/*
 * Hunt - A refined core library for D programming language.
 *
 * Copyright (C) 2018-2019 HuntLabs
 *
 * Website: https://www.huntlabs.net/
 *
 * Licensed under the Apache-2.0 License.
 *
 */

module hunt.math.Helper;

import std.math;
import hunt.Integer;
import hunt.Long;
import hunt.Exceptions;

/**
*/
final class MathHelper {

    /**
     * Don't let anyone instantiate this class.
     */
    private this() {}

    /**
     * The {@code double} value that is closer than any other to
     * <i>e</i>, the base of the natural logarithms.
     */
    enum 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.
     */
    enum double PI = 3.14159265358979323846;

    /**
     * Constant by which to multiply an angular value in degrees to obtain an
     * angular value in radians.
     */
    private enum double DEGREES_TO_RADIANS = 0.017453292519943295;

    /**
     * Constant by which to multiply an angular value in radians to obtain an
     * angular value in degrees.
     */
    private enum double RADIANS_TO_DEGREES = 57.29577951308232;

    /**
     * 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>
     *
     * <p>The computed result must be within 1 ulp of the exact result.
     * Results must be semi-monotonic.
     *
     * @param   a   an angle, in radians.
     * @return  the sine of the argument.
     */
    // @HotSpotIntrinsicCandidate
    // static double sin(double a) {
    //     return StrictMath.sin(a); // default impl. delegates to StrictMath
    // }

    // /**
    //  * 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>
    //  *
    //  * <p>The computed result must be within 1 ulp of the exact result.
    //  * Results must be semi-monotonic.
    //  *
    //  * @param   a   an angle, in radians.
    //  * @return  the cosine of the argument.
    //  */
    // @HotSpotIntrinsicCandidate
    // static double cos(double a) {
    //     return StrictMath.cos(a); // default impl. delegates to StrictMath
    // }

    // /**
    //  * 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>
    //  *
    //  * <p>The computed result must be within 1 ulp of the exact result.
    //  * Results must be semi-monotonic.
    //  *
    //  * @param   a   an angle, in radians.
    //  * @return  the tangent of the argument.
    //  */
    // @HotSpotIntrinsicCandidate
    // static double tan(double a) {
    //     return StrictMath.tan(a); // default impl. delegates to StrictMath
    // }

    // /**
    //  * 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>
    //  *
    //  * <p>The computed result must be within 1 ulp of the exact result.
    //  * Results must be semi-monotonic.
    //  *
    //  * @param   a   the value whose arc sine is to be returned.
    //  * @return  the arc sine of the argument.
    //  */
    // static double asin(double a) {
    //     return StrictMath.asin(a); // default impl. delegates to StrictMath
    // }

    // /**
    //  * 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>
    //  *
    //  * <p>The computed result must be within 1 ulp of the exact result.
    //  * Results must be semi-monotonic.
    //  *
    //  * @param   a   the value whose arc cosine is to be returned.
    //  * @return  the arc cosine of the argument.
    //  */
    // static double acos(double a) {
    //     return StrictMath.acos(a); // default impl. delegates to StrictMath
    // }

    // /**
    //  * 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>
    //  *
    //  * <p>The computed result must be within 1 ulp of the exact result.
    //  * Results must be semi-monotonic.
    //  *
    //  * @param   a   the value whose arc tangent is to be returned.
    //  * @return  the arc tangent of the argument.
    //  */
    // static double atan(double a) {
    //     return StrictMath.atan(a); // default impl. delegates to StrictMath
    // }

    // /**
    //  * 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.
    //  */
    // static double toRadians(double angdeg) {
    //     return angdeg * DEGREES_TO_RADIANS;
    // }

    // /**
    //  * 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.
    //  */
    // static double toDegrees(double angrad) {
    //     return angrad * RADIANS_TO_DEGREES;
    // }

    /**
     * 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>
     *
     * <p>The computed result must be within 1 ulp of the exact result.
     * Results must be semi-monotonic.
     *
     * @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.
     */
    // @HotSpotIntrinsicCandidate
    // static double exp(double a) {
    //     return StrictMath.exp(a); // default impl. delegates to StrictMath
    // }

    /**
     * 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>
     *
     * <p>The computed result must be within 1 ulp of the exact result.
     * Results must be semi-monotonic.
     *
     * @param   a   a value
     * @return  the value ln&nbsp;{@code a}, the natural logarithm of
     *          {@code a}.
     */
    // @HotSpotIntrinsicCandidate
    // static double log(double a) {
    //     return StrictMath.log(a); // default impl. delegates to StrictMath
    // }

    /**
     * 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>
     *
     * <p>The computed result must be within 1 ulp of the exact result.
     * Results must be semi-monotonic.
     *
     * @param   a   a value
     * @return  the base 10 logarithm of  {@code a}.
     */
    // @HotSpotIntrinsicCandidate
    // static double log10(double a) {
    //     return StrictMath.log10(a); // default impl. delegates to StrictMath
    // }

    /**
     * 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}.
     *          If the argument is NaN or less than zero, the result is NaN.
     */
    // @HotSpotIntrinsicCandidate
    // static double sqrt(double a) {
    //     return StrictMath.sqrt(a); // default impl. delegates to StrictMath
    //                                // Note that hardware sqrt instructions
    //                                // frequently can be directly used by JITs
    //                                // and should be much faster than doing
    //                                // Math.sqrt in software.
    // }


    /**
     * 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>
     *
     * <p>The computed result must be within 1 ulp of the exact result.
     *
     * @param   a   a value.
     * @return  the cube root of {@code a}.
     */
    // static double cbrt(double a) {
    //     return StrictMath.cbrt(a);
    // }

    /**
     * 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}.
     */
    // static double IEEEremainder(double f1, double f2) {
    //     return StrictMath.IEEEremainder(f1, f2); // delegate to StrictMath
    // }

    /**
     * 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 Math.ceil(x)} is exactly the
     * value of {@code -Math.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.
     */
    static double ceil(double a) {
        return std.math.ceil(a);
        // return StrictMath.ceil(a); // default impl. delegates to StrictMath
    }

    /**
     * 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.
     */
    static double floor(double a) {
        return std.math.floor(a);
        // return StrictMath.floor(a); // default impl. delegates to StrictMath
    }

    /**
     * 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, 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 {@code double} value.
     * @return  the closest floating-point value to {@code a} that is
     *          equal to a mathematical integer.
     */
    // static double rint(double a) {
    //     return StrictMath.rint(a); // default impl. delegates to StrictMath
    // }

    // /**
    //  * 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>
    //  *
    //  * <p>The computed result must be within 2 ulps of the exact result.
    //  * Results must be semi-monotonic.
    //  *
    //  * @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.
    //  */
    // @HotSpotIntrinsicCandidate
    // static double atan2(double y, double x) {
    //     return StrictMath.atan2(y, x); // default impl. delegates to StrictMath
    // }

    // /**
    //  * 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.)
    //  *
    //  * <p>The computed result must be within 1 ulp of the exact result.
    //  * Results must be semi-monotonic.
    //  *
    //  * @param   a   the base.
    //  * @param   b   the exponent.
    //  * @return  the value {@code a}<sup>{@code b}</sup>.
    //  */
    // @HotSpotIntrinsicCandidate
    // static double pow(double a, double b) {
    //     return StrictMath.pow(a, b); // default impl. delegates to StrictMath
    // }

