/*
 * Copyright 1999-2006 Sun Microsystems, Inc.  All rights reserved.
 * SUN PROPRIETARY/CONFIDENTIAL. Use is subject to license terms.
 *
 *
 *
 *
 *
 *
 *
 *
 *
 *
 *
 *
 *
 *
 *
 *
 *
 *
 *
 *
 */

package java.lang;
import java.util.Random;
import sun.misc.FpUtils;

/**
 * The class {@code StrictMath} contains methods for performing basic
 * numeric operations such as the elementary exponential, logarithm,
 * square root, and trigonometric functions.
 *
 * <p>To help ensure portability of Java programs, the definitions of
 * some of the numeric functions in this package require that they
 * produce the same results as certain published algorithms. These
 * algorithms are available from the well-known network library
 * {@code netlib} as the package "Freely Distributable Math
 * Library," <a
 * href="ftp://ftp.netlib.org/fdlibm.tar">{@code fdlibm}</a>. These
 * algorithms, which are written in the C programming language, are
 * then to be understood as executed with all floating-point
 * operations following the rules of Java floating-point arithmetic.
 *
 * <p>The Java math library is defined with respect to
 * {@code fdlibm} version 5.3. Where {@code fdlibm} provides
 * more than one definition for a function (such as
 * {@code acos}), use the "IEEE 754 core function" version
 * (residing in a file whose name begins with the letter
 * {@code e}).  The methods which require {@code fdlibm}
 * semantics are {@code sin}, {@code cos}, {@code tan},
 * {@code asin}, {@code acos}, {@code atan},
 * {@code exp}, {@code log}, {@code log10},
 * {@code cbrt}, {@code atan2}, {@code pow},
 * {@code sinh}, {@code cosh}, {@code tanh},
 * {@code hypot}, {@code expm1}, and {@code log1p}.
 *
 * @author  unascribed
 * @author  Joseph D. Darcy
 * @since   1.3
 */
public final class StrictMath {

    /**
     * Don't let anyone instantiate this class.
     */
    private StrictMath() {
    }
    /**
     * The {@code double} value that is closer than any other to
     * <i>e</i>, the base of the natural logarithms.
     */
    public static final double E = 2.7182818284590452354;
    /**
     * The {@code double} value that is closer than any other to
     * <i>pi</i>, the ratio of the circumference of a circle to its
     * diameter.
     */
    public static final double PI = 3.14159265358979323846;
   
    
    /**
     * Returns the trigonometric sine of an angle. Special cases:
     * <ul><li>If the argument is NaN or an infinity, then the
     * result is NaN.
     * <li>If the argument is zero, then the result is a zero with the
     * same sign as the argument.</ul>
     *
     * @param   a   an angle, in radians.
     * @return  the sine of the argument.
     */
    public static double sin(double x) {
        int hx = (int) (Double.doubleToRawLongBits(x) >> 32);
        int ix = hx & 0x7fffffff;
        return ix <= 0x3fe921fb ?
            __kernel_sin_(x, ix) :
            __ieee754_rem_pio2_(x, hx, sintype);
    }

    /**
     * Returns the trigonometric cosine of an angle. Special cases:
     * <ul><li>If the argument is NaN or an infinity, then the
     * result is NaN.</ul>
     *
     * @param   a   an angle, in radians.
     * @return  the cosine of the argument.
     */
    public static double cos(double x) {
        int hx = (int) (Double.doubleToRawLongBits(x) >> 32);
        int ix = hx & 0x7fffffff;
        return ix <= 0x3fe921fb  ?
            __kernel_cos_(x, 0, ix) :
            __ieee754_rem_pio2_(x, hx, costype);
    }

    /**
     * Returns the trigonometric tangent of an angle. Special cases:
     * <ul><li>If the argument is NaN or an infinity, then the result
     * is NaN.
     * <li>If the argument is zero, then the result is a zero with the
     * same sign as the argument.</ul>
     *
     * @param   a   an angle, in radians.
     * @return  the tangent of the argument.
     */
   public static double tan(double x) {
        final int hx = (int) (Double.doubleToRawLongBits(x) >> 32);
        return (hx&0x7fffffff) <= 0x3fe921fb ?
            __kernel_tan(x, 0d, 1, hx) :
            __ieee754_rem_pio2_(x, hx, tantype);
    }   

    /**
     * kernel tan function on [-pi/4, pi/4], pi/4 ~ 0.7854
     *
     * 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)))
     * 
     * @param x  is assumed to be bounded by ~pi/4 in magnitude.
     * @param y is the tail of x
     * @param k indicates whether tan (if k=1) or -1/tan (if k= -1) is returned.
     * @param hx high bits of x
     * @return
     */
    private static double __kernel_tan( double x, double y, int k, int hx) {
        double w,r;
        final int ix = hx & 0x7fffffff;
        if (ix < 0x3e300000 && (int) x == 0) { // |x| < 2**-28
            if (k == 1){
                return x;
            }
            if ((ix | hx) == 0){
                return one / abs(x); // generate inexact
            }
            // compute -1 / (x+y) carefully
            r = y;
            w = x + y;
        }else{
            if (ix >= 0x3FE59428) { // |x|>=0.67434
                if (hx < 0) {
                    x = 0.0d - x;
                    y = 0.0d - y;
                }
                x = (pio4 - x) + (pio4lo - y);
                y = 0.0;
            }
            final double 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]))
             */

            final double s = z * x;
            double v = z * (T2 + w*(T4 + w*(T6 + w*(T8 + w*(T10 + w*T12)))));
            r = (y+z*(s*((T1 + w*(T3 + w*(T5+w*(T7+w*(T9+w*T11)))))+v)+y))+T0*s;
            w = x + r;
            if (ix >= 0x3FE59428) {
                v = k;
                return (1-((hx>>30)&2))*(v-2.0d *(x-(((w*w)/(w+v))-r)));
            }
            if (k == 1) {
                return w;
            }
            // if allow error up to 2 ulp, simply return -1.0/(x+r) here
        }
        //  compute -1.0/(x+r) accurately
        final double a = negone / w;
        final double t = clearLow32bits(a);
        final double z = clearLow32bits(w);
        return t + a * ((1.0d + t * z) + t * (r - (z - x)));
    }

    
    private static final double
            S1 = -1.66666666666666324348e-01,
            S2 = 8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */
            S3 = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */
            S4 = 2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */
            S5 = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */
            S6 = 1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */

    /**
     * kernel sin 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 iy indicates whether y is 0. (if iy=0, y assume to be 0).
     *
     * Algorithm
     *      1. Since sin(-x) = -sin(x), we need only to consider positive x.
     *      2. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0.
     *      3. sin(x) is approximated by a polynomial of degree 13 on
     *         [0,pi/4]
     *                               3            13
     *              sin(x) ~ x + S1*x + ... + S6*x
     *         where
     *
     *      |sin(x)         2     4     6     8     10     12  |     -58
     *      |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x  +S6*x   )| <= 2
     *      |  x                                               |
     *
     *      4. sin(x+y) = sin(x) + sin'(x')*y
     *                  ~ sin(x) + (1-x*x/2)*y
     *         For better accuracy, let
     *                   3      2      2      2      2
     *              r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6))))
     *         then                   3    2
     *              sin(x) = x + (S1*x + (x *(r-y/2)+y))
     *
     * @param x
     * @param y
     * @return
     */
    private static double __kernel_sin(double x, double y, int ix) {
        if (ix < 0x3e400000 && (int) x == 0) {
            return x; // |x| < 2**-27  generate inexact
        }
        final double z = x * x;
        final double v = z * x;
        final double r = v * (S2 + z * (S3 + z * (S4 + z * (S5 + z * S6))));
        return x - ((z * (half * y - r) - y) - v * S1);
    }


    private static double __kernel_sin_(double x, int ix) {
        if (ix < 0x3e400000 && (int) x == 0) {
            return x; // |x| < 2**-27  generate inexact
        }
        final double z = x * x;
        return x + (z*x)*(S1 + z * (S2 + z * (S3 + z * (S4 + z * (S5 +z*S6)))));
    }


    private static final double
        two = 2.0d,
        one = Double.longBitsToDouble(0x3ff0000000000000L),
        negone = - one,
        C1 =  4.16666666666666019037e-02,
        C2 = -1.38888888888741095749e-03,
        C3 = 2.48015872894767294178e-05,
        C4 = -2.75573143513906633035e-07,
        C5 = 2.08757232129817482790e-09,
        C6 = -1.13596475577881948265e-11;


    /**
     * kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164
     * Input x is assumed to be bounded by ~pi/4 in magnitude.
     * Input y is the tail of x.
     *
     * Algorithm
     *      1. Since cos(-x) = cos(x), we need only to consider positive x.
     *      2. if x < 2^-27 (hx<0x3e400000 0), return 1 with inexact if x!=0.
     *      3. cos(x) is approximated by a polynomial of degree 14 on
     *         [0,pi/4]
     *                                       4            14
     *              cos(x) ~ 1 - x*x/2 + C1*x + ... + C6*x
     *         where the remez error is
     *
     *      |              2     4     6     8     10    12     14 |     -58
     *      |cos(x)-(1-.5*x +C1*x +C2*x +C3*x +C4*x +C5*x  +C6*x  )| <= 2
     *      |                                                      |
     *
     *                     4     6     8     10    12     14
     *      4. let r = C1*x +C2*x +C3*x +C4*x +C5*x  +C6*x  , then
     *             cos(x) = 1 - x*x/2 + r
     *         since cos(x+y) ~ cos(x) - sin(x)*y
     *                        ~ cos(x) - x*y,
     *         a correction term is necessary in cos(x) and hence
     *              cos(x+y) = 1 - (x*x/2 - (r - x*y))
     *         For better accuracy when x > 0.3, let qx = |x|/4 with
     *         the last 32 bits mask off, and if x > 0.78125, let qx = 0.28125.
     *         Then
     *              cos(x+y) = (1-qx) - ((x*x/2-qx) - (r-x*y)).
     *         Note that 1-qx and (x*x/2-qx) is EXACT here, and the
     *         magnitude of the latter is at least a quarter of x*x/2,
     *         thus, reducing the rounding error in the subtraction.
     *
     * @param x
     * @param y
     * @param ix
     * @return
     */
    private static double __kernel_cos_(double x, double y, int ix) {
        if (ix < 0x3e400000 && ((int) x) == 0) {
            return one; // x < 2**27  generate inexact
        }
        final double z = x * x;
        double r = z*(z*(C1 + z*(C2 + z*(C3 + z* (C4 + z*(C5 + z*C6)))))) - x*y;
        if (ix < 0x3FD33333) { //  |x| < 0.3
            return one - (0.5 * z - r);
        }
        final double qx = ix > 0x3fe90000 ? 0.28125 : // x > 0.78125
            Double.longBitsToDouble((long)(ix - 0x00200000) << 32); // x/4
        return (one - qx) - ((0.5 * z - qx) - r);
    }
    
    private static final int sintype = 0;
    private static final int costype = 1;
    private static final int tantype = 3;

    /**
     * Returns final values for tan , cos and sin.
     * 
     * @param trigtype
     * @param N
     * @param y0
     * @param y1
     * @author gustav trede
     * @return
     */
    private static double getTrigres(int trigtype, int N, double y0, double y1){
        int hx = ((int) (Double.doubleToRawLongBits(y0) >> 32));
        if (trigtype == tantype) {
            return __kernel_tan(y0, y1, 1 - ((N & 1) << 1), hx);
        }
        hx&=0x7fffffff;
        N = (N&3) - trigtype;
        double v= (N == 0 || N == 2) ?
            __kernel_sin(y0,y1,hx) :
            __kernel_cos_(y0,y1,hx);

        if (N == 0 || N == 1) {
            return trigtype == 0 ? v : 0.0d - v ;
        }
        return trigtype == 0 ? 0.0d - v : v ;
    }


    private static final double
        pio4   = 7.85398163397448278999e-01,
        pio4lo = 3.06161699786838301793e-17,
        T0  = 3.33333333333334091986e-01,
        T1  = 1.33333333333201242699e-01,
        T2  = 5.39682539762260521377e-02,
        T3  = 2.18694882948595424599e-02,
        T4  = 8.86323982359930005737e-03,
        T5  = 3.59207910759131235356e-03,
        T6  = 1.45620945432529025516e-03,
        T7  = 5.88041240820264096874e-04,
        T8  = 2.46463134818469906812e-04,
        T9  = 7.81794442939557092300e-05,
        T10 = 7.14072491382608190305e-05,
        T11 = -1.85586374855275456654e-05,
        T12 = 2.59073051863633712884e-05;


    /*
     * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi
     */
    private static final 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
    };
    
    private static final 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
    };

    private static final double 
        zero = 0.00000000000000000000e+00,
        half = 5.00000000000000000000e-01,
        /* 1.67772160000000000000e+07 */
        two24 = Double.longBitsToDouble(0x4170000000000000L),
        /* 6.36619772367581382433e-01 53 bits of 2/pi */
        invpio2 = Double.longBitsToDouble(0x3fe45f306dc9c883L),
        /* 1.57079632673412561417e+00 first  33 bit of pi/2 */
        pio2_1 = Double.longBitsToDouble(0x3ff921fb54400000L),
        /* 6.07710050650619224932e-11 pi/2 - pio2_1 */
        pio2_1t = Double.longBitsToDouble(0x3dd0b4611a626331L),
        /* 6.07710050630396597660e-11 second 33 bit of pi/2 */
        pio2_2 = Double.longBitsToDouble(0x3dd0b4611a600000L),
        /* 2.02226624879595063154e-21 pi/2 - (pio2_1+pio2_2) */
        pio2_2t = Double.longBitsToDouble(0x3ba3198a2e037073L),
        /* 2.02226624871116645580e-21 third  33 bit of pi/2 */
        pio2_3 = Double.longBitsToDouble(0x3ba3198a2e000000L),
        /* 8.47842766036889956997e-32 pi/2 - (pio2_1+pio2_2+pio2_3) */
        pio2_3t = Double.longBitsToDouble(0x397b839a252049c1L);

    private static double __ieee754_rem_pio2_(double x, int hx, int trigtype) {
        int ix = hx & 0x7fffffff;
        if (ix <= 0x413921fb) { // |x| ~<= 2^19*(pi/2)
            double y0, y1;
            int n;
            if (ix < 0x4002d97c) { // |x| < 3pi/4, special case with n=+-1
                if (hx > 0) {
                     x -= pio2_1;
                    if (ix != 0x3ff921fb) { // 33+53 bit pi is good enough
                        y0 = x - pio2_1t;
                        y1 = (x - y0) - pio2_1t;
                    } else { // near pi/2, use 33+33+53 bit pi
                        x -= pio2_2;
                        y0 = x - pio2_2t;
                        y1 = (x - y0) - pio2_2t;
                    }
                    n = 1;
                } else { // negative x
                    x+= pio2_1;
                    if (ix != 0x3ff921fb) { // 33+53 bit pi is good enough
                        y0 = x + pio2_1t;
                        y1 = (x - y0) + pio2_1t;
                    } else { // near pi/2, use 33+33+53 bit pi
                        x += pio2_2;
                        y0 = x + pio2_2t;
                        y1 = (x - y0) + pio2_2t;
                    }
                    n = -1;
                }
            }else{
                double t = abs(x);
                n = (int) (t * invpio2 + half);
                final double fn = n;
                double w = fn * pio2_1t; // 1st round good to 85 bit
                double r = t - fn * pio2_1;
                y0 = r - w;
                // quick check no cancellation
                if (n >= 32 || ix == npio2_hw[n - 1]) {
                    int i = ix-(((int)(Double.doubleToRawLongBits(y0)>>32))
                            &(0x7ff<<20));
                    if (i > (16 << 20)) { //2nd iteration needed, good to 118
                        w = fn * pio2_2;
                        t = r;
                        r -=  w;
                        w = fn * pio2_2t - ((t - r) - w);
                        y0 = r - w;
                        i = ix-(((int) (Double.doubleToRawLongBits(y0)>>32))
                                &(0x7ff<<20));
                        if (i > (49 << 20)) {//3rd iteration need, 151 bits acc
                            w = fn * pio2_3;
                            t = r;
                            r -=  w;
                            w = fn * pio2_3t - ((t - r) - w);
                            y0 = r - w;
                        }
                    }
                }
                y1 = (r - y0) - w;
                if (hx < 0) {
                    y1 = 0.0d - y1;
                    y0 = 0.0d - y0;                    
                    n = -n;
                }
            }
            return getTrigres(trigtype, n, y0, y1);
        }

        return ix >= 0x7ff00000 ?
            x-x : // x is inf or NaN
            __kernel_rem_pio2(x, hx, trigtype);
    }


    private static final double[] PIo2 = {
        1.57079625129699707031e+00,
        7.54978941586159635335e-08,
        5.39030252995776476554e-15,
        3.28200341580791294123e-22,
        1.27065575308067607349e-29,
        1.22933308981111328932e-36,
        2.73370053816464559624e-44,
        2.16741683877804819444e-51};

    private static final double twon24 = 5.96046447753906250000e-08;


    /**
     * Used for tlocal storage to save __kernel_rem_pio2 from  major mem allocs.
     * @author gustav trede
     */
    private static class Rempiostruct {
        final double[] f  = new double[20];
        final double[] q  = new double[20];
        final double[] fq = new double[20];
        final double[] x  = new double[3];
        final int[]    iq = new int[20];
    }
    
    private static final ThreadLocal<Rempiostruct> rempstruct =
            new ThreadLocal<Rempiostruct>() {
        @Override
        protected Rempiostruct initialValue() {
            return new Rempiostruct();
        }
    };

