2 * Copyright (c) 2005-2012 Michael Niedermayer <michaelni@gmx.at>
4 * This file is part of FFmpeg.
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.
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.
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
23 * miscellaneous math routines and tables
29 #include "mathematics.h"
30 #include "libavutil/common.h"
35 const uint8_t av_reverse
[256] = {
36 0x00,0x80,0x40,0xC0,0x20,0xA0,0x60,0xE0,0x10,0x90,0x50,0xD0,0x30,0xB0,0x70,0xF0,
37 0x08,0x88,0x48,0xC8,0x28,0xA8,0x68,0xE8,0x18,0x98,0x58,0xD8,0x38,0xB8,0x78,0xF8,
38 0x04,0x84,0x44,0xC4,0x24,0xA4,0x64,0xE4,0x14,0x94,0x54,0xD4,0x34,0xB4,0x74,0xF4,
39 0x0C,0x8C,0x4C,0xCC,0x2C,0xAC,0x6C,0xEC,0x1C,0x9C,0x5C,0xDC,0x3C,0xBC,0x7C,0xFC,
40 0x02,0x82,0x42,0xC2,0x22,0xA2,0x62,0xE2,0x12,0x92,0x52,0xD2,0x32,0xB2,0x72,0xF2,
41 0x0A,0x8A,0x4A,0xCA,0x2A,0xAA,0x6A,0xEA,0x1A,0x9A,0x5A,0xDA,0x3A,0xBA,0x7A,0xFA,
42 0x06,0x86,0x46,0xC6,0x26,0xA6,0x66,0xE6,0x16,0x96,0x56,0xD6,0x36,0xB6,0x76,0xF6,
43 0x0E,0x8E,0x4E,0xCE,0x2E,0xAE,0x6E,0xEE,0x1E,0x9E,0x5E,0xDE,0x3E,0xBE,0x7E,0xFE,
44 0x01,0x81,0x41,0xC1,0x21,0xA1,0x61,0xE1,0x11,0x91,0x51,0xD1,0x31,0xB1,0x71,0xF1,
45 0x09,0x89,0x49,0xC9,0x29,0xA9,0x69,0xE9,0x19,0x99,0x59,0xD9,0x39,0xB9,0x79,0xF9,
46 0x05,0x85,0x45,0xC5,0x25,0xA5,0x65,0xE5,0x15,0x95,0x55,0xD5,0x35,0xB5,0x75,0xF5,
47 0x0D,0x8D,0x4D,0xCD,0x2D,0xAD,0x6D,0xED,0x1D,0x9D,0x5D,0xDD,0x3D,0xBD,0x7D,0xFD,
48 0x03,0x83,0x43,0xC3,0x23,0xA3,0x63,0xE3,0x13,0x93,0x53,0xD3,0x33,0xB3,0x73,0xF3,
49 0x0B,0x8B,0x4B,0xCB,0x2B,0xAB,0x6B,0xEB,0x1B,0x9B,0x5B,0xDB,0x3B,0xBB,0x7B,0xFB,
50 0x07,0x87,0x47,0xC7,0x27,0xA7,0x67,0xE7,0x17,0x97,0x57,0xD7,0x37,0xB7,0x77,0xF7,
51 0x0F,0x8F,0x4F,0xCF,0x2F,0xAF,0x6F,0xEF,0x1F,0x9F,0x5F,0xDF,0x3F,0xBF,0x7F,0xFF,
55 int64_t av_gcd(int64_t a
, int64_t b
)
58 return av_gcd(b
, a
% b
);
63 int64_t av_rescale_rnd(int64_t a
, int64_t b
, int64_t c
, enum AVRounding rnd
)
68 av_assert2((unsigned)(rnd
&~AV_ROUND_PASS_MINMAX
)<=5 && (rnd
&~AV_ROUND_PASS_MINMAX
)!=4);
70 if (c
<= 0 || b
< 0 || !((unsigned)(rnd
&~AV_ROUND_PASS_MINMAX
)<=5 && (rnd
&~AV_ROUND_PASS_MINMAX
)!=4))
73 if (rnd
& AV_ROUND_PASS_MINMAX
) {
74 if (a
== INT64_MIN
|| a
== INT64_MAX
)
76 rnd
-= AV_ROUND_PASS_MINMAX
;
79 if (a
< 0 && a
!= INT64_MIN
)
80 return -av_rescale_rnd(-a
, b
, c
, rnd
^ ((rnd
>> 1) & 1));
82 if (rnd
== AV_ROUND_NEAR_INF
)
87 if (b
<= INT_MAX
&& c
<= INT_MAX
) {
89 return (a
* b
+ r
) / c
;
91 return a
/ c
* b
+ (a
% c
* b
+ r
) / c
;
94 uint64_t a0
= a
& 0xFFFFFFFF;
95 uint64_t a1
= a
>> 32;
