https://openjdk.java.net/ 
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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 jdk.internal.math.DoubleConsts;
import jdk.internal.HotSpotIntrinsicCandidate;


The class StrictMath contains methods for performing basic numeric operations such as the elementary exponential, logarithm, square root, and trigonometric functions. 
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 netlib as the package "Freely Distributable Math Library," fdlibm. 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.

The Java math library is defined with respect to fdlibm version 5.3. Where fdlibm provides more than one definition for a function (such as acos), use the "IEEE 754 core function" version (residing in a file whose name begins with the letter e). The methods which require fdlibm semantics are sin, cos, tan, asin, acos, atan, exp, log, log10, cbrt, atan2, pow, sinh, cosh, tanh, hypot, expm1, and log1p. 
 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 int or long and overflow errors need to be detected, the methods addExact, subtractExact, multiplyExact, and toIntExact throw an ArithmeticException when the results overflow. For other arithmetic operations such as divide, absolute value, increment by one, decrement by one, 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,  Joseph D. Darcy
Since:  1.3
/**
 * 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 by one, decrement by one, 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.

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

    
The double value that is closer than any other to e, the base of the natural logarithms.

/**
     * 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 double value that is closer than any other to pi, the ratio of the circumference of a circle to its
diameter.

/**
     * 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.

/**
     * 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.

/**
     * 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:

  • If the argument is NaN or an infinity, then the
result is NaN.

  • If the argument is zero, then the result is a zero with the
same sign as the argument.


Params:
  • a –   an angle, in radians.
Returns: the sine of the argument.
/**
     * 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:

  • If the argument is NaN or an infinity, then the
result is NaN.


Params:
  • a –   an angle, in radians.
Returns: the cosine of the argument.
/**
     * 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:

  • If the argument is NaN or an infinity, then the result
is NaN.

  • If the argument is zero, then the result is a zero with the
same sign as the argument.


Params:
  • a –   an angle, in radians.
Returns: the tangent of the argument.
/**
     * 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 -pi/2 through pi/2.  Special cases:

  • If the argument is NaN or its absolute value is greater
than 1, then the result is NaN.

  • If the argument is zero, then the result is a zero with the
same sign as the argument.


Params:
  • a –   the value whose arc sine is to be returned.
Returns: the arc sine of the argument.
/**
     * 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 pi.  Special case:

  • If the argument is NaN or its absolute value is greater
than 1, then the result is NaN.


Params:
  • a –   the value whose arc cosine is to be returned.
Returns: the arc cosine of the argument.
/**
     * 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 -pi/2 through pi/2.  Special cases:

  • If the argument is NaN, then the result is NaN.

  • If the argument is zero, then the result is a zero with the
same sign as the argument.


Params:
  • a –   the value whose arc tangent is to be returned.
Returns: the arc tangent of the argument.
/**
     * 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.

Params:
  • angdeg –   an angle, in degrees
Returns: the measurement of the angle angdeg in radians.
/**
     * 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
not expect cos(toRadians(90.0)) to exactly equal 0.0. 
Params:
  • angrad –   an angle, in radians
Returns: the measurement of the angle angrad in degrees.
/**
     * 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 e raised to the power of a double value. Special cases: 
  • If the argument is NaN, the result is NaN.

  • If the argument is positive infinity, then the result is
positive infinity.

  • If the argument is negative infinity, then the result is
positive zero.


Params:
  • a –   the exponent to raise e to.
Returns: the value ea,
         where e is the base of the natural logarithms.
/**
     * Returns Euler's number <i>e</i> raised to the power of a
     * {@code double} value. Special cases:
     * <ul><li>If the argument is NaN, the result is NaN.
     * <li>If the argument is positive infinity, then the result is
     * positive infinity.
     * <li>If the argument is negative infinity, then the result is
     * positive zero.</ul>
     *
     * @param   a   the exponent to raise <i>e</i> to.
     * @return  the value <i>e</i><sup>{@code a}</sup>,
     *          where <i>e</i> is the base of the natural logarithms.
     */
    public static double exp(double a) {
        return FdLibm.Exp.compute(a);
    }

    
Returns the natural logarithm (base e) of a double value. Special cases: 
  • If the argument is NaN or less than zero, then the result
is NaN.

  • If the argument is positive infinity, then the result is
positive infinity.

  • If the argument is positive zero or negative zero, then the
result is negative infinity.


Params:
  • a –   a value
Returns: the value ln a, the natural logarithm of 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&nbsp;{@code a}, the natural logarithm of
     *          {@code a}.
     */
    public static native double log(double a);

    
Returns the base 10 logarithm of a double value. Special cases: 
  • If the argument is NaN or less than zero, then the result
is NaN.

  • If the argument is positive infinity, then the result is
positive infinity.

  • If the argument is positive zero or negative zero, then the
result is negative infinity.

  •  If the argument is equal to 10n for
integer n, then the result is n.



Params:
  • a –   a value
Returns: the base 10 logarithm of a.
Since:1.5
/**
     * 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 double value. Special cases: 
  • If the argument is NaN or less than zero, then the result
is NaN.

  • If the argument is positive infinity, then the result is positive
infinity.

  • If the argument is positive zero or negative zero, then the
result is the same as the argument.
 Otherwise, the result is the double value closest to the true mathematical square root of the argument value. 
Params:
  • a –   a value.
Returns: the positive square root of 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 double value. For positive finite x, 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: 
    

  • If the argument is NaN, then the result is NaN.

  • If the argument is infinite, then the result is an infinity
with the same sign as the argument.

  • If the argument is zero, then the result is a zero with the
same sign as the argument.



Params:
  • a –   a value.
Returns: the cube root of a.
Since:1.5
/**
     * 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 double cbrt(double a) {
        return FdLibm.Cbrt.compute(a);
    }

    
Computes the remainder operation on two arguments as prescribed
by the IEEE 754 standard.
The remainder value is mathematically equal to
f1 - f2 × n,
where n is the mathematical integer closest to the exact mathematical value of the quotient f1/f2, and if two mathematical integers are equally close to f1/f2, then n 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:

  • 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.

  • If the first argument is finite and the second argument is
infinite, then the result is the same as the first argument.