    /**
     *
     * __kernel_rem_pio2 return the last three digits of N with
     *                y = x - N*pi/2
     * so that |y| < pi/2.
     *
     * The method is to compute the integer (mod 8) and fraction parts of
     * (2/pi)*x without doing the full multiplication. In general we
     * skip the part of the product that are known to be a huge integer
     * (more accurately, = 0 mod 8 ). Thus the number of operations are
     * independent of the exponent of the input.
     *
     * (2/pi) is represented by an array of 24-bit integers in two_over_pi[].
     *
     * Input parameters:
     *         x[]        The input value (must be positive) is broken into nx
     *                pieces of 24-bit integers in double precision format.
     *                x[i] will be the i-th 24 bit of x. The scaled exponent
     *                of x[0] is given in input parameter e0 (i.e., x[0]*2^e0
     *                match x's up to 24 bits.
     *
     *                Example of breaking a double positive z into x[0]+x[1]+x[2]:
     *                        e0 = ilogb(z)-23
     *                        z  = scalbn(z,-e0)
     *                for i = 0,1,2
     *                        x[i] = floor(z)
     *                        z    = (z-x[i])*2**24
     *
     *
     *        y[]        ouput result in an array of double precision numbers.
     *                The dimension of y[] is:
     *                        24-bit  precision        1
     *                        53-bit  precision        2
     *                        64-bit  precision        2
     *                        113-bit precision        3
     *                The actual value is the sum of them. Thus for 113-bit
     *                precison, one may have to do something like:
     *
     *                long double t,w,r_head, r_tail;
     *                t = (long double)y[2] + (long double)y[1];
     *                w = (long double)y[0];
     *                r_head = t+w;
     *                r_tail = w - (r_head - t);
     *
     *        e0        The exponent of x[0]
     *
     *        nx        dimension of x[]
     *
     *          prec        an integer indicating the precision:
     *                        0        24  bits (single)
     *                        1        53  bits (double)
     *                        2        64  bits (extended)
     *                        3        113 bits (quad)
     *
     *        two_over_pi[]
     *                integer array, contains the (24*i)-th to (24*i+23)-th
     *                bit of 2/pi after binary point. The corresponding
     *                floating value is
     *
     *                        two_over_pi[i] * 2^(-24(i+1)).
     *
     * External function:
     *        double scalbn(), floor();
     *
     *
     * Here is the description of some local variables:
     *
     *         jk    jk+1 is the initial number of terms of two_over_pi[] needed
     *                in the computation. The recommended value is 2,3,4,
     *                6 for single, double, extended,and quad.
     *
     *         jz        local integer variable indicating the number of
     *                terms of two_over_pi[] used.
     *
     *        jx        nx - 1
     *
     *        jv        index for pointing to the suitable two_over_pi[] for the
     *                computation. In general, we want
     *                        ( 2^e0*x[0] * two_over_pi[jv-1]*2^(-24jv) )/8
     *                is an integer. Thus
     *                        e0-3-24*jv >= 0 or (e0-3)/24 >= jv
     *                Hence jv = max(0,(e0-3)/24).
     *
     *        jp        jp+1 is the number of terms in PIo2[] needed, jp = jk.
     *
     *         q[]        double array with integral value, representing the
     *                24-bits chunk of the product of x and 2/pi.
     *
     *        q0        the corresponding exponent of q[0]. Note that the
     *                exponent for q[i] would be q0-24*i.
     *
     *        PIo2[]        double precision array, obtained by cutting pi/2
     *                into 24 bits chunks.
     *
     *        f[]        two_over_pi[] in floating point
     *
     *        iq[]        integer array by breaking up q[] in 24-bits chunk.
     *
     *        fq[]        final product of x*(2/pi) in fq[0],..,fq[jk]
     *
     *        ih        integer. If >0 it indicates q[] is >= 0.5, hence
     *                it also indicates the *sign* of the result.
     *
     * @param xv
     * @param hx
     * @param trig  trigtype
     * @return
     */
    private static double __kernel_rem_pio2(double xv, int hx, final int trig) {
        Rempiostruct rmp = rempstruct.get();
        double[] x = rmp.x;
        double[] f = rmp.f;
        double[] q = rmp.q;
        double[] fq = rmp.fq;
        int[] iq = rmp.iq;

        /* set z = scalbn(|x|,ilogb(x)-23) */
        long lx = Double.doubleToRawLongBits(xv);
        long exp = ((lx & 0x7ff0000000000000L ) >> 52) - 1046;
        lx = (lx - (exp << 52))&0x7fffffffffffffffL;
        double zz = Double.longBitsToDouble(lx);
        for (int i = 0; i < 2; i++) {
            x[i] = (int) zz;
            zz = (zz - x[i]) * two24;
        }
        x[2] = zz;
        int nx = 3;
        while (x[nx - 1] == zero) { /* skip zero term */
            nx--; 
        }
        double z, fw;
        int ih, n;
        int jk = 4;
        int jp = jk;
        /* determine jx,jv,q0, note that 3>q0 */
        int jx = nx - 1;
        int e0 = (int) exp;
        int jv = (e0 - 3) / 24;
        if (jv < 0) {
            jv = 0;
        }
        int q0 = e0 - (24 * (jv + 1));
        /* set up f[0] to f[jx+jk] where f[jx+jk] = two_over_pi[jv+jk] */
        int j = jv - jx;
        int m = jx + jk;
        for (int i = 0; i <= m; i++, j++) {
            f[i] = ((j < 0) ? zero : two_over_pi[j]);
        }

        /* compute q[0],q[1],...q[jk] */
        for (int i = 0; i <= jk; i++) {
            for (j = 0, fw = 0.0; j <= jx; j++) {
                fw += (x[j] * f[(jx + i) - j]);
            }
            q[i] = fw;
        }
        int jz = jk;
        while (true) { // recompute:
            /* distill q[] into iq[] reversingly */
            j = jz;
            z = q[jz];
            for (int i = 0; j > 0; i++, j--) {
                fw = ((int) (twon24 * z));
                iq[i] = (int) (z - (two24 * fw));
                z = q[j - 1] + fw;
            }
            /* compute n */
            z = scalb(z, q0); /* actual value of z */
            z -= (8.0 * floor(z * 0.125)); /* trim off integer >= 8 */
            n = (int) z;
            z -= n;
            ih = 0;
            if (q0 > 0) { /* need iq[jz-1] to determine n */
                int i = (iq[jz - 1] >> (24 - q0));
                n += i;
                iq[jz - 1] -= (i << (24 - q0));
                ih = iq[jz - 1] >> (23 - q0);
            } else if (q0 == 0) {
                ih = iq[jz - 1] >> 23;
            } else if (z >= 0.5) {
                ih = 2;
            }
            if (ih > 0) { /* q > 0.5 */
                n += 1;
                int carry = 0;
                for (int i = 0; i < jz; i++) { /* compute 1-q */
                    j = iq[i];
                    if (carry == 0) {
                        if (j != 0) {
                            carry = 1;
                            iq[i] = 0x1000000 - j;
                        }
                    } else {
                        iq[i] = 0xffffff - j;
                    }
                }
                /* rare case: chance is 1 in 12 */
                if (q0 == 1) {
                    iq[jz - 1] &= 0x7fffff;
                } else if (q0 == 2) {
                    iq[jz - 1] &= 0x3fffff;
                }
                if (ih == 2) {
                    z = one - z;
                    if (carry != 0) {
                        z -= scalb(one,q0);
                    }
                }
            }
            /* check if recomputation is needed */
            if (z == zero) {
                j = 0;
                for (int i = jz - 1; i >= jk; i--) {
                    j |= iq[i];
                }
                if (j == 0) { /* need recomputation */
                    int k = 1;
                    for (; iq[jk - k] == 0; k++) {
                    }/* k = no. of terms needed */
                    for (int i = jz + 1; i <= (jz + k); i++) {
                        // add q[jz+1] to q[jz+k]
                        f[jx + i] = two_over_pi[jv + i];
                        for (j = 0, fw = 0.0; j <= jx; j++) {
                            fw += (x[j] * f[(jx + i) - j]);
                        }
                        q[i] = fw;
                    }
                    jz += k;
                    continue; 
                }
            }
            break;
        }
        /* chop off zero terms */
        if (z == 0.0d) {
            jz--;
            q0 -= 24;
            while (iq[jz] == 0) {
                jz--;
                q0 -= 24;
            }
        } else { /* break z into 24-bit if necessary */
            z = scalb(z, -q0);
            if (z >= two24) {
                fw = (int) (twon24 * z);
                iq[jz] = (int) (z - (two24 * fw));
                jz++;
                q0 += 24;
                iq[jz] = (int) fw;
            } else {
                iq[jz] = (int) z;
            }
        }
        /* convert integer "bit" chunk to floating-point value */
        fw = scalb(one,q0);
        for (int i = jz; i >= 0; i--) {
            q[i] = fw * iq[i];
            fw *= twon24;
        }
        /* compute PIo2[0,...,jp]*q[jz,...,0] */
        for (int i = jz; i >= 0; i--) {
            int k = 0;
            for (fw = 0.0; (k <= jp) && (k <= (jz - i)); k++) {
                fw += PIo2[k] * q[i + k];
            }
            fq[jz - i] = fw;
        }
        /* compress fq[] into y[] */
        fw = 0.0d;
        for (int i = jz; i >= 0; i--) {
            fw += fq[i];
        }
        double y0 = (ih == 0) ? fw : (0.0d - fw);
        fw = fq[0] - fw;
        for (int i = 1; i <= jz; i++) {
            fw += fq[i];
        }
        double y1 = ((ih == 0) ? fw : (0.0d - fw));
        n &= 7;
        if (hx < 0) {
            y0 = 0.0d - y0;
            y1 = 0.0d - y1;
            n = -n;
        }
        return getTrigres(trig, n, y0, y1);
    }

    private static final double pio2_hi = 1.57079632679489655800e+00;
    private static final double pio2_lo = 6.12323399573676603587e-17;
    private static final double pio4_hi = 7.85398163397448278999e-01;
    private static final double PIret = PI + 2.0 * pio2_lo;

    /* coefficient for R(x^2) */
    private static final double pS0 = 1.66666666666666657415e-01;
    private static final double pS1 = -3.25565818622400915405e-01;
    private static final double pS2 = 2.01212532134862925881e-01;
    private static final double pS3 = -4.00555345006794114027e-02;
    private static final double pS4 = 7.91534994289814532176e-04;
    private static final double pS5 = 3.47933107596021167570e-05;
    private static final double qS1 = -2.40339491173441421878e+00;
    private static final double qS2 = 2.02094576023350569471e+00;
    private static final double qS3 = -6.88283971605453293030e-01;
    private static final double qS4 =  7.70381505559019352791e-02;


    /**
     * Returns the arc sine of a value; the returned angle is in the
     * range -<i>pi</i>/2 through <i>pi</i>/2.  Special cases:
     * <ul><li>If the argument is NaN or its absolute value is greater
     * than 1, then the result is NaN.
     * <li>If the argument is zero, then the result is a zero with the
     * same sign as the argument.</ul>
     *
     * @param   a   the value whose arc sine is to be returned.
     * @return  the arc sine of the argument.
     */
    public static double asin(double a) {
        /*
         *        asin(x)
         * Method :
         *        Since  asin(x) = x + x^3/6 + x^5*3/40 + x^7*15/336 + ...
         *        we approximate asin(x) on [0,0.5] by
         *                asin(x) = x + x*x^2*R(x^2)
         *        where
         *                R(x^2) is a rational approximation of (asin(x)-x)/x^3
         *        and its remez error is bounded by
         *                |(asin(x)-x)/x^3 - R(x^2)| < 2^(-58.75)
         *
         *        For x in [0.5,1]
         *                asin(x) = pi/2-2*asin(sqrt((1-x)/2))
         *        Let y = (1-x), z = y/2, s := sqrt(z),and pio2_hi+pio2_lo=pi/2;
         *        then for x>0.98
         *                asin(x) = pi/2 - 2*(s+s*z*R(z))
         *                        = pio2_hi - (2*(s+s*z*R(z)) - pio2_lo)
         *        For x<=0.98, let pio4_hi = pio2_hi/2, then
         *                f = hi part of s;
         *                c = sqrt(z) - f = (z-f*f)/(s+f)         ...f+c=sqrt(z)
         *        and
         *                asin(x) = pi/2 - 2*(s+s*z*R(z))
         *                        = pio4_hi+(pio4-2s)-(2s*z*R(z)-pio2_lo)
         *                        = pio4_hi+(pio4-2f)-(2s*z*R(z)-(pio2_lo+2c))
         *
         * Special cases:
         *        if x is NaN, return x itself;
         *        if |x|>1, return NaN with invalid signal.
         */
        int hx = __HI(a);
        int ix = hx & 0x7fffffff;
        if (ix >= 0x3ff00000) { /* |x|>= 1 */
            return ((ix - 0x3ff00000) | __LO(a)) == 0 ?
                a * pio2_hi + a * pio2_lo : //asin(1)=+-pi/2 with inexact
               (a-a)/(a-a); // asin(|x|>1) is NaN
        }
        if (ix < 0x3fe00000) { /* |x|<0.5 */            
            if (ix < 0x3e400000){ /* if |x| < 2**-27 */
                if(huge+a>one) return a; /* return x with inexact if x!=0*/
            }else
                return a + (a * getPdivQ(a*a));
        }
        // 1> |x|>= 0.5
        double t = (one - abs(a)) * 0.5;
        double pdivq = getPdivQ(t);
        double s = java.lang.StrictMath.sqrt(t);
        if (ix >= 0x3FEF3333) { /* if |x| > 0.975 */
            t = pio2_hi - (2.0 * (s + s * pdivq) - pio2_lo);
        } else {
            double w = clearLow32bits(s);
            double p = 2.0d * s * pdivq - (pio2_lo - 2.0d*((t-(w*w))/(s+w)));
            t = pio4_hi - (p - (pio4_hi - 2.0d * w));
        }
        return hx > 0 ? t : - t;
    }

    /**
     * Returns the arc cosine of a value; the returned angle is in the
     * range 0.0 through <i>pi</i>.  Special case:
     * <ul><li>If the argument is NaN or its absolute value is greater
     * than 1, then the result is NaN.</ul>
     *
     * @param   a   the value whose arc cosine is to be returned.
     * @return  the arc cosine of the argument.
     */
    public static double acos(double a) {
        /* Method :
         *        acos(x)  = pi/2 - asin(x)
         *        acos(-x) = pi/2 + asin(x)
         * For |x|<=0.5
         *        acos(x) = pi/2 - (x + x*x^2*R(x^2))        (see asin.c)
         * For x>0.5
         *         acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2)))
         *                = 2asin(sqrt((1-x)/2))
         *                = 2s + 2s*z*R(z)         ...z=(1-x)/2, s=sqrt(z)
         *                = 2f + (2c + 2s*z*R(z))
         *     where f=hi part of s, and c= (z-f*f)/(s+f) is the correction term
         *     for f so that f+c ~ sqrt(z).
         * For x<-0.5
         *        acos(x) = pi - 2asin(sqrt((1-|x|)/2))
         *          = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z)
         *
         * Special cases:
         *        if x is NaN, return x itself;
         *        if |x|>1, return NaN with invalid signal.
         */

        final int hx = __HI(a);
        final int ix = hx & 0x7fffffff;
        if (ix >= 0x3ff00000) { // |x| >= 1
            if (((ix - 0x3ff00000) | __LO(a)) == 0) { // |x|==1
                return a > 0 ? 0.0 : PIret;
            }
            return (a - a) / (a - a); // acos(|x|>1) is NaN
        }

        if (ix < 0x3fe00000) { // |x| < 0.5
            return ix <= 0x3c600000 ?
                pio2_hi + pio2_lo : //  |x|<2**-57
                pio2_hi - (a - (pio2_lo - a * getPdivQ(a * a)));
        }

        final double z = 0.5 * ((hx < 0) ? (one + a) : (one - a));
        final double s = java.lang.StrictMath.sqrt(z);
        final double pdivq = s * getPdivQ(z);

        if (hx < 0) { // x < -0.5            
            return PI - 2.0 * (s + (pdivq - pio2_lo));
        }        
        // x > 0.5        
        final double df = clearLow32bits(s);
        return 2.0 * (df + (pdivq + (z - df * df) / (s + df)));
    }

    private static double getPdivQ(double z){
        return (z*(pS0 + z*(pS1 + z*(pS2 + z*(pS3 + z*(pS4 + z*pS5)))))) /
                (one + z * (qS1 + z * (qS2 + (z * (qS3 + (z * qS4))))));
    }

    private static final double atanhi[] = {
        4.63647609000806093515e-01, // atan(0.5)hi
        7.85398163397448278999e-01, // atan(1.0)hi
        9.82793723247329054082e-01, // atan(1.5)hi
        1.57079632679489655800e+00};// atan(inf)hi
        

    private static final double atanlo[] = {
        2.26987774529616870924e-17, // atan(0.5)lo
        3.06161699786838301793e-17, // atan(1.0)lo
        1.39033110312309984516e-17, // atan(1.5)lo
        6.12323399573676603587e-17};// atan(inf)lo)

    private static final double
        ln2_hi = 6.93147180369123816490e-01,
        ln2_lo = 1.90821492927058770002e-10,
        Lg1    = 6.666666666666735130e-01,
        Lg2    = 3.999999999940941908e-01,
        Lg3    = 2.857142874366239149e-01,
        Lg4    = 2.222219843214978396e-01,
        Lg5    = 1.818357216161805012e-01,
        Lg6    = 1.531383769920937332e-01,
        Lg7    = 1.479819860511658591e-01,
        two54  = 1.80143985094819840000e+16,
        aT0 = 3.33333333333329318027e-01,
        aT1 = -1.99999999998764832476e-01,
        aT2 = 1.42857142725034663711e-01,
        aT3 = -1.11111104054623557880e-01,
        aT4 = 9.09088713343650656196e-02,
        aT5 = -7.69187620504482999495e-02,
        aT6 = 6.66107313738753120669e-02,
        aT7 = -5.83357013379057348645e-02,
        aT8 = 4.97687799461593236017e-02,
        aT9 = -3.65315727442169155270e-02,
        aT10 = 1.62858201153657823623e-02,
        atanhi3PLUSatanlo3 =  atanhi[3]  + atanlo[3],
        negatanhi3MINUSatanlo3 = -atanhi[3] - atanlo[3],
        pi_o_4 = 7.8539816339744827900e-01,
        pi_o_2 = 1.5707963267948965580e+00,
        pi_lo = 1.2246467991473531772e-16,
        huge = 1.0e+300,
        tiny = 1.0e-300;
  
