source: trunk/sys/libm/e_hypot.c @ 1

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1
2/* @(#)e_hypot.c 5.1 93/09/24 */
3/*
4 * ====================================================
5 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
6 *
7 * Developed at SunPro, a Sun Microsystems, Inc. business.
8 * Permission to use, copy, modify, and distribute this
9 * software is freely granted, provided that this notice
10 * is preserved.
11 * ====================================================
12 */
13
14/* __ieee754_hypot(x,y)
15 *
16 * Method :                 
17 *      If (assume round-to-nearest) z=x*x+y*y
18 *      has error less than sqrt(2)/2 ulp, than
19 *      sqrt(z) has error less than 1 ulp (exercise).
20 *
21 *      So, compute sqrt(x*x+y*y) with some care as
22 *      follows to get the error below 1 ulp:
23 *
24 *      Assume x>y>0;
25 *      (if possible, set rounding to round-to-nearest)
26 *      1. if x > 2y  use
27 *              x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y
28 *      where x1 = x with lower 32 bits cleared, x2 = x-x1; else
29 *      2. if x <= 2y use
30 *              t1*y1+((x-y)*(x-y)+(t1*y2+t2*y))
31 *      where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1,
32 *      y1= y with lower 32 bits chopped, y2 = y-y1.
33 *             
34 *      NOTE: scaling may be necessary if some argument is too
35 *            large or too tiny
36 *
37 * Special cases:
38 *      hypot(x,y) is INF if x or y is +INF or -INF; else
39 *      hypot(x,y) is NAN if x or y is NAN.
40 *
41 * Accuracy:
42 *      hypot(x,y) returns sqrt(x^2+y^2) with error less
43 *      than 1 ulps (units in the last place)
44 */
45
46#include <libm/fdlibm.h>
47
48#ifdef __STDC__
49static const double one = 1.0;
50#else
51static double one = 1.0;
52#endif
53
54#ifdef __STDC__
55        double __ieee754_hypot(double x, double y)
56#else
57        double __ieee754_hypot(x,y)
58        double x, y;
59#endif
60{
61        int n0;
62        double a=x,b=y,t1,t2,y1,y2,w;
63        int j,k,ha,hb;
64
65        n0 = ((*(int*)&one)>>29)^1;     /* high word index */
66        ha = *(n0+(int*)&x)&0x7fffffff; /* high word of  x */
67        hb = *(n0+(int*)&y)&0x7fffffff; /* high word of  y */
68        if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
69        *(n0+(int*)&a) = ha;    /* a <- |a| */
70        *(n0+(int*)&b) = hb;    /* b <- |b| */
71        if((ha-hb)>0x3c00000) {return a+b;} /* x/y > 2**60 */
72        k=0;
73        if(ha > 0x5f300000) {   /* a>2**500 */
74           if(ha >= 0x7ff00000) {       /* Inf or NaN */
75               w = a+b;                 /* for sNaN */
76               if(((ha&0xfffff)|*(1-n0+(int*)&a))==0) w = a;
77               if(((hb^0x7ff00000)|*(1-n0+(int*)&b))==0) w = b;
78               return w;
79           }
80           /* scale a and b by 2**-600 */
81           ha -= 0x25800000; hb -= 0x25800000;  k += 600;
82           *(n0+(int*)&a) = ha;
83           *(n0+(int*)&b) = hb;
84        }
85        if(hb < 0x20b00000) {   /* b < 2**-500 */
86            if(hb <= 0x000fffff) {      /* subnormal b or 0 */ 
87                if((hb|(*(1-n0+(int*)&b)))==0) return a;
88                t1=0;
89                *(n0+(int*)&t1) = 0x7fd00000;   /* t1=2^1022 */
90                b *= t1;
91                a *= t1;
92                k -= 1022;
93            } else {            /* scale a and b by 2^600 */
94                ha += 0x25800000;       /* a *= 2^600 */
95                hb += 0x25800000;       /* b *= 2^600 */
96                k -= 600;
97                *(n0+(int*)&a) = ha;
98                *(n0+(int*)&b) = hb;
99            }
100        }
101    /* medium size a and b */
102        w = a-b;
103        if (w>b) {
104            t1 = 0;
105            *(n0+(int*)&t1) = ha;
106            t2 = a-t1;
107            w  = sqrt(t1*t1-(b*(-b)-t2*(a+t1)));
108        } else {
109            a  = a+a;
110            y1 = 0;
111            *(n0+(int*)&y1) = hb;
112            y2 = b - y1;
113            t1 = 0;
114            *(n0+(int*)&t1) = ha+0x00100000;
115            t2 = a - t1;
116            w  = sqrt(t1*y1-(w*(-w)-(t1*y2+t2*b)));
117        }
118        if(k!=0) {
119            t1 = 1.0;
120            *(n0+(int*)&t1) += (k<<20);
121            return t1*w;
122        } else return w;
123}
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