Params:
  • f1 –   the dividend.
  • f2 –   the divisor.
Returns: the remainder when f1 is divided by f2.
/**
     * 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) double value that is greater than or equal to the argument and is equal to a mathematical integer. Special cases: 
  • If the argument value is already equal to a
mathematical integer, then the result is the same as the
argument.  
  • If the argument is NaN or an infinity or
positive zero or negative zero, then the result is the same as
the argument.  
  • If the argument value is less than zero but
greater than -1.0, then the result is negative zero.
 Note that the value of StrictMath.ceil(x) is exactly the value of -StrictMath.floor(-x). 
Params:
  • a –   a value.
Returns: 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.
/**
     * 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) double value that is less than or equal to the argument and is equal to a mathematical integer. Special cases: 
  • If the argument value is already equal to a
mathematical integer, then the result is the same as the
argument.  
  • If the argument is NaN or an infinity or
positive zero or negative zero, then the result is the same as
the argument.


Params:
  • a –   a value.
Returns: the largest (closest to positive infinity)
         floating-point value that less than or equal to the argument
         and is equal to a mathematical integer.
/**
     * 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.

Params:
  • a – the value to be floored or ceiled
  • negativeBoundary – result for values in (-1, 0)
  • positiveBoundary – result for values in (0, 1)
  • increment – value to add when the argument is non-integral
/**
     * 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 double value that is closest in value to the argument and is equal to a mathematical integer. If two 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: 
  • If the argument value is already equal to a mathematical
integer, then the result is the same as the argument.

  • If the argument is NaN or an infinity or positive zero or negative
zero, then the result is the same as the argument.


Author:Joseph D. Darcy
Params:
  • a –   a value.
Returns: the closest floating-point value to a that is equal to a mathematical integer.
/**
     * 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 theta from the conversion of rectangular coordinates (x, y) to polar coordinates (r, theta).
This method computes the phase theta by computing an arc tangent of y/x in the range of -pi to pi. Special
cases:

  • If either argument is NaN, then the result is NaN.

  • 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.

  • 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.

  • 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 double value closest to pi.

  • 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 double value closest to -pi.

  • 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 double value closest to pi/2.

  • 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 double value closest to -pi/2.

  • If both arguments are positive infinity, then the result is the double value closest to pi/4.

  • If the first argument is positive infinity and the second argument is negative infinity, then the result is the double value closest to 3*pi/4.

  • If the first argument is negative infinity and the second argument is positive infinity, then the result is the double value closest to -pi/4.

  • If both arguments are negative infinity, then the result is the double value closest to -3*pi/4.


Params:
  • y –   the ordinate coordinate
  • x –   the abscissa coordinate
Returns: the theta component of the point
         (r, theta)
         in polar coordinates that corresponds to the point
         (x, y) in Cartesian coordinates.
/**
     * Returns the angle <i>theta</i> from the conversion of rectangular
     * coordinates ({@code x},&nbsp;{@code y}) to polar
     * coordinates (r,&nbsp;<i>theta</i>).
     * This method computes the phase <i>theta</i> by computing an arc tangent
     * of {@code y/x} in the range of -<i>pi</i> to <i>pi</i>. Special
     * cases:
     * <ul><li>If either argument is NaN, then the result is NaN.
     * <li>If the first argument is positive zero and the second argument
     * is positive, or the first argument is positive and finite and the
     * second argument is positive infinity, then the result is positive
     * zero.
     * <li>If the first argument is negative zero and the second argument
     * is positive, or the first argument is negative and finite and the
     * second argument is positive infinity, then the result is negative zero.
     * <li>If the first argument is positive zero and the second argument
     * is negative, or the first argument is positive and finite and the
     * second argument is negative infinity, then the result is the
     * {@code double} value closest to <i>pi</i>.
     * <li>If the first argument is negative zero and the second argument
     * is negative, or the first argument is negative and finite and the
     * second argument is negative infinity, then the result is the
     * {@code double} value closest to -<i>pi</i>.
     * <li>If the first argument is positive and the second argument is
     * positive zero or negative zero, or the first argument is positive
     * infinity and the second argument is finite, then the result is the
     * {@code double} value closest to <i>pi</i>/2.
     * <li>If the first argument is negative and the second argument is
     * positive zero or negative zero, or the first argument is negative
     * infinity and the second argument is finite, then the result is the
     * {@code double} value closest to -<i>pi</i>/2.
     * <li>If both arguments are positive infinity, then the result is the
     * {@code double} value closest to <i>pi</i>/4.
     * <li>If the first argument is positive infinity and the second argument
     * is negative infinity, then the result is the {@code double}
     * value closest to 3*<i>pi</i>/4.
     * <li>If the first argument is negative infinity and the second argument
     * is positive infinity, then the result is the {@code double} value
     * closest to -<i>pi</i>/4.
     * <li>If both arguments are negative infinity, then the result is the
     * {@code double} value closest to -3*<i>pi</i>/4.</ul>
     *
     * @param   y   the ordinate coordinate
     * @param   x   the abscissa coordinate
     * @return  the <i>theta</i> component of the point
     *          (<i>r</i>,&nbsp;<i>theta</i>)
     *          in polar coordinates that corresponds to the point
     *          (<i>x</i>,&nbsp;<i>y</i>) in Cartesian coordinates.
     */
    public static native double atan2(double y, double x);

    
Returns the value of the first argument raised to the power of the
second argument. Special cases:

  • If the second argument is positive or negative zero, then the
result is 1.0.

  • If the second argument is 1.0, then the result is the same as the
first argument.

  • If the second argument is NaN, then the result is NaN.

  • If the first argument is NaN and the second argument is nonzero,
then the result is NaN.

  • If

      

    • the absolute value of the first argument is greater than 1
and the second argument is positive infinity, or

    • the absolute value of the first argument is less than 1 and
the second argument is negative infinity,

    
then the result is positive infinity.

  • If

      

    • the absolute value of the first argument is greater than 1 and
the second argument is negative infinity, or

    • the absolute value of the
first argument is less than 1 and the second argument is positive
infinity,

    
then the result is positive zero.

  • If the absolute value of the first argument equals 1 and the
second argument is infinite, then the result is NaN.

  • If

      

    • the first argument is positive zero and the second argument
is greater than zero, or

    • the first argument is positive infinity and the second
argument is less than zero,

    
then the result is positive zero.

  • If

      

    • the first argument is positive zero and the second argument
is less than zero, or

    • the first argument is positive infinity and the second
argument is greater than zero,

    
then the result is positive infinity.

  • If

      

    • the first argument is negative zero and the second argument
is greater than zero but not a finite odd integer, or

    • the first argument is negative infinity and the second
argument is less than zero but not a finite odd integer,

    
then the result is positive zero.

  • If

      

    • the first argument is negative zero and the second argument
is a positive finite odd integer, or

    • the first argument is negative infinity and the second
argument is a negative finite odd integer,

    
then the result is negative zero.

  • If

      

    • the first argument is negative zero and the second argument
is less than zero but not a finite odd integer, or

    • the first argument is negative infinity and the second
argument is greater than zero but not a finite odd integer,

    
then the result is positive infinity.

