e_hypot.cs

Go to the documentation of this file.

/*
 * Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved.
 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
 *
 * This code is free software; you can redistribute it and/or modify it
 * under the terms of the GNU General Public License version 2 only, as
 * published by the Free Software Foundation.  Oracle designates this
 * particular file as subject to the "Classpath" exception as provided
 * by Oracle in the LICENSE file that accompanied this code.
 *
 * This code is distributed in the hope that it will be useful, but WITHOUT
 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
 * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
 * version 2 for more details (a copy is included in the LICENSE file that
 * accompanied this code).
 *
 * You should have received a copy of the GNU General Public License version
 * 2 along with this work; if not, write to the Free Software Foundation,
 * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
 *
 * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
 * or visit www.oracle.com if you need additional information or have any
 * questions.
 */
 
/* __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)
 */
 
namespace IKVM.Runtime.Util.Java.Lang
{
    static partial class fdlibm
    {
        internal static double __ieee754_hypot(double x, double y)
        {
            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; }
            a = __HI(a, ha);   /* a <- |a| */
            b = __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;
                a = __HI(a, ha);
                b = __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;
                    t1 = __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;
                    a = __HI(a, ha);
                    b = __HI(b, hb);
                }
            }
            /* medium size a and b */
            w = a - b;
            if (w > b)
            {
                t1 = 0;
                t1 = __HI(t1, ha);
                t2 = a - t1;
                w = sqrt(t1 * t1 - (b * (-b) - t2 * (a + t1)));
            }
            else
            {
                a = a + a;
                y1 = 0;
                y1 = __HI(y1, hb);
                y2 = b - y1;
                t1 = 0;
                t1 = __HI(t1, ha + 0x00100000);
                t2 = a - t1;
                w = sqrt(t1 * y1 - (w * (-w) - (t1 * y2 + t2 * b)));
            }
            if (k != 0)
            {
                t1 = 1.0;
                t1 = __HI(t1, __HI(t1) + (k << 20));
                return t1 * w;
            }
            else return w;
        }
    }
}