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+
+/* @(#)e_hypot.c 1.3 95/01/18 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunSoft, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice 
+ * is preserved.
+ * ====================================================
+ */
+
+/* __ieee754_hypot(x,y)
+ *
+ * Method :                  
+ *	If (assume round-to-nearest) z=x*x+y*y 
+ *	has error less than ieee_sqrt(2)/2 ulp, than 
+ *	sqrt(z) has error less than 1 ulp (exercise).
+ *
+ *	So, compute ieee_sqrt(x*x+y*y) with some care as 
+ *	follows to get the error below 1 ulp:
+ *
+ *	Assume x>y>0;
+ *	(if possible, set rounding to round-to-nearest)
+ *	1. if x > 2y  use
+ *		x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y
+ *	where x1 = x with lower 32 bits cleared, x2 = x-x1; else
+ *	2. if x <= 2y use
+ *		t1*y1+((x-y)*(x-y)+(t1*y2+t2*y))
+ *	where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1, 
+ *	y1= y with lower 32 bits chopped, y2 = y-y1.
+ *		
+ *	NOTE: scaling may be necessary if some argument is too 
+ *	      large or too tiny
+ *
+ * Special cases:
+ *	hypot(x,y) is INF if x or y is +INF or -INF; else
+ *	hypot(x,y) is NAN if x or y is NAN.
+ *
+ * Accuracy:
+ * 	hypot(x,y) returns ieee_sqrt(x^2+y^2) with error less 
+ * 	than 1 ulps (units in the last place) 
+ */
+
+#include "fdlibm.h"
+
+#ifdef __STDC__
+	double __ieee754_hypot(double x, double y)
+#else
+	double __ieee754_hypot(x,y)
+	double x, y;
+#endif
+{
+	double a=x,b=y,t1,t2,y1,y2,w;
+	int j,k,ha,hb;
+
+	ha = __HI(x)&0x7fffffff;	/* high word of  x */
+	hb = __HI(y)&0x7fffffff;	/* high word of  y */
+	if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
+	__HI(a) = ha;	/* a <- |a| */
+	__HI(b) = hb;	/* b <- |b| */
+	if((ha-hb)>0x3c00000) {return a+b;} /* x/y > 2**60 */
+	k=0;
+	if(ha > 0x5f300000) {	/* a>2**500 */
+	   if(ha >= 0x7ff00000) {	/* Inf or NaN */
+	       w = a+b;			/* for sNaN */
+	       if(((ha&0xfffff)|__LO(a))==0) w = a;
+	       if(((hb^0x7ff00000)|__LO(b))==0) w = b;
+	       return w;
+	   }
+	   /* scale a and b by 2**-600 */
+	   ha -= 0x25800000; hb -= 0x25800000;	k += 600;
+	   __HI(a) = ha;
+	   __HI(b) = hb;
+	}
+	if(hb < 0x20b00000) {	/* b < 2**-500 */
+	    if(hb <= 0x000fffff) {	/* subnormal b or 0 */	
+		if((hb|(__LO(b)))==0) return a;
+		t1=0;
+		__HI(t1) = 0x7fd00000;	/* t1=2^1022 */
+		b *= t1;
+		a *= t1;
+		k -= 1022;
+	    } else {		/* scale a and b by 2^600 */
+	        ha += 0x25800000; 	/* a *= 2^600 */
+		hb += 0x25800000;	/* b *= 2^600 */
+		k -= 600;
+	   	__HI(a) = ha;
+	   	__HI(b) = hb;
+	    }
+	}
+    /* medium size a and b */
+	w = a-b;
+	if (w>b) {
+	    t1 = 0;
+	    __HI(t1) = ha;
+	    t2 = a-t1;
+	    w  = ieee_sqrt(t1*t1-(b*(-b)-t2*(a+t1)));
+	} else {
+	    a  = a+a;
+	    y1 = 0;
+	    __HI(y1) = hb;
+	    y2 = b - y1;
+	    t1 = 0;
+	    __HI(t1) = ha+0x00100000;
+	    t2 = a - t1;
+	    w  = ieee_sqrt(t1*y1-(w*(-w)-(t1*y2+t2*b)));
+	}
+	if(k!=0) {
+	    t1 = 1.0;
+	    __HI(t1) += (k<<20);
+	    return t1*w;
+	} else return w;
+}