e_rem_pio2.cs

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 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
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/* __ieee754_rem_pio2(x,y)
 *
 * return the remainder of x rem pi/2 in y_0_+y_1_
 * use __kernel_rem_pio2()
 */
 
namespace IKVM.Runtime.Util.Java.Lang
{
    static partial class fdlibm
    {
        /*
         * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi
         */
        static readonly int[] two_over_pi = {
0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62,
0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A,
0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129,
0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41,
0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8,
0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF,
0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5,
0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08,
0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3,
0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880,
0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B,
};
 
        static readonly int[] npio2_hw = {
0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C,
0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C,
0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A,
0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C,
0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB,
0x404858EB, 0x404921FB,
};
 
        /*
         * invpio2:  53 bits of 2/pi
         * pio2_1:   first  33 bit of pi/2
         * pio2_1t:  pi/2 - pio2_1
         * pio2_2:   second 33 bit of pi/2
         * pio2_2t:  pi/2 - (pio2_1+pio2_2)
         * pio2_3:   third  33 bit of pi/2
         * pio2_3t:  pi/2 - (pio2_1+pio2_2+pio2_3)
         */
 
        static int __ieee754_rem_pio2(double x, ref double y_0_, ref double y_1_)
        {
            const double
    zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
    half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
    two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
    invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
    pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */
    pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */
    pio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */
    pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */
    pio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */
    pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */
 
            double z, w, t, r, fn;
            int e0, i, j, nx, n, ix, hx;
 
            hx = __HI(x);           /* high word of x */
            ix = hx & 0x7fffffff;
            if (ix <= 0x3fe921fb)   /* |x| ~<= pi/4 , no need for reduction */
            { y_0_ = x; y_1_ = 0; return 0; }
            if (ix < 0x4002d97c)
            {  /* |x| < 3pi/4, special case with n=+-1 */
                if (hx > 0)
                {
                    z = x - pio2_1;
                    if (ix != 0x3ff921fb)
                    {    /* 33+53 bit pi is good enough */
                        y_0_ = z - pio2_1t;
                        y_1_ = (z - y_0_) - pio2_1t;
                    }
                    else
                    {                /* near pi/2, use 33+33+53 bit pi */
                        z -= pio2_2;
                        y_0_ = z - pio2_2t;
                        y_1_ = (z - y_0_) - pio2_2t;
                    }
                    return 1;
                }
                else
                {    /* negative x */
                    z = x + pio2_1;
                    if (ix != 0x3ff921fb)
                    {    /* 33+53 bit pi is good enough */
                        y_0_ = z + pio2_1t;
                        y_1_ = (z - y_0_) + pio2_1t;
                    }
                    else
                    {                /* near pi/2, use 33+33+53 bit pi */
                        z += pio2_2;
                        y_0_ = z + pio2_2t;
                        y_1_ = (z - y_0_) + pio2_2t;
                    }
                    return -1;
                }
            }
            if (ix <= 0x413921fb)
            { /* |x| ~<= 2^19*(pi/2), medium size */
                t = fabs(x);
                n = (int)(t * invpio2 + half);
                fn = (double)n;
                r = t - fn * pio2_1;
                w = fn * pio2_1t;    /* 1st round good to 85 bit */
                if (n < 32 && ix != npio2_hw[n - 1])
                {
                    y_0_ = r - w;     /* quick check no cancellation */
                }
                else
                {
                    j = ix >> 20;
                    y_0_ = r - w;
                    i = j - (((__HI(y_0_)) >> 20) & 0x7ff);
                    if (i > 16)
                    {  /* 2nd iteration needed, good to 118 */
                        t = r;
                        w = fn * pio2_2;
                        r = t - w;
                        w = fn * pio2_2t - ((t - r) - w);
                        y_0_ = r - w;
                        i = j - (((__HI(y_0_)) >> 20) & 0x7ff);
                        if (i > 49)
                        { /* 3rd iteration need, 151 bits acc */
                            t = r; /* will cover all possible cases */
                            w = fn * pio2_3;
                            r = t - w;
                            w = fn * pio2_3t - ((t - r) - w);
                            y_0_ = r - w;
                        }
                    }
                }
                y_1_ = (r - y_0_) - w;
                if (hx < 0) { y_0_ = -y_0_; y_1_ = -y_1_; return -n; }
                else return n;
            }
            /*
             * all other (large) arguments
             */
            if (ix >= 0x7ff00000)
            {            /* x is inf or NaN */
                y_0_ = y_1_ = x - x; return 0;
            }
            /* set z = scalbn(|x|,ilogb(x)-23) */
            z = x;
            e0 = (ix >> 20) - 1046;        /* e0 = ilogb(z)-23; */
            z = __HI(z, ix - (e0 << 20));
            double[] tx = new double[3];
            for (i = 0; i < 2; i++)
            {
                tx[i] = (double)((int)(z));
                z = (z - tx[i]) * two24;
            }
            tx[2] = z;
            nx = 3;
            while (tx[nx - 1] == zero) nx--;     /* skip zero term */
            double y_2_ = 0.0;
            n = __kernel_rem_pio2(tx, ref y_0_, ref y_1_, ref y_2_, e0, nx, 2, two_over_pi);
            if (hx < 0) { y_0_ = -y_0_; y_1_ = -y_1_; return -n; }
            return n;
        }
    }
}