  • If

      

    • the first argument is negative zero and the second argument
is a negative finite odd integer, or

    • the first argument is negative infinity and the second
argument is a positive finite odd integer,

    
then the result is negative infinity.

  • If the first argument is finite and less than zero

      

    •  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

    • 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

    • if the second argument is finite and not an integer, then
the result is NaN.

    

  • 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 double value.


(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 ceil or, equivalently, a fixed point of the method 
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.) 
Params:
  • a –   base.
  • b –   the exponent.
Returns: the value ab.
/**
     * Returns the value of the first argument raised to the power of the
     * second argument. Special cases:
     *
     * <ul><li>If the second argument is positive or negative zero, then the
     * result is 1.0.
     * <li>If the second argument is 1.0, then the result is the same as the
     * first argument.
     * <li>If the second argument is NaN, then the result is NaN.
     * <li>If the first argument is NaN and the second argument is nonzero,
     * then the result is NaN.
     *
     * <li>If
     * <ul>
     * <li>the absolute value of the first argument is greater than 1
     * and the second argument is positive infinity, or
     * <li>the absolute value of the first argument is less than 1 and
     * the second argument is negative infinity,
     * </ul>
     * then the result is positive infinity.
     *
     * <li>If
     * <ul>
     * <li>the absolute value of the first argument is greater than 1 and
     * the second argument is negative infinity, or
     * <li>the absolute value of the
     * first argument is less than 1 and the second argument is positive
     * infinity,
     * </ul>
     * then the result is positive zero.
     *
     * <li>If the absolute value of the first argument equals 1 and the
     * second argument is infinite, then the result is NaN.
     *
     * <li>If
     * <ul>
     * <li>the first argument is positive zero and the second argument
     * is greater than zero, or
     * <li>the first argument is positive infinity and the second
     * argument is less than zero,
     * </ul>
     * then the result is positive zero.
     *
     * <li>If
     * <ul>
     * <li>the first argument is positive zero and the second argument
     * is less than zero, or
     * <li>the first argument is positive infinity and the second
     * argument is greater than zero,
     * </ul>
     * then the result is positive infinity.
     *
     * <li>If
     * <ul>
     * <li>the first argument is negative zero and the second argument
     * is greater than zero but not a finite odd integer, or
     * <li>the first argument is negative infinity and the second
     * argument is less than zero but not a finite odd integer,
     * </ul>
     * then the result is positive zero.
     *
     * <li>If
     * <ul>
     * <li>the first argument is negative zero and the second argument
     * is a positive finite odd integer, or
     * <li>the first argument is negative infinity and the second
     * argument is a negative finite odd integer,
     * </ul>
     * then the result is negative zero.
     *
     * <li>If
     * <ul>
     * <li>the first argument is negative zero and the second argument
     * is less than zero but not a finite odd integer, or
     * <li>the first argument is negative infinity and the second
     * argument is greater than zero but not a finite odd integer,
     * </ul>
     * then the result is positive infinity.
     *
     * <li>If
     * <ul>
     * <li>the first argument is negative zero and the second argument
     * is a negative finite odd integer, or
     * <li>the first argument is negative infinity and the second
     * argument is a positive finite odd integer,
     * </ul>
     * then the result is negative infinity.
     *
     * <li>If the first argument is finite and less than zero
     * <ul>
     * <li> if the second argument is a finite even integer, the
     * result is equal to the result of raising the absolute value of
     * the first argument to the power of the second argument
     *
     * <li>if the second argument is a finite odd integer, the result
     * is equal to the negative of the result of raising the absolute
     * value of the first argument to the power of the second
     * argument
     *
     * <li>if the second argument is finite and not an integer, then
     * the result is NaN.
     * </ul>
     *
     * <li>If both arguments are integers, then the result is exactly equal
     * to the mathematical result of raising the first argument to the power
     * of the second argument if that result can in fact be represented
     * exactly as a {@code double} value.</ul>
     *
     * <p>(In the foregoing descriptions, a floating-point value is
     * considered to be an integer if and only if it is finite and a
     * fixed point of the method {@link #ceil ceil} or,
     * equivalently, a fixed point of the method {@link #floor
     * floor}. A value is a fixed point of a one-argument
     * method if and only if the result of applying the method to the
     * value is equal to the value.)
     *
     * @param   a   base.
     * @param   b   the exponent.
     * @return  the value {@code a}<sup>{@code b}</sup>.
     */
    public static double pow(double a, double b) {
        return FdLibm.Pow.compute(a, b);
    }

    
Returns the closest int to the argument, with ties rounding to positive infinity. 
Special cases:

  • If the argument is NaN, the result is 0.

  • If the argument is negative infinity or any value less than or equal to the value of Integer.MIN_VALUE, the result is equal to the value of Integer.MIN_VALUE. 
  • If the argument is positive infinity or any value greater than or equal to the value of Integer.MAX_VALUE, the result is equal to the value of Integer.MAX_VALUE.


Params:
  • a –   a floating-point value to be rounded to an integer.
See Also:
Returns: the value of the argument rounded to the nearest int value.
/**
     * 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
     */
    public static int round(float a) {
        return Math.round(a);
    }

    
Returns the closest long to the argument, with ties rounding to positive infinity. 
Special cases:

  • If the argument is NaN, the result is 0.

  • If the argument is negative infinity or any value less than or equal to the value of Long.MIN_VALUE, the result is equal to the value of Long.MIN_VALUE. 
  • If the argument is positive infinity or any value greater than or equal to the value of Long.MAX_VALUE, the result is equal to the value of Long.MAX_VALUE.


Params:
  • a –  a floating-point value to be rounded to a long.
See Also:
Returns: the value of the argument rounded to the nearest long value.
/**
     * 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
     */
    public static long round(double a) {
        return Math.round(a);
    }

    private static final class RandomNumberGeneratorHolder {
        static final Random randomNumberGenerator = new Random();
    }

    
Returns a double value with a positive sign, greater than or equal to 0.0 and less than 1.0. Returned values are chosen pseudorandomly with (approximately) uniform distribution from that range. 
When this method is first called, it creates a single new
pseudorandom-number generator, exactly as if by the expression

new java.util.Random()

This new pseudorandom-number generator is used thereafter for
all calls to this method and is used nowhere else.

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.

