/* @(#)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)
 */

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);
            (void)es;
            if (((high & 0x7fffffff) | low) == 0 && !issignalingl_inline(b))
                w = a;
            GET_LDOUBLE_WORDS(es, high, low, b);
            if (((eb ^ 0x7fff) | (high & 0x7fffffff) | low) == 0 && !issignalingl_inline(a))
                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);
            (void)es;
            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 = 1.0L;
        GET_LDOUBLE_EXP(es, t1);
        SET_LDOUBLE_EXP(t1, es + k);
        return check_oflowl(t1 * w);
    } else
        return w;
}
