1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
|
/*
* Copyright (c) 2005 Michael Niedermayer <michaelni@gmx.at>
*
* This file is part of FFmpeg.
*
* FFmpeg is free software; you can redistribute it and/or
* modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation; either
* version 2.1 of the License, or (at your option) any later version.
*
* FFmpeg is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public
* License along with FFmpeg; if not, write to the Free Software
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
*/
/**
* @file mathematics.c
* Miscellaneous math routines and tables.
*/
#include "common.h"
#include "mathematics.h"
const uint8_t ff_sqrt_tab[128]={
0, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5,
5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11
};
const uint8_t ff_log2_tab[256]={
0,0,1,1,2,2,2,2,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,
5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,
6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,
6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,
7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,
7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,
7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,
7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7
};
int64_t ff_gcd(int64_t a, int64_t b){
if(b) return ff_gcd(b, a%b);
else return a;
}
int64_t av_rescale_rnd(int64_t a, int64_t b, int64_t c, enum AVRounding rnd){
int64_t r=0;
assert(c > 0);
assert(b >=0);
assert(rnd >=0 && rnd<=5 && rnd!=4);
if(a<0 && a != INT64_MIN) return -av_rescale_rnd(-a, b, c, rnd ^ ((rnd>>1)&1));
if(rnd==AV_ROUND_NEAR_INF) r= c/2;
else if(rnd&1) r= c-1;
if(b<=INT_MAX && c<=INT_MAX){
if(a<=INT_MAX)
return (a * b + r)/c;
else
return a/c*b + (a%c*b + r)/c;
}else{
#if 1
uint64_t a0= a&0xFFFFFFFF;
uint64_t a1= a>>32;
uint64_t b0= b&0xFFFFFFFF;
uint64_t b1= b>>32;
uint64_t t1= a0*b1 + a1*b0;
uint64_t t1a= t1<<32;
int i;
a0 = a0*b0 + t1a;
a1 = a1*b1 + (t1>>32) + (a0<t1a);
a0 += r;
a1 += a0<r;
for(i=63; i>=0; i--){
// int o= a1 & 0x8000000000000000ULL;
a1+= a1 + ((a0>>i)&1);
t1+=t1;
if(/*o || */c <= a1){
a1 -= c;
t1++;
}
}
return t1;
}
#else
AVInteger ai;
ai= av_mul_i(av_int2i(a), av_int2i(b));
ai= av_add_i(ai, av_int2i(r));
return av_i2int(av_div_i(ai, av_int2i(c)));
}
#endif
}
int64_t av_rescale(int64_t a, int64_t b, int64_t c){
return av_rescale_rnd(a, b, c, AV_ROUND_NEAR_INF);
}
int64_t av_rescale_q(int64_t a, AVRational bq, AVRational cq){
int64_t b= bq.num * (int64_t)cq.den;
int64_t c= cq.num * (int64_t)bq.den;
return av_rescale_rnd(a, b, c, AV_ROUND_NEAR_INF);
}
#if 0
#include "integer.h"
#undef printf
main(){
int64_t a,b,c,d,e;
for(a=7; a<(1LL<<62); a+=a/3+1){
for(b=3; b<(1LL<<62); b+=b/4+1){
for(c=9; c<(1LL<<62); c+=(c*2)/5+3){
int64_t r= c/2;
AVInteger ai;
ai= av_mul_i(av_int2i(a), av_int2i(b));
ai= av_add_i(ai, av_int2i(r));
d= av_i2int(av_div_i(ai, av_int2i(c)));
e= av_rescale(a,b,c);
if((double)a * (double)b / (double)c > (1LL<<63))
continue;
if(d!=e) printf("%Ld*%Ld/%Ld= %Ld=%Ld\n", a, b, c, d, e);
}
}
}
}
#endif
|