    /**
     * Returns the arc tangent of a value; the returned angle is in the
     * range -<i>pi</i>/2 through <i>pi</i>/2.  Special cases:
     * <ul><li>If the argument is NaN, then the result is NaN.
     * <li>If the argument is zero, then the result is a zero with the
     * same sign as the argument.</ul>
     *
     * @param   a   the value whose arc tangent is to be returned.
     * @return  the arc tangent of the argument.
     */
    public static double atan(double a) {
        /*
         * Method
         *   1. Reduce x to positive by atan(x) = -atan(-x).
         *   2. According to the integer k=4t+0.25 chopped, t=x, the argument
         *      is further reduced to one of the following intervals and the
         *      arctangent of t is evaluated by the corresponding formula:
         *
         *      [0,7/16]      atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...)
         *      [7/16,11/16]  atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) )
         *      [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) )
         *      [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) )
         *      [39/16,INF]   atan(x) = atan(INF) + atan( -1/t )
         */
        
        int hx = __HI(a);
        int ix = hx & 0x7fffffff;
        if (ix >= 0x44100000) { /* if |x| >= 2^66 */
            if ((ix > 0x7ff00000) || (ix == 0x7ff00000 && __LO(a) != 0)) {
                return a+a; /* NaN */
            }
            return hx > 0 ? atanhi3PLUSatanlo3 : negatanhi3MINUSatanlo3;
        }
        int id;
        if (ix < 0x3fdc0000) { /* |x| < 0.4375 */
            if (ix < 0x3e200000 &&  /* |x| < 2^-29 */
                 (huge + a > one)) {
                    return a; /* raise inexact */
                }
            id = -1;
        } else {
            a = abs(a);
            if (ix < 0x3ff30000) { /* |x| < 1.1875 */
                if (ix < 0x3fe60000) { /* 7/16 <=|x|<11/16 */
                    id = 0;
                    a = (2.0d * a - one) / (2.0d + a);
                } else { /* 11/16<=|x|< 19/16 */
                    id = 1;
                    a = (a - one) / (a + one);
                }
            } else {
                if (ix < 0x40038000) { /* |x| < 2.4375 */
                    id = 2;
                    a = (a - 1.5d) / (one + 1.5d * a);
                } else { /* 2.4375 <= |x| < 2^66 */
                    id = 3;
                    a = negone / a;
                }
            }
        }

        /* end of argument reduction */
        double z = a * a;
        double w = z * z;

        /* break sum from i=0 to 10 aTi z**(i+1) into odd and even poly */
        double ss = a*(z*(aT0 + w*(aT2 + w*(aT4 + w*(aT6 +w*(aT8 + w*aT10)))))+
                w * (aT1 + w*(aT3 + w*(aT5 + w*(aT7 +w*aT9)))));
        if (id < 0) {
            return a - ss;
        }
        z = atanhi[id] - ((ss - atanlo[id]) - a);
        return hx < 0 ? 0.0d - z : z;
    }

    /**
     * Converts an angle measured in degrees to an approximately
     * equivalent angle measured in radians.  The conversion from
     * degrees to radians is generally inexact.
     *
     * @param   angdeg   an angle, in degrees
     * @return  the measurement of the angle {@code angdeg}
     *          in radians.
     */
    public static strictfp double toRadians(double angdeg) {
        return angdeg / 180.0 * PI;
    }

    /**
     * Converts an angle measured in radians to an approximately
     * equivalent angle measured in degrees.  The conversion from
     * radians to degrees is generally inexact; users should
     * <i>not</i> expect {@code cos(toRadians(90.0))} to exactly
     * equal {@code 0.0}.
     *
     * @param   angrad   an angle, in radians
     * @return  the measurement of the angle {@code angrad}
     *          in degrees.
     */
    public static strictfp double toDegrees(double angrad) {
        return angrad * 180.0 / PI;
    }

    private static final double
        ivln10      = 4.34294481903251816668e-01,
        log10_2hi   = 3.01029995663611771306e-01,
        log10_2lo   = 3.69423907715893078616e-13,
        halF[]      =  {0.5,-0.5},
        twom1000    = 9.33263618503218878990e-302,// 2**-1000=0x01700000,0
        o_threshold =  7.09782712893383973096e+02,
        u_threshold = -7.45133219101941108420e+02,
        ln2HI[]   = { 6.93147180369123816490e-01,-6.93147180369123816490e-01,},
        ln2LO[]   = { 1.90821492927058770002e-10,-1.90821492927058770002e-10,},
        invln2    =  1.44269504088896338700e+00,
        ln2HI0    = ln2HI[0],
        ln2LO0    = ln2LO[0];
   

    /**
     * Returns Euler's number <i>e</i> raised to the power of a
     * {@code double} value. Special cases:
     * <ul><li>If the argument is NaN, the result is NaN.
     * <li>If the argument is positive infinity, then the result is
     * positive infinity.
     * <li>If the argument is negative infinity, then the result is
     * positive zero.</ul>
     *
     * @param   a   the exponent to raise <i>e</i> to.
     * @return  the value <i>e</i><sup>{@code a}</sup>,
     *          where <i>e</i> is the base of the natural logarithms.
     */
    public static double exp(double a) {
        /* exp(x)
         * Returns the exponential of x.
         *
         * Method
         *   1. Argument reduction:
         *      Reduce x to an r so that |r| <= 0.5*ln2 ~ 0.34658.
         *        Given x, find r and integer k such that
         *
         *               x = k*ln2 + r,  |r| <= 0.5*ln2.
         *
         *      Here r will be represented as r = hi-lo for better
         *         accuracy.
         *
         *   2. Approximation of exp(r) by a special rational function on
         *        the interval [0,0.34658]:
         *        Write
         *       R(r**2) = r*(exp(r)+1)/(exp(r)-1) = 2 + r*r/6 - r**4/360 + ...
         *      We use a special Reme algorithm on [0,0.34658] to generate
         *         a polynomial of degree 5 to approximate R. The maximum error
         *          of this polynomial approximation is bounded by 2**-59. In
         *        other words,
         *            R(z) ~ 2.0 + P1*z + P2*z**2 + P3*z**3 + P4*z**4 + P5*z**5
         *         (where z=r*r, and the values of P1 to P5 are listed below)
         *        and
         *            |                  5          |     -59
         *             | 2.0+P1*z+...+P5*z   -  R(z) | <= 2
         *            |                             |
         *        The computation of exp(r) thus becomes
         *                             2*r
         *                exp(r) = 1 + -------
         *                              R - r
         *                          r*R1(r)
         *                       = 1 + r + ----------- (for better accuracy)
         *                                  2 - R1(r)
         *         where
         *                                   2       4             10
         *                R1(r) = r - (P1*r  + P2*r  + ... + P5*r   ).
         *
         *   3. Scale back to obtain exp(x):
         *        From step 1, we have
         *           exp(x) = 2^k * exp(r)
         *
         * Special cases:
         *        exp(INF) is INF, exp(NaN) is NaN;
         *        exp(-INF) is 0, and
         *        for finite argument, only exp(0)=1 is exact.
         *
         * Accuracy:
         *        according to an error analysis, the error is always less than
         *        1 ulp (unit in the last place).
         *
         * Misc. info.
         *        For IEEE double
         *            if x >  7.09782712893383973096e+02 then exp(x) overflow
         *            if x < -7.45133219101941108420e+02 then exp(x) underflow
         */
        int hx = __HI(a); /* high word of x */
        final int xsb = (hx >>> 31) & 1; /* sign bit of x */
        final boolean xsb0 = xsb == 0;
        hx &= 0x7fffffff; /* high word of |x| */

        /* filter out non-finite argument */
        if (hx >= 0x40862E42) { /* if |x|>=709.78... */
            if (hx >= 0x7ff00000) {
                if (((hx & 0xfffff) | __LO(a)) != 0) {
                    return a+a; /* NaN */
                }
                return xsb0 ? a : 0.0d; /* exp(+-inf)={inf,0} */
            }
            if (a > o_threshold) {
                return huge*huge; /* overflow */
            }
            if (a < u_threshold) {
                return twom1000 * twom1000; /* underflow */
            }
        }
        
        double hi = 0;
        double lo = 0;
        int k=0;
        /* argument reduction */
        if (hx > 0x3fd62e42) { /* if  |x| > 0.5 ln2 */
            if(hx < 0x3FF0A2B2) {	/* and |x| < 1.5 ln2 */
		hi = a-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb;
	    } else {
		k  = (int)(invln2*a+halF[xsb]);
                double t = k;
                hi = a - t * ln2HI0; /* t*ln2HI is exact here */
                lo = t * ln2LO0;
            }
            a = hi - lo;
        } else if (hx < 0x3e300000) { /* when |x|<2**-28 */
            if (huge + a > one) {
                return one + a; /* trigger inexact */
            }
        } 

        /* x is now in primary range */
        final double t = a * a;
        final double c = a - t * (P1 + t * (P2 + t * (P3 + t * (P4 + t * P5))));
        if (k == 0) {
            return one - (((a * c) / (c - 2.0)) - a);
        }        
        final long ybits = Double.doubleToRawLongBits(
                one - ((lo - ((a * c) / (2.0 - c))) - hi));
        return (k >= -1021) ?
            addToHighBits(ybits, k<<20) :
            addToHighBits(ybits, (k+1000)<<20)*twom1000;
    }



    /**
     * Returns the natural logarithm (base <i>e</i>) of a {@code double}
     * value. Special cases:
     * <ul><li>If the argument is NaN or less than zero, then the result
     * is NaN.
     * <li>If the argument is positive infinity, then the result is
     * positive infinity.
     * <li>If the argument is positive zero or negative zero, then the
     * result is negative infinity.</ul>
     *
     * @param   a   a value
     * @return  the value ln&nbsp;{@code a}, the natural logarithm of
     *          {@code a}.
     */
    public static double log(double x) {
        /* __ieee754_log(x)
         * Return the logrithm of x
         *
         * Method :
         *   1. Argument Reduction: find k and f such that
         *                        x = 2^k * (1+f),
         *           where  sqrt(2)/2 < 1+f < sqrt(2) .
         *
         *   2. Approximation of log(1+f).
         *        Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s)
         *                 = 2s + 2/3 s**3 + 2/5 s**5 + .....,
         *                      = 2s + s*R
         *      We use a special Reme algorithm on [0,0.1716] to generate
         *         a polynomial of degree 14 to approximate R The maximum error
         *        of this polynomial approximation is bounded by 2**-58.45. In
         *        other words,
         *                        2      4      6      8      10      12      14
         *            R(z) ~ Lg1*s +Lg2*s +Lg3*s +Lg4*s +Lg5*s  +Lg6*s  +Lg7*s
         *          (the values of Lg1 to Lg7 are listed in the program)
         *        and
         *            |      2          14          |     -58.45
         *            | Lg1*s +...+Lg7*s    -  R(z) | <= 2
         *            |                             |
         *        Note that 2s = f - s*f = f -hfsq + s*hfsq, where hfsq = f*f/2.
         *        In order to guarantee error in log below 1ulp, we compute log
         *        by
         *                log(1+f) = f - s*(f - R)       (if f is not too large)
         *                log(1+f) = f - (hfsq - s*(hfsq+R)).  (better accuracy)
         *
         *        3. Finally,  log(x) =k*ln2 + log(1+f).
         *                            =k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo)))
         *           Here ln2 is split into two floating point number:
         *                        ln2_hi + ln2_lo,
         *           where n*ln2_hi is always exact for |n| < 2000.
         *
         * Special cases:
         *        log(x) is NaN with signal if x < 0 (including -INF) ;
         *        log(+INF) is +INF; log(0) is -INF with signal;
         *        log(NaN) is that NaN with no signal.
         *
         * Accuracy:
         *        according to an error analysis, the error is always less than
         *        1 ulp (unit in the last place).
         */        
        int hx = (int) (Double.doubleToRawLongBits(x) >> 32);
        int k = 0;
        if (hx < 0x00100000) { /* x < 2**-1022  */
            if (((hx & 0x7fffffff) | (__LO(x)& 0xFFFFFFFF)) == 0) {
                return -two54/zero; /* log(+-0)=-inf */
            }
            if (hx < 0) {
                return (x-x)/zero; /* log(-#) = NaN */
            }
            k = -54;
            x *= two54; /* subnormal number, scale up x */
            hx = __HI(x); /* high word of x */
        }
        if (hx >= 0x7ff00000) {
            return x + x;
        }
        k += (hx >> 20) - 1023;
        hx &= 0x000fffff;
        final int i = (hx + 0x95f64) & 0x100000;
        k += i >> 20;
                    /* normalize x or x/2 */
        final double dkln2hi = k * ln2_hi;
        final double dkln2lo = k * ln2_lo;
        final boolean KisZero = k== 0;
        final double f = setHigh32bits(x, hx | (i ^ 0x3ff00000)) - 1.0;
        if ((0x000fffff & (2 + hx)) < 3) { /* |f| < 2**-20 */
            if (f == zero) {
                return KisZero ? zero : dkln2hi + dkln2lo;
            }
            double R = f * f * (0.5 - (0.33333333333333333 * f));
            return KisZero ? f - R  :  dkln2hi - ((R - dkln2lo) - f);
        }                                
        double s = f / (2.0 + f);
        final double z = s * s;
        final double w = z * z;
        final double R = w * (Lg2 + w * (Lg4 + w * Lg6)) +
                z * (Lg1 + w * (Lg3 + w * (Lg5 + w * Lg7)));
        if (((hx - 0x6147a)|(0x6b851 - hx)) > 0) {
            double hfsq = 0.5 * f * f;
            s *= hfsq + R;
            return KisZero ? f-(hfsq - s) : dkln2hi - ((hfsq -(s + dkln2lo))-f);
        }
        s *= f-R;
        return KisZero ? f-s : dkln2hi - ((s - dkln2lo) - f);
    }



    /**
     * Returns the base 10 logarithm of a {@code double} value.
     * Special cases:
     *
     * <ul><li>If the argument is NaN or less than zero, then the result
     * is NaN.
     * <li>If the argument is positive infinity, then the result is
     * positive infinity.
     * <li>If the argument is positive zero or negative zero, then the
     * result is negative infinity.
     * <li> If the argument is equal to 10<sup><i>n</i></sup> for
     * integer <i>n</i>, then the result is <i>n</i>.
     * </ul>
     *
     * @param   a   a value
     * @return  the base 10 logarithm of  {@code a}.
     * @since 1.5
     */
    public static double log10(double a) {
        /* __ieee754_log10(x)
         * Return the base 10 logarithm of x
         *
         * Method :
         *    Let log10_2hi = leading 40 bits of log10(2) and
         *        log10_2lo = log10(2) - log10_2hi,
         *        ivln10   = 1/log(10) rounded.
         *    Then
         *            n = ilogb(x),
         *            if(n<0)  n = n+1;
         *            x = scalbn(x,-n);
         *            log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x))
         *
         * Note 1:
         *    To guarantee log10(10**n)=n, where 10**n is normal, the rounding
         *    mode must set to Round-to-Nearest.
         * Note 2:
         *    [1/log(10)] rounded to 53 bits has error  .198   ulps;
         *    log10 is monotonic at all binary break points.
         *
         * Special cases:
         *    log10(x) is NaN with signal if x < 0;
         *    log10(+INF) is +INF with no signal; log10(0) is -INF with signal;
         *    log10(NaN) is that NaN with no signal;
         *    log10(10**N) = N  for N=0,1,...,22.
         */
        int hx = (int) (Double.doubleToRawLongBits(a) >> 32);
        int k = 0;
        if (hx < 0x00100000) { /* x < 2**-1022  */
                                        //unsigned low bits
            if (((hx & 0x7fffffff) | (__LO(a)&0xFFFFFFFF)) == 0) {
                return -two54/zero; /* log(+-0)=-inf */
            }
            if (hx < 0) {
                return (a-a)/zero; /* log(-#) = NaN */
            }
            k = -54;
            a *= two54; /* subnormal number, scale up x */
            hx = __HI(a);      /* high word of x */
        }
        if (hx >= 0x7ff00000) {
            return a + a;
        }
        k += (hx >> 20) - 1023;
        //i  = ((unsigned)k&0x80000000)>>31;
        final int i = (k & 0x80000000) >>> 31;
        hx = (hx & 0x000fffff) | ((0x3ff - i) << 20);
        final double y = k + i;
        return (y*log10_2lo + ivln10 * log(setHigh32bits(a, hx))) + y*log10_2hi;
    }

