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 /* __ieee754_hypot(x,y)
15  *
16  * Method :
17  *	If (assume round-to-nearest) z=x*x+y*y
18  *	has error less than ieee_sqrt(2)/2 ulp, than
19  *	sqrt(z) has error less than 1 ulp (exercise).
20  *
21  *	So, compute ieee_sqrt(x*x+y*y) with some care as
22  *	follows to get the error below 1 ulp:
23  *
24  *	Assume x>y>0;
25  *	(if possible, set rounding to round-to-nearest)
26  *	1. if x > 2y  use
27  *		x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y
28  *	where x1 = x with lower 32 bits cleared, x2 = x-x1; else
29  *	2. if x <= 2y use
30  *		t1*y1+((x-y)*(x-y)+(t1*y2+t2*y))
31  *	where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1,
32  *	y1= y with lower 32 bits chopped, y2 = y-y1.
33  *
34  *	NOTE: scaling may be necessary if some argument is too
35  *	      large or too tiny
36  *
37  * Special cases:
38  *	hypot(x,y) is INF if x or y is +INF or -INF; else
39  *	hypot(x,y) is NAN if x or y is NAN.
40  *
41  * Accuracy:
42  * 	hypot(x,y) returns ieee_sqrt(x^2+y^2) with error less
43  * 	than 1 ulps (units in the last place)
44  */
45 
46 #include "fdlibm.h"
47 
48 #ifdef __STDC__
__ieee754_hypot(double x,double y)49 	double __ieee754_hypot(double x, double y)
50 #else
51 	double __ieee754_hypot(x,y)
52 	double x, y;
53 #endif
54 {
55 	double a=x,b=y,t1,t2,y1,y2,w;
56 	int j,k,ha,hb;
57 
58 	ha = __HI(x)&0x7fffffff;	/* high word of  x */
59 	hb = __HI(y)&0x7fffffff;	/* high word of  y */
60 	if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
61 	__HI(a) = ha;	/* a <- |a| */
62 	__HI(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 	       w = a+b;			/* for sNaN */
68 	       if(((ha&0xfffff)|__LO(a))==0) w = a;
69 	       if(((hb^0x7ff00000)|__LO(b))==0) w = b;
70 	       return w;
71 	   }
72 	   /* scale a and b by 2**-600 */
73 	   ha -= 0x25800000; hb -= 0x25800000;	k += 600;
74 	   __HI(a) = ha;
75 	   __HI(b) = hb;
76 	}
77 	if(hb < 0x20b00000) {	/* b < 2**-500 */
78 	    if(hb <= 0x000fffff) {	/* subnormal b or 0 */
79 		if((hb|(__LO(b)))==0) return a;
80 		t1=0;
81 		__HI(t1) = 0x7fd00000;	/* t1=2^1022 */
82 		b *= t1;
83 		a *= t1;
84 		k -= 1022;
85 	    } else {		/* scale a and b by 2^600 */
86 	        ha += 0x25800000; 	/* a *= 2^600 */
87 		hb += 0x25800000;	/* b *= 2^600 */
88 		k -= 600;
89 	   	__HI(a) = ha;
90 	   	__HI(b) = hb;
91 	    }
92 	}
93     /* medium size a and b */
94 	w = a-b;
95 	if (w>b) {
96 	    t1 = 0;
97 	    __HI(t1) = ha;
98 	    t2 = a-t1;
99 	    w  = ieee_sqrt(t1*t1-(b*(-b)-t2*(a+t1)));
100 	} else {
101 	    a  = a+a;
102 	    y1 = 0;
103 	    __HI(y1) = hb;
104 	    y2 = b - y1;
105 	    t1 = 0;
106 	    __HI(t1) = ha+0x00100000;
107 	    t2 = a - t1;
108 	    w  = ieee_sqrt(t1*y1-(w*(-w)-(t1*y2+t2*b)));
109 	}
110 	if(k!=0) {
111 	    t1 = 1.0;
112 	    __HI(t1) += (k<<20);
113 	    return t1*w;
114 	} else return w;
115 }
116