s_cbrt.cs

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namespace IKVM.Runtime.Util.Java.Lang
{
    static partial class fdlibm
    {
        internal static double cbrt(double x)
        {
 
            /* cbrt(x)
             * Return cube root of x
             */
            const int
                    B1 = 715094163, /* B1 = (682-0.03306235651)*2**20 */
                    B2 = 696219795; /* B2 = (664-0.03306235651)*2**20 */
 
            const double
            C = 5.42857142857142815906e-01, /* 19/35     = 0x3FE15F15, 0xF15F15F1 */
            D = -7.05306122448979611050e-01, /* -864/1225 = 0xBFE691DE, 0x2532C834 */
            E = 1.41428571428571436819e+00, /* 99/70     = 0x3FF6A0EA, 0x0EA0EA0F */
            F = 1.60714285714285720630e+00, /* 45/28     = 0x3FF9B6DB, 0x6DB6DB6E */
            G = 3.57142857142857150787e-01; /* 5/14      = 0x3FD6DB6D, 0xB6DB6DB7 */
 
            int hx;
            double r, s, t = 0.0, w;
            int sign;
 
 
            hx = __HI(x);           /* high word of x */
            sign = hx & unchecked((int)0x80000000);             /* sign= sign(x) */
            hx ^= sign;
            if (hx >= 0x7ff00000) return (x + x); /* cbrt(NaN,INF) is itself */
            if ((hx | __LO(x)) == 0)
                return (x);          /* cbrt(0) is itself */
 
            x = __HI(x, hx);   /* x <- |x| */
            /* rough cbrt to 5 bits */
            if (hx < 0x00100000)               /* subnormal number */
            {
                t = __HI(t, 0x43500000);          /* set t= 2**54 */
                t *= x; t = __HI(t, __HI(t) / 3 + B2);
            }
            else
                t = __HI(t, hx / 3 + B1);
 
 
            /* new cbrt to 23 bits, may be implemented in single precision */
            r = t * t / x;
            s = C + r * t;
            t *= G + F / (s + E + D / s);
 
            /* chopped to 20 bits and make it larger than cbrt(x) */
            t = __LO(t, 0); t = __HI(t, __HI(t) + 0x00000001);
 
 
            /* one step newton iteration to 53 bits with error less than 0.667 ulps */
            s = t * t;          /* t*t is exact */
            r = x / s;
            w = t + t;
            r = (r - t) / (w + r);  /* r-s is exact */
            t = t + t * r;
 
            /* retore the sign bit */
            t = __HI(t, __HI(t) | sign);
            return (t);
        }
    }
}