    // /**
    //  * Returns the closest {@code int} to the argument, with ties
    //  * rounding to positive infinity.
    //  *
    //  * <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
    //  */
    // static int round(float a) {
    //     int intBits = Float.floatToRawIntBits(a);
    //     int biasedExp = (intBits & FloatConsts.EXP_BIT_MASK)
    //             >> (FloatConsts.SIGNIFICAND_WIDTH - 1);
    //     int shift = (FloatConsts.SIGNIFICAND_WIDTH - 2
    //             + FloatConsts.EXP_BIAS) - biasedExp;
    //     if ((shift & -32) == 0) { // shift >= 0 && shift < 32
    //         // a is a finite number such that pow(2,-32) <= ulp(a) < 1
    //         int r = ((intBits & FloatConsts.SIGNIF_BIT_MASK)
    //                 | (FloatConsts.SIGNIF_BIT_MASK + 1));
    //         if (intBits < 0) {
    //             r = -r;
    //         }
    //         // In the comments below each Java expression evaluates to the value
    //         // the corresponding mathematical expression:
    //         // (r) evaluates to a / ulp(a)
    //         // (r >> shift) evaluates to floor(a * 2)
    //         // ((r >> shift) + 1) evaluates to floor((a + 1/2) * 2)
    //         // (((r >> shift) + 1) >> 1) evaluates to floor(a + 1/2)
    //         return ((r >> shift) + 1) >> 1;
    //     } else {
    //         // a is either
    //         // - a finite number with abs(a) < exp(2,FloatConsts.SIGNIFICAND_WIDTH-32) < 1/2
    //         // - a finite number with ulp(a) >= 1 and hence a is a mathematical integer
    //         // - an infinity or NaN
    //         return (int) a;
    //     }
    // }

    // /**
    //  * Returns the closest {@code long} to the argument, with ties
    //  * rounding to positive infinity.
    //  *
    //  * <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
    //  */
    // static long round(double a) {
    //     long longBits = Double.doubleToRawLongBits(a);
    //     long biasedExp = (longBits & DoubleConsts.EXP_BIT_MASK)
    //             >> (DoubleConsts.SIGNIFICAND_WIDTH - 1);
    //     long shift = (DoubleConsts.SIGNIFICAND_WIDTH - 2
    //             + DoubleConsts.EXP_BIAS) - biasedExp;
    //     if ((shift & -64) == 0) { // shift >= 0 && shift < 64
    //         // a is a finite number such that pow(2,-64) <= ulp(a) < 1
    //         long r = ((longBits & DoubleConsts.SIGNIF_BIT_MASK)
    //                 | (DoubleConsts.SIGNIF_BIT_MASK + 1));
    //         if (longBits < 0) {
    //             r = -r;
    //         }
    //         // In the comments below each Java expression evaluates to the value
    //         // the corresponding mathematical expression:
    //         // (r) evaluates to a / ulp(a)
    //         // (r >> shift) evaluates to floor(a * 2)
    //         // ((r >> shift) + 1) evaluates to floor((a + 1/2) * 2)
    //         // (((r >> shift) + 1) >> 1) evaluates to floor(a + 1/2)
    //         return ((r >> shift) + 1) >> 1;
    //     } else {
    //         // a is either
    //         // - a finite number with abs(a) < exp(2,DoubleConsts.SIGNIFICAND_WIDTH-64) < 1/2
    //         // - a finite number with ulp(a) >= 1 and hence a is a mathematical integer
    //         // - an infinity or NaN
    //         return (long) a;
    //     }
    // }

    // private static final class RandomNumberGeneratorHolder {
    //     static final Random 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.
     *
     * @apiNote
     * As the largest {@code double} value less than {@code 1.0}
     * is {@code Math.nextDown(1.0)}, a value {@code x} in the closed range
     * {@code [x1,x2]} where {@code x1<=x2} may be defined by the statements
     *
     * <blockquote><pre>{@code
     * double f = Math.random()/Math.nextDown(1.0);
     * double x = x1*(1.0 - f) + x2*f;
     * }</pre></blockquote>
     *
     * @return  a pseudorandom {@code double} greater than or equal
     * to {@code 0.0} and less than {@code 1.0}.
     * @see #nextDown(double)
     * @see Random#nextDouble()
     */
    // static double random() {
    //     return RandomNumberGeneratorHolder.randomNumberGenerator.nextDouble();
    // }

    /**
     * Returns the sum of its arguments,
     * throwing an exception if the result overflows an {@code int}.
     *
     * @param x the first value
     * @param y the second value
     * @return the result
     * @throws ArithmeticException if the result overflows an int
     */
    // @HotSpotIntrinsicCandidate
    static int addExact(int x, int y) {
        int r = x + y;
        // HD 2-12 Overflow iff both arguments have the opposite sign of the result
        if (((x ^ r) & (y ^ r)) < 0) {
            throw new ArithmeticException("integer overflow");
        }
        return r;
    }

    /**
     * Returns the sum of its arguments,
     * throwing an exception if the result overflows a {@code long}.
     *
     * @param x the first value
     * @param y the second value
     * @return the result
     * @throws ArithmeticException if the result overflows a long
     */
    // @HotSpotIntrinsicCandidate
    static long addExact(long x, long y) {
        long r = x + y;
        // HD 2-12 Overflow iff both arguments have the opposite sign of the result
        if (((x ^ r) & (y ^ r)) < 0) {
            throw new ArithmeticException("long overflow");
        }
        return r;
    }

    /**
     * Returns the difference of the arguments,
     * throwing an exception if the result overflows an {@code int}.
     *
     * @param x the first value
     * @param y the second value to subtract from the first
     * @return the result
     * @throws ArithmeticException if the result overflows an int
     */
    // @HotSpotIntrinsicCandidate
    static int subtractExact(int x, int y) {
        int r = x - y;
        // HD 2-12 Overflow iff the arguments have different signs and
        // the sign of the result is different from the sign of x
        if (((x ^ y) & (x ^ r)) < 0) {
            throw new ArithmeticException("integer overflow");
        }
        return r;
    }

    /**
     * Returns the difference of the arguments,
     * throwing an exception if the result overflows a {@code long}.
     *
     * @param x the first value
     * @param y the second value to subtract from the first
     * @return the result
     * @throws ArithmeticException if the result overflows a long
     */
    // @HotSpotIntrinsicCandidate
    static long subtractExact(long x, long y) {
        long r = x - y;
        // HD 2-12 Overflow iff the arguments have different signs and
        // the sign of the result is different from the sign of x
        if (((x ^ y) & (x ^ r)) < 0) {
            throw new ArithmeticException("long overflow");
        }
        return r;
    }

    /**
     * Returns the product of the arguments,
     * throwing an exception if the result overflows an {@code int}.
     *
     * @param x the first value
     * @param y the second value
     * @return the result
     * @throws ArithmeticException if the result overflows an int
     */
    // @HotSpotIntrinsicCandidate
    static int multiplyExact(int x, int y) {
        long r = cast(long)x * cast(long)y;
        if (cast(int)r != r) {
            throw new ArithmeticException("integer overflow");
        }
        return cast(int)r;
    }

    /**
     * Returns the product of the arguments, throwing an exception if the result
     * overflows a {@code long}.
     *
     * @param x the first value
     * @param y the second value
     * @return the result
     * @throws ArithmeticException if the result overflows a long
     */
    static long multiplyExact(long x, int y) {
        return multiplyExact(x, cast(long)y);
    }

    /**
     * Returns the product of the arguments,
     * throwing an exception if the result overflows a {@code long}.
     *
     * @param x the first value
     * @param y the second value
     * @return the result
     * @throws ArithmeticException if the result overflows a long
     */
    // @HotSpotIntrinsicCandidate
    static long multiplyExact(long x, long y) {
        long r = x * y;
        long ax = abs(x);
        long ay = abs(y);
        if (((ax | ay) >>> 31 != 0)) {
            // Some bits greater than 2^31 that might cause overflow
            // Check the result using the divide operator
            // and check for the special case of Long.MIN_VALUE * -1
           if (((y != 0) && (r / y != x)) ||
               (x == Long.MIN_VALUE && y == -1)) {
                throw new ArithmeticException("long overflow");
            }
        }
        return r;
    }