    /**
     * Returns the correctly rounded positive square root of a
     * {@code double} value.
     * Special cases:
     * <ul><li>If the argument is NaN or less than zero, then the result
     * is NaN.
     * <li>If the argument is positive infinity, then the result is positive
     * infinity.
     * <li>If the argument is positive zero or negative zero, then the
     * result is the same as the argument.</ul>
     * Otherwise, the result is the {@code double} value closest to
     * the true mathematical square root of the argument value.
     *
     * @param   a   a value.
     * @return  the positive square root of {@code a}.
     */
    public static native double sqrt(double a);

    
    private static final int B1 = 715094163;//B1 = (682-0.03306235651)*2**20
    private static final long 
            B2highbits = 696219795L<<32;//(664-0.03306235651)*2**20   << 32

    private static final 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
            TWOpow54 = Double.longBitsToDouble(0x43500000L<<32);

    /**
     * Returns the cube root of a {@code double} value.  For
     * positive finite {@code x}, {@code cbrt(-x) ==
     * -cbrt(x)}; that is, the cube root of a negative value is
     * the negative of the cube root of that value's magnitude.
     * Special cases:
     *
     * <ul>
     *
     * <li>If the argument is NaN, then the result is NaN.
     *
     * <li>If the argument is infinite, then the result is an infinity
     * with the same sign as the argument.
     *
     * <li>If the argument is zero, then the result is a zero with the
     * same sign as the argument.
     *
     * </ul>
     *
     * @param   x   x value.
     * @return  the cube root of {@code x}.
     * @since 1.5
     */
    public static double cbrt(double x) {        
        long xb = Double.doubleToRawLongBits(x);
        long hx = xb >> 32; //todo check if faster to not store sign
        final long sign = hx & 0x80000000;// unsigned in c /* sign= sign(x) */
        hx ^= sign;
        if (hx >= 0x7ff00000L) {
            return x + x;       /* cbrt(NaN,INF) is itself */
        } 
        if ((hx | (xb & 0x00000000FFFFFFFFL) ) == 0) {
            return x;          /* cbrt(0) is itself */
        }
        
        x = setHigh32bits(xb, hx);  /* x <- |x| */
        /* rough cbrt to 5 bits */
        if (hx < 0x00100000L) {               /* subnormal number */
            //HI(t)=0x43500000; 		/* set t= 2**54 */
	    //t*=x; __HI(t)=__HI(t)/3+B2;
             long tb = Double.doubleToRawLongBits(TWOpow54 * x);
             hx = (tb&0x00000000FFFFFFFFL) | (tb/3  + B2highbits);
        } else {
            hx = (hx/3 + B1) << 32;
        }
        double t = Double.longBitsToDouble(hx);

        /* new cbrt to 23 bits, may be implemented in single precision */
        final double s = C_ + (t * t / x) * t;
        t *= G_ + F_ / (s + E_ + D_ / s);

        /* chopped to 20 bits and make it larger than cbrt(x) */
        //__LO(t)=0; __HI(t)+=0x00000001;
        t = Double.longBitsToDouble(
                ((Double.doubleToRawLongBits(t)>>32) + 0x00000001) <<32);
        //one step newton iteration to 53 bits with error less than 0.667 ulps
        final double r = x / (t * t);  /* t*t is exact */
        t += t*((r - t) / ((t + t) + r));  /* r-s is exact */
        /* retore the sign bit */
        return Double.longBitsToDouble(
                Double.doubleToRawLongBits(t) | (sign<<32));
    }

    /**
     * Computes the remainder operation on two arguments as prescribed
     * by the IEEE 754 standard.
     * The remainder value is mathematically equal to
     * <code>f1&nbsp;-&nbsp;f2</code>&nbsp;&times;&nbsp;<i>n</i>,
     * where <i>n</i> is the mathematical integer closest to the exact
     * mathematical value of the quotient {@code f1/f2}, and if two
     * mathematical integers are equally close to {@code f1/f2},
     * then <i>n</i> is the integer that is even. If the remainder is
     * zero, its sign is the same as the sign of the first argument.
     * Special cases:
     * <ul><li>If either argument is NaN, or the first argument is infinite,
     * or the second argument is positive zero or negative zero, then the
     * result is NaN.
     * <li>If the first argument is finite and the second argument is
     * infinite, then the result is the same as the first argument.</ul>
     *
     * @param   f1   the dividend.
     * @param   f2   the divisor.
     * @return  the remainder when {@code f1} is divided by
     *          {@code f2}.
     */
    public static double IEEEremainder(double f1, double f2) {
        /* __ieee754_remainder(x,p)
         * Return :
         *      returns  x REM p  =  x - [x/p]*p as if in infinite
         *      precise arithmetic, where [x/p] is the (infinite bit)
         *      integer nearest x/p (in half way case choose the even one).
         * Method :
         *      Based on fmod() return x-[x/p]chopped*p exactlp.
         */        
        //todo need to verify that this implementation  works.
        long t = Double.doubleToRawLongBits(f1);
        int hx = (int) (t >> 32);
        final long sx = (long)(hx & 0x80000000)<<32; //unsigned in c
        hx &= 0x7fffffff;
        
        int lx = (int) t; //unsigned in c
        t = Double.doubleToRawLongBits(f2);
        int hp = (int) (t >> 32) & 0x7fffffff;
        int lp = (int) t; //unsigned in c

        /* purge off exception values */
        if (((hp | lp) == 0) ||         /* p = 0 */
                (hx >= 0x7ff00000) ||   /* x not finite */
                ((hp >= 0x7ff00000) &&  /* p is NaN */
                (((hp - 0x7ff00000) | lp) != 0))) {
            return (f1 * f2) / (f1 * f2);
        }

        if (hp <= 0x7fdfffff) {
            //f1 = __ieee754_fmod(f1,f2+f2);  /* now x < 2p */
            f1 = f1 % (f2 + f2); /* now x < 2p */
        }

        if (((hx - hp) | (lx - lp)) == 0) {
            return zero * f1;
        }

        f1 = abs(f1);
        f2 = abs(f2);
        if (hp < 0x00200000) {
            if ((f1 + f1) > f2) {
                f1 -= f2;
                if ((f1 + f1) >= f2) {
                    f1 -= f2;
                }
            }
        } else {
            final double p_half = 0.5 * f2;
            if (f1 > p_half) {
                f1 -= f2;
                if (f1 >= p_half) {
                    f1 -= f2;
                }
            }
        }        
        return setHigh32bitsXOR(f1, sx);
    }


    /**
     * Returns the smallest (closest to negative infinity)
     * {@code double} value that is greater than or equal to the
     * argument and is equal to a mathematical integer. Special cases:
     * <ul><li>If the argument value is already equal to a
     * mathematical integer, then the result is the same as the
     * argument.  <li>If the argument is NaN or an infinity or
     * positive zero or negative zero, then the result is the same as
     * the argument.  <li>If the argument value is less than zero but
     * greater than -1.0, then the result is negative zero.</ul> Note
     * that the value of {@code StrictMath.ceil(x)} is exactly the
     * value of {@code -StrictMath.floor(-x)}.
     *
     * @param   a   a value.
     * @return  the smallest (closest to negative infinity)
     *          floating-point value that is greater than or equal to
     *          the argument and is equal to a mathematical integer.
     */
    public static double ceil(double a) {
        return floorOrCeil(a, false);
    }

    /**
     * Returns the largest (closest to positive infinity)
     * {@code double} value that is less than or equal to the
     * argument and is equal to a mathematical integer. Special cases:
     * <ul><li>If the argument value is already equal to a
     * mathematical integer, then the result is the same as the
     * argument.  <li>If the argument is NaN or an infinity or
     * positive zero or negative zero, then the result is the same as
     * the argument.</ul>
     *
     * @param   a   a value.
     * @return  the largest (closest to positive infinity)
     *          floating-point value that less than or equal to the argument
     *          and is equal to a mathematical integer.
     */
    public static double floor(double a) {    
        return floorOrCeil(a, true);
    }


    /**
     * FDLIBM 5.3 s_ceil.c and s_floor.c combined in one method.
     * @param x value to perform floor or ceil on.
     * @param isfloor true if floor operation, false if ceil
     * @author gustav trede
     * @return
     */   
    private static double floorOrCeil(double x, boolean isfloor){
        long xb = Double.doubleToRawLongBits(x);
        long i0 = xb >> 32;
        long i1 = (int)xb;
        final int j0 = (int) (((i0 >> 20) & 0x7ff) - 0x3ff);
        if(j0<20) {
            if(j0<0) {  /* raise inexact if x != 0 */
                if(huge+x>0.0d) {/* return 0*sign(x) if |x|<1 */
                    if (isfloor){ //floor version
                        if(i0>=0 ) {
                            i0=i1=0;
                        }
                        else if(((i0&0x7fffffff)|i1)!=0){
                            i0=0xbff00000;
                            i1=0;
                        }
                    }else{   // ceil version
                        if(i0<0) {
                            i0=0x80000000;
                            i1=0;
                        }
                        else if((i0|i1)!=0) {
                            i0=0x3ff00000;
                            i1=0;
                        }
                    }
                }
            } else {
                int i = (0x000fffff)>>>j0; // unsigned declared in c
                if(((i0&i)|i1)==0) {
                    return x; /* x is integral */
                }
                if(huge+x>0.0d) { /* raise inexact flag */
                    if(isfloor && i0<0  || !isfloor && i0>0){
                        i0 += (0x00100000)>>j0;
                    }
                    i0 &= (~i);
                    i1=0;
                }
            }
        } else if (j0>51){
            return j0==0x400 ? x+x : x; /* inf or NaN , integral */
        } else {
            //i = ((unsigned)(0xffffffff))>>(j0-20);
            int i = 0xffffffff>>>(j0-20); // unsigned declared in c
            if((i1&i)==0){
                return x;     /* x is integral */
            }
            if(huge+x>0.0d){            /* raise inexact flag */
                if(isfloor && i0<0 || !isfloor && i0>0 ) {
                    if(j0==20){
                        i0+=1;
                    }else {
                        //unsigned j = i1+(1<<(52-j0));
                        //if(j<i1)
                        long j = i1 + (1L << (52 - j0));
                        if((j&0x7fffffffffffffffL)<(i1&0x7fffffffffffffffL)){
                            i0+=1;       /* got a carry */
                        }
                        i1 = j;
                    }
                }
                i1 &= ~i;
            }
        }
        return Double.longBitsToDouble((i0<<32) | ( i1 & 0x00000000FFFFFFFFL) );
    }

    /**
     * Returns the {@code double} value that is closest in value
     * to the argument and is equal to a mathematical integer. If two
     * {@code double} values that are mathematical integers are
     * equally close to the value of the argument, the result is the
     * integer value that is even. Special cases:
     * <ul><li>If the argument value is already equal to a mathematical
     * integer, then the result is the same as the argument.
     * <li>If the argument is NaN or an infinity or positive zero or negative
     * zero, then the result is the same as the argument.</ul>
     *
     * @param   a   a value.
     * @return  the closest floating-point value to {@code a} that is
     *          equal to a mathematical integer.
     * @author Joseph D. Darcy
     */
    public static double rint(double a) {
        /*
         * If the absolute value of a is not less than 2^52, it
         * is either a finite integer (the double format does not have
         * enough significand bits for a number that large to have any
         * fractional portion), an infinity, or a NaN.  In any of
         * these cases, rint of the argument is the argument.
         *
         * Otherwise, the sum (twoToThe52 + a ) will properly round
         * away any fractional portion of a since ulp(twoToThe52) ==
         * 1.0; subtracting out twoToThe52 from this sum will then be
         * exact and leave the rounded integer portion of a.
         *
         * This method does *not* need to be declared strictfp to get
         * fully reproducible results.  Whether or not a method is
         * declared strictfp can only make a difference in the
         * returned result if some operation would overflow or
         * underflow with strictfp semantics.  The operation
         * (twoToThe52 + a ) cannot overflow since large values of a
         * are screened out; the add cannot underflow since twoToThe52
         * is too large.  The subtraction ((twoToThe52 + a ) -
         * twoToThe52) will be exact as discussed above and thus
         * cannot overflow or meaningfully underflow.  Finally, the
         * last multiply in the return statement is by plus or minus
         * 1.0, which is exact too.
         */
        double twoToThe52 = (double) (1L << 52); // 2^52
        double sign = FpUtils.rawCopySign(1.0, a); // preserve sign info
        a = Math.abs(a);

        if (a < twoToThe52) { // E_min <= ilogb(a) <= 51
            a = ((twoToThe52 + a) - twoToThe52);
        }

        return sign * a; // restore original sign
    }

    /**
     * Returns the angle <i>theta</i> from the conversion of rectangular
     * coordinates ({@code x},&nbsp;{@code y}) to polar
     * coordinates (r,&nbsp;<i>theta</i>).
     * This method computes the phase <i>theta</i> by computing an arc tangent
     * of {@code y/x} in the range of -<i>pi</i> to <i>pi</i>. Special
     * cases:
     * <ul><li>If either argument is NaN, then the result is NaN.
     * <li>If the first argument is positive zero and the second argument
     * is positive, or the first argument is positive and finite and the
     * second argument is positive infinity, then the result is positive
     * zero.
     * <li>If the first argument is negative zero and the second argument
     * is positive, or the first argument is negative and finite and the
     * second argument is positive infinity, then the result is negative zero.
     * <li>If the first argument is positive zero and the second argument
     * is negative, or the first argument is positive and finite and the
     * second argument is negative infinity, then the result is the
     * {@code double} value closest to <i>pi</i>.
     * <li>If the first argument is negative zero and the second argument
     * is negative, or the first argument is negative and finite and the
     * second argument is negative infinity, then the result is the
     * {@code double} value closest to -<i>pi</i>.
     * <li>If the first argument is positive and the second argument is
     * positive zero or negative zero, or the first argument is positive
     * infinity and the second argument is finite, then the result is the
     * {@code double} value closest to <i>pi</i>/2.
     * <li>If the first argument is negative and the second argument is
     * positive zero or negative zero, or the first argument is negative
     * infinity and the second argument is finite, then the result is the
     * {@code double} value closest to -<i>pi</i>/2.
     * <li>If both arguments are positive infinity, then the result is the
     * {@code double} value closest to <i>pi</i>/4.
     * <li>If the first argument is positive infinity and the second argument
     * is negative infinity, then the result is the {@code double}
     * value closest to 3*<i>pi</i>/4.
     * <li>If the first argument is negative infinity and the second argument
     * is positive infinity, then the result is the {@code double} value
     * closest to -<i>pi</i>/4.
     * <li>If both arguments are negative infinity, then the result is the
     * {@code double} value closest to -3*<i>pi</i>/4.</ul>
     *
     * @param   y   the ordinate coordinate
     * @param   x   the abscissa coordinate
     * @return  the <i>theta</i> component of the point
     *          (<i>r</i>,&nbsp;<i>theta</i>)
     *          in polar coordinates that corresponds to the point
     *          (<i>x</i>,&nbsp;<i>y</i>) in Cartesian coordinates.
     */
    public static double atan2(double y, double x) {
        /* __ieee754_atan2(y,x)
         * Method :
         *      1. Reduce y to positive by atan2(y,x)=-atan2(-y,x).
         *      2. Reduce x to positive by (if x and y are unexceptional):
         *              ARG (x+iy) = arctan(y/x)           ... if x > 0,
         *              ARG (x+iy) = pi - arctan[y/(-x)]   ... if x < 0,
         *
         * Special cases:
         *
         *      ATAN2((anything), NaN ) is NaN;
         *      ATAN2(NAN , (anything) ) is NaN;
         *      ATAN2(+-0, +(anything but NaN)) is +-0  ;
         *      ATAN2(+-0, -(anything but NaN)) is +-pi ;
         *      ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2;
         *      ATAN2(+-(anything but INF and NaN), +INF) is +-0 ;
         *      ATAN2(+-(anything but INF and NaN), -INF) is +-pi;
         *      ATAN2(+-INF,+INF ) is +-pi/4 ;
         *      ATAN2(+-INF,-INF ) is +-3pi/4;
         *      ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2;
         *
         */
        long t = Double.doubleToRawLongBits(x);
        int hx = (int) (t >> 32);
        int lx = (int) t;
        int ix = hx & 0x7fffffff;  
        t = Double.doubleToRawLongBits(y);
        int hy = (int) (t >> 32);
        int ly = (int) t;
        int iy = hy & 0x7fffffff;
        if (((ix | ((lx | -lx) >>> 31)) > 0x7ff00000) ||
                ((iy | ((ly | -ly) >>> 31)) > 0x7ff00000)) {/* x or y is NaN */
            return x + y;
        }
        if (((hx - 0x3ff00000) | lx) == 0) {
            return atan(y); /* x=1.0 */
        }
        int m = ((hy >> 31) & 1) | ((hx >> 30) & 2); /* 2*sign(x)+sign(y) */

        /* when y = 0 */
        if ((iy | ly) == 0) {
            switch (m) {
                case 0:
                case 1: return y; /* atan(+-0,+anything)=+-0 */
                case 2: return PI + tiny; /* atan(+0,-anything) = pi */
                case 3: return -PI - tiny; /* atan(-0,-anything) =-pi */
            }
        }

        /* when x = 0 */
        if ((ix | lx) == 0) {
            return hy < 0? -pi_o_2 - tiny : pi_o_2 + tiny;
        }

        /* when x is INF */
        if (ix == 0x7ff00000) {
            if (iy == 0x7ff00000) {
                switch (m) {
                    case 0: return pi_o_4 + tiny; /* atan(+INF,+INF) */
                    case 1: return -pi_o_4 - tiny; /* atan(-INF,+INF) */
                    case 2: return (3.0 * pi_o_4) + tiny; /*atan(+INF,-INF)*/
                    case 3: return (-3.0 * pi_o_4) - tiny; /*atan(-INF,-INF)*/
                }
            } else {
                switch (m) {
                    case 0: return zero; /* atan(+...,+INF) */
                    case 1: return -zero; /* atan(-...,+INF) */
                    case 2: return PI + tiny; /* atan(+...,-INF) */
                    case 3: return -PI - tiny; /* atan(-...,-INF) */
                }
            }
        }

