/* @(#)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.
 * ====================================================
 */

/* hypotl(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*yy1+((x-y)*(x-y)+(t1*y2+t2*y))
 *      where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1,
 *      yy1= y with lower 32 bits chopped, y2 = y-yy1.
 *
 *      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"

long double
hypotl(long double x, long double y)
{
        long double a,b,t1,t2,yy1,y2,w;
        u_int32_t j,k,ea,eb;

        GET_LDOUBLE_EXP(ea,x);
        ea &= 0x7fff;
        GET_LDOUBLE_EXP(eb,y);
        eb &= 0x7fff;
        if(eb > ea) {a=y;b=x;j=ea; ea=eb;eb=j;} else {a=x;b=y;}
        SET_LDOUBLE_EXP(a,ea);  /* a <- |a| */
        SET_LDOUBLE_EXP(b,eb);  /* b <- |b| */
        if((ea-eb)>0x46) {return a+b;} /* x/y > 2**70 */
        k=0;
        if(ea > 0x5f3f) {       /* a>2**8000 */
           if(ea == 0x7fff) {   /* Inf or NaN */
               u_int32_t es,high,low;
               w = a+b;                 /* for sNaN */
               GET_LDOUBLE_WORDS(es,high,low,a);
               if(((high&0x7fffffff)|low)==0) w = a;
               GET_LDOUBLE_WORDS(es,high,low,b);
               if(((eb^0x7fff)|(high&0x7fffffff)|low)==0) w = b;
               return w;
           }
           /* scale a and b by 2**-9600 */
           ea -= 0x2580; eb -= 0x2580;  k += 9600;
           SET_LDOUBLE_EXP(a,ea);
           SET_LDOUBLE_EXP(b,eb);
        }
        if(eb < 0x20bf) {       /* b < 2**-8000 */
            if(eb == 0) {       /* subnormal b or 0 */
                u_int32_t es,high,low;
                GET_LDOUBLE_WORDS(es,high,low,b);
                if((high|low)==0) return a;
                SET_LDOUBLE_WORDS(t1, 0x7ffd, 0, 0);    /* t1=2^16382 */
                b *= t1;
                a *= t1;
                k -= 16382;
            } else {            /* scale a and b by 2^9600 */
                ea += 0x2580;   /* a *= 2^9600 */
                eb += 0x2580;   /* b *= 2^9600 */
                k -= 9600;
                SET_LDOUBLE_EXP(a,ea);
                SET_LDOUBLE_EXP(b,eb);
            }
        }
    /* medium size a and b */
        w = a-b;
        if (w>b) {
            u_int32_t high;
            GET_LDOUBLE_MSW(high,a);
            SET_LDOUBLE_WORDS(t1,ea,high,0);
            t2 = a-t1;
            w  = sqrtl(t1*t1-(b*(-b)-t2*(a+t1)));
        } else {
            u_int32_t high;
            GET_LDOUBLE_MSW(high,b);
            a  = a+a;
            SET_LDOUBLE_WORDS(yy1,eb,high,0);
            y2 = b - yy1;
            GET_LDOUBLE_MSW(high,a);
            SET_LDOUBLE_WORDS(t1,ea+1,high,0);
            t2 = a - t1;
            w  = sqrtl(t1*yy1-(w*(-w)-(t1*y2+t2*b)));
        }
        if(k!=0) {
            u_int32_t es;
            t1 = 1.0;
            GET_LDOUBLE_EXP(es,t1);
            SET_LDOUBLE_EXP(t1,es+k);
            return t1*w;
        } else return w;
}
DEF_STD(hypotl);