1
2/*
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5 *
6 * Developed at SunSoft, 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*y1+((x-y)*(x-y)+(t1*y2+t2*y))
30 *	where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1,
31 *	y1= y with lower 32 bits chopped, y2 = y-y1.
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
47#include "math.h"
48#include "math_private.h"
49
50double
51hypot(double x, double y)
52{
53	double a,b,t1,t2,y1,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	a = fabs(a);
62	b = fabs(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	       /* Use original arg order iff result is NaN; quieten sNaNs. */
69	       w = fabsl(x+0.0L)-fabs(y+0);
70	       GET_LOW_WORD(low,a);
71	       if(((ha&0xfffff)|low)==0) w = a;
72	       GET_LOW_WORD(low,b);
73	       if(((hb^0x7ff00000)|low)==0) w = b;
74	       return w;
75	   }
76	   /* scale a and b by 2**-600 */
77	   ha -= 0x25800000; hb -= 0x25800000;	k += 600;
78	   SET_HIGH_WORD(a,ha);
79	   SET_HIGH_WORD(b,hb);
80	}
81	if(hb < 0x20b00000) {	/* b < 2**-500 */
82	    if(hb <= 0x000fffff) {	/* subnormal b or 0 */
83	        u_int32_t low;
84		GET_LOW_WORD(low,b);
85		if((hb|low)==0) return a;
86		t1=0;
87		SET_HIGH_WORD(t1,0x7fd00000);	/* t1=2^1022 */
88		b *= t1;
89		a *= t1;
90		k -= 1022;
91	    } else {		/* scale a and b by 2^600 */
92	        ha += 0x25800000; 	/* a *= 2^600 */
93		hb += 0x25800000;	/* b *= 2^600 */
94		k -= 600;
95		SET_HIGH_WORD(a,ha);
96		SET_HIGH_WORD(b,hb);
97	    }
98	}
99    /* medium size a and b */
100	w = a-b;
101	if (w>b) {
102	    t1 = 0;
103	    SET_HIGH_WORD(t1,ha);
104	    t2 = a-t1;
105	    w  = sqrt(t1*t1-(b*(-b)-t2*(a+t1)));
106	} else {
107	    a  = a+a;
108	    y1 = 0;
109	    SET_HIGH_WORD(y1,hb);
110	    y2 = b - y1;
111	    t1 = 0;
112	    SET_HIGH_WORD(t1,ha+0x00100000);
113	    t2 = a - t1;
114	    w  = sqrt(t1*y1-(w*(-w)-(t1*y2+t2*b)));
115	}
116	if(k!=0) {
117	    t1 = 0.0;
118	    SET_HIGH_WORD(t1,(1023+k)<<20);
119	    return t1*w;
120	} else return w;
121}
122
123#if LDBL_MANT_DIG == 53
124__weak_reference(hypot, hypotl);
125#endif
126