        /* when y is INF */
        if (iy == 0x7ff00000) {
            return hy < 0 ? -pi_o_2 - tiny : pi_o_2 + tiny;
        }

        /* compute y/x */
        double z;
        int k = (iy - ix) >> 20;
        if (k > 60) { /* |y/x| >  2**60 */
            z = pi_o_2 + (0.5 * pi_lo);
        } else if ((hx < 0) && (k < -60)) {
            z = 0.0; /* |y|/x < -2**60 */
        } else {
            z = atan(abs(y / x)); /* safe to do y/x */
        }

        switch (m) {
            case 0:  return z; /* atan(+,+) */
            case 1:  return setHigh32bitsXOR(z,(0x80000000L<<32));// atan(-,+)
            case 2:  return PI - (z - pi_lo); /* atan(+,-) */
            default: return (z - pi_lo) - PI; /* atan(-,-) */
        }
    }

    
    private static final double bp[] = {1.0, 1.5,},
            dp_h[] = {0.0, 5.84962487220764160156e-01,},
            dp_l[] = {0.0, 1.35003920212974897128e-08,},
            two53 = 9007199254740992.0,
            /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
            L1 = 5.99999999999994648725e-01,
            L2 = 4.28571428578550184252e-01,
            L3 = 3.33333329818377432918e-01,
            L4 = 2.72728123808534006489e-01,
            L5 = 2.30660745775561754067e-01,
            L6 = 2.06975017800338417784e-01,
            P1 = 1.66666666666666019037e-01,
            P2 = -2.77777777770155933842e-03,
            P3 = 6.61375632143793436117e-05,
            P4 = -1.65339022054652515390e-06,
            P5 = 4.13813679705723846039e-08,
            lg2   = 6.93147180559945286227e-01,
            lg2_h = 6.93147182464599609375e-01,
            lg2_l = -1.90465429995776804525e-09,
            ovt   = 8.0085662595372944372e-0017,//-(1024-log2(ovfl+.5ulp))
            cp    = 9.61796693925975554329e-01, //=2/(3ln2)
            cp_h  = 9.61796700954437255859e-01, //=(float)cp
            cp_l  = -7.02846165095275826516e-09,//=tail of cp_h
            ivln2 = 1.44269504088896338700e+00,  //=1/ln2
            ivln2_h = 1.44269502162933349609e+00,//=24b 1/ln2
            ivln2_l = 1.92596299112661746887e-08;//=1/ln2 tail


    /**
     * Returns the value of the first argument raised to the power of the
     * second argument. Special cases:
     *
     * <ul><li>If the second argument is positive or negative zero, then the
     * result is 1.0.
     * <li>If the second argument is 1.0, then the result is the same as the
     * first argument.
     * <li>If the second argument is NaN, then the result is NaN.
     * <li>If the first argument is NaN and the second argument is nonzero,
     * then the result is NaN.
     *
     * <li>If
     * <ul>
     * <li>the absolute value of the first argument is greater than 1
     * and the second argument is positive infinity, or
     * <li>the absolute value of the first argument is less than 1 and
     * the second argument is negative infinity,
     * </ul>
     * then the result is positive infinity.
     *
     * <li>If
     * <ul>
     * <li>the absolute value of the first argument is greater than 1 and
     * the second argument is negative infinity, or
     * <li>the absolute value of the
     * first argument is less than 1 and the second argument is positive
     * infinity,
     * </ul>
     * then the result is positive zero.
     *
     * <li>If the absolute value of the first argument equals 1 and the
     * second argument is infinite, then the result is NaN.
     *
     * <li>If
     * <ul>
     * <li>the first argument is positive zero and the second argument
     * is greater than zero, or
     * <li>the first argument is positive infinity and the second
     * argument is less than zero,
     * </ul>
     * then the result is positive zero.
     *
     * <li>If
     * <ul>
     * <li>the first argument is positive zero and the second argument
     * is less than zero, or
     * <li>the first argument is positive infinity and the second
     * argument is greater than zero,
     * </ul>
     * then the result is positive infinity.
     *
     * <li>If
     * <ul>
     * <li>the first argument is negative zero and the second argument
     * is greater than zero but not a finite odd integer, or
     * <li>the first argument is negative infinity and the second
     * argument is less than zero but not a finite odd integer,
     * </ul>
     * then the result is positive zero.
     *
     * <li>If
     * <ul>
     * <li>the first argument is negative zero and the second argument
     * is a positive finite odd integer, or
     * <li>the first argument is negative infinity and the second
     * argument is a negative finite odd integer,
     * </ul>
     * then the result is negative zero.
     *
     * <li>If
     * <ul>
     * <li>the first argument is negative zero and the second argument
     * is less than zero but not a finite odd integer, or
     * <li>the first argument is negative infinity and the second
     * argument is greater than zero but not a finite odd integer,
     * </ul>
     * then the result is positive infinity.
     *
     * <li>If
     * <ul>
     * <li>the first argument is negative zero and the second argument
     * is a negative finite odd integer, or
     * <li>the first argument is negative infinity and the second
     * argument is a positive finite odd integer,
     * </ul>
     * then the result is negative infinity.
     *
     * <li>If the first argument is finite and less than zero
     * <ul>
     * <li> if the second argument is a finite even integer, the
     * result is equal to the result of raising the absolute value of
     * the first argument to the power of the second argument
     *
     * <li>if the second argument is a finite odd integer, the result
     * is equal to the negative of the result of raising the absolute
     * value of the first argument to the power of the second
     * argument
     *
     * <li>if the second argument is finite and not an integer, then
     * the result is NaN.
     * </ul>
     *
     * <li>If both arguments are integers, then the result is exactly equal
     * to the mathematical result of raising the first argument to the power
     * of the second argument if that result can in fact be represented
     * exactly as a {@code double} value.</ul>
     *
     * <p>(In the foregoing descriptions, a floating-point value is
     * considered to be an integer if and only if it is finite and a
     * fixed point of the method {@link #ceil ceil} or,
     * equivalently, a fixed point of the method {@link #floor
     * floor}. A value is a fixed point of a one-argument
     * method if and only if the result of applying the method to the
     * value is equal to the value.)
     *
     * @param   a   base.
     * @param   b   the exponent.
     * @return  the value {@code a}<sup>{@code b}</sup>.
     */
    public static double pow(double x, double y){
        /* __ieee754_pow(x,y) return x**y
        *
        *		      n
        * Method:  Let x =  2   * (1+f)
        *	1. Compute and return log2(x) in two pieces:
        *		log2(x) = w1 + w2,
        *	   where w1 has 53-24 = 29 bit trailing zeros.
        *	2. Perform y*log2(x) = n+y' by simulating muti-precision
        *	   arithmetic, where |y'|<=0.5.
        *	3. Return x**y = 2**n*exp(y'*log2)
        *
        * Special cases:
        *	1.  (anything) ** 0  is 1
        *	2.  (anything) ** 1  is itself
        *	3.  (anything) ** NAN is NAN
        *	4.  NAN ** (anything except 0) is NAN
        *	5.  +-(|x| > 1) **  +INF is +INF
        *	6.  +-(|x| > 1) **  -INF is +0
        *	7.  +-(|x| < 1) **  +INF is +0
        *	8.  +-(|x| < 1) **  -INF is +INF
        *	9.  +-1         ** +-INF is NAN
        *	10. +0 ** (+anything except 0, NAN)               is +0
        *	11. -0 ** (+anything except 0, NAN, odd integer)  is +0
        *	12. +0 ** (-anything except 0, NAN)               is +INF
        *	13. -0 ** (-anything except 0, NAN, odd integer)  is +INF
        *	14. -0 ** (odd integer) = -( +0 ** (odd integer) )
        *	15. +INF ** (+anything except 0,NAN) is +INF
        *	16. +INF ** (-anything except 0,NAN) is +0
        *	17. -INF ** (anything)  = -0 ** (-anything)
        *	18. (-anything) ** (integer) is
                                        (-1)**(integer)*(+anything**integer)
        *	19. (-anything except 0 and inf) ** (non-integer) is NAN
        *
        * Accuracy:
        *	pow(x,y) returns x**y nearly rounded. In particular
        *			pow(integer,integer)
        *	always returns the correct integer provided it is
        *	representable.
        *
        */       

        //i0 = ((*(int*)&one)>>29)^1; i1=1-i0;

        long xb = Double.doubleToRawLongBits(x);
        int hx = (int) (xb >> 32);
        int lx = (int) xb&0x7fffffff;  //unsigned
        int ix = hx & 0x7fffffff;
        xb = Double.doubleToRawLongBits(y);
        int hy = (int) (xb >> 32);
        int ly = (int) xb& 0x7fffffff; //unsigned
        int iy = hy & 0x7fffffff;

        /* y==zero: x**0 = 1 */
        if((iy|ly)==0) return one;

        /* +-NaN return x+y */
        if(ix > 0x7ff00000 || ((ix==0x7ff00000)&&(lx!=0)) ||
           iy > 0x7ff00000 || ((iy==0x7ff00000)&&(ly!=0)))
                return x+y;

        /* determine if y is an odd int when x < 0
        * yisint = 0	... y is not an integer
        * yisint = 1	... y is an odd int
        * yisint = 2	... y is an even int
        */
        int yisint  = 0;
        if(hx<0) {
            if(iy>=0x43400000) yisint = 2; /* even integer y */
            else if(iy>=0x3ff00000) {
                int k = (iy>>20)-0x3ff;	   /* exponent */
                if(k>20) {
                    int j = ly>>(52-k);
                    if((j<<(52-k))==ly) yisint = 2-(j&1);
                } else if(ly==0) {
                    int j = iy>>(20-k);
                    if((j<<(20-k))==iy) yisint = 2-(j&1);
                }
            }
        }

        /* special value of y */
        if(ly==0) {
            if (iy==0x7ff00000) {	/* y is +-inf */
                if(((ix-0x3ff00000)|lx)==0)
                    return  y - y;	/* inf**+-1 is NaN */
                return (ix >= 0x3ff00000) ? /* (|x|>1)**+-inf = inf,0 */
                    (hy>=0)? y: zero : /* (|x|<1)**-,+inf = inf,0 */
                    (hy<0)?-y: zero;
            }
            if(iy==0x3ff00000) {	/* y is  +-1 */
                return (hy<0) ? one/x : x;
            }
            if(hy==0x40000000) return x*x; /* y is  2 */
            if(hy==0x3fe00000) {	/* y is  0.5 */
                if(hx>=0)	/* x >= +0 */
                return Math.sqrt(x);
            }
        }

        double ax   = abs(x);
        /* special value of x */
        if(lx==0) {
            if(ix==0x7ff00000||ix==0||ix==0x3ff00000){
                double z = ax;			/*x is +-0,+-inf,+-1*/
                if(hy<0) z = one/z;	/* z = (1/|x|) */
                if(hx<0) {
                    if(((ix-0x3ff00000)|yisint)==0) {
                        z = (z-z)/(z-z); /* (-1)**non-int is NaN */
                    } else if(yisint==1)
                        z = -z;		/* (x<0)**odd = -(|x|**odd) */
                }
                return z;
            }
        }

        int n = (hx>>31)+1;

        /* (x<0)**(non-int) is NaN */
        if((n|yisint)==0) return (x-x)/(x-x);

        double s = one; /* s (sign of result -ve**odd) = -1 else = 1 */
        if((n|(yisint-1))==0) s = -one;/* (-ve)**(odd int) */

        double t1,t2;
        /* |y| is huge */
        if(iy>0x41e00000) { /* if |y| > 2**31 */
            if(iy>0x43f00000){	/* if |y| > 2**64, must o/uflow */
                if(ix<=0x3fefffff) return (hy<0)? huge*huge:tiny*tiny;
                if(ix>=0x3ff00000) return (hy>0)? huge*huge:tiny*tiny;
            }
        /* over/underflow if x is not close to one */
            if(ix<0x3fefffff) return (hy<0)? s*huge*huge:s*tiny*tiny;
            if(ix>0x3ff00000) return (hy>0)? s*huge*huge:s*tiny*tiny;
        /* now |1-x| is tiny <= 2**-20, suffice to compute
           log(x) by x-x^2/2+x^3/3-x^4/4 */
            double t = ax-one;		/* t has 20 trailing zeros */
            double w = (t*t)*(0.5-t*(0.3333333333333333333333-t*0.25));
            double u = ivln2_h*t;	/* ivln2_h has 21 sig. bits */
            double v = t*ivln2_l-w*ivln2;
            t1 = clearLow32bits(u+v);
            t2 = v-(t1-u);
        } else {           
            n = 0;
        /* take care subnormal number */
            if(ix<0x00100000)
                {ax *= two53; n -= 53; ix = __HI(ax); }
            n  += ((ix)>>20)-0x3ff;
            int j  = ix&0x000fffff;
        /* determine interval */
            ix = j|0x3ff00000;		/* normalize ix */
            int k=0;
            if(j<=0x3988E) ;		/* |x|<sqrt(3/2) */
            else if(j<0xBB67A) k=1;	/* |x|<sqrt(3)   */
            else {n+=1;ix -= 0x00100000;}

            ax = setHigh32bits(ax, ix); //__HI(ax) = ix;

        /* compute ss = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
            double u = ax-bp[k];		/* bp[0]=1.0, bp[1]=1.5 */
            double v = one/(ax+bp[k]);
            double ss = u*v;
            double s_h = clearLow32bits(ss);
        /* t_h=ax+bp[k] High */
            //__HI(t_h)=((ix>>1)|0x20000000)+0x00080000+(k<<18);
            double t_h = setHigh32bitsDontMask(zerobitshigh,
                    ((ix>>1)|0x20000000)+0x00080000+(k<<18));
            double s_l = v*((u-s_h*t_h)-s_h*(ax - (t_h-bp[k])));
        /* compute log(ax) */
            double s2 = ss*ss;
            double r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6)))))
                    + s_l*(s_h+ss);
            s2  = s_h*s_h;
            t_h = clearLow32bits(3.0+s2+r);
        /* u+v = ss*(1+...) */
            u = s_h*t_h;
            v = s_l*t_h+(r-((t_h-3.0)-s2))*ss;
        /* 2/(3log2)*(ss+...) */
            double p_h = clearLow32bits(u+v); //__LO(p_h) = 0;
            double z_h = cp_h*p_h;		/* cp_h+cp_l = 2/(3*log2) */
            double z_l = cp_l*p_h+(v-(p_h-u))*cp+dp_l[k];
        /* log2(ax) = (ss+..)*2/(3*log2) = n + dp_h + z_h + z_l */
            double t = n;
            t1 = clearLow32bits((((z_h+z_l)+dp_h[k])+t)); //__LO(t1) = 0;
            t2 = z_l-(((t1-t)-dp_h[k])-z_h);
        }

        /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
        double y1 = clearLow32bits(y); //__LO(y1) = 0;
        double p_l = (y-y1)*t1+y*t2;
        double p_h = y1*t1;
        double z = p_l+p_h;
        long zb = Double.doubleToRawLongBits(z);
        int j = (int) (zb >> 32);
        if (j>=0x40900000) {				/* z >= 1024 */
            if(((j-0x40900000)|((int) zb))!=0)		/* if z > 1024 */
                return s*huge*huge;			/* overflow */
            else {
                if(p_l+ovt>z-p_h) return s*huge*huge;	/* overflow */
            }
        } else if((j&0x7fffffff)>=0x4090cc00 ) {	/* z <= -1075 */
            if(((j-0xc090cc00)|((int) zb))!=0) 		/* z < -1075 */
                return s*tiny*tiny;		/* underflow */
            else {
                if(p_l<=z-p_h) return s*tiny*tiny;	/* underflow */
            }
        }
        /*
        * compute 2**(p_h+p_l)
        */
        int i = j&0x7fffffff;        
        n = 0;
        if(i>0x3fe00000) {		/* if |z| > 0.5, set n = [z+0.5] */
            n = j+(0x00100000>>((i>>20)-0x3ff+1));
            final int k = ((n&0x7fffffff)>>20)-0x3ff;	/* new k for n */
            double t = setHigh32bitsDontMask(zerobitshigh,(n&~(0x000fffff>>k)));
            n = ((n&0x000fffff)|0x00100000)>>(20-k);
            if(j<0) n = -n;
            p_h -= t;
        }
        double t = clearLow32bits(p_l+p_h);//__LO(t) = 0;
        double u = t*lg2_h;
        double v = (p_l-(t-p_h))*lg2+t*lg2_l;
        z = u+v;
        double w = v-(z-u);
        t  = z*z;
        t1  = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
        z  = one-(((z*t1)/(t1-two)-(w+z*w))-z);
        j  = __HI(z) + (n<<20);
        return s*((j>>20)<=0 ? 
            scalb(z,n) :	/* subnormal output */
            addToHighBits(z, (long)n<<(20) ));//__HI(z) += (n<<20);
    }


     
    /**
     * Returns the closest {@code int} to the argument. The
     * result is rounded to an integer by adding 1/2, taking the
     * floor of the result, and casting the result to type {@code int}.
     * In other words, the result is equal to the value of the expression:
     * <p>{@code (int)Math.floor(a + 0.5f)}
     *
     * <p>Special cases:
     * <ul><li>If the argument is NaN, the result is 0.
     * <li>If the argument is negative infinity or any value less than or
     * equal to the value of {@code Integer.MIN_VALUE}, the result is
     * equal to the value of {@code Integer.MIN_VALUE}.
     * <li>If the argument is positive infinity or any value greater than or
     * equal to the value of {@code Integer.MAX_VALUE}, the result is
     * equal to the value of {@code Integer.MAX_VALUE}.</ul>
     *
     * @param   a   a floating-point value to be rounded to an integer.
     * @return  the value of the argument rounded to the nearest
     *          {@code int} value.
     * @see     java.lang.Integer#MAX_VALUE
     * @see     java.lang.Integer#MIN_VALUE
     */
    public static int round(float a) {
        return (int) floor(a + 0.5f);
    }

