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
|
/* @(#)e_hypot.c 5.1 93/09/24 */
/*
* ====================================================
* 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.
* ====================================================
*/
#if defined(LIBM_SCCS) && !defined(lint)
static char rcsid[] = "$NetBSD: e_hypot.c,v 1.9 1995/05/12 04:57:27 jtc Exp $";
#endif
/* __ieee754_hypot(x,y)
*
* Method :
* If (assume round-to-nearest) z=x*x+y*y
* has error less than sqrt(2)/2 ulp, than
* sqrt(z) has error less than 1 ulp (exercise).
*
* So, compute sqrt(x*x+y*y) with some care as
* follows to get the error below 1 ulp:
*
* Assume x>y>0;
* (if possible, set rounding to round-to-nearest)
* 1. if x > 2y use
* x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y
* where x1 = x with lower 32 bits cleared, x2 = x-x1; else
* 2. if x <= 2y use
* t1*y1+((x-y)*(x-y)+(t1*y2+t2*y))
* where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1,
* y1= y with lower 32 bits chopped, y2 = y-y1.
*
* NOTE: scaling may be necessary if some argument is too
* large or too tiny
*
* Special cases:
* hypot(x,y) is INF if x or y is +INF or -INF; else
* hypot(x,y) is NAN if x or y is NAN.
*
* Accuracy:
* hypot(x,y) returns sqrt(x^2+y^2) with error less
* than 1 ulps (units in the last place)
*/
#include "math.h"
#include "math_private.h"
#ifdef __STDC__
double __ieee754_hypot(double x, double y)
#else
double __ieee754_hypot(x,y)
double x, y;
#endif
{
double a=x,b=y,t1,t2,y1,y2,w;
int32_t j,k,ha,hb;
GET_HIGH_WORD(ha,x);
ha &= 0x7fffffff;
GET_HIGH_WORD(hb,y);
hb &= 0x7fffffff;
if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
SET_HIGH_WORD(a,ha); /* a <- |a| */
SET_HIGH_WORD(b,hb); /* b <- |b| */
if((ha-hb)>0x3c00000) {return a+b;} /* x/y > 2**60 */
k=0;
if(ha > 0x5f300000) { /* a>2**500 */
if(ha >= 0x7ff00000) { /* Inf or NaN */
u_int32_t low;
w = a+b; /* for sNaN */
GET_LOW_WORD(low,a);
if(((ha&0xfffff)|low)==0) w = a;
GET_LOW_WORD(low,b);
if(((hb^0x7ff00000)|low)==0) w = b;
return w;
}
/* scale a and b by 2**-600 */
ha -= 0x25800000; hb -= 0x25800000; k += 600;
SET_HIGH_WORD(a,ha);
SET_HIGH_WORD(b,hb);
}
if(hb < 0x20b00000) { /* b < 2**-500 */
if(hb <= 0x000fffff) { /* subnormal b or 0 */
u_int32_t low;
GET_LOW_WORD(low,b);
if((hb|low)==0) return a;
t1=0;
SET_HIGH_WORD(t1,0x7fd00000); /* t1=2^1022 */
b *= t1;
a *= t1;
k -= 1022;
} else { /* scale a and b by 2^600 */
ha += 0x25800000; /* a *= 2^600 */
hb += 0x25800000; /* b *= 2^600 */
k -= 600;
SET_HIGH_WORD(a,ha);
SET_HIGH_WORD(b,hb);
}
}
/* medium size a and b */
w = a-b;
if (w>b) {
t1 = 0;
SET_HIGH_WORD(t1,ha);
t2 = a-t1;
w = __ieee754_sqrt(t1*t1-(b*(-b)-t2*(a+t1)));
} else {
a = a+a;
y1 = 0;
SET_HIGH_WORD(y1,hb);
y2 = b - y1;
t1 = 0;
SET_HIGH_WORD(t1,ha+0x00100000);
t2 = a - t1;
w = __ieee754_sqrt(t1*y1-(w*(-w)-(t1*y2+t2*b)));
}
if(k!=0) {
u_int32_t high;
t1 = 1.0;
GET_HIGH_WORD(high,t1);
SET_HIGH_WORD(t1,high+(k<<20));
return t1*w;
} else return w;
}
|
