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
|
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/*
* __ieee754_fmod(x,y)
* Return x mod y in exact arithmetic
* Method: shift and subtract
*/
#include <math.h>
#include <math_private.h>
static const double one = 1.0, Zero[] = { 0.0, -0.0, };
double
__ieee754_fmod (double x, double y)
{
int32_t n, hx, hy, hz, ix, iy, sx, i;
u_int32_t lx, ly, lz;
EXTRACT_WORDS (hx, lx, x);
EXTRACT_WORDS (hy, ly, y);
sx = hx & 0x80000000; /* sign of x */
hx ^= sx; /* |x| */
hy &= 0x7fffffff; /* |y| */
/* purge off exception values */
if ((hy | ly) == 0 || (hx >= 0x7ff00000) || /* y=0,or x not finite */
((hy | ((ly | -ly) >> 31)) > 0x7ff00000)) /* or y is NaN */
return (x * y) / (x * y);
if (hx <= hy)
{
if ((hx < hy) || (lx < ly))
return x; /* |x|<|y| return x */
if (lx == ly)
return Zero[(u_int32_t) sx >> 31]; /* |x|=|y| return x*0*/
}
/* determine ix = ilogb(x) */
if (__builtin_expect (hx < 0x00100000, 0)) /* subnormal x */
{
if (hx == 0)
{
for (ix = -1043, i = lx; i > 0; i <<= 1)
ix -= 1;
}
else
{
for (ix = -1022, i = (hx << 11); i > 0; i <<= 1)
ix -= 1;
}
}
else
ix = (hx >> 20) - 1023;
/* determine iy = ilogb(y) */
if (__builtin_expect (hy < 0x00100000, 0)) /* subnormal y */
{
if (hy == 0)
{
for (iy = -1043, i = ly; i > 0; i <<= 1)
iy -= 1;
}
else
{
for (iy = -1022, i = (hy << 11); i > 0; i <<= 1)
iy -= 1;
}
}
else
iy = (hy >> 20) - 1023;
/* set up {hx,lx}, {hy,ly} and align y to x */
if (__builtin_expect (ix >= -1022, 1))
hx = 0x00100000 | (0x000fffff & hx);
else /* subnormal x, shift x to normal */
{
n = -1022 - ix;
if (n <= 31)
{
hx = (hx << n) | (lx >> (32 - n));
lx <<= n;
}
else
{
hx = lx << (n - 32);
lx = 0;
}
}
if (__builtin_expect (iy >= -1022, 1))
hy = 0x00100000 | (0x000fffff & hy);
else /* subnormal y, shift y to normal */
{
n = -1022 - iy;
if (n <= 31)
{
hy = (hy << n) | (ly >> (32 - n));
ly <<= n;
}
else
{
hy = ly << (n - 32);
ly = 0;
}
}
/* fix point fmod */
n = ix - iy;
while (n--)
{
hz = hx - hy; lz = lx - ly; if (lx < ly)
hz -= 1;
if (hz < 0)
{
hx = hx + hx + (lx >> 31); lx = lx + lx;
}
else
{
if ((hz | lz) == 0) /* return sign(x)*0 */
return Zero[(u_int32_t) sx >> 31];
hx = hz + hz + (lz >> 31); lx = lz + lz;
}
}
hz = hx - hy; lz = lx - ly; if (lx < ly)
hz -= 1;
if (hz >= 0)
{
hx = hz; lx = lz;
}
/* convert back to floating value and restore the sign */
if ((hx | lx) == 0) /* return sign(x)*0 */
return Zero[(u_int32_t) sx >> 31];
while (hx < 0x00100000) /* normalize x */
{
hx = hx + hx + (lx >> 31); lx = lx + lx;
iy -= 1;
}
if (__builtin_expect (iy >= -1022, 1)) /* normalize output */
{
hx = ((hx - 0x00100000) | ((iy + 1023) << 20));
INSERT_WORDS (x, hx | sx, lx);
}
else /* subnormal output */
{
n = -1022 - iy;
if (n <= 20)
{
lx = (lx >> n) | ((u_int32_t) hx << (32 - n));
hx >>= n;
}
else if (n <= 31)
{
lx = (hx << (32 - n)) | (lx >> n); hx = sx;
}
else
{
lx = hx >> (n - 32); hx = sx;
}
INSERT_WORDS (x, hx | sx, lx);
x *= one; /* create necessary signal */
}
return x; /* exact output */
}
strong_alias (__ieee754_fmod, __fmod_finite)
|
