/*

 * Copyright (c) 1998, 2016, Oracle and/or its affiliates. All rights reserved.

 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.

 *

 * This code is free software; you can redistribute it and/or modify it

 * under the terms of the GNU General Public License version 2 only, as

 * published by the Free Software Foundation.  Oracle designates this

 * particular file as subject to the "Classpath" exception as provided

 * by Oracle in the LICENSE file that accompanied this code.

 *

 * This code is distributed in the hope that it will be useful, but WITHOUT

 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or

 * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License

 * version 2 for more details (a copy is included in the LICENSE file that

 * accompanied this code).

 *

 * You should have received a copy of the GNU General Public License version

 * 2 along with this work; if not, write to the Free Software Foundation,

 * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.

 *

 * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA

 * or visit www.oracle.com if you need additional information or have any

 * questions.

 */

/**

 * A transliteration of the "Freely Distributable Math Library"

 * algorithms from C into Java. That is, this port of the algorithms

 * is as close to the C originals as possible while still being

 * readable legal Java.

 */

public class FdlibmTranslit {

    private FdlibmTranslit() {

        throw new UnsupportedOperationException("No FdLibmTranslit instances for you.");

    }

    /**

     * Return the low-order 32 bits of the double argument as an int.

     */

    private static int __LO(double x) {

        long transducer = Double.doubleToRawLongBits(x);

        return (int)transducer;

    }

    /**

     * Return a double with its low-order bits of the second argument

     * and the high-order bits of the first argument..

     */

    private static double __LO(double x, int low) {

        long transX = Double.doubleToRawLongBits(x);

        return Double.longBitsToDouble((transX & 0xFFFF_FFFF_0000_0000L) |

                                       (low    & 0x0000_0000_FFFF_FFFFL));

    }

    /**

     * Return the high-order 32 bits of the double argument as an int.

     */

    private static int __HI(double x) {

        long transducer = Double.doubleToRawLongBits(x);

        return (int)(transducer >> 32);

    }

    /**

     * Return a double with its high-order bits of the second argument

     * and the low-order bits of the first argument..

     */

    private static double __HI(double x, int high) {

        long transX = Double.doubleToRawLongBits(x);

        return Double.longBitsToDouble((transX & 0x0000_0000_FFFF_FFFFL) |

                                       ( ((long)high)) << 32 );

    }

    public static double hypot(double x, double y) {

        return Hypot.compute(x, y);

    }

    /**

     * cbrt(x)

     * Return cube root of x

     */

    public static class Cbrt {

        // unsigned

        private static final int B1 = 715094163; /* B1 = (682-0.03306235651)*2**20 */

        private static final int B2 = 696219795; /* B2 = (664-0.03306235651)*2**20 */

        private static final double C =  5.42857142857142815906e-01; /* 19/35     = 0x3FE15F15, 0xF15F15F1 */

        private static final double D = -7.05306122448979611050e-01; /* -864/1225 = 0xBFE691DE, 0x2532C834 */

        private static final double E =  1.41428571428571436819e+00; /* 99/70     = 0x3FF6A0EA, 0x0EA0EA0F */

        private static final double F =  1.60714285714285720630e+00; /* 45/28     = 0x3FF9B6DB, 0x6DB6DB6E */

        private static final double G =  3.57142857142857150787e-01; /* 5/14      = 0x3FD6DB6D, 0xB6DB6DB7 */

        public static strictfp double compute(double x) {

            int     hx;

            double  r, s, t=0.0, w;

            int sign; // unsigned

            hx = __HI(x);           // high word of x

            sign = hx & 0x80000000;             // sign= sign(x)

            hx  ^= sign;

            if (hx >= 0x7ff00000)

                return (x+x); // cbrt(NaN,INF) is itself

            if ((hx | __LO(x)) == 0)

                return(x);          // cbrt(0) is itself

            x = __HI(x, hx);   // x <- |x|

            // rough cbrt to 5 bits

            if (hx < 0x00100000) {               // subnormal number

                t = __HI(t, 0x43500000);          // set t= 2**54

                t *= x;

                t = __HI(t, __HI(t)/3+B2);

            } else {

                t = __HI(t, hx/3+B1);

            }

            // new cbrt to 23 bits, may be implemented in single precision

            r = t * t/x;

            s = C + r*t;

            t *= G + F/(s + E + D/s);

            // chopped to 20 bits and make it larger than cbrt(x)

            t = __LO(t, 0);

            t = __HI(t, __HI(t)+0x00000001);

            // one step newton iteration to 53 bits with error less than 0.667 ulps

            s = t * t;          // t*t is exact

            r = x / s;

            w = t + t;

            r= (r - t)/(w + r);  // r-s is exact

            t= t + t*r;

            // retore the sign bit

            t = __HI(t, __HI(t) | sign);

            return(t);

        }

    }

    /**

     * 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)

     */

    static class Hypot {

        public static double compute(double x, double y) {

            double a = x;

            double b = y;

            double t1, t2, y1, y2, w;

            int j, k, ha, hb;

            ha = __HI(x) & 0x7fffffff;        // high word of  x

            hb = __HI(y) & 0x7fffffff;        // high word of  y

            if(hb > ha) {

                a = y;

                b = x;

                j = ha;

                ha = hb;

                hb = j;

            } else {

                a = x;

                b = y;

