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
|
/* Rewritten for 64-bit machines by Ulrich Drepper <drepper@gmail.com>. */
/*
* ====================================================
* 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>
#include <stdint.h>
static const double one = 1.0, Zero[] = {0.0, -0.0,};
double
__ieee754_fmod (double x, double y)
{
int32_t n,ix,iy;
int64_t hx,hy,hz,sx,i;
EXTRACT_WORDS64(hx,x);
EXTRACT_WORDS64(hy,y);
sx = hx&UINT64_C(0x8000000000000000); /* sign of x */
hx ^=sx; /* |x| */
hy &= UINT64_C(0x7fffffffffffffff); /* |y| */
/* purge off exception values */
if(__builtin_expect(hy==0
|| hx >= UINT64_C(0x7ff0000000000000)
|| hy > UINT64_C(0x7ff0000000000000), 0))
/* y=0,or x not finite or y is NaN */
return (x*y)/(x*y);
if(__builtin_expect(hx<=hy, 0)) {
if(hx<hy) return x; /* |x|<|y| return x */
return Zero[(uint64_t)sx>>63]; /* |x|=|y| return x*0*/
}
/* determine ix = ilogb(x) */
if(__builtin_expect(hx<UINT64_C(0x0010000000000000), 0)) {
/* subnormal x */
for (ix = -1022,i=(hx<<11); i>0; i<<=1) ix -=1;
} else ix = (hx>>52)-1023;
/* determine iy = ilogb(y) */
if(__builtin_expect(hy<UINT64_C(0x0010000000000000), 0)) { /* subnormal y */
for (iy = -1022,i=(hy<<11); i>0; i<<=1) iy -=1;
} else iy = (hy>>52)-1023;
/* set up hx, hy and align y to x */
if(__builtin_expect(ix >= -1022, 1))
hx = UINT64_C(0x0010000000000000)|(UINT64_C(0x000fffffffffffff)&hx);
else { /* subnormal x, shift x to normal */
n = -1022-ix;
hx<<=n;
}
if(__builtin_expect(iy >= -1022, 1))
hy = UINT64_C(0x0010000000000000)|(UINT64_C(0x000fffffffffffff)&hy);
else { /* subnormal y, shift y to normal */
n = -1022-iy;
hy<<=n;
}
/* fix point fmod */
n = ix - iy;
while(n--) {
hz=hx-hy;
if(hz<0){hx = hx+hx;}
else {
if(hz==0) /* return sign(x)*0 */
return Zero[(uint64_t)sx>>63];
hx = hz+hz;
}
}
hz=hx-hy;
if(hz>=0) {hx=hz;}
/* convert back to floating value and restore the sign */
if(hx==0) /* return sign(x)*0 */
return Zero[(uint64_t)sx>>63];
while(hx<UINT64_C(0x0010000000000000)) { /* normalize x */
hx = hx+hx;
iy -= 1;
}
if(__builtin_expect(iy>= -1022, 1)) { /* normalize output */
hx = ((hx-UINT64_C(0x0010000000000000))|((uint64_t)(iy+1023)<<52));
INSERT_WORDS64(x,hx|sx);
} else { /* subnormal output */
n = -1022 - iy;
hx>>=n;
INSERT_WORDS64(x,hx|sx);
x *= one; /* create necessary signal */
}
return x; /* exact output */
}
strong_alias (__ieee754_fmod, __fmod_finite)
|
