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

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package java.lang;

import java.util.Random;

import sun.misc.DoubleConsts;

import jdk.internal.HotSpotIntrinsicCandidate;

/**

 * The class {@code StrictMath} contains methods for performing basic

 * numeric operations such as the elementary exponential, logarithm,

 * square root, and trigonometric functions.

 *

 * <p>To help ensure portability of Java programs, the definitions of

 * some of the numeric functions in this package require that they

 * produce the same results as certain published algorithms. These

 * algorithms are available from the well-known network library

 * {@code netlib} as the package "Freely Distributable Math

 * Library," <a

 * href="ftp://ftp.netlib.org/fdlibm.tar">{@code fdlibm}</a>. These

 * algorithms, which are written in the C programming language, are

 * then to be understood as executed with all floating-point

 * operations following the rules of Java floating-point arithmetic.

 *

 * <p>The Java math library is defined with respect to

 * {@code fdlibm} version 5.3. Where {@code fdlibm} provides

 * more than one definition for a function (such as

 * {@code acos}), use the "IEEE 754 core function" version

 * (residing in a file whose name begins with the letter

 * {@code e}).  The methods which require {@code fdlibm}

 * semantics are {@code sin}, {@code cos}, {@code tan},

 * {@code asin}, {@code acos}, {@code atan},

 * {@code exp}, {@code log}, {@code log10},

 * {@code cbrt}, {@code atan2}, {@code pow},

 * {@code sinh}, {@code cosh}, {@code tanh},

 * {@code hypot}, {@code expm1}, and {@code log1p}.

 *

 * <p>

 * The platform uses signed two's complement integer arithmetic with

 * int and long primitive types.  The developer should choose

 * the primitive type to ensure that arithmetic operations consistently

 * produce correct results, which in some cases means the operations

 * will not overflow the range of values of the computation.

 * The best practice is to choose the primitive type and algorithm to avoid

 * overflow. In cases where the size is {@code int} or {@code long} and

 * overflow errors need to be detected, the methods {@code addExact},

 * {@code subtractExact}, {@code multiplyExact}, and {@code toIntExact}

 * throw an {@code ArithmeticException} when the results overflow.

 * For other arithmetic operations such as divide, absolute value,

 * increment, decrement, and negation overflow occurs only with

 * a specific minimum or maximum value and should be checked against

 * the minimum or maximum as appropriate.

 *

 * @author  unascribed

 * @author  Joseph D. Darcy

 * @since   1.3

 */

public final class StrictMath {

    /**

     * Don't let anyone instantiate this class.

     */

    private StrictMath() {}

    /**

     * The {@code double} value that is closer than any other to

     * <i>e</i>, the base of the natural logarithms.

     */

    public static final double E = 2.7182818284590452354;

    /**

     * The {@code double} value that is closer than any other to

     * <i>pi</i>, the ratio of the circumference of a circle to its

     * diameter.

     */

    public static final double PI = 3.14159265358979323846;

    /**

     * Constant by which to multiply an angular value in degrees to obtain an

     * angular value in radians.

     */

    private static final double DEGREES_TO_RADIANS = 0.017453292519943295;

    /**

     * Constant by which to multiply an angular value in radians to obtain an

     * angular value in degrees.

     */

    private static final 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>

     *

     * @param   a   an angle, in radians.

     * @return  the sine of the argument.

     */

    public static native double sin(double a);

    /**

     * Returns the trigonometric cosine of an angle. Special cases:

     * <ul><li>If the argument is NaN or an infinity, then the

     * result is NaN.</ul>

     *

     * @param   a   an angle, in radians.

     * @return  the cosine of the argument.

     */

    public static native double cos(double a);

    /**

     * Returns the trigonometric tangent of an angle. Special cases:

     * <ul><li>If the argument is NaN or an infinity, then the result

     * is NaN.

     * <li>If the argument is zero, then the result is a zero with the

     * same sign as the argument.</ul>

     *

     * @param   a   an angle, in radians.