    /**
     * Returns the argument incremented by one, throwing an exception if the
     * result overflows an {@code int}.
     *
     * @param a the value to increment
     * @return the result
     * @throws ArithmeticException if the result overflows an int
     */
    // @HotSpotIntrinsicCandidate
    static int incrementExact(int a) {
        if (a == Integer.MAX_VALUE) {
            throw new ArithmeticException("integer overflow");
        }

        return a + 1;
    }

    /**
     * Returns the argument incremented by one, throwing an exception if the
     * result overflows a {@code long}.
     *
     * @param a the value to increment
     * @return the result
     * @throws ArithmeticException if the result overflows a long
     */
    // @HotSpotIntrinsicCandidate
    static long incrementExact(long a) {
        if (a == Long.MAX_VALUE) {
            throw new ArithmeticException("long overflow");
        }

        return a + 1L;
    }

    /**
     * Returns the argument decremented by one, throwing an exception if the
     * result overflows an {@code int}.
     *
     * @param a the value to decrement
     * @return the result
     * @throws ArithmeticException if the result overflows an int
     */
    // @HotSpotIntrinsicCandidate
    static int decrementExact(int a) {
        if (a == Integer.MIN_VALUE) {
            throw new ArithmeticException("integer overflow");
        }

        return a - 1;
    }

    /**
     * Returns the argument decremented by one, throwing an exception if the
     * result overflows a {@code long}.
     *
     * @param a the value to decrement
     * @return the result
     * @throws ArithmeticException if the result overflows a long
     */
    // @HotSpotIntrinsicCandidate
    static long decrementExact(long a) {
        if (a == Long.MIN_VALUE) {
            throw new ArithmeticException("long overflow");
        }

        return a - 1L;
    }

    /**
     * Returns the negation of the argument, throwing an exception if the
     * result overflows an {@code int}.
     *
     * @param a the value to negate
     * @return the result
     * @throws ArithmeticException if the result overflows an int
     */
    // @HotSpotIntrinsicCandidate
    static int negateExact(int a) {
        if (a == Integer.MIN_VALUE) {
            throw new ArithmeticException("integer overflow");
        }

        return -a;
    }

    /**
     * Returns the negation of the argument, throwing an exception if the
     * result overflows a {@code long}.
     *
     * @param a the value to negate
     * @return the result
     * @throws ArithmeticException if the result overflows a long
     */
    // @HotSpotIntrinsicCandidate
    static long negateExact(long a) {
        if (a == Long.MIN_VALUE) {
            throw new ArithmeticException("long overflow");
        }

        return -a;
    }

    /**
     * Returns the value of the {@code long} argument;
     * throwing an exception if the value overflows an {@code int}.
     *
     * @param value the long value
     * @return the argument as an int
     * @throws ArithmeticException if the {@code argument} overflows an int
     */
    static int toIntExact(long value) {
        if (cast(int)value != value) {
            throw new ArithmeticException("integer overflow");
        }
        return cast(int)value;
    }

    /**
     * Returns the exact mathematical product of the arguments.
     *
     * @param x the first value
     * @param y the second value
     * @return the result
     */
    static long multiplyFull(int x, int y) {
        return cast(long)x * cast(long)y;
    }

    /**
     * Returns as a {@code long} the most significant 64 bits of the 128-bit
     * product of two 64-bit factors.
     *
     * @param x the first value
     * @param y the second value
     * @return the result
     */
    // @HotSpotIntrinsicCandidate
    static long multiplyHigh(long x, long y) {
        if (x < 0 || y < 0) {
            // Use technique from section 8-2 of Henry S. Warren, Jr.,
            // Hacker's Delight (2nd ed.) (Addison Wesley, 2013), 173-174.
            long x1 = x >> 32;
            long x2 = x & 0xFFFFFFFFL;
            long y1 = y >> 32;
            long y2 = y & 0xFFFFFFFFL;
            long z2 = x2 * y2;
            long t = x1 * y2 + (z2 >>> 32);
            long z1 = t & 0xFFFFFFFFL;
            long z0 = t >> 32;
            z1 += x2 * y1;
            return x1 * y1 + z0 + (z1 >> 32);
        } else {
            // Use Karatsuba technique with two base 2^32 digits.
            long x1 = x >>> 32;
            long y1 = y >>> 32;
            long x2 = x & 0xFFFFFFFFL;
            long y2 = y & 0xFFFFFFFFL;
            long A = x1 * y1;
            long B = x2 * y2;
            long C = (x1 + x2) * (y1 + y2);
            long K = C - A - B;
            return (((B >>> 32) + K) >>> 32) + A;
        }
    }

    /**
     * Returns the largest (closest to positive infinity)
     * {@code int} value that is less than or equal to the algebraic quotient.
     * There is one special case, if the dividend is the
     * {@linkplain Integer#MIN_VALUE Integer.MIN_VALUE} and the divisor is {@code -1},
     * then integer overflow occurs and
     * the result is equal to {@code Integer.MIN_VALUE}.
     * <p>
     * Normal integer division operates under the round to zero rounding mode
     * (truncation).  This operation instead acts under the round toward
     * negative infinity (floor) rounding mode.
     * The floor rounding mode gives different results from truncation
     * when the exact result is negative.
     * <ul>
     *   <li>If the signs of the arguments are the same, the results of
     *       {@code floorDiv} and the {@code /} operator are the same.  <br>
     *       For example, {@code floorDiv(4, 3) == 1} and {@code (4 / 3) == 1}.</li>
     *   <li>If the signs of the arguments are different,  the quotient is negative and
     *       {@code floorDiv} returns the integer less than or equal to the quotient
     *       and the {@code /} operator returns the integer closest to zero.<br>
     *       For example, {@code floorDiv(-4, 3) == -2},
     *       whereas {@code (-4 / 3) == -1}.
     *   </li>
     * </ul>
     *
     * @param x the dividend
     * @param y the divisor
     * @return the largest (closest to positive infinity)
     * {@code int} value that is less than or equal to the algebraic quotient.
     * @throws ArithmeticException if the divisor {@code y} is zero
     * @see #floorMod(int, int)
     * @see #floor(double)
     */
    static int floorDiv(int x, int y) {
        int r = x / y;
        // if the signs are different and modulo not zero, round down
        if ((x ^ y) < 0 && (r * y != x)) {
            r--;
        }
        return r;
    }

    /**
     * Returns the largest (closest to positive infinity)
     * {@code long} value that is less than or equal to the algebraic quotient.
     * There is one special case, if the dividend is the
     * {@linkplain Long#MIN_VALUE Long.MIN_VALUE} and the divisor is {@code -1},
     * then integer overflow occurs and
     * the result is equal to {@code Long.MIN_VALUE}.
     * <p>
     * Normal integer division operates under the round to zero rounding mode
     * (truncation).  This operation instead acts under the round toward
     * negative infinity (floor) rounding mode.
     * The floor rounding mode gives different results from truncation
     * when the exact result is negative.
     * <p>
     * For examples, see {@link #floorDiv(int, int)}.
     *
     * @param x the dividend
     * @param y the divisor
     * @return the largest (closest to positive infinity)
     * {@code int} value that is less than or equal to the algebraic quotient.
     * @throws ArithmeticException if the divisor {@code y} is zero
     * @see #floorMod(long, int)
     * @see #floor(double)
     */
    static long floorDiv(long x, int y) {
        return floorDiv(x, cast(long)y);
    }