            }

            a = __HI(a, ha);   // a <- |a|

            b = __HI(b, hb);   // b <- |b|

            if ((ha - hb) > 0x3c00000) {

                return a + b;  // x / y > 2**60

            }

            k=0;

            if (ha > 0x5f300000) {   // a>2**500

                if (ha >= 0x7ff00000) {       // Inf or NaN

                    w = a + b;                // for sNaN

                    if (((ha & 0xfffff) | __LO(a)) == 0)

                        w = a;

                    if (((hb ^ 0x7ff00000) | __LO(b)) == 0)

                        w = b;

                    return w;

                }

                // scale a and b by 2**-600

                ha -= 0x25800000;

                hb -= 0x25800000;

                k += 600;

                a = __HI(a, ha);

                b = __HI(b, hb);

            }

            if (hb < 0x20b00000) {   // b < 2**-500

                if (hb <= 0x000fffff) {      // subnormal b or 0 */

                    if ((hb | (__LO(b))) == 0)

                        return a;

                    t1 = 0;

                    t1 = __HI(t1, 0x7fd00000);  // t1=2^1022

                    b *= t1;

                    a *= t1;

                    k -= 1022;

                } else {            // scale a and b by 2^600

                    ha += 0x25800000;       // a *= 2^600

                    hb += 0x25800000;       // b *= 2^600

                    k -= 600;

                    a = __HI(a, ha);

                    b = __HI(b, hb);

                }

            }

            // medium size a and b

            w = a - b;

            if (w > b) {

                t1 = 0;

                t1 = __HI(t1, ha);

                t2 = a - t1;

                w  = Math.sqrt(t1*t1 - (b*(-b) - t2 * (a + t1)));

            } else {

                a  = a + a;

                y1 = 0;

                y1 = __HI(y1, hb);

                y2 = b - y1;

                t1 = 0;

                t1 = __HI(t1, ha + 0x00100000);

                t2 = a - t1;

                w  = Math.sqrt(t1*y1 - (w*(-w) - (t1*y2 + t2*b)));

            }

            if (k != 0) {

                t1 = 1.0;

                int t1_hi = __HI(t1);

                t1_hi += (k << 20);

                t1 = __HI(t1, t1_hi);

                return t1 * w;

            } else

                return w;

        }

    }

    /**

     * 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

     *

     * 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.

     */

    static class Exp {

        private static final double one     = 1.0;

        private static final double[] halF = {0.5,-0.5,};

        private static final double huge    = 1.0e+300;

        private static final double twom1000= 9.33263618503218878990e-302;      /* 2**-1000=0x01700000,0*/

        private static final double o_threshold=  7.09782712893383973096e+02;   /* 0x40862E42, 0xFEFA39EF */

        private static final double u_threshold= -7.45133219101941108420e+02;   /* 0xc0874910, 0xD52D3051 */

        private static final double[] ln2HI   ={ 6.93147180369123816490e-01,    /* 0x3fe62e42, 0xfee00000 */

                                                 -6.93147180369123816490e-01};  /* 0xbfe62e42, 0xfee00000 */

        private static final double[] ln2LO   ={ 1.90821492927058770002e-10,    /* 0x3dea39ef, 0x35793c76 */

                                                 -1.90821492927058770002e-10,}; /* 0xbdea39ef, 0x35793c76 */

        private static final double invln2 =  1.44269504088896338700e+00;       /* 0x3ff71547, 0x652b82fe */

        private static final double P1   =  1.66666666666666019037e-01;         /* 0x3FC55555, 0x5555553E */

        private static final double P2   = -2.77777777770155933842e-03;         /* 0xBF66C16C, 0x16BEBD93 */

        private static final double P3   =  6.61375632143793436117e-05;         /* 0x3F11566A, 0xAF25DE2C */

        private static final double P4   = -1.65339022054652515390e-06;         /* 0xBEBBBD41, 0xC5D26BF1 */

        private static final double P5   =  4.13813679705723846039e-08;         /* 0x3E663769, 0x72BEA4D0 */

        public static strictfp double compute(double x) {

            double y,hi=0,lo=0,c,t;

            int k=0,xsb;

            /*unsigned*/ int hx;

            hx  = __HI(x);  /* high word of x */

            xsb = (hx>>31)&1;               /* sign bit of x */

            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(x))!=0)

                        return x+x;                /* NaN */

                    else return (xsb==0)? x:0.0;    /* exp(+-inf)={inf,0} */

                }

                if(x > o_threshold) return huge*huge; /* overflow */

                if(x < u_threshold) return twom1000*twom1000; /* underflow */

            }

            /* argument reduction */

            if(hx > 0x3fd62e42) {           /* if  |x| > 0.5 ln2 */

                if(hx < 0x3FF0A2B2) {       /* and |x| < 1.5 ln2 */

                    hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb;

                } else {

                    k  = (int)(invln2*x+halF[xsb]);

                    t  = k;

                    hi = x - t*ln2HI[0];    /* t*ln2HI is exact here */

                    lo = t*ln2LO[0];

                }

                x  = hi - lo;

            }

            else if(hx < 0x3e300000)  {     /* when |x|<2**-28 */

                if(huge+x>one) return one+x;/* trigger inexact */

            }

            else k = 0;

            /* x is now in primary range */

            t  = x*x;

            c  = x - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));

            if(k==0)        return one-((x*c)/(c-2.0)-x);

            else            y = one-((lo-(x*c)/(2.0-c))-hi);

            if(k >= -1021) {

                y = __HI(y, __HI(y) + (k<<20)); /* add k to y's exponent */

                return y;

            } else {

                y = __HI(y, __HI(y) + ((k+1000)<<20));/* add k to y's exponent */

                return y*twom1000;

            }

        }

    }

}