    /**
     * Returns the closest {@code long} to the argument. The result
     * is rounded to an integer by adding 1/2, taking the floor of the
     * result, and casting the result to type {@code long}. In other
     * words, the result is equal to the value of the expression:
     * <p>{@code (long)Math.floor(a + 0.5d)}
     *
     * <p>Special cases:
     * <ul><li>If the argument is NaN, the result is 0.
     * <li>If the argument is negative infinity or any value less than or
     * equal to the value of {@code Long.MIN_VALUE}, the result is
     * equal to the value of {@code Long.MIN_VALUE}.
     * <li>If the argument is positive infinity or any value greater than or
     * equal to the value of {@code Long.MAX_VALUE}, the result is
     * equal to the value of {@code Long.MAX_VALUE}.</ul>
     *
     * @param   a  a floating-point value to be rounded to a
     *          {@code long}.
     * @return  the value of the argument rounded to the nearest
     *          {@code long} value.
     * @see     java.lang.Long#MAX_VALUE
     * @see     java.lang.Long#MIN_VALUE
     */
    public static long round(double a) {
        return (long) floor(a + 0.5d);
    }

    private static  Random randomNumberGenerator;

    private static  synchronized void initRNG() {
        if (randomNumberGenerator == null) {
            randomNumberGenerator = new Random();
        }
    }

    /**
     * Returns a {@code double} value with a positive sign, greater
     * than or equal to {@code 0.0} and less than {@code 1.0}.
     * Returned values are chosen pseudorandomly with (approximately)
     * uniform distribution from that range.
     *
     * <p>When this method is first called, it creates a single new
     * pseudorandom-number generator, exactly as if by the expression
     * <blockquote>{@code new java.util.Random}</blockquote> This
     * new pseudorandom-number generator is used thereafter for all
     * calls to this method and is used nowhere else.
     *
     * <p>This method is properly synchronized to allow correct use by
     * more than one thread. However, if many threads need to generate
     * pseudorandom numbers at a great rate, it may reduce contention
     * for each thread to have its own pseudorandom number generator.
     *
     * @return  a pseudorandom {@code double} greater than or equal
     * to {@code 0.0} and less than {@code 1.0}.
     * @see     java.util.Random#nextDouble()
     */
    public static double random() {
        if (randomNumberGenerator == null) {
            initRNG();
        }
        return randomNumberGenerator.nextDouble();
    }

    /**
     * Returns the absolute value of an {@code int} value..
     * If the argument is not negative, the argument is returned.
     * If the argument is negative, the negation of the argument is returned.
     *
     * <p>Note that if the argument is equal to the value of
     * {@link Integer#MIN_VALUE}, the most negative representable
     * {@code int} value, the result is that same value, which is
     * negative.
     *
     * @param   a   the  argument whose absolute value is to be determined.
     * @return  the absolute value of the argument.
     */
    public static int abs(int a) {
        return (a < 0) ? -a : a;
    }

    /**
     * Returns the absolute value of a {@code long} value.
     * If the argument is not negative, the argument is returned.
     * If the argument is negative, the negation of the argument is returned.
     *
     * <p>Note that if the argument is equal to the value of
     * {@link Long#MIN_VALUE}, the most negative representable
     * {@code long} value, the result is that same value, which
     * is negative.
     *
     * @param   a   the  argument whose absolute value is to be determined.
     * @return  the absolute value of the argument.
     */
    public static long abs(long a) {
        return (a < 0) ? -a : a;
    }

    /**
     * Returns the absolute value of a {@code float} value.
     * If the argument is not negative, the argument is returned.
     * If the argument is negative, the negation of the argument is returned.
     * Special cases:
     * <ul><li>If the argument is positive zero or negative zero, the
     * result is positive zero.
     * <li>If the argument is infinite, the result is positive infinity.
     * <li>If the argument is NaN, the result is NaN.</ul>
     * In other words, the result is the same as the value of the expression:
     * <p>{@code Float.intBitsToFloat(0x7fffffff & Float.floatToIntBits(a))}
     *
     * @param   a   the argument whose absolute value is to be determined
     * @return  the absolute value of the argument.
     */
    public static float abs(float a) {
        return (a <= 0.0F) ? 0.0F - a : a;
    }

    /**
     * Returns the absolute value of a {@code double} value.
     * If the argument is not negative, the argument is returned.
     * If the argument is negative, the negation of the argument is returned.
     * Special cases:
     * <ul><li>If the argument is positive zero or negative zero, the result
     * is positive zero.
     * <li>If the argument is infinite, the result is positive infinity.
     * <li>If the argument is NaN, the result is NaN.</ul>
     * In other words, the result is the same as the value of the expression:
     * <p>{@code Double.longBitsToDouble((Double.doubleToLongBits(a)<<1)>>>1)}
     *
     * @param   a   the argument whose absolute value is to be determined
     * @return  the absolute value of the argument.
     */
    public static double abs(double a) {
        return (a <= 0.0D) ? 0.0D - a : a;
    }

    /**
     * Returns the greater of two {@code int} values. That is, the
     * result is the argument closer to the value of
     * {@link Integer#MAX_VALUE}. If the arguments have the same value,
     * the result is that same value.
     *
     * @param   a   an argument.
     * @param   b   another argument.
     * @return  the larger of {@code a} and {@code b}.
     */
    public static int max(int a, int b) {
        return (a >= b) ? a : b;
    }

    /**
     * Returns the greater of two {@code long} values. That is, the
     * result is the argument closer to the value of
     * {@link Long#MAX_VALUE}. If the arguments have the same value,
     * the result is that same value.
     *
     * @param   a   an argument.
     * @param   b   another argument.
     * @return  the larger of {@code a} and {@code b}.
     */
    public static long max(long a, long b) {
        return (a >= b) ? a : b;
    }

    private final static long
            negativeZeroFloatBits = Float.floatToIntBits(-0.0f),
            negativeZeroDoubleBits = Double.doubleToLongBits(-0.0d);

    /**
     * Returns the greater of two {@code float} values.  That is,
     * the result is the argument closer to positive infinity. If the
     * arguments have the same value, the result is that same
     * value. If either value is NaN, then the result is NaN.  Unlike
     * the numerical comparison operators, this method considers
     * negative zero to be strictly smaller than positive zero. If one
     * argument is positive zero and the other negative zero, the
     * result is positive zero.
     *
     * @param   a   an argument.
     * @param   b   another argument.
     * @return  the larger of {@code a} and {@code b}.
     */
    public static float max(float a, float b) {
        if (a != a) {
            return a;   // a is NaN
        }
        if ((a == 0.0f) && (b == 0.0f)
                && (Float.floatToIntBits(a) == negativeZeroFloatBits)) {
            return b;
        }
        return (a >= b) ? a : b;
    }

    /**
     * Returns the greater of two {@code double} values.  That
     * is, the result is the argument closer to positive infinity. If
     * the arguments have the same value, the result is that same
     * value. If either value is NaN, then the result is NaN.  Unlike
     * the numerical comparison operators, this method considers
     * negative zero to be strictly smaller than positive zero. If one
     * argument is positive zero and the other negative zero, the
     * result is positive zero.
     *
     * @param   a   an argument.
     * @param   b   another argument.
     * @return  the larger of {@code a} and {@code b}.
     */
    public static double max(double a, double b) {
        if (a != a) {
            return a;   // a is NaN
        }
        if ((a == 0.0d) && (b == 0.0d)
                && (Double.doubleToLongBits(a) == negativeZeroDoubleBits)) {
            return b;
        }
        return (a >= b) ? a : b;
    }

    /**
     * Returns the smaller of two {@code int} values. That is,
     * the result the argument closer to the value of
     * {@link Integer#MIN_VALUE}.  If the arguments have the same
     * value, the result is that same value.
     *
     * @param   a   an argument.
     * @param   b   another argument.
     * @return  the smaller of {@code a} and {@code b}.
     */
    public static int min(int a, int b) {
        return (a <= b) ? a : b;
    }

    /**
     * Returns the smaller of two {@code long} values. That is,
     * the result is the argument closer to the value of
     * {@link Long#MIN_VALUE}. If the arguments have the same
     * value, the result is that same value.
     *
     * @param   a   an argument.
     * @param   b   another argument.
     * @return  the smaller of {@code a} and {@code b}.
     */
    public static long min(long a, long b) {
        return (a <= b) ? a : b;
    }

    /**
     * Returns the smaller of two {@code float} values.  That is,
     * the result is the value closer to negative infinity. If the
     * arguments have the same value, the result is that same
     * value. If either value is NaN, then the result is NaN.  Unlike
     * the numerical comparison operators, this method considers
     * negative zero to be strictly smaller than positive zero.  If
     * one argument is positive zero and the other is negative zero,
     * the result is negative zero.
     *
     * @param   a   an argument.
     * @param   b   another argument.
     * @return  the smaller of {@code a} and {@code b.}
     */
    public static float min(float a, float b) {
        if (a != a) {
            return a;   // a is NaN
        }
        if ((a == 0.0f) && (b == 0.0f)
                && (Float.floatToIntBits(b) == negativeZeroFloatBits)) {
            return b;
        }
        return (a <= b) ? a : b;
    }

    /**
     * Returns the smaller of two {@code double} values.  That
     * is, the result is the value closer to negative infinity. If the
     * arguments have the same value, the result is that same
     * value. If either value is NaN, then the result is NaN.  Unlike
     * the numerical comparison operators, this method considers
     * negative zero to be strictly smaller than positive zero. If one
     * argument is positive zero and the other is negative zero, the
     * result is negative zero.
     *
     * @param   a   an argument.
     * @param   b   another argument.
     * @return  the smaller of {@code a} and {@code b}.
     */
    public static double min(double a, double b) {
        if (a != a) {
            return a;   // a is NaN
        }
        if ((a == 0.0d) && (b == 0.0d)
                && (Double.doubleToLongBits(b) == negativeZeroDoubleBits)) {
            return b;
        }
        return (a <= b) ? a : b;
    }

    /**
     * Returns the size of an ulp of the argument.  An ulp of a
     * {@code double} value is the positive distance between this
     * floating-point value and the {@code double} value next
     * larger in magnitude.  Note that for non-NaN <i>x</i>,
     * <code>ulp(-<i>x</i>) == ulp(<i>x</i>)</code>.
     *
     * <p>Special Cases:
     * <ul>
     * <li> If the argument is NaN, then the result is NaN.
     * <li> If the argument is positive or negative infinity, then the
     * result is positive infinity.
     * <li> If the argument is positive or negative zero, then the result is
     * {@code Double.MIN_VALUE}.
     * <li> If the argument is &plusmn;{@code Double.MAX_VALUE}, then
     * the result is equal to 2<sup>971</sup>.
     * </ul>
     *
     * @param d the floating-point value whose ulp is to be returned
     * @return the size of an ulp of the argument
     * @author Joseph D. Darcy
     * @since 1.5
     */
    public static double ulp(double d) {
        return sun.misc.FpUtils.ulp(d);
    }

    /**
     * Returns the size of an ulp of the argument.  An ulp of a
     * {@code float} value is the positive distance between this
     * floating-point value and the {@code float} value next
     * larger in magnitude.  Note that for non-NaN <i>x</i>,
     * <code>ulp(-<i>x</i>) == ulp(<i>x</i>)</code>.
     *
     * <p>Special Cases:
     * <ul>
     * <li> If the argument is NaN, then the result is NaN.
     * <li> If the argument is positive or negative infinity, then the
     * result is positive infinity.
     * <li> If the argument is positive or negative zero, then the result is
     * {@code Float.MIN_VALUE}.
     * <li> If the argument is &plusmn;{@code Float.MAX_VALUE}, then
     * the result is equal to 2<sup>104</sup>.
     * </ul>
     *
     * @param f the floating-point value whose ulp is to be returned
     * @return the size of an ulp of the argument
     * @author Joseph D. Darcy
     * @since 1.5
     */
    public static float ulp(float f) {
        return sun.misc.FpUtils.ulp(f);
    }

    /**
     * Returns the signum function of the argument; zero if the argument
     * is zero, 1.0 if the argument is greater than zero, -1.0 if the
     * argument is less than zero.
     *
     * <p>Special Cases:
     * <ul>
     * <li> If the argument is NaN, then the result is NaN.
     * <li> If the argument is positive zero or negative zero, then the
     *      result is the same as the argument.
     * </ul>
     *
     * @param d the floating-point value whose signum is to be returned
     * @return the signum function of the argument
     * @author Joseph D. Darcy
     * @since 1.5
     */
    public static double signum(double d) {
        return sun.misc.FpUtils.signum(d);
    }

    /**
     * Returns the signum function of the argument; zero if the argument
     * is zero, 1.0f if the argument is greater than zero, -1.0f if the
     * argument is less than zero.
     *
     * <p>Special Cases:
     * <ul>
     * <li> If the argument is NaN, then the result is NaN.
     * <li> If the argument is positive zero or negative zero, then the
     *      result is the same as the argument.
     * </ul>
     *
     * @param f the floating-point value whose signum is to be returned
     * @return the signum function of the argument
     * @author Joseph D. Darcy
     * @since 1.5
     */
    public static float signum(float f) {
        return sun.misc.FpUtils.signum(f);
    }

    private static final double shuge = 1.0e307;
    /**
     * Returns the hyperbolic sine of a {@code double} value.
     * The hyperbolic sine of <i>x</i> is defined to be
     * (<i>e<sup>x</sup>&nbsp;-&nbsp;e<sup>-x</sup></i>)/2
     * where <i>e</i> is {@linkplain Math#E Euler's number}.
     *
     * <p>Special cases:
     * <ul>
     *
     * <li>If the argument is NaN, then the result is NaN.
     *
     * <li>If the argument is infinite, then the result is an infinity
     * with the same sign as the argument.
     *
     * <li>If the argument is zero, then the result is a zero with the
     * same sign as the argument.
     *
     * </ul>
     *
     * @param   x The number whose hyperbolic sine is to be returned.
     * @return  The hyperbolic sine of {@code x}.
     * @since 1.5
     */
    public static double sinh(double x) {
        /* __ieee754_sinh(x)
         * Method :
         * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2
         *      1. Replace x by |x| (sinh(-x) = -sinh(x)).
         *      2.
         *                                                  E + E/(E+1)
         *          0    <= x <= 22     :  sinh(x) := --------------, E=expm1(x)
         *                                                      2
         *
         *          22       <= x <= lnovft :  sinh(x) := exp(x)/2
         *          lnovft   <= x <= ln2ovft:  sinh(x) := exp(x/2)/2 * exp(x/2)
         *          ln2ovft  <  x           :  sinh(x) := x*shuge (overflow)
         *
         * Special cases:
         *      sinh(x) is |x| if x is +INF, -INF, or NaN.
         *      only sinh(0)=0 is exact for finite x.
         */

        final long xb = Double.doubleToLongBits(x);
        final double h = (xb >> 32) < 0 ? -0.5 : 0.5;
        final int ix = (int) ((xb >> 32) & 0x7fffffff);
        
        if(ix >= 0x7ff00000) { /* x is INF or NaN */
            return x+x;
        }
        
        /* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */
        if (ix < 0x40360000) {          /* |x|<22 */
            if (ix<0x3e300000)          /* |x|<2**-28 */
                if(shuge+x>one) {
                    return x;/* sinh(tiny) = tiny with inexact */
                }
            final double t = expm1(abs(x));
            return (ix<0x3ff00000) ? h*(2.0*t-t*t/(t+one)) : h*(t+t/(t+one));
        }

        /* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */
        if (ix < 0x40862E42)  return h*exp(abs(x));

        // |x| in [log(Double.MAX_VALUE), overflowthreshold]
        if (ix < 0x408633ce || (ix == 0x408633ce && 
                (xb & 0x00000000ffffffffL) <= 0x8fb9f87dL)){
            final double w = exp(0.5 * abs(x));
            return (h * w) * w;
        }
        /* |x| > overflowthresold, sinh(x) overflow */
        return x*shuge;

    }

    /**
     * Returns the hyperbolic cosine of a {@code double} value.
     * The hyperbolic cosine of <i>x</i> is defined to be
     * (<i>e<sup>x</sup>&nbsp;+&nbsp;e<sup>-x</sup></i>)/2
     * where <i>e</i> is {@linkplain Math#E Euler's number}.
     *
     * <p>Special cases:
     * <ul>
     *
     * <li>If the argument is NaN, then the result is NaN.
     *
     * <li>If the argument is infinite, then the result is positive
     * infinity.
     *
     * <li>If the argument is zero, then the result is {@code 1.0}.
     *
     * </ul>
     *
     * @param   x The number whose hyperbolic cosine is to be returned.
     * @return  The hyperbolic cosine of {@code x}.
     * @since 1.5
     */
    public static double cosh(double x) {
        /* __ieee754_cosh(x)
         * Method :
         * mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2
         *      1. Replace x by |x| (cosh(x) = cosh(-x)).
         *      2.
         *                                                     [ exp(x) - 1 ]^2
         *          0       <= x <= ln2/2  :  cosh(x) := 1 + -------------------
         *                                                         2*exp(x)
         *
         *                                                exp(x) +  1/exp(x)
         *          ln2/2    <= x <= 22     :  cosh(x) := -------------------
         *                                                        2
         *          22       <= x <= lnovft :  cosh(x) := exp(x)/2
         *          lnovft   <= x <= ln2ovft:  cosh(x) := exp(x/2)/2 * exp(x/2)
         *          ln2ovft  <  x           :  cosh(x) := huge*huge (overflow)
         *
         * Special cases:
         *      cosh(x) is |x| if x is +INF, -INF, or NaN.
         *      only cosh(0)=1 is exact for finite x.
         */

        final long xb = Double.doubleToRawLongBits(x);
        final int ix = ((int) (xb >> 32)) & 0x7fffffff;