    /**
     * Returns the largest (closest to positive infinity)
     * {@code long} value that is less than or equal to the algebraic quotient.
     * There is one special case, if the dividend is the
     * {@linkplain Long#MIN_VALUE Long.MIN_VALUE} and the divisor is {@code -1},
     * then integer overflow occurs and
     * the result is equal to {@code Long.MIN_VALUE}.
     * <p>
     * Normal integer division operates under the round to zero rounding mode
     * (truncation).  This operation instead acts under the round toward
     * negative infinity (floor) rounding mode.
     * The floor rounding mode gives different results from truncation
     * when the exact result is negative.
     * <p>
     * For examples, see {@link #floorDiv(int, int)}.
     *
     * @param x the dividend
     * @param y the divisor
     * @return the largest (closest to positive infinity)
     * {@code long} value that is less than or equal to the algebraic quotient.
     * @throws ArithmeticException if the divisor {@code y} is zero
     * @see #floorMod(long, long)
     * @see #floor(double)
     */
    static long floorDiv(long x, long y) {
        long r = x / y;
        // if the signs are different and modulo not zero, round down
        if ((x ^ y) < 0 && (r * y != x)) {
            r--;
        }
        return r;
    }

    /**
     * Returns the floor modulus of the {@code int} arguments.
     * <p>
     * The floor modulus is {@code x - (floorDiv(x, y) * y)},
     * has the same sign as the divisor {@code y}, and
     * is in the range of {@code -abs(y) < r < +abs(y)}.
     *
     * <p>
     * The relationship between {@code floorDiv} and {@code floorMod} is such that:
     * <ul>
     *   <li>{@code floorDiv(x, y) * y + floorMod(x, y) == x}
     * </ul>
     * <p>
     * The difference in values between {@code floorMod} and
     * the {@code %} operator is due to the difference between
     * {@code floorDiv} that returns the integer less than or equal to the quotient
     * and the {@code /} operator that returns the integer closest to zero.
     * <p>
     * Examples:
     * <ul>
     *   <li>If the signs of the arguments are the same, the results
     *       of {@code floorMod} and the {@code %} operator are the same.  <br>
     *       <ul>
     *       <li>{@code floorMod(4, 3) == 1}; &nbsp; and {@code (4 % 3) == 1}</li>
     *       </ul>
     *   <li>If the signs of the arguments are different, the results differ from the {@code %} operator.<br>
     *      <ul>
     *      <li>{@code floorMod(+4, -3) == -2}; &nbsp; and {@code (+4 % -3) == +1} </li>
     *      <li>{@code floorMod(-4, +3) == +2}; &nbsp; and {@code (-4 % +3) == -1} </li>
     *      <li>{@code floorMod(-4, -3) == -1}; &nbsp; and {@code (-4 % -3) == -1 } </li>
     *      </ul>
     *   </li>
     * </ul>
     * <p>
     * If the signs of arguments are unknown and a positive modulus
     * is needed it can be computed as {@code (floorMod(x, y) + abs(y)) % abs(y)}.
     *
     * @param x the dividend
     * @param y the divisor
     * @return the floor modulus {@code x - (floorDiv(x, y) * y)}
     * @throws ArithmeticException if the divisor {@code y} is zero
     * @see #floorDiv(int, int)
     */
    static int floorMod(int x, int y) {
        return x - floorDiv(x, y) * y;
    }

    /**
     * Returns the floor modulus of the {@code long} and {@code int} arguments.
     * <p>
     * The floor modulus is {@code x - (floorDiv(x, y) * y)},
     * has the same sign as the divisor {@code y}, and
     * is in the range of {@code -abs(y) < r < +abs(y)}.
     *
     * <p>
     * The relationship between {@code floorDiv} and {@code floorMod} is such that:
     * <ul>
     *   <li>{@code floorDiv(x, y) * y + floorMod(x, y) == x}
     * </ul>
     * <p>
     * For examples, see {@link #floorMod(int, int)}.
     *
     * @param x the dividend
     * @param y the divisor
     * @return the floor modulus {@code x - (floorDiv(x, y) * y)}
     * @throws ArithmeticException if the divisor {@code y} is zero
     * @see #floorDiv(long, int)
     */
    static int floorMod(long x, int y) {
        // Result cannot overflow the range of int.
        return cast(int)(x - floorDiv(x, y) * y);
    }

    /**
     * Returns the floor modulus of the {@code long} arguments.
     * <p>
     * The floor modulus is {@code x - (floorDiv(x, y) * y)},
     * has the same sign as the divisor {@code y}, and
     * is in the range of {@code -abs(y) < r < +abs(y)}.
     *
     * <p>
     * The relationship between {@code floorDiv} and {@code floorMod} is such that:
     * <ul>
     *   <li>{@code floorDiv(x, y) * y + floorMod(x, y) == x}
     * </ul>
     * <p>
     * For examples, see {@link #floorMod(int, int)}.
     *
     * @param x the dividend
     * @param y the divisor
     * @return the floor modulus {@code x - (floorDiv(x, y) * y)}
     * @throws ArithmeticException if the divisor {@code y} is zero
     * @see #floorDiv(long, long)
     */
    static long floorMod(long x, long y) {
        return x - floorDiv(x, y) * y;
    }

    /**
     * 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.
     */
    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.
     */
    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>
     *
     * @apiNote As implied by the above, one valid implementation of
     * this method is given by the expression below which computes a
     * {@code float} with the same exponent and significand as the
     * argument but with a guaranteed zero sign bit indicating a
     * positive value:<br>
     * {@code Float.intBitsToFloat(0x7fffffff & Float.floatToRawIntBits(a))}
     *
     * @param   a   the argument whose absolute value is to be determined
     * @return  the absolute value of the argument.
     */
    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>
     *
     * @apiNote As implied by the above, one valid implementation of
     * this method is given by the expression below which computes a
     * {@code double} with the same exponent and significand as the
     * argument but with a guaranteed zero sign bit indicating a
     * positive value:<br>
     * {@code Double.longBitsToDouble((Double.doubleToRawLongBits(a)<<1)>>>1)}
     *
     * @param   a   the argument whose absolute value is to be determined
     * @return  the absolute value of the argument.
     */
    // @HotSpotIntrinsicCandidate
    static double abs(double a) {
        return std.math.abs(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}.
     */
    // @HotSpotIntrinsicCandidate
    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}.
     */
    static long max(long a, long b) {
        return (a >= b) ? a : b;
    }