     * @return  the tangent of the argument.

     */

    public static native double tan(double a);

    /**

     * Returns the arc sine of a value; the returned angle is in the

     * range -<i>pi</i>/2 through <i>pi</i>/2.  Special cases:

     * <ul><li>If the argument is NaN or its absolute value is greater

     * than 1, then the result is NaN.

     * <li>If the argument is zero, then the result is a zero with the

     * same sign as the argument.</ul>

     *

     * @param   a   the value whose arc sine is to be returned.

     * @return  the arc sine of the argument.

     */

    public static native double asin(double a);

    /**

     * Returns the arc cosine of a value; the returned angle is in the

     * range 0.0 through <i>pi</i>.  Special case:

     * <ul><li>If the argument is NaN or its absolute value is greater

     * than 1, then the result is NaN.</ul>

     *

     * @param   a   the value whose arc cosine is to be returned.

     * @return  the arc cosine of the argument.

     */

    public static native double acos(double a);

    /**

     * Returns the arc tangent of a value; the returned angle is in the

     * range -<i>pi</i>/2 through <i>pi</i>/2.  Special cases:

     * <ul><li>If the argument is NaN, then the result is NaN.

     * <li>If the argument is zero, then the result is a zero with the

     * same sign as the argument.</ul>

     *

     * @param   a   the value whose arc tangent is to be returned.

     * @return  the arc tangent of the argument.

     */

    public static native double atan(double a);

    /**

     * Converts an angle measured in degrees to an approximately

     * equivalent angle measured in radians.  The conversion from

     * degrees to radians is generally inexact.

     *

     * @param   angdeg   an angle, in degrees

     * @return  the measurement of the angle {@code angdeg}

     *          in radians.

     */

    public static strictfp double toRadians(double angdeg) {

        // Do not delegate to Math.toRadians(angdeg) because

        // this method has the strictfp modifier.

        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.

     */

    public static strictfp double toDegrees(double angrad) {

        // Do not delegate to Math.toDegrees(angrad) because

        // this method has the strictfp modifier.

        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>

     *

     * @param   a   the exponent to raise <i>e</i> to.

     * @return  the value <i>e</i><sup>{@code a}</sup>,

     *          where <i>e</i> is the base of the natural logarithms.

     */

    public static native double exp(double a);

    /**

     * Returns the natural logarithm (base <i>e</i>) of a {@code double}

     * value. Special cases:

     * <ul><li>If the argument is NaN or less than zero, then the result

     * is NaN.

     * <li>If the argument is positive infinity, then the result is

     * positive infinity.

     * <li>If the argument is positive zero or negative zero, then the

     * result is negative infinity.</ul>

     *

     * @param   a   a value

     * @return  the value ln {@code a}, the natural logarithm of

     *          {@code a}.

     */

    public static native double log(double a);

    /**

     * Returns the base 10 logarithm of a {@code double} value.

     * Special cases:

     *

     * <ul><li>If the argument is NaN or less than zero, then the result

     * is NaN.

     * <li>If the argument is positive infinity, then the result is

     * positive infinity.

     * <li>If the argument is positive zero or negative zero, then the

     * result is negative infinity.

     * <li> If the argument is equal to 10<sup><i>n</i></sup> for

     * integer <i>n</i>, then the result is <i>n</i>.

     * </ul>

     *

     * @param   a   a value

     * @return  the base 10 logarithm of  {@code a}.

     * @since 1.5

     */

    public static native double log10(double a);

    /**

     * 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}.

     */

    @HotSpotIntrinsicCandidate

    public static native double sqrt(double a);

    /**

     * Returns the cube root of a {@code double} value.  For

     * positive finite {@code x}, {@code cbrt(-x) ==

     * -cbrt(x)}; that is, the cube root of a negative value is

     * the negative of the cube root of that value's magnitude.

     * Special cases:

     *

     * <ul>

     *

     * <li>If the argument is NaN, then the result is NaN.

