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
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
|
#include "aftypes.h"
/* this table was generated for AF_ANGLE_PI = 256 */
#define AF_ANGLE_MAX_ITERS 8
static const FT_Fixed
af_angle_arctan_table[9] =
{
90, 64, 38, 20, 10, 5, 3, 1, 1
};
static FT_Int
af_angle_prenorm( FT_Vector* vec )
{
FT_Fixed x, y, z;
FT_Int shift;
x = vec->x;
y = vec->y;
z = ( ( x >= 0 ) ? x : - x ) | ( (y >= 0) ? y : -y );
shift = 0;
if ( z < ( 1L << 27 ) )
{
do
{
shift++;
z <<= 1;
} while ( z < ( 1L << 27 ) );
vec->x = x << shift;
vec->y = y << shift;
}
else if ( z > ( 1L << 28 ) )
{
do
{
shift++;
z >>= 1;
} while ( z > ( 1L << 28 ) );
vec->x = x >> shift;
vec->y = y >> shift;
shift = -shift;
}
return shift;
}
static void
af_angle_pseudo_polarize( FT_Vector* vec )
{
FT_Fixed theta;
FT_Fixed yi, i;
FT_Fixed x, y;
const FT_Fixed *arctanptr;
x = vec->x;
y = vec->y;
/* Get the vector into the right half plane */
theta = 0;
if ( x < 0 )
{
x = -x;
y = -y;
theta = 2 * AF_ANGLE_PI2;
}
if ( y > 0 )
theta = - theta;
arctanptr = af_angle_arctan_table;
if ( y < 0 )
{
/* Rotate positive */
yi = y + ( x << 1 );
x = x - ( y << 1 );
y = yi;
theta -= *arctanptr++; /* Subtract angle */
}
else
{
/* Rotate negative */
yi = y - ( x << 1 );
x = x + ( y << 1 );
y = yi;
theta += *arctanptr++; /* Add angle */
}
i = 0;
do
{
if ( y < 0 )
{
/* Rotate positive */
yi = y + ( x >> i );
x = x - ( y >> i );
y = yi;
theta -= *arctanptr++;
}
else
{
/* Rotate negative */
yi = y - ( x >> i );
x = x + ( y >> i );
y = yi;
theta += *arctanptr++;
}
} while ( ++i < AF_TRIG_MAX_ITERS );
/* round theta */
if ( theta >= 0 )
theta = ( theta + 2 ) & -4;
else
theta = - (( -theta + 2 ) & -4);
vec->x = x;
vec->y = theta;
}
/* documentation is in fttrigon.h */
FT_LOCAL_DEF( AF_Angle )
af_angle_atan( FT_Fixed dx,
FT_Fixed dy )
{
FT_Vector v;
if ( dx == 0 && dy == 0 )
return 0;
v.x = dx;
v.y = dy;
af_angle_prenorm( &v );
af_angle_pseudo_polarize( &v );
return v.y;
}
FT_LOCAL_DEF( AF_Angle )
af_angle_diff( AF_Angle angle1,
AF_Angle angle2 )
{
AF_Angle delta = angle2 - angle1;
delta %= AF_ANGLE_2PI;
if ( delta < 0 )
delta += AF_ANGLE_2PI;
if ( delta > AF_ANGLE_PI )
delta -= AF_ANGLE_2PI;
return delta;
}
/* well, this needs to be somewhere, right :-)
*/
FT_LOCAL_DEF( void )
af_sort_pos( FT_UInt count,
FT_Pos* table )
{
FT_Int i, j;
FT_Pos swap;
for ( i = 1; i < count; i++ )
{
for ( j = i; j > 0; j-- )
{
if ( table[j] > table[j - 1] )
break;
swap = table[j];
table[j] = table[j - 1];
table[j - 1] = swap;
}
}
}
|