    // // Use raw bit-wise conversions on guaranteed non-NaN arguments.
    // private static final long negativeZeroFloatBits  = Float.floatToRawIntBits(-0.0f);
    // private static final long negativeZeroDoubleBits = Double.doubleToRawLongBits(-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}.
     */
    static float max(float a, float b) {
        // if (a != a)
        //     return a;   // a is NaN
        // if ((a == 0.0f) &&
        //     (b == 0.0f) &&
        //     (Float.floatToRawIntBits(a) == negativeZeroFloatBits)) {
        //     // Raw conversion ok since NaN can't map to -0.0.
        //     return b;
        // }
        // return (a >= b) ? a : b;
        import std.algorithm.comparison : max;
        return max(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}.
     */
    static double max(double a, double b) {
        // if (a != a)
        //     return a;   // a is NaN
        // if ((a == 0.0d) &&
        //     (b == 0.0d) &&
        //     (Double.doubleToRawLongBits(a) == negativeZeroDoubleBits)) {
        //     // Raw conversion ok since NaN can't map to -0.0.
        //     return b;
        // }
        // return (a >= b) ? a : b;
        import std.algorithm.comparison : max;
        return max(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}.
     */
    // @HotSpotIntrinsicCandidate
    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}.
     */
    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}.
     */
    // static float min(float a, float b) {
    //     if (a != a)
    //         return a;   // a is NaN
    //     if ((a == 0.0f) &&
    //         (b == 0.0f) &&
    //         (Float.floatToRawIntBits(b) == negativeZeroFloatBits)) {
    //         // Raw conversion ok since NaN can't map to -0.0.
    //         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}.
    //  */
    // static double min(double a, double b) {
    //     if (a != a)
    //         return a;   // a is NaN
    //     if ((a == 0.0d) &&
    //         (b == 0.0d) &&
    //         (Double.doubleToRawLongBits(b) == negativeZeroDoubleBits)) {
    //         // Raw conversion ok since NaN can't map to -0.0.
    //         return b;
    //     }
    //     return (a <= b) ? a : b;
    // }

    // /**
    //  * Returns the fused multiply add of the three arguments; that is,
    //  * returns the exact product of the first two arguments summed
    //  * with the third argument and then rounded once to the nearest
    //  * {@code double}.
    //  *
    //  * The rounding is done using the {@linkplain
    //  * java.math.RoundingMode#HALF_EVEN round to nearest even
    //  * rounding mode}.
    //  *
    //  * In contrast, if {@code a * b + c} is evaluated as a regular
    //  * floating-point expression, two rounding errors are involved,
    //  * the first for the multiply operation, the second for the
    //  * addition operation.
    //  *
    //  * <p>Special cases:
    //  * <ul>
    //  * <li> If any argument is NaN, the result is NaN.
    //  *
    //  * <li> If one of the first two arguments is infinite and the
    //  * other is zero, the result is NaN.
    //  *
    //  * <li> If the exact product of the first two arguments is infinite
    //  * (in other words, at least one of the arguments is infinite and
    //  * the other is neither zero nor NaN) and the third argument is an
    //  * infinity of the opposite sign, the result is NaN.
    //  *
    //  * </ul>
    //  *
    //  * <p>Note that {@code fma(a, 1.0, c)} returns the same
    //  * result as ({@code a + c}).  However,
    //  * {@code fma(a, b, +0.0)} does <em>not</em> always return the
    //  * same result as ({@code a * b}) since
    //  * {@code fma(-0.0, +0.0, +0.0)} is {@code +0.0} while
    //  * ({@code -0.0 * +0.0}) is {@code -0.0}; {@code fma(a, b, -0.0)} is
    //  * equivalent to ({@code a * b}) however.
    //  *
    //  * @apiNote This method corresponds to the fusedMultiplyAdd
    //  * operation defined in IEEE 754-2008.
    //  *
    //  * @param a a value
    //  * @param b a value
    //  * @param c a value
    //  *
    //  * @return (<i>a</i>&nbsp;&times;&nbsp;<i>b</i>&nbsp;+&nbsp;<i>c</i>)
    //  * computed, as if with unlimited range and precision, and rounded
    //  * once to the nearest {@code double} value
    //  *
    //  */
    // @HotSpotIntrinsicCandidate
    // static double fma(double a, double b, double c) {
    //     /*
    //      * Infinity and NaN arithmetic is not quite the same with two
    //      * roundings as opposed to just one so the simple expression
    //      * "a * b + c" cannot always be used to compute the correct
    //      * result.  With two roundings, the product can overflow and
    //      * if the addend is infinite, a spurious NaN can be produced
    //      * if the infinity from the overflow and the infinite addend
    //      * have opposite signs.
    //      */

    //     // First, screen for and handle non-finite input values whose
    //     // arithmetic is not supported by BigDecimal.
    //     if (Double.isNaN(a) || Double.isNaN(b) || Double.isNaN(c)) {
    //         return Double.NaN;
    //     } else { // All inputs non-NaN
    //         boolean infiniteA = Double.isInfinite(a);
    //         boolean infiniteB = Double.isInfinite(b);
    //         boolean infiniteC = Double.isInfinite(c);
    //         double result;

    //         if (infiniteA || infiniteB || infiniteC) {
    //             if (infiniteA && b == 0.0 ||
    //                 infiniteB && a == 0.0 ) {
    //                 return Double.NaN;
    //             }
    //             // Store product in a double field to cause an
    //             // overflow even if non-strictfp evaluation is being
    //             // used.
    //             double product = a * b;
    //             if (Double.isInfinite(product) && !infiniteA && !infiniteB) {
    //                 // Intermediate overflow; might cause a
    //                 // spurious NaN if added to infinite c.
    //                 assert Double.isInfinite(c);
    //                 return c;
    //             } else {
    //                 result = product + c;
    //                 assert !Double.isFinite(result);
    //                 return result;
    //             }
    //         } else { // All inputs finite
    //             BigDecimal product = (new BigDecimal(a)).multiply(new BigDecimal(b));
    //             if (c == 0.0) { // Positive or negative zero
    //                 // If the product is an exact zero, use a
    //                 // floating-point expression to compute the sign
    //                 // of the zero final result. The product is an
    //                 // exact zero if and only if at least one of a and
    //                 // b is zero.
    //                 if (a == 0.0 || b == 0.0) {
    //                     return a * b + c;
    //                 } else {
    //                     // The sign of a zero addend doesn't matter if
    //                     // the product is nonzero. The sign of a zero
    //                     // addend is not factored in the result if the
    //                     // exact product is nonzero but underflows to
    //                     // zero; see IEEE-754 2008 section 6.3 "The
    //                     // sign bit".
    //                     return product.doubleValue();
    //                 }
    //             } else {
    //                 return product.add(new BigDecimal(c)).doubleValue();
    //             }
    //         }
    //     }
    // }

    // /**
    //  * Returns the fused multiply add of the three arguments; that is,
    //  * returns the exact product of the first two arguments summed
    //  * with the third argument and then rounded once to the nearest
    //  * {@code float}.
    //  *
    //  * The rounding is done using the {@linkplain
    //  * java.math.RoundingMode#HALF_EVEN round to nearest even
    //  * rounding mode}.
    //  *
    //  * In contrast, if {@code a * b + c} is evaluated as a regular
    //  * floating-point expression, two rounding errors are involved,
    //  * the first for the multiply operation, the second for the
    //  * addition operation.
    //  *
    //  * <p>Special cases:
    //  * <ul>
    //  * <li> If any argument is NaN, the result is NaN.
    //  *
    //  * <li> If one of the first two arguments is infinite and the
    //  * other is zero, the result is NaN.
    //  *
    //  * <li> If the exact product of the first two arguments is infinite
    //  * (in other words, at least one of the arguments is infinite and
    //  * the other is neither zero nor NaN) and the third argument is an
    //  * infinity of the opposite sign, the result is NaN.
    //  *
    //  * </ul>
    //  *
    //  * <p>Note that {@code fma(a, 1.0f, c)} returns the same
    //  * result as ({@code a + c}).  However,
    //  * {@code fma(a, b, +0.0f)} does <em>not</em> always return the
    //  * same result as ({@code a * b}) since
    //  * {@code fma(-0.0f, +0.0f, +0.0f)} is {@code +0.0f} while
    //  * ({@code -0.0f * +0.0f}) is {@code -0.0f}; {@code fma(a, b, -0.0f)} is
    //  * equivalent to ({@code a * b}) however.
    //  *
    //  * @apiNote This method corresponds to the fusedMultiplyAdd
    //  * operation defined in IEEE 754-2008.
    //  *
    //  * @param a a value
    //  * @param b a value
    //  * @param c a value
    //  *
    //  * @return (<i>a</i>&nbsp;&times;&nbsp;<i>b</i>&nbsp;+&nbsp;<i>c</i>)
    //  * computed, as if with unlimited range and precision, and rounded
    //  * once to the nearest {@code float} value
    //  *
    //  */
    // @HotSpotIntrinsicCandidate
    // static float fma(float a, float b, float c) {
    //     /*
    //      *  Since the double format has more than twice the precision
    //      *  of the float format, the multiply of a * b is exact in
    //      *  double. The add of c to the product then incurs one
    //      *  rounding error. Since the double format moreover has more
    //      *  than (2p + 2) precision bits compared to the p bits of the
    //      *  float format, the two roundings of (a * b + c), first to
    //      *  the double format and then secondarily to the float format,
    //      *  are equivalent to rounding the intermediate result directly
    //      *  to the float format.
    //      *
    //      * In terms of strictfp vs default-fp concerns related to
    //      * overflow and underflow, since
    //      *
    //      * (Float.MAX_VALUE * Float.MAX_VALUE) << Double.MAX_VALUE
    //      * (Float.MIN_VALUE * Float.MIN_VALUE) >> Double.MIN_VALUE
    //      *
    //      * neither the multiply nor add will overflow or underflow in
    //      * double. Therefore, it is not necessary for this method to
    //      * be declared strictfp to have reproducible
    //      * behavior. However, it is necessary to explicitly store down
    //      * to a float variable to avoid returning a value in the float
    //      * extended value set.
    //      */
    //     float result = (float)(((double) a * (double) b ) + (double) c);
    //     return result;
    // }

