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#include <sys/cdefs.h>
15__FBSDID("$FreeBSD$");
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 <float.h>
50
51#include "math.h"
52#include "math_private.h"
53
54double
55__ieee754_hypot(double x, double y)
56{
57	double a,b,t1,t2,y1,y2,w;
58	int32_t j,k,ha,hb;
59
60	GET_HIGH_WORD(ha,x);
61	ha &= 0x7fffffff;
62	GET_HIGH_WORD(hb,y);
63	hb &= 0x7fffffff;
64	if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
65	a = fabs(a);
66	b = fabs(b);
67	if((ha-hb)>0x3c00000) {return a+b;} /* x/y > 2**60 */
68	k=0;
69	if(ha > 0x5f300000) {	/* a>2**500 */
70	   if(ha >= 0x7ff00000) {	/* Inf or NaN */
71	       u_int32_t low;
72	       /* Use original arg order iff result is NaN; quieten sNaNs. */
73	       w = fabs(x+0.0)-fabs(y+0.0);
74	       GET_LOW_WORD(low,a);
75	       if(((ha&0xfffff)|low)==0) w = a;
76	       GET_LOW_WORD(low,b);
77	       if(((hb^0x7ff00000)|low)==0) w = b;
78	       return w;
79	   }
80	   /* scale a and b by 2**-600 */
81	   ha -= 0x25800000; hb -= 0x25800000;	k += 600;
82	   SET_HIGH_WORD(a,ha);
83	   SET_HIGH_WORD(b,hb);
84	}
85	if(hb < 0x20b00000) {	/* b < 2**-500 */
86	    if(hb <= 0x000fffff) {	/* subnormal b or 0 */
87	        u_int32_t low;
88		GET_LOW_WORD(low,b);
89		if((hb|low)==0) return a;
90		t1=0;
91		SET_HIGH_WORD(t1,0x7fd00000);	/* t1=2^1022 */
92		b *= t1;
93		a *= t1;
94		k -= 1022;
95	    } else {		/* scale a and b by 2^600 */
96	        ha += 0x25800000; 	/* a *= 2^600 */
97		hb += 0x25800000;	/* b *= 2^600 */
98		k -= 600;
99		SET_HIGH_WORD(a,ha);
100		SET_HIGH_WORD(b,hb);
101	    }
102	}
103    /* medium size a and b */
104	w = a-b;
105	if (w>b) {
106	    t1 = 0;
107	    SET_HIGH_WORD(t1,ha);
108	    t2 = a-t1;
109	    w  = sqrt(t1*t1-(b*(-b)-t2*(a+t1)));
110	} else {
111	    a  = a+a;
112	    y1 = 0;
113	    SET_HIGH_WORD(y1,hb);
114	    y2 = b - y1;
115	    t1 = 0;
116	    SET_HIGH_WORD(t1,ha+0x00100000);
117	    t2 = a - t1;
118	    w  = sqrt(t1*y1-(w*(-w)-(t1*y2+t2*b)));
119	}
120	if(k!=0) {
121	    u_int32_t high;
122	    t1 = 1.0;
123	    GET_HIGH_WORD(high,t1);
124	    SET_HIGH_WORD(t1,high+(k<<20));
125	    return t1*w;
126	} else return w;
127}
128
129#if LDBL_MANT_DIG == 53
130__weak_reference(hypot, hypotl);
131#endif
132