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 */
130enum 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 */
170int64_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 */
182int64_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 */
193int64_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 */
204int64_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 */
213int64_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 */
228int 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 */
249int64_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 */
276int64_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 repeatly 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 */
289int64_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 */
294double av_bessel_i0(double x);
295
296/**
297 * @}
298 */
299
300#endif /* AVUTIL_MATHEMATICS_H */
301