FFmpeg
 All Data Structures Namespaces Files Functions Variables Typedefs Enumerations Enumerator Macros Groups Pages
mathematics.h
Go to the documentation of this file.
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  */
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 */
#define av_const
Definition: attributes.h:76
const char * b
Definition: vf_curves.c:113
AVRounding
Rounding methods.
Definition: mathematics.h:79
Macro definitions for various function/variable attributes.
Round toward +infinity.
Definition: mathematics.h:83
int64_t duration
Definition: movenc.c:63
int64_t av_rescale_q(int64_t a, AVRational bq, AVRational cq) av_const
Rescale a 64-bit integer by 2 rational numbers.
Definition: mathematics.c:142
Round away from zero.
Definition: mathematics.h:81
Round to nearest and halfway cases away from zero.
Definition: mathematics.h:84
int64_t av_const av_gcd(int64_t a, int64_t b)
Compute the greatest common divisor of two integer operands.
Definition: mathematics.c:37
int av_compare_ts(int64_t ts_a, AVRational tb_a, int64_t ts_b, AVRational tb_b)
Compare two timestamps each in its own time base.
Definition: mathematics.c:147
int64_t av_rescale(int64_t a, int64_t b, int64_t c) av_const
Rescale a 64-bit integer with rounding to nearest.
Definition: mathematics.c:129
Round toward zero.
Definition: mathematics.h:80
int64_t av_rescale_rnd(int64_t a, int64_t b, int64_t c, enum AVRounding rnd) av_const
Rescale a 64-bit integer with specified rounding.
Definition: mathematics.c:58
int64_t av_rescale_delta(AVRational in_tb, int64_t in_ts, AVRational fs_tb, int duration, int64_t *last, AVRational out_tb)
Rescale a timestamp while preserving known durations.
Definition: mathematics.c:168
Rational number (pair of numerator and denominator).
Definition: rational.h:58
Round toward -infinity.
Definition: mathematics.h:82
Utilties for rational number calculation.
int64_t av_add_stable(AVRational ts_tb, int64_t ts, AVRational inc_tb, int64_t inc)
Add a value to a timestamp.
Definition: mathematics.c:191
static double c[64]
#define rnd()
Definition: checkasm.h:67
Flag telling rescaling functions to pass INT64_MIN/MAX through unchanged, avoiding special cases for ...
Definition: mathematics.h:108
int64_t av_rescale_q_rnd(int64_t a, AVRational bq, AVRational cq, enum AVRounding rnd) av_const
Rescale a 64-bit integer by 2 rational numbers with specified rounding.
Definition: mathematics.c:134
int64_t av_compare_mod(uint64_t a, uint64_t b, uint64_t mod)
Compare the remainders of two integer operands divided by a common divisor.
Definition: mathematics.c:160