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

/* 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 _NEED_FLOAT64

__float64
hypot64(__float64 x, __float64 y)
{
    __float64 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 */
            __uint32_t low;
            w = a + b; /* for sNaN */
            GET_LOW_WORD(low, a);
            if (((ha & 0xfffff) | low) == 0 && !issignaling(b))
                w = a;
            GET_LOW_WORD(low, b);
            if (((hb ^ 0x7ff00000) | low) == 0 && !issignaling(a))
                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 */
            __uint32_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 = sqrt64(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 = sqrt64(t1 * y1 - (w * (-w) - (t1 * y2 + t2 * b)));
    }
    if (k != 0) {
        __uint32_t high;
        t1 = _F_64(1.0);
        GET_HIGH_WORD(high, t1);
        SET_HIGH_WORD(t1, high + (k << 20));
        w *= t1;
    }
    return check_oflow(w);
}

_MATH_ALIAS_d_dd(hypot)

#endif /* _NEED_FLOAT64 */