        /* x is INF or NaN */
        if(ix>=0x7ff00000){
            return x*x;
        }
        
        /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
        if (ix < 0x3fd62e43) {
            final double t = expm1(abs(x));
            final double w = one + t;
            // for tiny arguments return 1.
            return  (ix < 0x3c800000) ? w :  one + (t * t) / (w + w);
        }

       /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
        if (ix < 0x40360000) {
            final double t = exp(abs(x));
            return half * t + half / t;
        }

        /* |x| in [22, log(maxdouble)] return half*exp(|x|) */
        if (ix < 0x40862e42) {
            return half * exp(abs(x));
        }

         /* |x| in [log(maxdouble), overflowthresold] */
        if (ix < 0x408633ce || (ix == 0x408633ce &&
                (xb & 0x00000000ffffffffL) <= 0x8fb9f87dL)){
            final double w = exp(half * abs(x));
            return (half * w) * w;
        }
         /* |x| > overflowthresold, cosh(x) overflow */
        return huge*huge;
    }

    /**
     * Returns the hyperbolic tangent of a {@code double} value.
     * The hyperbolic tangent of <i>x</i> is defined to be
     * (<i>e<sup>x</sup>&nbsp;-&nbsp;e<sup>-x</sup></i>)/(<i>e<sup>x</sup>&nbsp;+&nbsp;e<sup>-x</sup></i>),
     * in other words, {@linkplain Math#sinh
     * sinh(<i>x</i>)}/{@linkplain Math#cosh cosh(<i>x</i>)}.  Note
     * that the absolute value of the exact tanh is always less than
     * 1.
     *
     * <p>Special cases:
     * <ul>
     *
     * <li>If the argument is NaN, then the result is NaN.
     *
     * <li>If the argument is zero, then the result is a zero with the
     * same sign as the argument.
     *
     * <li>If the argument is positive infinity, then the result is
     * {@code +1.0}.
     *
     * <li>If the argument is negative infinity, then the result is
     * {@code -1.0}.
     *
     * </ul>
     *
     * @param   x The number whose hyperbolic tangent is to be returned.
     * @return  The hyperbolic tangent of {@code x}.
     * @since 1.5
     */
    public static double tanh(double x) {
        /* Tanh(x)
         * Return the Hyperbolic Tangent of x
         *
         * Method :
         *                                     x    -x
         *                                    e  - e
         *      0. tanh(x) is defined to be -----------
         *                                     x    -x
         *                                    e  + e
         *      1. reduce x to non-negative by tanh(-x) = -tanh(x).
         *      2.  0      <= x <= 2**-55 : tanh(x) := x*(one+x)
         *                                              -t
         *          2**-55 <  x <=  1     : tanh(x) := -----; t = expm1(-2x)
         *                                             t + 2
         *                                                   2
         *          1      <= x <=  22.0  : tanh(x) := 1-  ----- ; t=expm1(2x)
         *                                                 t + 2
         *          22.0   <  x <= INF    : tanh(x) := 1.
         *
         * Special cases:
         *      tanh(NaN) is NaN;
         *      only tanh(0)=0 is exact for finite argument.
         */

        /* High word of |x|. */
        final int hx = (int) (Double.doubleToRawLongBits(x) >> 32);
        final int ix = hx & 0x7fffffff;

        /* x is INF or NaN */
        if (ix >= 0x7ff00000) {
            return hx>=0 ?
                one / x + one : /* tanh(+-inf)=+-1 */
                one / x - one;  /* tanh(NaN) = NaN */
        }

        double z;
        /* |x| < 22 */
        if (ix < 0x40360000) {          /* |x|<22 */
            if (ix < 0x3c800000) {          /* |x|<2**-55 */
                return x * (one + x);       /* tanh(small) = small */
            }
            x = abs(x);
            if (ix >= 0x3ff00000) {       /* |x|>=1  */
                z = one - two / (expm1(2.0d * x) + two);
            } else {
                double t = expm1(-two * x);
                z = -t / (t + two);
            }
            /* |x| > 22, return +-1 */
        } else {
            z = one - tiny;    /* raised inexact flag */
        }
        return hx >= 0 ? z : 0.0d - z;
    }

    private static final double TWOpow1022 = setHigh32bits(0x7fd00000);
    private static final long 
            onebits = Double.doubleToLongBits(one),
            clearHighmask = 0x00000000FFFFFFFFL,
            onebitshigh = onebits&clearHighmask,
            zerobitshigh = Double.doubleToLongBits(zero)&clearHighmask;


    /**
     * Returns sqrt(<i>x</i><sup>2</sup>&nbsp;+<i>y</i><sup>2</sup>)
     * without intermediate overflow or underflow.
     *
     * <p>Special cases:
     * <ul>
     *
     * <li> If either argument is infinite, then the result
     * is positive infinity.
     *
     * <li> If either argument is NaN and neither argument is infinite,
     * then the result is NaN.
     *
     * </ul>
     *
     * @param x a value
     * @param y a value
     * @return sqrt(<i>x</i><sup>2</sup>&nbsp;+<i>y</i><sup>2</sup>)
     * without intermediate overflow or underflow
     * @since 1.5
     */ 
    public static double hypot(double a, double b) {
        /* __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)
         */

        long hx = (Double.doubleToRawLongBits(a) >>> 32)&0x7fffffff;
        long hy = (Double.doubleToRawLongBits(b) >>> 32)&0x7fffffff;
	if(hy > hx) {
            double at = a;
            a=b;
            b=at;
            long j=hx;
            hx=hy;
            hy=j;
        }
        
         a= abs(a);
         b= abs(b);

	//a = setHigh32bits(a,hx);
      //  b = setHigh32bits(b,hy);


        //System.err.println("a1 ");
        if (hx - hy > 0x3c00000) {
            return a + b;
        } /* x/y > 2**60 */
//System.err.println("a2");
        int k = 0;
        if (hx > 0x5f300000) {   /* a>2**500 */
           // System.err.println("b1 "+hx +" >= "+ 0x7ff00000);
            if (hx >= 0x7ff00000) {       /* Inf or NaN */
             //  System.err.println("b2");
               return Double.isInfinite(a) || Double.isInfinite(b) ?
                   Double.POSITIVE_INFINITY :
                   Double.NaN;
            }
            /* scale a and b by 2**-600 */
            k = 600;
            a = setHigh32bits(a, hx -= 0x25800000);
            b = setHigh32bits(b, hy -= 0x25800000);
        }
        if (hy < 0x20b00000) {   /* b < 2**-500 */
            if (hy <= 0x000fffff) {      /* subnormal b or 0 */
                //if ((hy | (bbits&clearHighmask)) == 0) {
                if ((hy | __LO(b)) == 0) {
                    return a;
                }
                b *= TWOpow1022; 
                a *= TWOpow1022;
                k -= 1022;
            } else {          /* scale a and b by 2^600 */
                k -= 600;
                a = setHigh32bits(a, hx += 0x25800000); /* a *= 2^600 */
                b = setHigh32bits(b, hy += 0x25800000); /* b *= 2^600 */
            }
        }

        /* medium size a and b */
        double w = a - b;
        if (w > b) {
            final double t1 = Double.longBitsToDouble(hx << 32);
            w = t1*t1 - (b * -b - (a - t1) * (a + t1));
        } else {
            final double y1 = Double.longBitsToDouble(hy << 32);
            final double t1 = Double.longBitsToDouble((hx+0x00100000) << 32);
            w = t1*y1 - (w * -w - (t1*(b - y1) + b*((a+a)-t1)));
        }
        w = java.lang.StrictMath.sqrt(w);
        return k!=0 ?  w*setHhighbitsAddSome(onebits, (long)k << (20+32)) : w;
    }

    /* scaled coefficients related to expm1 */
    private static final double
            Q1 = -3.33333333333331316428e-02, /* BFA11111 111110F4 */
            Q2 = 1.58730158725481460165e-03, /* 3F5A01A0 19FE5585 */
            Q3 = -7.93650757867487942473e-05, /* BF14CE19 9EAADBB7 */
            Q4 = 4.00821782732936239552e-06, /* 3ED0CFCA 86E65239 */
            Q5 = -2.01099218183624371326e-07; /* BE8AFDB7 6E09C32D */


    /**
     * Returns <i>e</i><sup>x</sup>&nbsp;-1.  Note that for values of
     * <i>x</i> near 0, the exact sum of
     * {@code expm1(x)}&nbsp;+&nbsp;1 is much closer to the true
     * result of <i>e</i><sup>x</sup> than {@code exp(x)}.
     *
     * <p>Special cases:
     * <ul>
     * <li>If the argument is NaN, the result is NaN.
     *
     * <li>If the argument is positive infinity, then the result is
     * positive infinity.
     *
     * <li>If the argument is negative infinity, then the result is
     * -1.0.
     *
     * <li>If the argument is zero, then the result is a zero with the
     * same sign as the argument.
     *
     * </ul>
     *
     * @param   x   the exponent to raise <i>e</i> to in the computation of
     *              <i>e</i><sup>{@code x}</sup>&nbsp;-1.
     * @return  the value <i>e</i><sup>{@code x}</sup>&nbsp;-&nbsp;1.
     * @since 1.5
     */
    public static double expm1(double x) {
        /* expm1(x)
         * Returns exp(x)-1, the exponential of x minus 1.
         *
         * Method
         *   1. Argument reduction:
         *      Given x, find r and integer k such that
         *
         *               x = k*ln2 + r,  |r| <= 0.5*ln2 ~ 0.34658
         *
         *      Here a correction term c will be computed to compensate
         *      the error in r when rounded to a floating-point number.
         *
         *   2. Approximating expm1(r) by a special rational function on
         *      the interval [0,0.34658]:
         *      Since
         *          r*(exp(r)+1)/(exp(r)-1) = 2+ r^2/6 - r^4/360 + ...
         *      we define R1(r*r) by
         *          r*(exp(r)+1)/(exp(r)-1) = 2+ r^2/6 * R1(r*r)
         *      That is,
         *          R1(r**2) = 6/r *((exp(r)+1)/(exp(r)-1) - 2/r)
         *                   = 6/r * ( 1 + 2.0*(1/(exp(r)-1) - 1/r))
         *                   = 1 - r^2/60 + r^4/2520 - r^6/100800 + ...
         *      We use a special Reme algorithm on [0,0.347] to generate
         *      a polynomial of degree 5 in r*r to approximate R1. The
         *      maximum error of this polynomial approximation is bounded
         *      by 2**-61. In other words,
         *          R1(z) ~ 1.0 + Q1*z + Q2*z**2 + Q3*z**3 + Q4*z**4 + Q5*z**5
         *      where   Q1  =  -1.6666666666666567384E-2,
         *              Q2  =   3.9682539681370365873E-4,
         *              Q3  =  -9.9206344733435987357E-6,
         *              Q4  =   2.5051361420808517002E-7,
         *              Q5  =  -6.2843505682382617102E-9;
         *      (where z=r*r, and the values of Q1 to Q5 are listed below)
         *      with error bounded by
         *          |                  5           |     -61
         *          | 1.0+Q1*z+...+Q5*z   -  R1(z) | <= 2
         *          |                              |
         *
         *      expm1(r) = exp(r)-1 is then computed by the following
         *      specific way which minimize the accumulation rounding error:
         *                             2     3
         *                            r     r    [ 3 - (R1 + R1*r/2)  ]
         *            expm1(r) = r + --- + --- * [--------------------]
         *                            2     2    [ 6 - r*(3 - R1*r/2) ]
         *
         *      To compensate the error in the argument reduction, we use
         *              expm1(r+c) = expm1(r) + c + expm1(r)*c
         *                         ~ expm1(r) + c + r*c
         *      Thus c+r*c will be added in as the correction terms for
         *      expm1(r+c). Now rearrange the term to avoid optimization
         *      screw up:
         *                      (      2                                    2 )
         *                      ({  ( r    [ R1 -  (3 - R1*r/2) ]  )  }    r  )
         *       expm1(r+c)~r - ({r*(--- * [--------------------]-c)-c} - --- )
         *                      ({  ( 2    [ 6 - r*(3 - R1*r/2) ]  )  }    2  )
         *                      (                                             )
         *
         *                 = r - E
         *   3. Scale back to obtain expm1(x):
         *      From step 1, we have
         *         expm1(x) = either 2^k*[expm1(r)+1] - 1
         *                  = or     2^k*[expm1(r) + (1-2^-k)]
         *   4. Implementation notes:
         *      (A). To save one multiplication, we scale the coefficient Qi
         *           to Qi*2^i, and replace z by (x^2)/2.
         *      (B). To achieve maximum accuracy, we compute expm1(x) by
         *        (i)   if x < -56*ln2, return -1.0, (raise inexact if x!=inf)
         *        (ii)  if k=0, return r-E
         *        (iii) if k=-1, return 0.5*(r-E)-0.5
         *        (iv)  if k=1 if r < -0.25, return 2*((r+0.5)- E)
         *                     else          return  1.0+2.0*(r-E);
         *        (v)   if (k<-2||k>56) return 2^k(1-(E-r)) - 1 (or exp(x)-1)
         *        (vi)  if k <= 20, return 2^k((1-2^-k)-(E-r)), else
         *        (vii) return 2^k(1-((E+2^-k)-r))
         *
         * Special cases:
         *      expm1(INF) is INF, expm1(NaN) is NaN;
         *      expm1(-INF) is -1, and
         *      for finite argument, only expm1(0)=0 is exact.
         *
         * Accuracy:
         *      according to an error analysis, the error is always less than
         *      1 ulp (unit in the last place).
         *
         * Misc. info.
         *      For IEEE double
         *          if x >  7.09782712893383973096e+02 then expm1(x) overflow
         *
         * Constants:
         * The hexadecimal values are the intended ones for the following
         * constants. The decimal values may be used, provided that the
         * compiler will convert from decimal to binary accurately enough
         * to produce the hexadecimal values shown.
         */
        
        long xb = Double.doubleToRawLongBits(x);
        int hx = (int) (xb >> 32);    /* high word of x  UNSIGNED */
        final boolean xsbzero = (hx & 0x80000000)==0;  /* sign bit of x */
        //double y = xsbzero ? x : 0.0d - x; /* y = |x| */
        hx &= 0x7fffffff;     /* high word of |x| */

        /* filter out huge and non-finite argument */
        if (hx >= 0x4043687A) {                  /* if |x|>=56*ln2 */
            if (hx >= 0x40862E42) {              /* if |x|>=709.78... */
                if (hx >= 0x7ff00000) {
                    return  (((hx & 0xfffff) | (int)xb) != 0) ?
                            x + x :     /* NaN */
                            xsbzero ? x : -1.0 ; /* exp(+-inf)={inf,-1} */
                }
                if (x > o_threshold) {
                    return huge*huge; /* overflow */
                }
            }
            /* x < -56*ln2, return -1.0 with inexact */
            if (!xsbzero && (x + tiny < 0.0) ) {          /* raise inexact */
                return tiny - one;        /* return -1 */
            }
        }

        double hi,lo,c=0;
        int k = 0;
        /* argument reduction */
        if (hx > 0x3fd62e42) {           /* if  |x| > 0.5 ln2 */
            if (hx < 0x3FF0A2B2) {       /* and |x| < 1.5 ln2 */
                if (xsbzero) {
                    hi = x - ln2_hi;
                    lo = ln2_lo;
                    k = 1;
                } else {
                    hi = x + ln2_hi;
                    lo = -ln2_lo;
                    k = -1;
                }
            } else {
                // loss of precision here ?:
                k = (int) (invln2 * x + (xsbzero ? 0.5 : - 0.5));
                hi = x - k * ln2_hi;      /* t*ln2_hi is exact here */
                lo = k * ln2_lo;
            }
            x = hi - lo;
            c = (hi - x) - lo;
        } else if (hx < 0x3c900000) {      /* when |x|<2**-54, return x */
             /* return x with inexact flags when x!=0 */
            return x - ((huge + x) - (huge + x));
        }

        /* x is now in primary range */
        final double hfx = 0.5 * x;
        final double hxs = x * hfx;
        final double r1 = one + hxs * (Q1 + hxs*(Q2+hxs*(Q3+hxs*(Q4+hxs*Q5))));
        final double t = 3.0 - r1 * hfx;
        double e = hxs * ((r1 - t) / (6.0 - x * t));
        if (k == 0) {
            return x - (x * e - hxs);          /* c is 0 */
        } 
        e = (x * (e - c) - c) - hxs;
        if (k == -1) {
            return 0.5 * (x - e) - 0.5;
        }
        if (k == 1) {
            return  x < -0.25 ? -2.0 * (e - (x + 0.5)) : one + 2.0 * (x - e);
        }
        if (k <= -2 || k > 56) {   /* suffice to return exp(x)-1 */
            /* add k to y's exponent */
            return setHhighbitsAddSome(one - (e - x), (long)k << (20+32)) - one;
        }
        final double y = k < 20 ?  /* 1-2^-k */
            setHigh32bitsDontMask(onebitshigh,0x3ff00000-(0x200000>>k))-(e-x) :            
            (x-(e+setHigh32bitsDontMask(onebitshigh,(0x3ff-k)<<20)))+one;//2^-k
        /* add k to y's exponent */
        return setHhighbitsAddSome(y, (long)k << (20+32));
    }
    
    private static final double
            Lp1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */
            Lp2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */
            Lp3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */
            Lp4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */
            Lp5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */
            Lp6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */
            Lp7 = 1.479819860511658591e-01;  /* 3FC2F112 DF3E5244 */
            