96 uint64_t b0
= b
& 0xFFFFFFFF;
97 uint64_t b1
= b
>> 32;
98 uint64_t t1
= a0
* b1
+ a1
* b0
;
99 uint64_t t1a
= t1
<< 32;
103 a1
= a1
* b1
+ (t1
>> 32) + (a0
< t1a
);
107 for (i
= 63; i
>= 0; i
--) {
108 a1
+= a1
+ ((a0
>> i
) & 1);
119 ai
= av_mul_i(av_int2i(a
), av_int2i(b
));
120 ai
= av_add_i(ai
, av_int2i(r
));
122 return av_i2int(av_div_i(ai
, av_int2i(c
)));
127 int64_t av_rescale(int64_t a
, int64_t b
, int64_t c
)
129 return av_rescale_rnd(a
, b
, c
, AV_ROUND_NEAR_INF
);
132 int64_t av_rescale_q_rnd(int64_t a
, AVRational bq
, AVRational cq
,
135 int64_t b
= bq
.num
* (int64_t)cq
.den
;
136 int64_t c
= cq
.num
* (int64_t)bq
.den
;
137 return av_rescale_rnd(a
, b
, c
, rnd
);
140 int64_t av_rescale_q(int64_t a
, AVRational bq
, AVRational cq
)
142 return av_rescale_q_rnd(a
, bq
, cq
, AV_ROUND_NEAR_INF
);
145 int av_compare_ts(int64_t ts_a
, AVRational tb_a
, int64_t ts_b
, AVRational tb_b
)
147 int64_t a
= tb_a
.num
* (int64_t)tb_b
.den
;
148 int64_t b
= tb_b
.num
* (int64_t)tb_a
.den
;
149 if ((FFABS(ts_a
)|a
|FFABS(ts_b
)|b
) <= INT_MAX
)
150 return (ts_a
*a
> ts_b
*b
) - (ts_a
*a
< ts_b
*b
);
151 if (av_rescale_rnd(ts_a
, a
, b
, AV_ROUND_DOWN
) < ts_b
)
153 if (av_rescale_rnd(ts_b
, b
, a
, AV_ROUND_DOWN
) < ts_a
)
158 int64_t av_compare_mod(uint64_t a
, uint64_t b
, uint64_t mod
)
160 int64_t c
= (a
- b
) & (mod
- 1);
166 int64_t av_rescale_delta(AVRational in_tb
, int64_t in_ts
, AVRational fs_tb
, int duration
, int64_t *last
, AVRational out_tb
){
169 av_assert0(in_ts
!= AV_NOPTS_VALUE
);
170 av_assert0(duration
>= 0);
172 if (*last
== AV_NOPTS_VALUE
|| !duration
|| in_tb
.num
*(int64_t)out_tb
.den
<= out_tb
.num
*(int64_t)in_tb
.den
) {
174 *last
= av_rescale_q(in_ts
, in_tb
, fs_tb
) + duration
;
175 return av_rescale_q(in_ts
, in_tb
, out_tb
);
178 a
= av_rescale_q_rnd(2*in_ts
-1, in_tb
, fs_tb
, AV_ROUND_DOWN
) >>1;
179 b
= (av_rescale_q_rnd(2*in_ts
+1, in_tb
, fs_tb
, AV_ROUND_UP
)+1)>>1;
180 if (*last
< 2*a
- b
|| *last
> 2*b
- a
)
183 this = av_clip64(*last
, a
, b
);
184 *last
= this + duration
;
186 return av_rescale_q(this, fs_tb
, out_tb
);
189 int64_t av_add_stable(AVRational ts_tb
, int64_t ts
, AVRational inc_tb
, int64_t inc
)
194 inc_tb
= av_mul_q(inc_tb
, (AVRational
) {inc
, 1});
196 m
= inc_tb
.num
* (int64_t)ts_tb
.den
;
197 d
= inc_tb
.den
* (int64_t)ts_tb
.num
;
205 int64_t old
= av_rescale_q(ts
, ts_tb
, inc_tb
);
206 int64_t old_ts
= av_rescale_q(old
, inc_tb
, ts_tb
);
207 return av_rescale_q(old
+ 1, inc_tb
, ts_tb
) + (ts
- old_ts
);