1/* @(#)e_hypot.c 5.1 93/09/24 */
2/*
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5 *
6 * Developed at SunPro, a Sun Microsystems, Inc. business.
7 * Permission to use, copy, modify, and distribute this
8 * software is freely granted, provided that this notice
9 * is preserved.
10 * ====================================================
11 */
12
13#if defined(LIBM_SCCS) && !defined(lint)
14static char rcsid[] = "$NetBSD: e_hypot.c,v 1.9 1995/05/12 04:57:27 jtc Exp $";
15#endif
16
17/* __ieee754_hypot(x,y)
18 *
19 * Method :
20 *	If (assume round-to-nearest) z=x*x+y*y
21 *	has error less than sqrt(2)/2 ulp, than
22 *	sqrt(z) has error less than 1 ulp (exercise).
23 *
24 *	So, compute sqrt(x*x+y*y) with some care as
25 *	follows to get the error below 1 ulp:
26 *
27 *	Assume x>y>0;
28 *	(if possible, set rounding to round-to-nearest)
29 *	1. if x > 2y  use
30 *		x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y
31 *	where x1 = x with lower 32 bits cleared, x2 = x-x1; else
32 *	2. if x <= 2y use
33 *		t1*y1+((x-y)*(x-y)+(t1*y2+t2*y))
34 *	where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1,
35 *	y1= y with lower 32 bits chopped, y2 = y-y1.
36 *
37 *	NOTE: scaling may be necessary if some argument is too
38 *	      large or too tiny
39 *
40 * Special cases:
41 *	hypot(x,y) is INF if x or y is +INF or -INF; else
42 *	hypot(x,y) is NAN if x or y is NAN.
43 *
44 * Accuracy:
45 * 	hypot(x,y) returns sqrt(x^2+y^2) with error less
46 * 	than 1 ulps (units in the last place)
47 */
48
49#include "math.h"
50#include "math_private.h"
51
52#ifdef __STDC__
53	double __ieee754_hypot(double x, double y)
54#else
55	double __ieee754_hypot(x,y)
56	double x, y;
57#endif
58{
59	double a,b,t1,t2,y1,y2,w;
60	int32_t j,k,ha,hb;
61
62	GET_HIGH_WORD(ha,x);
63	ha &= 0x7fffffff;
64	GET_HIGH_WORD(hb,y);
65	hb &= 0x7fffffff;
66	if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
67	SET_HIGH_WORD(a,ha);	/* a <- |a| */
68	SET_HIGH_WORD(b,hb);	/* b <- |b| */
69	if((ha-hb)>0x3c00000) {return a+b;} /* x/y > 2**60 */
70	k=0;
71	if(ha > 0x5f300000) {	/* a>2**500 */
72	   if(ha >= 0x7ff00000) {	/* Inf or NaN */
73	       u_int32_t low;
74	       w = a+b;			/* for sNaN */
75	       GET_LOW_WORD(low,a);
76	       if(((ha&0xfffff)|low)==0) w = a;
77	       GET_LOW_WORD(low,b);
78	       if(((hb^0x7ff00000)|low)==0) w = b;
79	       return w;
80	   }
81	   /* scale a and b by 2**-600 */
82	   ha -= 0x25800000; hb -= 0x25800000;	k += 600;
83	   SET_HIGH_WORD(a,ha);
84	   SET_HIGH_WORD(b,hb);
85	}
86	if(hb < 0x20b00000) {	/* b < 2**-500 */
87	    if(hb <= 0x000fffff) {	/* subnormal b or 0 */
88	        u_int32_t low;
89		GET_LOW_WORD(low,b);
90		if((hb|low)==0) return a;
91		t1=0;
92		SET_HIGH_WORD(t1,0x7fd00000);	/* t1=2^1022 */
93		b *= t1;
94		a *= t1;
95		k -= 1022;
96	    } else {		/* scale a and b by 2^600 */
97	        ha += 0x25800000; 	/* a *= 2^600 */
98		hb += 0x25800000;	/* b *= 2^600 */
99		k -= 600;
100		SET_HIGH_WORD(a,ha);
101		SET_HIGH_WORD(b,hb);
102	    }
103	}
104    /* medium size a and b */
105	w = a-b;
106	if (w>b) {
107	    t1 = 0;
108	    SET_HIGH_WORD(t1,ha);
109	    t2 = a-t1;
110	    w  = __ieee754_sqrt(t1*t1-(b*(-b)-t2*(a+t1)));
111	} else {
112	    a  = a+a;
113	    y1 = 0;
114	    SET_HIGH_WORD(y1,hb);
115	    y2 = b - y1;
116	    t1 = 0;
117	    SET_HIGH_WORD(t1,ha+0x00100000);
118	    t2 = a - t1;
119	    w  = __ieee754_sqrt(t1*y1-(w*(-w)-(t1*y2+t2*b)));
120	}
121	if(k!=0) {
122	    u_int32_t high;
123	    t1 = 1.0;
124	    GET_HIGH_WORD(high,t1);
125	    SET_HIGH_WORD(t1,high+(k<<20));
126	    return t1*w;
127	} else return w;
128}
129