     *

     * <li>If the argument is infinite, then the result is an infinity

     * with the same sign as the argument.

     *

     * <li>If the argument is zero, then the result is a zero with the

     * same sign as the argument.

     *

     * </ul>

     *

     * @param   a   a value.

     * @return  the cube root of {@code a}.

     * @since 1.5

     */

    public static native double cbrt(double 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}.

     */

    public static native double IEEEremainder(double f1, double f2);

    /**

     * Returns the smallest (closest to negative infinity)

     * {@code double} value that is greater than or equal to the

     * argument and is equal to a mathematical integer. Special cases:

     * <ul><li>If the argument value is already equal to a

     * mathematical integer, then the result is the same as the

     * argument.  <li>If the argument is NaN or an infinity or

     * positive zero or negative zero, then the result is the same as

     * the argument.  <li>If the argument value is less than zero but

     * greater than -1.0, then the result is negative zero.</ul> Note

     * that the value of {@code StrictMath.ceil(x)} is exactly the

     * value of {@code -StrictMath.floor(-x)}.

     *

     * @param   a   a value.

     * @return  the smallest (closest to negative infinity)

     *          floating-point value that is greater than or equal to

     *          the argument and is equal to a mathematical integer.

     */

    public static double ceil(double a) {

        return floorOrCeil(a, -0.0, 1.0, 1.0);

    }

    /**

     * Returns the largest (closest to positive infinity)

     * {@code double} value that is less than or equal to the

     * argument and is equal to a mathematical integer. Special cases:

     * <ul><li>If the argument value is already equal to a

     * mathematical integer, then the result is the same as the

     * argument.  <li>If the argument is NaN or an infinity or

     * positive zero or negative zero, then the result is the same as

     * the argument.</ul>

     *

     * @param   a   a value.

     * @return  the largest (closest to positive infinity)

     *          floating-point value that less than or equal to the argument

     *          and is equal to a mathematical integer.

     */

    public static double floor(double a) {

        return floorOrCeil(a, -1.0, 0.0, -1.0);

    }

    /**

     * Internal method to share logic between floor and ceil.

     *

     * @param a the value to be floored or ceiled

     * @param negativeBoundary result for values in (-1, 0)

     * @param positiveBoundary result for values in (0, 1)

     * @param increment value to add when the argument is non-integral

     */

    private static double floorOrCeil(double a,

                                      double negativeBoundary,

                                      double positiveBoundary,

                                      double sign) {

        int exponent = Math.getExponent(a);

        if (exponent < 0) {

            /*

             * Absolute value of argument is less than 1.

             * floorOrceil(-0.0) => -0.0

             * floorOrceil(+0.0) => +0.0

             */

            return ((a == 0.0) ? a :

                    ( (a < 0.0) ?  negativeBoundary : positiveBoundary) );

        } else if (exponent >= 52) {

            /*

             * Infinity, NaN, or a value so large it must be integral.

             */

            return a;

        }

        // Else the argument is either an integral value already XOR it

        // has to be rounded to one.

        assert exponent >= 0 && exponent <= 51;

        long doppel = Double.doubleToRawLongBits(a);

        long mask   = DoubleConsts.SIGNIF_BIT_MASK >> exponent;

        if ( (mask & doppel) == 0L )

            return a; // integral value

        else {

            double result = Double.longBitsToDouble(doppel & (~mask));

            if (sign*a > 0.0)

                result = result + sign;

            return result;

        }

    }

    /**

     * Returns the {@code double} value that is closest in value

     * to the argument and is equal to a mathematical integer. If two

     * {@code double} values that are mathematical integers are

     * equally close to the value of the argument, the result is the

     * integer value that is even. Special cases:

     * <ul><li>If the argument value is already equal to a mathematical

     * integer, then the result is the same as the argument.

     * <li>If the argument is NaN or an infinity or positive zero or negative

     * zero, then the result is the same as the argument.</ul>

     *

     * @param   a   a value.

     * @return  the closest floating-point value to {@code a} that is

     *          equal to a mathematical integer.

