/* @(#)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 sqrt(2)/2 ulp, than 

 *	sqrt(z) has error less than 1 ulp (exercise).

 *

 *	So, compute 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 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  = 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  = 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;

}