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

    
Returns the sum of its arguments, throwing an exception if the result overflows an int. 
Params:
  • x – the first value
  • y – the second value
Throws:
See Also:
Returns:the result
Since:1.8
/**
     * 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
     * @see Math#addExact(int,int)
     * @since 1.8
     */
    public static int addExact(int x, int y) {
        return Math.addExact(x, y);
    }

    
Returns the sum of its arguments, throwing an exception if the result overflows a long. 
Params:
  • x – the first value
  • y – the second value
Throws:
See Also:
Returns:the result
Since:1.8
/**
     * 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
     * @see Math#addExact(long,long)
     * @since 1.8
     */
    public static long addExact(long x, long y) {
        return Math.addExact(x, y);
    }

    
Returns the difference of the arguments, throwing an exception if the result overflows an int. 
Params:
  • x – the first value
  • y – the second value to subtract from the first
Throws:
See Also:
Returns:the result
Since:1.8
/**
     * 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
     * @see Math#subtractExact(int,int)
     * @since 1.8
     */
    public static int subtractExact(int x, int y) {
        return Math.subtractExact(x, y);
    }

    
Returns the difference of the arguments, throwing an exception if the result overflows a long. 
Params:
  • x – the first value
  • y – the second value to subtract from the first
Throws:
See Also:
Returns:the result
Since:1.8
/**
     * 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
     * @see Math#subtractExact(long,long)
     * @since 1.8
     */
    public static long subtractExact(long x, long y) {
        return Math.subtractExact(x, y);
    }

    
Returns the product of the arguments, throwing an exception if the result overflows an int. 
Params:
  • x – the first value
  • y – the second value
Throws:
See Also:
Returns:the result
Since:1.8
/**
     * 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
     * @see Math#multiplyExact(int,int)
     * @since 1.8
     */
    public static int multiplyExact(int x, int y) {
        return Math.multiplyExact(x, y);
    }

    
Returns the product of the arguments, throwing an exception if the result overflows a long. 
Params:
  • x – the first value
  • y – the second value
Throws:
See Also:
Returns:the result
Since:9
/**
     * 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
     * @see Math#multiplyExact(long,int)
     * @since 9
     */
    public static long multiplyExact(long x, int y) {
        return Math.multiplyExact(x, y);
    }

    
Returns the product of the arguments, throwing an exception if the result overflows a long. 
Params:
  • x – the first value
  • y – the second value
Throws:
See Also:
Returns:the result
Since:1.8
/**
     * 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
     * @see Math#multiplyExact(long,long)
     * @since 1.8
     */
    public static long multiplyExact(long x, long y) {
        return Math.multiplyExact(x, y);
    }

    
Returns the value of the long argument; throwing an exception if the value overflows an int. 
Params:
  • value – the long value
Throws:
See Also:
Returns:the argument as an int
Since:1.8
/**
     * 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
     * @see Math#toIntExact(long)
     * @since 1.8
     */
    public static int toIntExact(long value) {
        return Math.toIntExact(value);
    }

    
Returns the exact mathematical product of the arguments.

Params:
  • x – the first value
  • y – the second value
See Also:
Returns:the result
Since:9
/**
     * Returns the exact mathematical product of the arguments.
     *
     * @param x the first value
     * @param y the second value
     * @return the result
     * @see Math#multiplyFull(int,int)
     * @since 9
     */
    public static long multiplyFull(int x, int y) {
        return Math.multiplyFull(x, y);
    }

    
Returns as a long the most significant 64 bits of the 128-bit product of two 64-bit factors. 
Params:
  • x – the first value
  • y – the second value
See Also:
Returns:the result
Since:9
/**
     * 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
     * @see Math#multiplyHigh(long,long)
     * @since 9
     */
    public static long multiplyHigh(long x, long y) {
        return Math.multiplyHigh(x, y);
    }

    
Returns the largest (closest to positive infinity) int value that is less than or equal to the algebraic quotient. There is one special case, if the dividend is the Integer.MIN_VALUE and the divisor is -1, then integer overflow occurs and the result is equal to the Integer.MIN_VALUE. 
 See Math.floorDiv for examples and a comparison to the integer division / operator. 
Params:
  • x – the dividend
  • y – the divisor
Throws:
See Also:
Returns:the largest (closest to positive infinity) int value that is less than or equal to the algebraic quotient.
Since:1.8
/**
     * 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 the {@code Integer.MIN_VALUE}.
     * <p>
     * See {@link Math#floorDiv(int, int) Math.floorDiv} for examples and
     * a comparison to the integer division {@code /} operator.
     *
     * @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 Math#floorDiv(int, int)
     * @see Math#floor(double)
     * @since 1.8
     */
    public static int floorDiv(int x, int y) {
        return Math.floorDiv(x, y);
    }

    
Returns the largest (closest to positive infinity) long value that is less than or equal to the algebraic quotient. There is one special case, if the dividend is the Long.MIN_VALUE and the divisor is -1, then integer overflow occurs and the result is equal to Long.MIN_VALUE. 
 See Math.floorDiv for examples and a comparison to the integer division / operator. 
Params:
  • x – the dividend
  • y – the divisor
Throws:
See Also:
Returns:the largest (closest to positive infinity) int value that is less than or equal to the algebraic quotient.
Since:9
/**
     * 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>
     * See {@link Math#floorDiv(int, int) Math.floorDiv} for examples and
     * a comparison to the integer division {@code /} operator.
     *
     * @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 Math#floorDiv(long, int)
     * @see Math#floor(double)
     * @since 9
     */
    public static long floorDiv(long x, int y) {
        return Math.floorDiv(x, y);
    }

    
Returns the largest (closest to positive infinity) long value that is less than or equal to the algebraic quotient. There is one special case, if the dividend is the Long.MIN_VALUE and the divisor is -1, then integer overflow occurs and the result is equal to the Long.MIN_VALUE. 
 See Math.floorDiv for examples and a comparison to the integer division / operator. 
Params:
  • x – the dividend
  • y – the divisor
Throws:
See Also:
Returns:the largest (closest to positive infinity) long value that is less than or equal to the algebraic quotient.
Since:1.8
/**
     * 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 the {@code Long.MIN_VALUE}.
     * <p>
     * See {@link Math#floorDiv(int, int) Math.floorDiv} for examples and
     * a comparison to the integer division {@code /} operator.
     *
     * @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 Math#floorDiv(long, long)
     * @see Math#floor(double)
     * @since 1.8
     */
    public static long floorDiv(long x, long y) {
        return Math.floorDiv(x, y);
    }

    
Returns the floor modulus of the int arguments. 
 The floor modulus is x - (floorDiv(x, y) * y), has the same sign as the divisor y, and is in the range of -abs(y) < r < +abs(y). 
 The relationship between floorDiv and floorMod is such that: 
    
