64_t a, AVRational bq, AVRational cq) av_const; 207 208 /** 209 * Rescale a 64-bit integer by 2 rational numbers with specified rounding. 210 * 211 * The operation is mathematically equivalent to `a * bq / cq`. 212 * 213 * @see av_rescale(), av_rescale_rnd(), av_rescale_q() 214 */ 215 int64_t av_rescale_q_rnd(int64_t a, AVRational bq, AVRational cq, 216 enum AVRounding rnd) av_const; 217 218 /** 219 * Compare two timestamps each in its own time base. 220 * 221 * @return One of the following values: 222 * - -1 if `ts_a` is before `ts_b` 223 * - 1 if `ts_a` is after `ts_b` 224 * - 0 if they represent the same position 225 * 226 * @warning 227 * The result of the function is undefined if one of the timestamps is outside 228 * the `int64_t` range when represented in the other's timebase. 229 */ 230 int av_compare_ts(int64_t ts_a, AVRational tb_a, int64_t ts_b, AVRational tb_b); 231 232 /** 233 * Compare the remainders of two integer operands divided by a common divisor. 234 * 235 * In other words, compare the least significant `log2(mod)` bits of integers 236 * `a` and `b`. 237 * 238 * @code{.c} 239 * av_compare_mod(0x11, 0x02, 0x10) < 0 // since 0x11 % 0x10 (0x1) < 0x02 % 240 * 0x10 (0x2) av_compare_mod(0x11, 0x02, 0x20) > 0 // since 0x11 % 0x20 (0x11) 241 * > 0x02 % 0x20 (0x02) 242 * @endcode 243 * 244 * @param a Operand 245 * @param b Operand 246 * @param mod Divisor; must be a power of 2 247 * @return 248 * - a negative value if `a % mod < b % mod` 249 * - a positive value if `a % mod > b % mod` 250 * - zero if `a % mod == b % mod` 251 */ 252 int64_t av_compare_mod(uint64_t a, uint64_t b, uint64_t mod); 253 254 /** 255 * Rescale a timestamp while preserving known durations. 256 * 257 * This function is designed to be called per audio packet to scale the input 258 * timestamp to a different time base. Compared to a simple av_rescale_q() 259 * call, this function is robust against possible inconsistent frame durations. 260 * 261 * The `last` parameter is a state variable that must be preserved for all 262 * subsequent calls for the same stream. For the first call, `*last` should be 263 * initialized to #AV_NOPTS_VALUE. 264 * 265 * @param[in] in_tb Input time base 266 * @param[in] in_ts Input timestamp 267 * @param[in] fs_tb Duration time base; typically this is finer-grained 268 * (greater) than `in_tb` and `out_tb` 269 * @param[in] duration Duration till the next call to this function (i.e. 270 * duration of the current packet/frame) 271 * @param[in,out] last Pointer to a timestamp expressed in terms of 272 * `fs_tb`, acting as a state variable 273 * @param[in] out_tb Output timebase 274 * @return Timestamp expressed in terms of `out_tb` 275 * 276 * @note In the context of this function, "duration" is in term of samples, not 277 * seconds. 278 */ 279 int64_t av_rescale_delta(AVRational in_tb, int64_t in_ts, AVRational fs_tb, 280 int duration, int64_t* last, AVRational out_tb); 281 282 /** 283 * Add a value to a timestamp. 284 * 285 * This function guarantees that when the same value is repeatly added that 286 * no accumulation of rounding errors occurs. 287 * 288 * @param[in] ts Input timestamp 289 * @param[in] ts_tb Input timestamp time base 290 * @param[in] inc Value to be added 291 * @param[in] inc_tb Time base of `inc` 292 */ 293 int64_t av_add_stable(AVRational ts_tb, int64_t ts, AVRational inc_tb, 294 int64_t inc); 295 296 /** 297 * 0th order modified bessel function of the first kind. 298 */ 299 double av_bessel_i0(double x); 300 301 /** 302 * @} 303 */ 304 305 #endif /* AVUTIL_MATHEMATICS_H */