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
|
/* @(#)e_fmod.c 1.3 95/01/18 */
/*-
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
#include <sys/cdefs.h>
/* __FBSDID("$FreeBSD: src/lib/msun/src/s_remquof.c,v 1.1 2005/03/25 04:40:44 das Exp $"); */
#include "math.h"
#include "math_private.h"
static const float Zero[] = {0.0, -0.0,};
/*
* Return the IEEE remainder and set *quo to the last n bits of the
* quotient, rounded to the nearest integer. We choose n=31 because
* we wind up computing all the integer bits of the quotient anyway as
* a side-effect of computing the remainder by the shift and subtract
* method. In practice, this is far more bits than are needed to use
* remquo in reduction algorithms.
*/
float
remquof(float x, float y, int *quo)
{
int32_t n,hx,hy,hz,ix,iy,sx,i;
u_int32_t q,sxy;
GET_FLOAT_WORD(hx,x);
GET_FLOAT_WORD(hy,y);
sxy = (hx ^ hy) & 0x80000000;
sx = hx&0x80000000; /* sign of x */
hx ^=sx; /* |x| */
hy &= 0x7fffffff; /* |y| */
/* purge off exception values */
if(hy==0||hx>=0x7f800000||hy>0x7f800000) /* y=0,NaN;or x not finite */
return (x*y)/(x*y);
if(hx<hy) {
q = 0;
goto fixup; /* |x|<|y| return x or x-y */
} else if(hx==hy) {
*quo = 1;
return Zero[(u_int32_t)sx>>31]; /* |x|=|y| return x*0*/
}
/* determine ix = ilogb(x) */
if(hx<0x00800000) { /* subnormal x */
for (ix = -126,i=(hx<<8); i>0; i<<=1) ix -=1;
} else ix = (hx>>23)-127;
/* determine iy = ilogb(y) */
if(hy<0x00800000) { /* subnormal y */
for (iy = -126,i=(hy<<8); i>0; i<<=1) iy -=1;
} else iy = (hy>>23)-127;
/* set up {hx,lx}, {hy,ly} and align y to x */
if(ix >= -126)
hx = 0x00800000|(0x007fffff&hx);
else { /* subnormal x, shift x to normal */
n = -126-ix;
hx <<= n;
}
if(iy >= -126)
hy = 0x00800000|(0x007fffff&hy);
else { /* subnormal y, shift y to normal */
n = -126-iy;
hy <<= n;
}
/* fix point fmod */
n = ix - iy;
q = 0;
while(n--) {
hz=hx-hy;
if(hz<0) hx = hx << 1;
else {hx = hz << 1; q++;}
q <<= 1;
}
hz=hx-hy;
if(hz>=0) {hx=hz;q++;}
/* convert back to floating value and restore the sign */
if(hx==0) { /* return sign(x)*0 */
*quo = (sxy ? -q : q);
return Zero[(u_int32_t)sx>>31];
}
while(hx<0x00800000) { /* normalize x */
hx <<= 1;
iy -= 1;
}
if(iy>= -126) { /* normalize output */
hx = ((hx-0x00800000)|((iy+127)<<23));
} else { /* subnormal output */
n = -126 - iy;
hx >>= n;
}
fixup:
SET_FLOAT_WORD(x,hx);
y = fabsf(y);
if (y < 0x1p-125f) {
if (x+x>y || (x+x==y && (q & 1))) {
q++;
x-=y;
}
} else if (x>0.5f*y || (x==0.5f*y && (q & 1))) {
q++;
x-=y;
}
GET_FLOAT_WORD(hx,x);
SET_FLOAT_WORD(x,hx^sx);
q &= 0x7fffffff;
*quo = (sxy ? -q : q);
return x;
}
|
