1
2/* @(#)e_hypot.c 1.3 95/01/18 */
3/*
4 * ====================================================
5 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
6 *
7 * Developed at SunSoft, 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 ieee_sqrt(2)/2 ulp, than
19 *	sqrt(z) has error less than 1 ulp (exercise).
20 *
21 *	So, compute ieee_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 ieee_sqrt(x^2+y^2) with error less
43 * 	than 1 ulps (units in the last place)
44 */
45
46#include "fdlibm.h"
47
48#ifdef __STDC__
49	double __ieee754_hypot(double x, double y)
50#else
51	double __ieee754_hypot(x,y)
52	double x, y;
53#endif
54{
55	double a=x,b=y,t1,t2,y1,y2,w;
56	int j,k,ha,hb;
57
58	ha = __HI(x)&0x7fffffff;	/* high word of  x */
59	hb = __HI(y)&0x7fffffff;	/* high word of  y */
60	if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
61	__HI(a) = ha;	/* a <- |a| */
62	__HI(b) = hb;	/* b <- |b| */
63	if((ha-hb)>0x3c00000) {return a+b;} /* x/y > 2**60 */
64	k=0;
65	if(ha > 0x5f300000) {	/* a>2**500 */
66	   if(ha >= 0x7ff00000) {	/* Inf or NaN */
67	       w = a+b;			/* for sNaN */
68	       if(((ha&0xfffff)|__LO(a))==0) w = a;
69	       if(((hb^0x7ff00000)|__LO(b))==0) w = b;
70	       return w;
71	   }
72	   /* scale a and b by 2**-600 */
73	   ha -= 0x25800000; hb -= 0x25800000;	k += 600;
74	   __HI(a) = ha;
75	   __HI(b) = hb;
76	}
77	if(hb < 0x20b00000) {	/* b < 2**-500 */
78	    if(hb <= 0x000fffff) {	/* subnormal b or 0 */
79		if((hb|(__LO(b)))==0) return a;
80		t1=0;
81		__HI(t1) = 0x7fd00000;	/* t1=2^1022 */
82		b *= t1;
83		a *= t1;
84		k -= 1022;
85	    } else {		/* scale a and b by 2^600 */
86	        ha += 0x25800000; 	/* a *= 2^600 */
87		hb += 0x25800000;	/* b *= 2^600 */
88		k -= 600;
89	   	__HI(a) = ha;
90	   	__HI(b) = hb;
91	    }
92	}
93    /* medium size a and b */
94	w = a-b;
95	if (w>b) {
96	    t1 = 0;
97	    __HI(t1) = ha;
98	    t2 = a-t1;
99	    w  = ieee_sqrt(t1*t1-(b*(-b)-t2*(a+t1)));
100	} else {
101	    a  = a+a;
102	    y1 = 0;
103	    __HI(y1) = hb;
104	    y2 = b - y1;
105	    t1 = 0;
106	    __HI(t1) = ha+0x00100000;
107	    t2 = a - t1;
108	    w  = ieee_sqrt(t1*y1-(w*(-w)-(t1*y2+t2*b)));
109	}
110	if(k!=0) {
111	    t1 = 1.0;
112	    __HI(t1) += (k<<20);
113	    return t1*w;
114	} else return w;
115}
116