k_tan.cs

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 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
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 * 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).
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/* __kernel_tan( x, y, k )
 * kernel tan function on [-pi/4, pi/4], pi/4 ~ 0.7854
 * Input x is assumed to be bounded by ~pi/4 in magnitude.
 * Input y is the tail of x.
 * Input k indicates whether tan (if k=1) or
 * -1/tan (if k= -1) is returned.
 *
 * Algorithm
 *      1. Since tan(-x) = -tan(x), we need only to consider positive x.
 *      2. if x < 2^-28 (hx<0x3e300000 0), return x with inexact if x!=0.
 *      3. tan(x) is approximated by a odd polynomial of degree 27 on
 *         [0,0.67434]
 *                               3             27
 *              tan(x) ~ x + T1*x + ... + T13*x
 *         where
 *
 *              |tan(x)         2     4            26   |     -59.2
 *              |----- - (1+T1*x +T2*x +.... +T13*x    )| <= 2
 *              |  x                                    |
 *
 *         Note: tan(x+y) = tan(x) + tan'(x)*y
 *                        ~ tan(x) + (1+x*x)*y
 *         Therefore, for better accuracy in computing tan(x+y), let
 *                   3      2      2       2       2
 *              r = x *(T2+x *(T3+x *(...+x *(T12+x *T13))))
 *         then
 *                                  3    2
 *              tan(x+y) = x + (T1*x + (x *(r+y)+y))
 *
 *      4. For x in [0.67434,pi/4],  let y = pi/4 - x, then
 *              tan(x) = tan(pi/4-y) = (1-tan(y))/(1+tan(y))
 *                     = 1 - 2*(tan(y) - (tan(y)^2)/(1+tan(y)))
 */
 
namespace IKVM.Runtime.Util.Java.Lang
{
    static partial class fdlibm
    {
        static double __kernel_tan(double x, double y, int iy)
        {
            const double
    one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
    pio4 = 7.85398163397448278999e-01, /* 0x3FE921FB, 0x54442D18 */
    pio4lo = 3.06161699786838301793e-17, /* 0x3C81A626, 0x33145C07 */
    T_0_ =
    3.33333333333334091986e-01, /* 0x3FD55555, 0x55555563 */
    T_1_ =
    1.33333333333201242699e-01, /* 0x3FC11111, 0x1110FE7A */
    T_2_ =
    5.39682539762260521377e-02, /* 0x3FABA1BA, 0x1BB341FE */
    T_3_ =
    2.18694882948595424599e-02, /* 0x3F9664F4, 0x8406D637 */
    T_4_ =
    8.86323982359930005737e-03, /* 0x3F8226E3, 0xE96E8493 */
    T_5_ =
    3.59207910759131235356e-03, /* 0x3F6D6D22, 0xC9560328 */
    T_6_ =
    1.45620945432529025516e-03, /* 0x3F57DBC8, 0xFEE08315 */
    T_7_ =
    5.88041240820264096874e-04, /* 0x3F4344D8, 0xF2F26501 */
    T_8_ =
    2.46463134818469906812e-04, /* 0x3F3026F7, 0x1A8D1068 */
    T_9_ =
    7.81794442939557092300e-05, /* 0x3F147E88, 0xA03792A6 */
    T_10_ =
    7.14072491382608190305e-05, /* 0x3F12B80F, 0x32F0A7E9 */
    T_11_ =
    -1.85586374855275456654e-05, /* 0xBEF375CB, 0xDB605373 */
    T_12_ =
    2.59073051863633712884e-05; /* 0x3EFB2A70, 0x74BF7AD4 */
 
            double z, r, v, w, s;
            int ix, hx;
            hx = __HI(x);   /* high word of x */
            ix = hx & 0x7fffffff;     /* high word of |x| */
            if (ix < 0x3e300000)
            {                     /* x < 2**-28 */
                if ((int)x == 0)
                {                       /* generate inexact */
                    if (((ix | __LO(x)) | (iy + 1)) == 0)
                        return one / fabs(x);
                    else
                    {
                        if (iy == 1)
                            return x;
                        else
                        {    /* compute -1 / (x+y) carefully */
                            double a, t;
 
                            z = w = x + y;
                            z = __LO(z, 0);
                            v = y - (z - x);
                            t = a = -one / w;
                            t = __LO(t, 0);
                            s = one + t * z;
                            return t + a * (s + t * v);
                        }
                    }
                }
            }
            if (ix >= 0x3FE59428)
            {                    /* |x|>=0.6744 */
                if (hx < 0) { x = -x; y = -y; }
                z = pio4 - x;
                w = pio4lo - y;
                x = z + w; y = 0.0;
            }
            z = x * x;
            w = z * z;
            /* Break x^5*(T[1]+x^2*T[2]+...) into
             *    x^5(T[1]+x^4*T[3]+...+x^20*T[11]) +
             *    x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12]))
             */
            r = T_1_ + w * (T_3_ + w * (T_5_ + w * (T_7_ + w * (T_9_ + w * T_11_))));
            v = z * (T_2_ + w * (T_4_ + w * (T_6_ + w * (T_8_ + w * (T_10_ + w * T_12_)))));
            s = z * x;
            r = y + z * (s * (r + v) + y);
            r += T_0_ * s;
            w = x + r;
            if (ix >= 0x3FE59428)
            {
                v = (double)iy;
                return (double)(1 - ((hx >> 30) & 2)) * (v - 2.0 * (x - (w * w / (w + v) - r)));
            }
            if (iy == 1) return w;
            else
            {          /* if allow error up to 2 ulp,
                           simply return -1.0/(x+r) here */
                /*  compute -1.0/(x+r) accurately */
                double a, t;
                z = w;
                z = __LO(z, 0);
                v = r - (z - x);     /* z+v = r+x */
                t = a = -1.0 / w;    /* a = -1.0/w */
                t = __LO(t, 0);
                s = 1.0 + t * z;
                return t + a * (s + t * v);
            }
        }
    }
}