    // /**
    //  * Returns the size of an ulp of the argument.  An ulp, unit in
    //  * the last place, 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
    //  */
    // static double ulp(double d) {
    //     int exp = getExponent(d);

    //     switch(exp) {
    //     case Double.MAX_EXPONENT + 1:       // NaN or infinity
    //         return Math.abs(d);

    //     case Double.MIN_EXPONENT - 1:       // zero or subnormal
    //         return Double.MIN_VALUE;

    //     default:
    //         assert exp <= Double.MAX_EXPONENT && exp >= Double.MIN_EXPONENT;

    //         // ulp(x) is usually 2^(SIGNIFICAND_WIDTH-1)*(2^ilogb(x))
    //         exp = exp - (DoubleConsts.SIGNIFICAND_WIDTH-1);
    //         if (exp >= Double.MIN_EXPONENT) {
    //             return powerOfTwoD(exp);
    //         }
    //         else {
    //             // return a subnormal result; left shift integer
    //             // representation of Double.MIN_VALUE appropriate
    //             // number of positions
    //             return Double.longBitsToDouble(1L <<
    //             (exp - (Double.MIN_EXPONENT - (DoubleConsts.SIGNIFICAND_WIDTH-1)) ));
    //         }
    //     }
    // }

    // /**
    //  * Returns the size of an ulp of the argument.  An ulp, unit in
    //  * the last place, 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
    //  */
    // static float ulp(float f) {
    //     int exp = getExponent(f);

    //     switch(exp) {
    //     case Float.MAX_EXPONENT+1:        // NaN or infinity
    //         return Math.abs(f);

    //     case Float.MIN_EXPONENT-1:        // zero or subnormal
    //         return Float.MIN_VALUE;

    //     default:
    //         assert exp <= Float.MAX_EXPONENT && exp >= Float.MIN_EXPONENT;

    //         // ulp(x) is usually 2^(SIGNIFICAND_WIDTH-1)*(2^ilogb(x))
    //         exp = exp - (FloatConsts.SIGNIFICAND_WIDTH-1);
    //         if (exp >= Float.MIN_EXPONENT) {
    //             return powerOfTwoF(exp);
    //         } else {
    //             // return a subnormal result; left shift integer
    //             // representation of FloatConsts.MIN_VALUE appropriate
    //             // number of positions
    //             return Float.intBitsToFloat(1 <<
    //             (exp - (Float.MIN_EXPONENT - (FloatConsts.SIGNIFICAND_WIDTH-1)) ));
    //         }
    //     }
    // }

    // /**
    //  * 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
    //  */
    // static double signum(double d) {
    //     return (d == 0.0 || Double.isNaN(d))?d:copySign(1.0, 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
    //  */
    // static float signum(float f) {
    //     return (f == 0.0f || Float.isNaN(f))?f:copySign(1.0f, f);
    // }

    // /**
    //  * 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>
    //  *
    //  * <p>The computed result must be within 2.5 ulps of the exact result.
    //  *
    //  * @param   x The number whose hyperbolic sine is to be returned.
    //  * @return  The hyperbolic sine of {@code x}.
    //  */
    // static double sinh(double x) {
    //     return StrictMath.sinh(x);
    // }

    // /**
    //  * 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>
    //  *
    //  * <p>The computed result must be within 2.5 ulps of the exact result.
    //  *
    //  * @param   x The number whose hyperbolic cosine is to be returned.
    //  * @return  The hyperbolic cosine of {@code x}.
    //  */
    // static double cosh(double x) {
    //     return StrictMath.cosh(x);
    // }

    // /**
    //  * 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>
    //  *
    //  * <p>The computed result must be within 2.5 ulps of the exact result.
    //  * The result of {@code tanh} for any finite input must have
    //  * an absolute value less than or equal to 1.  Note that once the
    //  * exact result of tanh is within 1/2 of an ulp of the limit value
    //  * of &plusmn;1, correctly signed &plusmn;{@code 1.0} should
    //  * be returned.
    //  *
    //  * @param   x The number whose hyperbolic tangent is to be returned.
    //  * @return  The hyperbolic tangent of {@code x}.
    //  */
    // static double tanh(double x) {
    //     return StrictMath.tanh(x);
    // }

    // /**
    //  * 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>
    //  *
    //  * <p>The computed result must be within 1 ulp of the exact
    //  * result.  If one parameter is held constant, the results must be
    //  * semi-monotonic in the other parameter.
    //  *
    //  * @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
    //  */
    // static double hypot(double x, double y) {
    //     return StrictMath.hypot(x, y);
    // }

    // /**
    //  * 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>
    //  *
    //  * <p>The computed result must be within 1 ulp of the exact result.
    //  * Results must be semi-monotonic.  The result of
    //  * {@code expm1} for any finite input must be greater than or
    //  * equal to {@code -1.0}.  Note that once the exact result of
    //  * <i>e</i><sup>{@code x}</sup>&nbsp;-&nbsp;1 is within 1/2
    //  * ulp of the limit value -1, {@code -1.0} should be
    //  * returned.
    //  *
    //  * @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.
    //  */
    // static double expm1(double x) {
    //     return StrictMath.expm1(x);
    // }

    // /**
    //  * 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>
    //  *
    //  * <p>The computed result must be within 1 ulp of the exact result.
    //  * Results must be semi-monotonic.
    //  *
    //  * @param   x   a value
    //  * @return the value ln({@code x}&nbsp;+&nbsp;1), the natural
    //  * log of {@code x}&nbsp;+&nbsp;1
    //  */
    // static double log1p(double x) {
    //     return StrictMath.log1p(x);
    // }