  
  • floorDiv(x, y) * y + floorMod(x, y) == x 


 See Math.floorMod for examples and a comparison to the % operator. 
Params:
  • x – the dividend
  • y – the divisor
Throws:
See Also:
Returns:the floor modulus x - (floorDiv(x, y) * y)
Since:1.8
/**
     * 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>
     * See {@link Math#floorMod(int, int) Math.floorMod} for examples and
     * a comparison to the {@code %} operator.
     *
     * @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 Math#floorMod(int, int)
     * @see StrictMath#floorDiv(int, int)
     * @since 1.8
     */
    public static int floorMod(int x, int y) {
        return Math.floorMod(x , y);
    }

    
Returns the floor modulus of the long and int arguments. 
 The floor modulus is x - (floorDiv(x, y) * y), has the same sign as the divisor y, and is in the range of -abs(y) < r < +abs(y). 
 The relationship between floorDiv and floorMod is such that: 
    
  
  • floorDiv(x, y) * y + floorMod(x, y) == x 


 See Math.floorMod for examples and a comparison to the % operator. 
Params:
  • x – the dividend
  • y – the divisor
Throws:
See Also:
Returns:the floor modulus x - (floorDiv(x, y) * y)
Since:9
/**
     * 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>
     * See {@link Math#floorMod(int, int) Math.floorMod} for examples and
     * a comparison to the {@code %} operator.
     *
     * @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 Math#floorMod(long, int)
     * @see StrictMath#floorDiv(long, int)
     * @since 9
     */
    public static int floorMod(long x, int y) {
        return Math.floorMod(x , y);
    }

    
Returns the floor modulus of the long arguments. 
 The floor modulus is x - (floorDiv(x, y) * y), has the same sign as the divisor y, and is in the range of -abs(y) < r < +abs(y). 
 The relationship between floorDiv and floorMod is such that: 
    
  
  • floorDiv(x, y) * y + floorMod(x, y) == x 


 See Math.floorMod for examples and a comparison to the % operator. 
Params:
  • x – the dividend
  • y – the divisor
Throws:
See Also:
Returns:the floor modulus x - (floorDiv(x, y) * y)
Since:1.8
/**
     * 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>
     * See {@link Math#floorMod(int, int) Math.floorMod} for examples and
     * a comparison to the {@code %} operator.
     *
     * @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 Math#floorMod(long, long)
     * @see StrictMath#floorDiv(long, long)
     * @since 1.8
     */
    public static long floorMod(long x, long y) {
        return Math.floorMod(x, y);
    }

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

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

    
Returns the absolute value of a 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: 
  • If the argument is positive zero or negative zero, the
result is positive zero.

  • If the argument is infinite, the result is positive infinity.

  • If the argument is NaN, the result is NaN.


Params:
  • a –   the argument whose absolute value is to be determined
API Note:As implied by the above, one valid implementation of this method is given by the expression below which computes a float with the same exponent and significand as the argument but with a guaranteed zero sign bit indicating a positive value: 
 Float.intBitsToFloat(0x7fffffff & Float.floatToRawIntBits(a))
Returns: the absolute value of the argument.
/**
     * 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.
     */
    public static float abs(float a) {
        return Math.abs(a);
    }

    
Returns the absolute value of a 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: 
  • If the argument is positive zero or negative zero, the result
is positive zero.

  • If the argument is infinite, the result is positive infinity.

  • If the argument is NaN, the result is NaN.


Params:
  • a –   the argument whose absolute value is to be determined
API Note:As implied by the above, one valid implementation of this method is given by the expression below which computes a double with the same exponent and significand as the argument but with a guaranteed zero sign bit indicating a positive value: 
 Double.longBitsToDouble((Double.doubleToRawLongBits(a)<<1)>>>1)
Returns: the absolute value of the argument.
/**
     * 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.
     */
    public static double abs(double a) {
        return Math.abs(a);
    }

    
Returns the greater of two int values. That is, the result is the argument closer to the value of Integer.MAX_VALUE. If the arguments have the same value, the result is that same value. 
Params:
  • a –   an argument.
  • b –   another argument.
Returns: the larger of a and b.
/**
     * 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
    public static int max(int a, int b) {
        return Math.max(a, b);
    }

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

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

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

    
Returns the smaller of two int values. That is, the result the argument closer to the value of Integer.MIN_VALUE. If the arguments have the same value, the result is that same value. 
Params:
  • a –   an argument.
  • b –   another argument.
Returns: the smaller of a and 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
    public static int min(int a, int b) {
        return Math.min(a, b);
    }

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

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

    
Returns the smaller of two 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. 
Params:
  • a –   an argument.
  • b –   another argument.
Returns: the smaller of a and b.
/**
     * Returns the smaller of two {@code double} values.  That
     * is, the result is the value closer to negative infinity. If the
     * arguments have the same value, the result is that same
     * value. If either value is NaN, then the result is NaN.  Unlike
     * the numerical comparison operators, this method considers
     * negative zero to be strictly smaller than positive zero. If one
     * argument is positive zero and the other is negative zero, the
     * result is negative zero.
     *
     * @param   a   an argument.
     * @param   b   another argument.
     * @return  the smaller of {@code a} and {@code b}.
     */
    public static double min(double a, double b) {
        return Math.min(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 double. The rounding is done using the round to nearest even
rounding mode. In contrast, if 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. 
Special cases:

    

  •  If any argument is NaN, the result is NaN.

  •  If one of the first two arguments is infinite and the
other is zero, the result is NaN.

  •  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.



Note that fusedMac(a, 1.0, c) returns the same result as (a + c). However, fusedMac(a, b, +0.0) does not always return the same result as (a * b) since fusedMac(-0.0, +0.0, +0.0) is +0.0 while (-0.0 * +0.0) is -0.0; fusedMac(a, b, -0.0) is equivalent to (a * b) however. 
Params:
  • a – a value
  • b – a value
  • c – a value
API Note:This method corresponds to the fusedMultiplyAdd
operation defined in IEEE 754-2008.
Returns:(a × b + c) computed, as if with unlimited range and precision, and rounded once to the nearest double value
Since:9
/**
     * 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 fusedMac(a, 1.0, c)} returns the same
     * result as ({@code a + c}).  However,
     * {@code fusedMac(a, b, +0.0)} does <em>not</em> always return the
     * same result as ({@code a * b}) since
     * {@code fusedMac(-0.0, +0.0, +0.0)} is {@code +0.0} while
     * ({@code -0.0 * +0.0}) is {@code -0.0}; {@code fusedMac(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
     *
     * @since 9
     */
    public static double fma(double a, double b, double c) {
        return Math.fma(a, b, c);
    }

    
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 float. The rounding is done using the round to nearest even
rounding mode. In contrast, if 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. 
Special cases:

    

  •  If any argument is NaN, the result is NaN.

