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/* hypot(x,y)
14 *
15 * Method :
16 *	If (assume round-to-nearest) z=x*x+y*y
17 *	has error less than sqrt(2)/2 ulp, than
18 *	sqrt(z) has error less than 1 ulp (exercise).
19 *
20 *	So, compute sqrt(x*x+y*y) with some care as
21 *	follows to get the error below 1 ulp:
22 *
23 *	Assume x>y>0;
24 *	(if possible, set rounding to round-to-nearest)
25 *	1. if x > 2y  use
26 *		x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y
27 *	where x1 = x with lower 32 bits cleared, x2 = x-x1; else
28 *	2. if x <= 2y use
29 *		t1*yy1+((x-y)*(x-y)+(t1*y2+t2*y))
30 *	where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1,
31 *	yy1= y with lower 32 bits chopped, y2 = y-yy1.
32 *
33 *	NOTE: scaling may be necessary if some argument is too
34 *	      large or too tiny
35 *
36 * Special cases:
37 *	hypot(x,y) is INF if x or y is +INF or -INF; else
38 *	hypot(x,y) is NAN if x or y is NAN.
39 *
40 * Accuracy:
41 * 	hypot(x,y) returns sqrt(x^2+y^2) with error less
42 * 	than 1 ulps (units in the last place)
43 */
44
45#include <float.h>
46#include <math.h>
47
48#include "math_private.h"
49
50double
51hypot(double x, double y)
52{
53	double a=x,b=y,t1,t2,yy1,y2,w;
54	int32_t j,k,ha,hb;
55
56	GET_HIGH_WORD(ha,x);
57	ha &= 0x7fffffff;
58	GET_HIGH_WORD(hb,y);
59	hb &= 0x7fffffff;
60	if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
61	SET_HIGH_WORD(a,ha);	/* a <- |a| */
62	SET_HIGH_WORD(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	       u_int32_t low;
68	       w = a+b;			/* for sNaN */
69	       GET_LOW_WORD(low,a);
70	       if(((ha&0xfffff)|low)==0) w = a;
71	       GET_LOW_WORD(low,b);
72	       if(((hb^0x7ff00000)|low)==0) w = b;
73	       return w;
74	   }
75	   /* scale a and b by 2**-600 */
76	   ha -= 0x25800000; hb -= 0x25800000;	k += 600;
77	   SET_HIGH_WORD(a,ha);
78	   SET_HIGH_WORD(b,hb);
79	}
80	if(hb < 0x20b00000) {	/* b < 2**-500 */
81	    if(hb <= 0x000fffff) {	/* subnormal b or 0 */
82	        u_int32_t low;
83		GET_LOW_WORD(low,b);
84		if((hb|low)==0) return a;
85		t1=0;
86		SET_HIGH_WORD(t1,0x7fd00000);	/* t1=2^1022 */
87		b *= t1;
88		a *= t1;
89		k -= 1022;
90	    } else {		/* scale a and b by 2^600 */
91	        ha += 0x25800000; 	/* a *= 2^600 */
92		hb += 0x25800000;	/* b *= 2^600 */
93		k -= 600;
94		SET_HIGH_WORD(a,ha);
95		SET_HIGH_WORD(b,hb);
96	    }
97	}
98    /* medium size a and b */
99	w = a-b;
100	if (w>b) {
101	    t1 = 0;
102	    SET_HIGH_WORD(t1,ha);
103	    t2 = a-t1;
104	    w  = sqrt(t1*t1-(b*(-b)-t2*(a+t1)));
105	} else {
106	    a  = a+a;
107	    yy1 = 0;
108	    SET_HIGH_WORD(yy1,hb);
109	    y2 = b - yy1;
110	    t1 = 0;
111	    SET_HIGH_WORD(t1,ha+0x00100000);
112	    t2 = a - t1;
113	    w  = sqrt(t1*yy1-(w*(-w)-(t1*y2+t2*b)));
114	}
115	if(k!=0) {
116	    u_int32_t high;
117	    t1 = 1.0;
118	    GET_HIGH_WORD(high,t1);
119	    SET_HIGH_WORD(t1,high+(k<<20));
120	    return t1*w;
121	} else return w;
122}
123DEF_STD(hypot);
124LDBL_MAYBE_CLONE(hypot);
125