    // /**
    //  * Returns the first floating-point argument with the sign of the
    //  * second floating-point argument.  Note that unlike the {@link
    //  * StrictMath#copySign(double, double) StrictMath.copySign}
    //  * method, this method does not require NaN {@code sign}
    //  * arguments to be treated as positive values; implementations are
    //  * permitted to treat some NaN arguments as positive and other NaN
    //  * arguments as negative to allow greater performance.
    //  *
    //  * @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}.
    //  */
    // static double copySign(double magnitude, double sign) {
    //     return Double.longBitsToDouble((Double.doubleToRawLongBits(sign) &
    //                                     (DoubleConsts.SIGN_BIT_MASK)) |
    //                                    (Double.doubleToRawLongBits(magnitude) &
    //                                     (DoubleConsts.EXP_BIT_MASK |
    //                                      DoubleConsts.SIGNIF_BIT_MASK)));
    // }

    // /**
    //  * Returns the first floating-point argument with the sign of the
    //  * second floating-point argument.  Note that unlike the {@link
    //  * StrictMath#copySign(float, float) StrictMath.copySign}
    //  * method, this method does not require NaN {@code sign}
    //  * arguments to be treated as positive values; implementations are
    //  * permitted to treat some NaN arguments as positive and other NaN
    //  * arguments as negative to allow greater performance.
    //  *
    //  * @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}.
    //  */
    // static float copySign(float magnitude, float sign) {
    //     return Float.intBitsToFloat((Float.floatToRawIntBits(sign) &
    //                                  (FloatConsts.SIGN_BIT_MASK)) |
    //                                 (Float.floatToRawIntBits(magnitude) &
    //                                  (FloatConsts.EXP_BIT_MASK |
    //                                   FloatConsts.SIGNIF_BIT_MASK)));
    // }

    // /**
    //  * 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
    //  * @return the unbiased exponent of the argument
    //  */
    // static int getExponent(float f) {
    //     /*
    //      * Bitwise convert f to integer, mask out exponent bits, shift
    //      * to the right and then subtract out float's bias adjust to
    //      * get true exponent value
    //      */
    //     return ((Float.floatToRawIntBits(f) & FloatConsts.EXP_BIT_MASK) >>
    //             (FloatConsts.SIGNIFICAND_WIDTH - 1)) - FloatConsts.EXP_BIAS;
    // }

    // /**
    //  * 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
    //  * @return the unbiased exponent of the argument
    //  */
    // static int getExponent(double d) {
    //     /*
    //      * Bitwise convert d to long, mask out exponent bits, shift
    //      * to the right and then subtract out double's bias adjust to
    //      * get true exponent value.
    //      */
    //     return (int)(((Double.doubleToRawLongBits(d) & DoubleConsts.EXP_BIT_MASK) >>
    //                   (DoubleConsts.SIGNIFICAND_WIDTH - 1)) - DoubleConsts.EXP_BIAS);
    // }

    // /**
    //  * 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}.
    //  */
    // static double nextAfter(double start, double direction) {
    //     /*
    //      * The cases:
    //      *
    //      * nextAfter(+infinity, 0)  == MAX_VALUE
    //      * nextAfter(+infinity, +infinity)  == +infinity
    //      * nextAfter(-infinity, 0)  == -MAX_VALUE
    //      * nextAfter(-infinity, -infinity)  == -infinity
    //      *
    //      * are naturally handled without any additional testing
    //      */

    //     /*
    //      * IEEE 754 floating-point numbers are lexicographically
    //      * ordered if treated as signed-magnitude integers.
    //      * Since Java's integers are two's complement,
    //      * incrementing the two's complement representation of a
    //      * logically negative floating-point value *decrements*
    //      * the signed-magnitude representation. Therefore, when
    //      * the integer representation of a floating-point value
    //      * is negative, the adjustment to the representation is in
    //      * the opposite direction from what would initially be expected.
    //      */

    //     // Branch to descending case first as it is more costly than ascending
    //     // case due to start != 0.0d conditional.
    //     if (start > direction) { // descending
    //         if (start != 0.0d) {
    //             final long transducer = Double.doubleToRawLongBits(start);
    //             return Double.longBitsToDouble(transducer + ((transducer > 0L) ? -1L : 1L));
    //         } else { // start == 0.0d && direction < 0.0d
    //             return -Double.MIN_VALUE;
    //         }
    //     } else if (start < direction) { // ascending
    //         // Add +0.0 to get rid of a -0.0 (+0.0 + -0.0 => +0.0)
    //         // then bitwise convert start to integer.
    //         final long transducer = Double.doubleToRawLongBits(start + 0.0d);
    //         return Double.longBitsToDouble(transducer + ((transducer >= 0L) ? 1L : -1L));
    //     } else if (start == direction) {
    //         return direction;
    //     } else { // isNaN(start) || isNaN(direction)
    //         return 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}.
    //  */
    // static float nextAfter(float start, double direction) {
    //     /*
    //      * The cases:
    //      *
    //      * nextAfter(+infinity, 0)  == MAX_VALUE
    //      * nextAfter(+infinity, +infinity)  == +infinity
    //      * nextAfter(-infinity, 0)  == -MAX_VALUE
    //      * nextAfter(-infinity, -infinity)  == -infinity
    //      *
    //      * are naturally handled without any additional testing
    //      */

    //     /*
    //      * IEEE 754 floating-point numbers are lexicographically
    //      * ordered if treated as signed-magnitude integers.
    //      * Since Java's integers are two's complement,
    //      * incrementing the two's complement representation of a
    //      * logically negative floating-point value *decrements*
    //      * the signed-magnitude representation. Therefore, when
    //      * the integer representation of a floating-point value
    //      * is negative, the adjustment to the representation is in
    //      * the opposite direction from what would initially be expected.
    //      */

    //     // Branch to descending case first as it is more costly than ascending
    //     // case due to start != 0.0f conditional.
    //     if (start > direction) { // descending
    //         if (start != 0.0f) {
    //             final int transducer = Float.floatToRawIntBits(start);
    //             return Float.intBitsToFloat(transducer + ((transducer > 0) ? -1 : 1));
    //         } else { // start == 0.0f && direction < 0.0f
    //             return -Float.MIN_VALUE;
    //         }
    //     } else if (start < direction) { // ascending
    //         // Add +0.0 to get rid of a -0.0 (+0.0 + -0.0 => +0.0)
    //         // then bitwise convert start to integer.
    //         final int transducer = Float.floatToRawIntBits(start + 0.0f);
    //         return Float.intBitsToFloat(transducer + ((transducer >= 0) ? 1 : -1));
    //     } else if (start == direction) {
    //         return (float)direction;
    //     } else { // isNaN(start) || isNaN(direction)
    //         return start + (float)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.
    //  */
    // static double nextUp(double d) {
    //     // Use a single conditional and handle the likely cases first.
    //     if (d < Double.POSITIVE_INFINITY) {
    //         // Add +0.0 to get rid of a -0.0 (+0.0 + -0.0 => +0.0).
    //         final long transducer = Double.doubleToRawLongBits(d + 0.0D);
    //         return Double.longBitsToDouble(transducer + ((transducer >= 0L) ? 1L : -1L));
    //     } else { // d is NaN or +Infinity
    //         return 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.
    //  */
    // static float nextUp(float f) {
    //     // Use a single conditional and handle the likely cases first.
    //     if (f < Float.POSITIVE_INFINITY) {
    //         // Add +0.0 to get rid of a -0.0 (+0.0 + -0.0 => +0.0).
    //         final int transducer = Float.floatToRawIntBits(f + 0.0F);
    //         return Float.intBitsToFloat(transducer + ((transducer >= 0) ? 1 : -1));
    //     } else { // f is NaN or +Infinity
    //         return f;
    //     }
    // }