  •  If one of the first two arguments is infinite and the
other is zero, the result is NaN.

  •  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.



Note that fma(a, 1.0f, c) returns the same result as (a + c). However, fma(a, b, +0.0f) does not always return the same result as (a * b) since fma(-0.0f, +0.0f, +0.0f) is +0.0f while (-0.0f * +0.0f) is -0.0f; fma(a, b, -0.0f) is equivalent to (a * b) however. 
Params:
  • a – a value
  • b – a value
  • c – a value
API Note:This method corresponds to the fusedMultiplyAdd
operation defined in IEEE 754-2008.
Returns:(a × b + c) computed, as if with unlimited range and precision, and rounded once to the nearest float value
Since:9
/**
     * 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
     *
     * @since 9
     */
    public static float fma(float a, float b, float c) {
        return Math.fma(a, b, c);
    }

    
Returns the size of an ulp of the argument. An ulp, unit in the last place, of a double value is the positive distance between this floating-point value and the 
double value next larger in magnitude. Note that for non-NaN x, ulp(-x) == ulp(x).

Special Cases:

    

  •  If the argument is NaN, then the result is NaN.

  •  If the argument is positive or negative infinity, then the
result is positive infinity.

  •  If the argument is positive or negative zero, then the result is Double.MIN_VALUE. 
  •  If the argument is ±Double.MAX_VALUE, then the result is equal to 2971.



Author:Joseph D. Darcy
Params:
  • d – the floating-point value whose ulp is to be returned
Returns:the size of an ulp of the argument
Since:1.5
/**
     * 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
     * @since 1.5
     */
    public static double ulp(double d) {
        return Math.ulp(d);
    }

    
Returns the size of an ulp of the argument. An ulp, unit in the last place, of a float value is the positive distance between this floating-point value and the 
float value next larger in magnitude. Note that for non-NaN x, ulp(-x) == ulp(x).

Special Cases:

    

  •  If the argument is NaN, then the result is NaN.

  •  If the argument is positive or negative infinity, then the
result is positive infinity.

  •  If the argument is positive or negative zero, then the result is Float.MIN_VALUE. 
  •  If the argument is ±Float.MAX_VALUE, then the result is equal to 2104.



Author:Joseph D. Darcy
Params:
  • f – the floating-point value whose ulp is to be returned
Returns:the size of an ulp of the argument
Since:1.5
/**
     * 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
     * @since 1.5
     */
    public static float ulp(float f) {
        return Math.ulp(f);
    }

    
Returns the signum function of the argument; zero if the argument
is zero, 1.0 if the argument is greater than zero, -1.0 if the
argument is less than zero.

Special Cases:

    

  •  If the argument is NaN, then the result is NaN.

  •  If the argument is positive zero or negative zero, then the
     result is the same as the argument.



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

    
Returns the signum function of the argument; zero if the argument
is zero, 1.0f if the argument is greater than zero, -1.0f if the
argument is less than zero.

Special Cases:

    

  •  If the argument is NaN, then the result is NaN.

  •  If the argument is positive zero or negative zero, then the
     result is the same as the argument.



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

    
Returns the hyperbolic sine of a double value. The hyperbolic sine of x is defined to be
(ex - e-x)/2
where e is Euler's number. 
Special cases:

    

  • If the argument is NaN, then the result is NaN.

  • If the argument is infinite, then the result is an infinity
with the same sign as the argument.

  • If the argument is zero, then the result is a zero with the
same sign as the argument.



Params:
  • x – The number whose hyperbolic sine is to be returned.
Returns: The hyperbolic sine of x.
Since:1.5
/**
     * Returns the hyperbolic sine of a {@code double} value.
     * The hyperbolic sine of <i>x</i> is defined to be
     * (<i>e<sup>x</sup>&nbsp;-&nbsp;e<sup>-x</sup></i>)/2
     * where <i>e</i> is {@linkplain Math#E Euler's number}.
     *
     * <p>Special cases:
     * <ul>
     *
     * <li>If the argument is NaN, then the result is NaN.
     *
     * <li>If the argument is infinite, then the result is an infinity
     * with the same sign as the argument.
     *
     * <li>If the argument is zero, then the result is a zero with the
     * same sign as the argument.
     *
     * </ul>
     *
     * @param   x The number whose hyperbolic sine is to be returned.
     * @return  The hyperbolic sine of {@code x}.
     * @since 1.5
     */
    public static native double sinh(double x);

    
Returns the hyperbolic cosine of a double value. The hyperbolic cosine of x is defined to be
(ex + e-x)/2
where e is Euler's number. 
Special cases:

    

  • If the argument is NaN, then the result is NaN.

  • If the argument is infinite, then the result is positive
infinity.

  • If the argument is zero, then the result is 1.0. 


Params:
  • x – The number whose hyperbolic cosine is to be returned.
Returns: The hyperbolic cosine of x.
Since:1.5
/**
     * Returns the hyperbolic cosine of a {@code double} value.
     * The hyperbolic cosine of <i>x</i> is defined to be
     * (<i>e<sup>x</sup>&nbsp;+&nbsp;e<sup>-x</sup></i>)/2
     * where <i>e</i> is {@linkplain Math#E Euler's number}.
     *
     * <p>Special cases:
     * <ul>
     *
     * <li>If the argument is NaN, then the result is NaN.
     *
     * <li>If the argument is infinite, then the result is positive
     * infinity.
     *
     * <li>If the argument is zero, then the result is {@code 1.0}.
     *
     * </ul>
     *
     * @param   x The number whose hyperbolic cosine is to be returned.
     * @return  The hyperbolic cosine of {@code x}.
     * @since 1.5
     */
    public static native double cosh(double x);

    
Returns the hyperbolic tangent of a double value. The hyperbolic tangent of x is defined to be
(ex - e-x)/(ex + e-x), in other words, 
sinh(x)/cosh(x). Note that the absolute value of the exact tanh is always less than 1. 
Special cases:

    

  • If the argument is NaN, then the result is NaN.

  • If the argument is zero, then the result is a zero with the
same sign as the argument.

  • If the argument is positive infinity, then the result is +1.0. 
  • If the argument is negative infinity, then the result is -1.0. 


