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/* @(#)e_hypot.c 5.1 93/09/24 */

/*

 * ====================================================

 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.

 *

 * Developed at SunPro, a Sun Microsystems, Inc. business.

 * Permission to use, copy, modify, and distribute this

 * software is freely granted, provided that this notice

 * is preserved.

 * ====================================================

 */

#if defined(LIBM_SCCS) && !defined(lint)

static char rcsid[] = "$NetBSD: e_hypot.c,v 1.9 1995/05/12 04:57:27 jtc Exp $";

#endif

/* __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 "math.h"

#include "math_private.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;

        int32_t j,k,ha,hb;

        GET_HIGH_WORD(ha,x);

        ha &= 0x7fffffff;

        GET_HIGH_WORD(hb,y);

        hb &= 0x7fffffff;

        if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}

        SET_HIGH_WORD(a,ha);    /* a <- |a| */

        SET_HIGH_WORD(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 */

               u_int32_t low;

               w = a+b;                 /* for sNaN */

               GET_LOW_WORD(low,a);

               if(((ha&0xfffff)|low)==0) w = a;

               GET_LOW_WORD(low,b);

               if(((hb^0x7ff00000)|low)==0) w = b;

               return w;

           }

           /* scale a and b by 2**-600 */

           ha -= 0x25800000; hb -= 0x25800000;  k += 600;

           SET_HIGH_WORD(a,ha);

           SET_HIGH_WORD(b,hb);

        }

        if(hb < 0x20b00000) {   /* b < 2**-500 */

            if(hb <= 0x000fffff) {      /* subnormal b or 0 */

                u_int32_t low;

                GET_LOW_WORD(low,b);

                if((hb|low)==0) return a;

                t1=0;

                SET_HIGH_WORD(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;

                SET_HIGH_WORD(a,ha);

                SET_HIGH_WORD(b,hb);

            }

        }

    /* medium size a and b */

        w = a-b;

        if (w>b) {

            t1 = 0;

            SET_HIGH_WORD(t1,ha);

            t2 = a-t1;

            w  = __ieee754_sqrt(t1*t1-(b*(-b)-t2*(a+t1)));

        } else {

            a  = a+a;

            y1 = 0;

            SET_HIGH_WORD(y1,hb);

            y2 = b - y1;

            t1 = 0;

            SET_HIGH_WORD(t1,ha+0x00100000);

            t2 = a - t1;

            w  = __ieee754_sqrt(t1*y1-(w*(-w)-(t1*y2+t2*b)));

        }

        if(k!=0) {

            u_int32_t high;

            t1 = 1.0;

            GET_HIGH_WORD(high,t1);

            SET_HIGH_WORD(t1,high+(k<<20));

            return t1*w;

        } else return w;

}