    // /**
    //  * Returns the floating-point value adjacent to {@code d} in
    //  * the direction of negative infinity.  This method is
    //  * semantically equivalent to {@code nextAfter(d,
    //  * Double.NEGATIVE_INFINITY)}; however, a
    //  * {@code nextDown} 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 negative infinity, the result is
    //  * negative infinity.
    //  *
    //  * <li> If the argument is zero, the result is
    //  * {@code -Double.MIN_VALUE}
    //  *
    //  * </ul>
    //  *
    //  * @param d  starting floating-point value
    //  * @return The adjacent floating-point value closer to negative
    //  * infinity.
    //  */
    // static double nextDown(double d) {
    //     if (Double.isNaN(d) || d == Double.NEGATIVE_INFINITY)
    //         return d;
    //     else {
    //         if (d == 0.0)
    //             return -Double.MIN_VALUE;
    //         else
    //             return Double.longBitsToDouble(Double.doubleToRawLongBits(d) +
    //                                            ((d > 0.0d)?-1L:+1L));
    //     }
    // }

    // /**
    //  * Returns the floating-point value adjacent to {@code f} in
    //  * the direction of negative infinity.  This method is
    //  * semantically equivalent to {@code nextAfter(f,
    //  * Float.NEGATIVE_INFINITY)}; however, a
    //  * {@code nextDown} 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 negative infinity, the result is
    //  * negative infinity.
    //  *
    //  * <li> If the argument is zero, the result is
    //  * {@code -Float.MIN_VALUE}
    //  *
    //  * </ul>
    //  *
    //  * @param f  starting floating-point value
    //  * @return The adjacent floating-point value closer to negative
    //  * infinity.
    //  */
    // static float nextDown(float f) {
    //     if (Float.isNaN(f) || f == Float.NEGATIVE_INFINITY)
    //         return f;
    //     else {
    //         if (f == 0.0f)
    //             return -Float.MIN_VALUE;
    //         else
    //             return Float.intBitsToFloat(Float.floatToRawIntBits(f) +
    //                                         ((f > 0.0f)?-1:+1));
    //     }
    // }

    // /**
    //  * Returns {@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>
    //  */
    // static double scalb(double d, int scaleFactor) {
    //     /*
    //      * This method does not need to be declared strictfp to
    //      * compute the same correct result on all platforms.  When
    //      * scaling up, it does not matter what order the
    //      * multiply-store operations are done; the result will be
    //      * finite or overflow regardless of the operation ordering.
    //      * However, to get the correct result when scaling down, a
    //      * particular ordering must be used.
    //      *
    //      * When scaling down, the multiply-store operations are
    //      * sequenced so that it is not possible for two consecutive
    //      * multiply-stores to return subnormal results.  If one
    //      * multiply-store result is subnormal, the next multiply will
    //      * round it away to zero.  This is done by first multiplying
    //      * by 2 ^ (scaleFactor % n) and then multiplying several
    //      * times by 2^n as needed where n is the exponent of number
    //      * that is a covenient power of two.  In this way, at most one
    //      * real rounding error occurs.  If the double value set is
    //      * being used exclusively, the rounding will occur on a
    //      * multiply.  If the double-extended-exponent value set is
    //      * being used, the products will (perhaps) be exact but the
    //      * stores to d are guaranteed to round to the double value
    //      * set.
    //      *
    //      * It is _not_ a valid implementation to first multiply d by
    //      * 2^MIN_EXPONENT and then by 2 ^ (scaleFactor %
    //      * MIN_EXPONENT) since even in a strictfp program double
    //      * rounding on underflow could occur; e.g. if the scaleFactor
    //      * argument was (MIN_EXPONENT - n) and the exponent of d was a
    //      * little less than -(MIN_EXPONENT - n), meaning the final
    //      * result would be subnormal.
    //      *
    //      * Since exact reproducibility of this method can be achieved
    //      * without any undue performance burden, there is no
    //      * compelling reason to allow double rounding on underflow in
    //      * scalb.
    //      */

    //     // magnitude of a power of two so large that scaling a finite
    //     // nonzero value by it would be guaranteed to over or
    //     // underflow; due to rounding, scaling down takes an
    //     // additional power of two which is reflected here
    //     final int MAX_SCALE = Double.MAX_EXPONENT + -Double.MIN_EXPONENT +
    //                           DoubleConsts.SIGNIFICAND_WIDTH + 1;
    //     int exp_adjust = 0;
    //     int scale_increment = 0;
    //     double exp_delta = Double.NaN;

    //     // Make sure scaling factor is in a reasonable range

    //     if(scaleFactor < 0) {
    //         scaleFactor = Math.max(scaleFactor, -MAX_SCALE);
    //         scale_increment = -512;
    //         exp_delta = twoToTheDoubleScaleDown;
    //     }
    //     else {
    //         scaleFactor = Math.min(scaleFactor, MAX_SCALE);
    //         scale_increment = 512;
    //         exp_delta = twoToTheDoubleScaleUp;
    //     }

    //     // Calculate (scaleFactor % +/-512), 512 = 2^9, using
    //     // technique from "Hacker's Delight" section 10-2.
    //     int t = (scaleFactor >> 9-1) >>> 32 - 9;
    //     exp_adjust = ((scaleFactor + t) & (512 -1)) - t;

    //     d *= powerOfTwoD(exp_adjust);
    //     scaleFactor -= exp_adjust;

    //     while(scaleFactor != 0) {
    //         d *= exp_delta;
    //         scaleFactor -= scale_increment;
    //     }
    //     return d;
    // }

    // /**
    //  * Returns {@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>
    //  */
    // static float scalb(float f, int scaleFactor) {
    //     // magnitude of a power of two so large that scaling a finite
    //     // nonzero value by it would be guaranteed to over or
    //     // underflow; due to rounding, scaling down takes an
    //     // additional power of two which is reflected here
    //     final int MAX_SCALE = Float.MAX_EXPONENT + -Float.MIN_EXPONENT +
    //                           FloatConsts.SIGNIFICAND_WIDTH + 1;

    //     // Make sure scaling factor is in a reasonable range
    //     scaleFactor = Math.max(Math.min(scaleFactor, MAX_SCALE), -MAX_SCALE);

    //     /*
    //      * Since + MAX_SCALE for float fits well within the double
    //      * exponent range and + float -> double conversion is exact
    //      * the multiplication below will be exact. Therefore, the
    //      * rounding that occurs when the double product is cast to
    //      * float will be the correctly rounded float result.  Since
    //      * all operations other than the final multiply will be exact,
    //      * it is not necessary to declare this method strictfp.
    //      */
    //     return (float)((double)f*powerOfTwoD(scaleFactor));
    // }

    // // Constants used in scalb
    // static double twoToTheDoubleScaleUp = powerOfTwoD(512);
    // static double twoToTheDoubleScaleDown = powerOfTwoD(-512);

    // /**
    //  * Returns a floating-point power of two in the normal range.
    //  */
    // static double powerOfTwoD(int n) {
    //     assert(n >= Double.MIN_EXPONENT && n <= Double.MAX_EXPONENT);
    //     return Double.longBitsToDouble((((long)n + (long)DoubleConsts.EXP_BIAS) <<
    //                                     (DoubleConsts.SIGNIFICAND_WIDTH-1))
    //                                    & DoubleConsts.EXP_BIT_MASK);
    // }

    // /**
    //  * Returns a floating-point power of two in the normal range.
    //  */
    // static float powerOfTwoF(int n) {
    //     assert(n >= Float.MIN_EXPONENT && n <= Float.MAX_EXPONENT);
    //     return Float.intBitsToFloat(((n + FloatConsts.EXP_BIAS) <<
    //                                  (FloatConsts.SIGNIFICAND_WIDTH-1))
    //                                 & FloatConsts.EXP_BIT_MASK);
    // }
}