Params:
  • x – The number whose hyperbolic tangent is to be returned.
Returns: The hyperbolic tangent of x.
Since:1.5
/**
     * Returns the hyperbolic tangent of a {@code double} value.
     * The hyperbolic tangent of <i>x</i> is defined to be
     * (<i>e<sup>x</sup>&nbsp;-&nbsp;e<sup>-x</sup></i>)/(<i>e<sup>x</sup>&nbsp;+&nbsp;e<sup>-x</sup></i>),
     * in other words, {@linkplain Math#sinh
     * sinh(<i>x</i>)}/{@linkplain Math#cosh cosh(<i>x</i>)}.  Note
     * that the absolute value of the exact tanh is always less than
     * 1.
     *
     * <p>Special cases:
     * <ul>
     *
     * <li>If the argument is NaN, then the result is NaN.
     *
     * <li>If the argument is zero, then the result is a zero with the
     * same sign as the argument.
     *
     * <li>If the argument is positive infinity, then the result is
     * {@code +1.0}.
     *
     * <li>If the argument is negative infinity, then the result is
     * {@code -1.0}.
     *
     * </ul>
     *
     * @param   x The number whose hyperbolic tangent is to be returned.
     * @return  The hyperbolic tangent of {@code x}.
     * @since 1.5
     */
    public static native double tanh(double x);

    
Returns sqrt(x2 +y2)
without intermediate overflow or underflow.

Special cases:

    

  •  If either argument is infinite, then the result
is positive infinity.

  •  If either argument is NaN and neither argument is infinite,
then the result is NaN.



Params:
  • x – a value
  • y – a value
Returns:sqrt(x2 +y2)
without intermediate overflow or underflow
Since:1.5
/**
     * Returns sqrt(<i>x</i><sup>2</sup>&nbsp;+<i>y</i><sup>2</sup>)
     * without intermediate overflow or underflow.
     *
     * <p>Special cases:
     * <ul>
     *
     * <li> If either argument is infinite, then the result
     * is positive infinity.
     *
     * <li> If either argument is NaN and neither argument is infinite,
     * then the result is NaN.
     *
     * </ul>
     *
     * @param x a value
     * @param y a value
     * @return sqrt(<i>x</i><sup>2</sup>&nbsp;+<i>y</i><sup>2</sup>)
     * without intermediate overflow or underflow
     * @since 1.5
     */
    public static double hypot(double x, double y) {
        return FdLibm.Hypot.compute(x, y);
    }

    
Returns ex -1.  Note that for values of
x near 0, the exact sum of expm1(x) + 1 is much closer to the true result of ex than exp(x). 
Special cases:

    

  • If the argument is NaN, the result is NaN.

  • If the argument is positive infinity, then the result is
positive infinity.

  • If the argument is negative infinity, then the result is
-1.0.

  • If the argument is zero, then the result is a zero with the
same sign as the argument.



Params:
  • x –   the exponent to raise e to in the computation of
             ex -1.
Returns: the value ex - 1.
Since:1.5
/**
     * Returns <i>e</i><sup>x</sup>&nbsp;-1.  Note that for values of
     * <i>x</i> near 0, the exact sum of
     * {@code expm1(x)}&nbsp;+&nbsp;1 is much closer to the true
     * result of <i>e</i><sup>x</sup> than {@code exp(x)}.
     *
     * <p>Special cases:
     * <ul>
     * <li>If the argument is NaN, the result is NaN.
     *
     * <li>If the argument is positive infinity, then the result is
     * positive infinity.
     *
     * <li>If the argument is negative infinity, then the result is
     * -1.0.
     *
     * <li>If the argument is zero, then the result is a zero with the
     * same sign as the argument.
     *
     * </ul>
     *
     * @param   x   the exponent to raise <i>e</i> to in the computation of
     *              <i>e</i><sup>{@code x}</sup>&nbsp;-1.
     * @return  the value <i>e</i><sup>{@code x}</sup>&nbsp;-&nbsp;1.
     * @since 1.5
     */
    public static native double expm1(double x);

    
Returns the natural logarithm of the sum of the argument and 1. Note that for small values x, the result of log1p(x) is much closer to the true result of ln(1 + x) than the floating-point evaluation of log(1.0+x). 
Special cases:

    

  • If the argument is NaN or less than -1, then the result is
NaN.

  • If the argument is positive infinity, then the result is
positive infinity.

  • If the argument is negative one, then the result is
negative infinity.

  • If the argument is zero, then the result is a zero with the
same sign as the argument.



Params:
  • x –   a value
Returns:the value ln(x + 1), the natural log of x + 1
Since:1.5
/**
     * Returns the natural logarithm of the sum of the argument and 1.
     * Note that for small values {@code x}, the result of
     * {@code log1p(x)} is much closer to the true result of ln(1
     * + {@code x}) than the floating-point evaluation of
     * {@code log(1.0+x)}.
     *
     * <p>Special cases:
     * <ul>
     *
     * <li>If the argument is NaN or less than -1, then the result is
     * NaN.
     *
     * <li>If the argument is positive infinity, then the result is
     * positive infinity.
     *
     * <li>If the argument is negative one, then the result is
     * negative infinity.
     *
     * <li>If the argument is zero, then the result is a zero with the
     * same sign as the argument.
     *
     * </ul>
     *
     * @param   x   a value
     * @return the value ln({@code x}&nbsp;+&nbsp;1), the natural
     * log of {@code x}&nbsp;+&nbsp;1
     * @since 1.5
     */
    public static native double log1p(double x);

    
Returns the first floating-point argument with the sign of the second floating-point argument. For this method, a NaN sign argument is always treated as if it were positive. 
Params:
  • magnitude –  the parameter providing the magnitude of the result
  • sign –   the parameter providing the sign of the result
Returns:a value with the magnitude of magnitude and the sign of sign.
Since:1.6
/**
     * Returns the first floating-point argument with the sign of the
     * second floating-point argument.  For this method, a NaN
     * {@code sign} argument is always treated as if it were
     * positive.
     *
     * @param magnitude  the parameter providing the magnitude of the result
     * @param sign   the parameter providing the sign of the result
     * @return a value with the magnitude of {@code magnitude}
     * and the sign of {@code sign}.
     * @since 1.6
     */
    public static double copySign(double magnitude, double sign) {
        return Math.copySign(magnitude, (Double.isNaN(sign)?1.0d:sign));
    }

    
Returns the first floating-point argument with the sign of the second floating-point argument. For this method, a NaN sign argument is always treated as if it were positive. 
Params:
  • magnitude –  the parameter providing the magnitude of the result
  • sign –   the parameter providing the sign of the result
Returns:a value with the magnitude of magnitude and the sign of sign.
Since:1.6
/**
     * Returns the first floating-point argument with the sign of the
     * second floating-point argument.  For this method, a NaN
     * {@code sign} argument is always treated as if it were
     * positive.
     *
     * @param magnitude  the parameter providing the magnitude of the result
     * @param sign   the parameter providing the sign of the result
     * @return a value with the magnitude of {@code magnitude}
     * and the sign of {@code sign}.
     * @since 1.6
     */
    public static float copySign(float magnitude, float sign) {
        return Math.copySign(magnitude, (Float.isNaN(sign)?1.0f:sign));
    }
    