    /**
     * Returns the natural logarithm of the sum of the argument and 1.
     * Note that for small values {@code x}, the result of
     * {@code log1p(x)} is much closer to the true result of ln(1
     * + {@code x}) than the floating-point evaluation of
     * {@code log(1.0+x)}.
     *
     * <p>Special cases:
     * <ul>
     *
     * <li>If the argument is NaN or less than -1, then the result is
     * NaN.
     *
     * <li>If the argument is positive infinity, then the result is
     * positive infinity.
     *
     * <li>If the argument is negative one, then the result is
     * negative infinity.
     *
     * <li>If the argument is zero, then the result is a zero with the
     * same sign as the argument.
     *
     * </ul>
     *
     * @param   x   a value
     * @return the value ln({@code x}&nbsp;+&nbsp;1), the natural
     * log of {@code x}&nbsp;+&nbsp;1
     * @since 1.5
     */
    public static double log1p(double x) {
        /* double log1p(double x)
         *
         * Method :
         *   1. Argument Reduction: find k and f such that
         *                      1+x = 2^k * (1+f),
         *         where  sqrt(2)/2 < 1+f < sqrt(2) .
         *
         *      Note. If k=0, then f=x is exact. However, if k!=0, then f
         *      may not be representable exactly. In that case, a correction
         *      term is need. Let u=1+x rounded. Let c = (1+x)-u, then
         *      log(1+x) - log(u) ~ c/u. Thus, we proceed to compute log(u),
         *      and add back the correction term c/u.
         *      (Note: when x > 2**53, one can simply return log(x))
         *
         *   2. Approximation of log1p(f).
         *      Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s)
         *               = 2s + 2/3 s**3 + 2/5 s**5 + .....,
         *               = 2s + s*R
         *      We use a special Reme algorithm on [0,0.1716] to generate
         *      a polynomial of degree 14 to approximate R The maximum error
         *      of this polynomial approximation is bounded by 2**-58.45. In
         *      other words,
         *                      2      4      6      8      10      12      14
         *          R(z) ~ Lp1*s +Lp2*s +Lp3*s +Lp4*s +Lp5*s  +Lp6*s  +Lp7*s
         *      (the values of Lp1 to Lp7 are listed in the program)
         *      and
         *          |      2          14          |     -58.45
         *          | Lp1*s +...+Lp7*s    -  R(z) | <= 2
         *          |                             |
         *      Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2.
         *      In order to guarantee error in log below 1ulp, we compute log
         *      by
         *              log1p(f) = f - (hfsq - s*(hfsq+R)).
         *
         *      3. Finally, log1p(x) = k*ln2 + log1p(f).
         *                           = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo)))
         *         Here ln2 is split into two floating point number:
         *                      ln2_hi + ln2_lo,
         *         where n*ln2_hi is always exact for |n| < 2000.
         *
         * Special cases:
         *      log1p(x) is NaN with signal if x < -1 (including -INF) ;
         *      log1p(+INF) is +INF; log1p(-1) is -INF with signal;
         *      log1p(NaN) is that NaN with no signal.
         *
         * Accuracy:
         *      according to an error analysis, the error is always less than
         *      1 ulp (unit in the last place).
         *
         * Constants:
         * The hexadecimal values are the intended ones for the following
         * constants. The decimal values may be used, provided that the
         * compiler will convert from decimal to binary accurately enough
         * to produce the hexadecimal values shown.
         *
         * Note: Assuming log() return accurate answer, the following
         *       algorithm can be used to compute log1p(x) to within a few ULP:
         *
         *              u = 1+x;
         *              if(u==1.0) return x ; else
         *                         return log(u)*(x/(u-1.0));
         *
         *       See HP-15C Advanced Functions Handbook, p.193.
         */
        double f = 0 ;
        int k=1,  hu=0;
        final int hx = __HI(x);           /* high word of x */
        final int ax = hx & 0x7fffffff;        
        if (hx < 0x3FDA827A) {                  /* x < 0.41422  */
            if (ax >= 0x3ff00000) {                /* x <= -1.0 */
                return x == -1.0d  ? -two54 / zero :   /* log1p(-1)=-inf */
                    (x - x) / (x - x);   /* log1p(x<-1)=NaN */
            }
            if (ax < 0x3e200000) {                 /* |x| < 2**-29 */
                if (two54 + x > zero /* raise inexact */
                        && ax < 0x3c900000) /* |x| < 2**-54 */ {
                    return x;
                } 
                return x - x * x * 0.5;                
            }
            if (hx > 0 || hx <= ((int) 0xbfd2bec3)) { /* -0.2929<x<0.41422 */
                k = 0;
                f = x;
                hu = 1;
            }  
        }
        
        if (hx >= 0x7ff00000) {
            return x + x;
        }
        double c;
        if (k != 0) {
            final double u = hx < 0x43400000 ? 1.0 + x : x ;
            long ub = Double.doubleToRawLongBits(u);              
            hu = (int) (ub >> 32); /* high word of u */
            k = (hu >> 20) - 1023;
            c = hx < 0x43400000 ? (k > 0 ? 1.0-(u - x) : x - (u - 1.0))/u : 0;
            int newhu;
            if ((hu&=0x000fffff) < 0x6a09e) {
                newhu = hu | 0x3ff00000;   /* normalize u */
            } else {
                k += 1;
                newhu = hu | 0x3fe00000;        /* normalize u/2 */
                hu = (0x00100000 - hu) >> 2;
            }
            f = setHigh32bits(ub, newhu) -1.0;
        }
        else c=0;

        double hfsq = 0.5 * f * f;
        if (hu == 0) {     /* |f| < 2**-20 */
            if (f == zero) {
                return k == 0 ? zero : k * ln2_hi + (c + k * ln2_lo) ;
            }
            final double R = hfsq * (1.0 - 0.66666666666666666 * f);
            return k == 0 ? f - R :  k * ln2_hi - ((R - (k * ln2_lo + c)) - f);
        }
        final double s = f / (2.0 + f);
        final double z = s * s;
        final double R =
                s*(hfsq +z*(Lp1+z*(Lp2+z*(Lp3+z*(Lp4+z*(Lp5+z*(Lp6+z*Lp7)))))));
        return k == 0 ? f - (hfsq - R) :
            k * ln2_hi - ((hfsq - (R + (k * ln2_lo + c))) - f);
    }

    /**
     * Returns the first floating-point argument with the sign of the
     * second floating-point argument.  For this method, a NaN
     * {@code sign} argument is always treated as if it were
     * positive.
     *
     * @param magnitude  the parameter providing the magnitude of the result
     * @param sign   the parameter providing the sign of the result
     * @return a value with the magnitude of {@code magnitude}
     * and the sign of {@code sign}.
     * @since 1.6
     */
    public static double copySign(double magnitude, double sign) {
        return sun.misc.FpUtils.copySign(magnitude, sign);
    }

    /**
     * Returns the first floating-point argument with the sign of the
     * second floating-point argument.  For this method, a NaN
     * {@code sign} argument is always treated as if it were
     * positive.
     *
     * @param magnitude  the parameter providing the magnitude of the result
     * @param sign   the parameter providing the sign of the result
     * @return a value with the magnitude of {@code magnitude}
     * and the sign of {@code sign}.
     * @since 1.6
     */
    public static float copySign(float magnitude, float sign) {
        return sun.misc.FpUtils.copySign(magnitude, sign);
    }

    /**
     * Returns the unbiased exponent used in the representation of a
     * {@code float}.  Special cases:
     *
     * <ul>
     * <li>If the argument is NaN or infinite, then the result is
     * {@link Float#MAX_EXPONENT} + 1.
     * <li>If the argument is zero or subnormal, then the result is
     * {@link Float#MIN_EXPONENT} -1.
     * </ul>
     * @param f a {@code float} value
     * @since 1.6
     */
    public static int getExponent(float f) {
        return sun.misc.FpUtils.getExponent(f);
    }

    /**
     * Returns the unbiased exponent used in the representation of a
     * {@code double}.  Special cases:
     *
     * <ul>
     * <li>If the argument is NaN or infinite, then the result is
     * {@link Double#MAX_EXPONENT} + 1.
     * <li>If the argument is zero or subnormal, then the result is
     * {@link Double#MIN_EXPONENT} -1.
     * </ul>
     * @param d a {@code double} value
     * @since 1.6
     */
    public static int getExponent(double d) {
        return sun.misc.FpUtils.getExponent(d);
    }

    /**
     * Returns the floating-point number adjacent to the first
     * argument in the direction of the second argument.  If both
     * arguments compare as equal the second argument is returned.
     *
     * <p>Special cases:
     * <ul>
     * <li> If either argument is a NaN, then NaN is returned.
     *
     * <li> If both arguments are signed zeros, {@code direction}
     * is returned unchanged (as implied by the requirement of
     * returning the second argument if the arguments compare as
     * equal).
     *
     * <li> If {@code start} is
     * &plusmn;{@link Double#MIN_VALUE} and {@code direction}
     * has a value such that the result should have a smaller
     * magnitude, then a zero with the same sign as {@code start}
     * is returned.
     *
     * <li> If {@code start} is infinite and
     * {@code direction} has a value such that the result should
     * have a smaller magnitude, {@link Double#MAX_VALUE} with the
     * same sign as {@code start} is returned.
     *
     * <li> If {@code start} is equal to &plusmn;
     * {@link Double#MAX_VALUE} and {@code direction} has a
     * value such that the result should have a larger magnitude, an
     * infinity with same sign as {@code start} is returned.
     * </ul>
     *
     * @param start  starting floating-point value
     * @param direction value indicating which of
     * {@code start}'s neighbors or {@code start} should
     * be returned
     * @return The floating-point number adjacent to {@code start} in the
     * direction of {@code direction}.
     * @since 1.6
     */
    public static double nextAfter(double start, double direction) {
        return sun.misc.FpUtils.nextAfter(start, direction);
    }

    /**
     * Returns the floating-point number adjacent to the first
     * argument in the direction of the second argument.  If both
     * arguments compare as equal a value equivalent to the second argument
     * is returned.
     *
     * <p>Special cases:
     * <ul>
     * <li> If either argument is a NaN, then NaN is returned.
     *
     * <li> If both arguments are signed zeros, a value equivalent
     * to {@code direction} is returned.
     *
     * <li> If {@code start} is
     * &plusmn;{@link Float#MIN_VALUE} and {@code direction}
     * has a value such that the result should have a smaller
     * magnitude, then a zero with the same sign as {@code start}
     * is returned.
     *
     * <li> If {@code start} is infinite and
     * {@code direction} has a value such that the result should
     * have a smaller magnitude, {@link Float#MAX_VALUE} with the
     * same sign as {@code start} is returned.
     *
     * <li> If {@code start} is equal to &plusmn;
     * {@link Float#MAX_VALUE} and {@code direction} has a
     * value such that the result should have a larger magnitude, an
     * infinity with same sign as {@code start} is returned.
     * </ul>
     *
     * @param start  starting floating-point value
     * @param direction value indicating which of
     * {@code start}'s neighbors or {@code start} should
     * be returned
     * @return The floating-point number adjacent to {@code start} in the
     * direction of {@code direction}.
     * @since 1.6
     */
    public static float nextAfter(float start, double direction) {
        return sun.misc.FpUtils.nextAfter(start, direction);
    }

    /**
     * Returns the floating-point value adjacent to {@code d} in
     * the direction of positive infinity.  This method is
     * semantically equivalent to {@code nextAfter(d,
     * Double.POSITIVE_INFINITY)}; however, a {@code nextUp}
     * implementation may run faster than its equivalent
     * {@code nextAfter} call.
     *
     * <p>Special Cases:
     * <ul>
     * <li> If the argument is NaN, the result is NaN.
     *
     * <li> If the argument is positive infinity, the result is
     * positive infinity.
     *
     * <li> If the argument is zero, the result is
     * {@link Double#MIN_VALUE}
     *
     * </ul>
     *
     * @param d starting floating-point value
     * @return The adjacent floating-point value closer to positive
     * infinity.
     * @since 1.6
     */
    public static double nextUp(double d) {
        return sun.misc.FpUtils.nextUp(d);
    }

    /**
     * Returns the floating-point value adjacent to {@code f} in
     * the direction of positive infinity.  This method is
     * semantically equivalent to {@code nextAfter(f,
     * Float.POSITIVE_INFINITY)}; however, a {@code nextUp}
     * implementation may run faster than its equivalent
     * {@code nextAfter} call.
     *
     * <p>Special Cases:
     * <ul>
     * <li> If the argument is NaN, the result is NaN.
     *
     * <li> If the argument is positive infinity, the result is
     * positive infinity.
     *
     * <li> If the argument is zero, the result is
     * {@link Float#MIN_VALUE}
     *
     * </ul>
     *
     * @param f starting floating-point value
     * @return The adjacent floating-point value closer to positive
     * infinity.
     * @since 1.6
     */
    public static float nextUp(float f) {
        return sun.misc.FpUtils.nextUp(f);
    }
    

    /**
     * Return {@code d} &times;
     * 2<sup>{@code scaleFactor}</sup> rounded as if performed
     * by a single correctly rounded floating-point multiply to a
     * member of the double value set.  See the Java
     * Language Specification for a discussion of floating-point
     * value sets.  If the exponent of the result is between {@link
     * Double#MIN_EXPONENT} and {@link Double#MAX_EXPONENT}, the
     * answer is calculated exactly.  If the exponent of the result
     * would be larger than {@code Double.MAX_EXPONENT}, an
     * infinity is returned.  Note that if the result is subnormal,
     * precision may be lost; that is, when {@code scalb(x, n)}
     * is subnormal, {@code scalb(scalb(x, n), -n)} may not equal
     * <i>x</i>.  When the result is non-NaN, the result has the same
     * sign as {@code d}.
     *
     * <p>Special cases:
     * <ul>
     * <li> If the first argument is NaN, NaN is returned.
     * <li> If the first argument is infinite, then an infinity of the
     * same sign is returned.
     * <li> If the first argument is zero, then a zero of the same
     * sign is returned.
     * </ul>
     *
     * @param d number to be scaled by a power of two.
     * @param scaleFactor power of 2 used to scale {@code d}
     * @return {@code d} &times; 2<sup>{@code scaleFactor}</sup>
     * @since 1.6
     */
    public static double scalb(double d, int scaleFactor) {
        return sun.misc.FpUtils.scalb(d, scaleFactor);
    }

    /**
     * Return {@code f} &times;
     * 2<sup>{@code scaleFactor}</sup> rounded as if performed
     * by a single correctly rounded floating-point multiply to a
     * member of the float value set.  See the Java
     * Language Specification for a discussion of floating-point
     * value sets.  If the exponent of the result is between {@link
     * Float#MIN_EXPONENT} and {@link Float#MAX_EXPONENT}, the
     * answer is calculated exactly.  If the exponent of the result
     * would be larger than {@code Float.MAX_EXPONENT}, an
     * infinity is returned.  Note that if the result is subnormal,
     * precision may be lost; that is, when {@code scalb(x, n)}
     * is subnormal, {@code scalb(scalb(x, n), -n)} may not equal
     * <i>x</i>.  When the result is non-NaN, the result has the same
     * sign as {@code f}.
     *
     * <p>Special cases:
     * <ul>
     * <li> If the first argument is NaN, NaN is returned.
     * <li> If the first argument is infinite, then an infinity of the
     * same sign is returned.
     * <li> If the first argument is zero, then a zero of the same
     * sign is returned.
     * </ul>
     *
     * @param f number to be scaled by a power of two.
     * @param scaleFactor power of 2 used to scale {@code f}
     * @return {@code f} &times; 2<sup>{@code scaleFactor}</sup>
     * @since 1.6
     */
    public static float scalb(float f, int scaleFactor) {
        return sun.misc.FpUtils.scalb(f, scaleFactor);
    }
   

    public static double setHhighbitsAddSome(double x, long highadd) {
        return setHhighbitsAddSome(Double.doubleToRawLongBits(x), highadd);
    }

    public static double setHhighbitsORSome(double x, long highOR) {
        return Double.longBitsToDouble(
                Double.doubleToRawLongBits(x) | (highOR<<32) );
    }

    public static double setHhighbitsAddSome(long xl, long highadd) {
        return Double.longBitsToDouble((xl&clearHighmask)|(xl + highadd));
    }

    private static int __HI(double x) {
        return (int) (Double.doubleToRawLongBits(x) >> 32);
    }

    private static int __LO(double x) {
        return (int) Double.doubleToRawLongBits(x);
    }

    private static double clearLow32bits(double x){
        return Double.longBitsToDouble(
                Double.doubleToRawLongBits(x) & 0xFFFFFFFF00000000L);
    }

    private static double setHigh32bits(double x, long newhigh) {
        return setHigh32bits(Double.doubleToRawLongBits(x), newhigh);
    }

    private static double setHigh32bitsXOR(double x, long toXor) {
       return Double.longBitsToDouble((Double.doubleToRawLongBits(x))^toXor);
    }

    private static double addToHighBits(double x, long toadd) {
        return addToHighBits(Double.doubleToRawLongBits(x), toadd);
    }

    private static double addToHighBits(long x, long toadd) {
        return Double.longBitsToDouble(
                (x&clearHighmask) | (((x>>32) + toadd)<<32) );
    }


    private static double setHigh32bits(long x, long newhigh) {
        return Double.longBitsToDouble(
                (x&clearHighmask) | (newhigh << 32));
    }

    private static double setHigh32bitsDontMask(long x, long newhigh) {
        return Double.longBitsToDouble(x | (newhigh << 32));
    }

    private static double setHigh32bits(long newhigh) {
        return Double.longBitsToDouble((newhigh << 32));
    }
   
}