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#ifndef lint
15static char rcsid[] = "$FreeBSD: src/lib/msun/src/e_hypot.c,v 1.9 2005/02/04 18:26:05 das Exp $";
16#endif
17
18/* __ieee754_hypot(x,y)
19 *
20 * Method :
21 *	If (assume round-to-nearest) z=x*x+y*y
22 *	has error less than sqrt(2)/2 ulp, than
23 *	sqrt(z) has error less than 1 ulp (exercise).
24 *
25 *	So, compute sqrt(x*x+y*y) with some care as
26 *	follows to get the error below 1 ulp:
27 *
28 *	Assume x>y>0;
29 *	(if possible, set rounding to round-to-nearest)
30 *	1. if x > 2y  use
31 *		x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y
32 *	where x1 = x with lower 32 bits cleared, x2 = x-x1; else
33 *	2. if x <= 2y use
34 *		t1*y1+((x-y)*(x-y)+(t1*y2+t2*y))
35 *	where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1,
36 *	y1= y with lower 32 bits chopped, y2 = y-y1.
37 *
38 *	NOTE: scaling may be necessary if some argument is too
39 *	      large or too tiny
40 *
41 * Special cases:
42 *	hypot(x,y) is INF if x or y is +INF or -INF; else
43 *	hypot(x,y) is NAN if x or y is NAN.
44 *
45 * Accuracy:
46 * 	hypot(x,y) returns sqrt(x^2+y^2) with error less
47 * 	than 1 ulps (units in the last place)
48 */
49
50#include "math.h"
51#include "math_private.h"
52
53double
54__ieee754_hypot(double x, double y)
55{
56	double a=x,b=y,t1,t2,y1,y2,w;
57	int32_t j,k,ha,hb;
58
59	GET_HIGH_WORD(ha,x);
60	ha &= 0x7fffffff;
61	GET_HIGH_WORD(hb,y);
62	hb &= 0x7fffffff;
63	if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
64	SET_HIGH_WORD(a,ha);	/* a <- |a| */
65	SET_HIGH_WORD(b,hb);	/* b <- |b| */
66	if((ha-hb)>0x3c00000) {return a+b;} /* x/y > 2**60 */
67	k=0;
68	if(ha > 0x5f300000) {	/* a>2**500 */
69	   if(ha >= 0x7ff00000) {	/* Inf or NaN */
70	       u_int32_t low;
71	       w = a+b;			/* for sNaN */
72	       GET_LOW_WORD(low,a);
73	       if(((ha&0xfffff)|low)==0) w = a;
74	       GET_LOW_WORD(low,b);
75	       if(((hb^0x7ff00000)|low)==0) w = b;
76	       return w;
77	   }
78	   /* scale a and b by 2**-600 */
79	   ha -= 0x25800000; hb -= 0x25800000;	k += 600;
80	   SET_HIGH_WORD(a,ha);
81	   SET_HIGH_WORD(b,hb);
82	}
83	if(hb < 0x20b00000) {	/* b < 2**-500 */
84	    if(hb <= 0x000fffff) {	/* subnormal b or 0 */
85	        u_int32_t low;
86		GET_LOW_WORD(low,b);
87		if((hb|low)==0) return a;
88		t1=0;
89		SET_HIGH_WORD(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		SET_HIGH_WORD(a,ha);
98		SET_HIGH_WORD(b,hb);
99	    }
100	}
101    /* medium size a and b */
102	w = a-b;
103	if (w>b) {
104	    t1 = 0;
105	    SET_HIGH_WORD(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	    SET_HIGH_WORD(y1,hb);
112	    y2 = b - y1;
113	    t1 = 0;
114	    SET_HIGH_WORD(t1,ha+0x00100000);
115	    t2 = a - t1;
116	    w  = sqrt(t1*y1-(w*(-w)-(t1*y2+t2*b)));
117	}
118	if(k!=0) {
119	    u_int32_t high;
120	    t1 = 1.0;
121	    GET_HIGH_WORD(high,t1);
122	    SET_HIGH_WORD(t1,high+(k<<20));
123	    return t1*w;
124	} else return w;
125}
126