Returns the unbiased exponent used in the representation of a float. Special cases: 

Params:
  • f – a float value
Returns:the unbiased exponent of the argument
Since:1.6
/**
     * 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
     * @since 1.6
     */
    public static int getExponent(float f) {
        return Math.getExponent(f);
    }

    
Returns the unbiased exponent used in the representation of a double. Special cases: 

Params:
  • d – a double value
Returns:the unbiased exponent of the argument
Since:1.6
/**
     * 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
     * @since 1.6
     */
    public static int getExponent(double d) {
        return Math.getExponent(d);
    }

    
Returns the floating-point number adjacent to the first
argument in the direction of the second argument.  If both
arguments compare as equal the second argument is returned.

Special cases:

    

  •  If either argument is a NaN, then NaN is returned.

  •  If both arguments are signed zeros, direction is returned unchanged (as implied by the requirement of returning the second argument if the arguments compare as equal). 
  •  If start is ±Double.MIN_VALUE and direction has a value such that the result should have a smaller magnitude, then a zero with the same sign as start is returned. 
  •  If start is infinite and direction has a value such that the result should have a smaller magnitude, Double.MAX_VALUE with the same sign as start is returned. 
  •  If start is equal to ± Double.MAX_VALUE and direction has a value such that the result should have a larger magnitude, an infinity with same sign as start is returned. 


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

    
Returns the floating-point number adjacent to the first
argument in the direction of the second argument.  If both
arguments compare as equal a value equivalent to the second argument
is returned.

Special cases:

    

  •  If either argument is a NaN, then NaN is returned.

  •  If both arguments are signed zeros, a value equivalent to direction is returned. 
  •  If start is ±Float.MIN_VALUE and direction has a value such that the result should have a smaller magnitude, then a zero with the same sign as start is returned. 
  •  If start is infinite and direction has a value such that the result should have a smaller magnitude, Float.MAX_VALUE with the same sign as start is returned. 
  •  If start is equal to ± Float.MAX_VALUE and direction has a value such that the result should have a larger magnitude, an infinity with same sign as start is returned. 


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

    
Returns the floating-point value adjacent to d in the direction of positive infinity. This method is semantically equivalent to nextAfter(d,
Double.POSITIVE_INFINITY); however, a nextUp implementation may run faster than its equivalent nextAfter call. 
Special Cases:

    

  •  If the argument is NaN, the result is NaN.

  •  If the argument is positive infinity, the result is
positive infinity.

  •  If the argument is zero, the result is Double.MIN_VALUE 


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

    
Returns the floating-point value adjacent to f in the direction of positive infinity. This method is semantically equivalent to nextAfter(f,
Float.POSITIVE_INFINITY); however, a nextUp implementation may run faster than its equivalent nextAfter call. 
Special Cases:

    

  •  If the argument is NaN, the result is NaN.

  •  If the argument is positive infinity, the result is
positive infinity.

  •  If the argument is zero, the result is Float.MIN_VALUE 


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

    
Returns the floating-point value adjacent to d in the direction of negative infinity. This method is semantically equivalent to nextAfter(d,
Double.NEGATIVE_INFINITY); however, a nextDown implementation may run faster than its equivalent nextAfter call. 
Special Cases:

    

  •  If the argument is NaN, the result is NaN.

  •  If the argument is negative infinity, the result is
negative infinity.

  •  If the argument is zero, the result is -Double.MIN_VALUE 


Params:
  • d –  starting floating-point value
Returns:The adjacent floating-point value closer to negative
infinity.
Since:1.8
/**
     * 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.
     * @since 1.8
     */
    public static double nextDown(double d) {
        return Math.nextDown(d);
    }

    
Returns the floating-point value adjacent to f in the direction of negative infinity. This method is semantically equivalent to nextAfter(f,
Float.NEGATIVE_INFINITY); however, a nextDown implementation may run faster than its equivalent nextAfter call. 
Special Cases:

    

  •  If the argument is NaN, the result is NaN.

  •  If the argument is negative infinity, the result is
negative infinity.

  •  If the argument is zero, the result is -Float.MIN_VALUE 


Params:
  • f –  starting floating-point value
Returns:The adjacent floating-point value closer to negative
infinity.
Since:1.8
/**
     * 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.
     * @since 1.8
     */
    public static float nextDown(float f) {
        return Math.nextDown(f);
    }

    
Returns d × 2scaleFactor 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 Double.MIN_EXPONENT and Double.MAX_EXPONENT, the answer is calculated exactly. If the exponent of the result would be larger than Double.MAX_EXPONENT, an infinity is returned. Note that if the result is subnormal, precision may be lost; that is, when scalb(x, n) is subnormal, scalb(scalb(x, n), -n) may not equal x. When the result is non-NaN, the result has the same sign as d. 
Special cases:

    

  •  If the first argument is NaN, NaN is returned.

  •  If the first argument is infinite, then an infinity of the
same sign is returned.

  •  If the first argument is zero, then a zero of the same
sign is returned.



Params:
  • d – number to be scaled by a power of two.
  • scaleFactor – power of 2 used to scale d
Returns:d × 2scaleFactor
Since:1.6
/**
     * 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>
     * @since 1.6
     */
    public static double scalb(double d, int scaleFactor) {
        return Math.scalb(d, scaleFactor);
    }

    
Returns f × 2scaleFactor 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 Float.MIN_EXPONENT and Float.MAX_EXPONENT, the answer is calculated exactly. If the exponent of the result would be larger than Float.MAX_EXPONENT, an infinity is returned. Note that if the result is subnormal, precision may be lost; that is, when scalb(x, n) is subnormal, scalb(scalb(x, n), -n) may not equal x. When the result is non-NaN, the result has the same sign as f. 
Special cases:

    

  •  If the first argument is NaN, NaN is returned.

  •  If the first argument is infinite, then an infinity of the
same sign is returned.

  •  If the first argument is zero, then a zero of the same
sign is returned.



Params:
  • f – number to be scaled by a power of two.
  • scaleFactor – power of 2 used to scale f
Returns:f × 2scaleFactor
Since:1.6
/**
     * 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>
     * @since 1.6
     */
    public static float scalb(float f, int scaleFactor) {
        return Math.scalb(f, scaleFactor);
    }
}