     * @author Joseph D. Darcy

     */

    public static double rint(double a) {

        /*

         * If the absolute value of a is not less than 2^52, it

         * is either a finite integer (the double format does not have

         * enough significand bits for a number that large to have any

         * fractional portion), an infinity, or a NaN.  In any of

         * these cases, rint of the argument is the argument.

         *

         * Otherwise, the sum (twoToThe52 + a ) will properly round

         * away any fractional portion of a since ulp(twoToThe52) ==

         * 1.0; subtracting out twoToThe52 from this sum will then be

         * exact and leave the rounded integer portion of a.

         *

         * This method does *not* need to be declared strictfp to get

         * fully reproducible results.  Whether or not a method is

         * declared strictfp can only make a difference in the

         * returned result if some operation would overflow or

         * underflow with strictfp semantics.  The operation

         * (twoToThe52 + a ) cannot overflow since large values of a

         * are screened out; the add cannot underflow since twoToThe52

         * is too large.  The subtraction ((twoToThe52 + a ) -

         * twoToThe52) will be exact as discussed above and thus

         * cannot overflow or meaningfully underflow.  Finally, the

         * last multiply in the return statement is by plus or minus

         * 1.0, which is exact too.

         */

        double twoToThe52 = (double)(1L << 52); // 2^52

        double sign = Math.copySign(1.0, a); // preserve sign info

        a = Math.abs(a);

        if (a < twoToThe52) { // E_min <= ilogb(a) <= 51

            a = ((twoToThe52 + a ) - twoToThe52);

        }

        return sign * a; // restore original sign

    }

    /**

     * Returns the angle <i>theta</i> from the conversion of rectangular

     * coordinates ({@code x}, {@code y}) to polar

     * coordinates (r,&nbsp;<i>theta</i>).

     * This method computes the phase <i>theta</i> by computing an arc tangent

     * of {@code y/x} in the range of -<i>pi</i> to <i>pi</i>. Special

     * cases:

     * <ul><li>If either argument is NaN, then the result is NaN.

     * <li>If the first argument is positive zero and the second argument

     * is positive, or the first argument is positive and finite and the

     * second argument is positive infinity, then the result is positive

     * zero.

     * <li>If the first argument is negative zero and the second argument

     * is positive, or the first argument is negative and finite and the

     * second argument is positive infinity, then the result is negative zero.

     * <li>If the first argument is positive zero and the second argument

     * is negative, or the first argument is positive and finite and the

     * second argument is negative infinity, then the result is the

     * {@code double} value closest to <i>pi</i>.

     * <li>If the first argument is negative zero and the second argument

     * is negative, or the first argument is negative and finite and the

     * second argument is negative infinity, then the result is the

     * {@code double} value closest to -<i>pi</i>.

     * <li>If the first argument is positive and the second argument is

     * positive zero or negative zero, or the first argument is positive

     * infinity and the second argument is finite, then the result is the

     * {@code double} value closest to <i>pi</i>/2.

     * <li>If the first argument is negative and the second argument is

     * positive zero or negative zero, or the first argument is negative

     * infinity and the second argument is finite, then the result is the

     * {@code double} value closest to -<i>pi</i>/2.

     * <li>If both arguments are positive infinity, then the result is the

     * {@code double} value closest to <i>pi</i>/4.

     * <li>If the first argument is positive infinity and the second argument

     * is negative infinity, then the result is the {@code double}

     * value closest to 3*<i>pi</i>/4.

     * <li>If the first argument is negative infinity and the second argument

     * is positive infinity, then the result is the {@code double} value

     * closest to -<i>pi</i>/4.

     * <li>If both arguments are negative infinity, then the result is the

     * {@code double} value closest to -3*<i>pi</i>/4.</ul>

     *

     * @param   y   the ordinate coordinate

     * @param   x   the abscissa coordinate

     * @return  the <i>theta</i> component of the point

     *          (<i>r</i>,&nbsp;<i>theta</i>)