java.lang

## Class Math

- java.lang.Object
- - java.lang.Math

-     public final class Math
      extends Object

  The class `Math` contains methods for performing basic numeric operations such as the elementary exponential, logarithm, square root, and trigonometric functions.

  Unlike some of the numeric methods of class `StrictMath`, all implementations of the equivalent functions of class `Math` are not defined to return the bit-for-bit same results. This relaxation permits better-performing implementations where strict reproducibility is not required.

  By default many of the `Math` methods simply call the equivalent method in `StrictMath` for their implementation. Code generators are encouraged to use platform-specific native libraries or microprocessor instructions, where available, to provide higher-performance implementations of `Math` methods. Such higher-performance implementations still must conform to the specification for `Math`.

  The quality of implementation specifications concern two properties, accuracy of the returned result and monotonicity of the method. Accuracy of the floating-point `Math` methods is measured in terms of ulps, units in the last place. For a given floating-point format, an ulp of a specific real number value is the distance between the two floating-point values bracketing that numerical value. When discussing the accuracy of a method as a whole rather than at a specific argument, the number of ulps cited is for the worst-case error at any argument. If a method always has an error less than 0.5 ulps, the method always returns the floating-point number nearest the exact result; such a method is correctly rounded. A correctly rounded method is generally the best a floating-point approximation can be; however, it is impractical for many floating-point methods to be correctly rounded. Instead, for the `Math` class, a larger error bound of 1 or 2 ulps is allowed for certain methods. Informally, with a 1 ulp error bound, when the exact result is a representable number, the exact result should be returned as the computed result; otherwise, either of the two floating-point values which bracket the exact result may be returned. For exact results large in magnitude, one of the endpoints of the bracket may be infinite. Besides accuracy at individual arguments, maintaining proper relations between the method at different arguments is also important. Therefore, most methods with more than 0.5 ulp errors are required to be semi-monotonic: whenever the mathematical function is non-decreasing, so is the floating-point approximation, likewise, whenever the mathematical function is non-increasing, so is the floating-point approximation. Not all approximations that have 1 ulp accuracy will automatically meet the monotonicity requirements.

  Since:
    JDK1.0

- - ### Field Summary

    Fields
    Modifier and Type | Field and Description
    --- | ---
    `static double` | `E` The `double` value that is closer than any other to e, the base of the natural logarithms.
    `static double` | `PI` The `double` value that is closer than any other to pi, the ratio of the circumference of a circle to its diameter.

  - ### Method Summary

    Methods
    Modifier and Type | Method and Description
    --- | ---
    `static double` | `abs(double a)` Returns the absolute value of a `double` value.
    `static float` | `abs(float a)` Returns the absolute value of a `float` value.
    `static int` | `abs(int a)` Returns the absolute value of an `int` value.
    `static long` | `abs(long a)` Returns the absolute value of a `long` value.
    `static double` | `acos(double a)` Returns the arc cosine of a value; the returned angle is in the range 0.0 through pi.
    `static double` | `asin(double a)` Returns the arc sine of a value; the returned angle is in the range -pi/2 through pi/2.
    `static double` | `atan(double a)` Returns the arc tangent of a value; the returned angle is in the range -pi/2 through pi/2.
    `static double` | `atan2(double y, double x)` Returns the angle theta from the conversion of rectangular coordinates (`x`, `y`) to polar coordinates (r, theta).
    `static double` | `cbrt(double a)` Returns the cube root of a `double` value.
    `static double` | `ceil(double a)` 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.
    `static double` | `copySign(double magnitude, double sign)` Returns the first floating-point argument with the sign of the second floating-point argument.
    `static float` | `copySign(float magnitude, float sign)` Returns the first floating-point argument with the sign of the second floating-point argument.
    `static double` | `cos(double a)` Returns the trigonometric cosine of an angle.
    `static double` | `cosh(double x)` Returns the hyperbolic cosine of a `double` value.
    `static double` | `exp(double a)` Returns Euler's number e raised to the power of a `double` value.
    `static double` | `expm1(double x)` Returns ex -1.
    `static double` | `floor(double a)` 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.
    `static int` | `getExponent(double d)` Returns the unbiased exponent used in the representation of a `double`.
    `static int` | `getExponent(float f)` Returns the unbiased exponent used in the representation of a `float`.
    `static double` | `hypot(double x, double y)` Returns sqrt(x2 +y2) without intermediate overflow or underflow.
    `static double` | `IEEEremainder(double f1, double f2)` Computes the remainder operation on two arguments as prescribed by the IEEE 754 standard.
    `static double` | `log(double a)` Returns the natural logarithm (base e) of a `double` value.
    `static double` | `log10(double a)` Returns the base 10 logarithm of a `double` value.
    `static double` | `log1p(double x)` Returns the natural logarithm of the sum of the argument and 1.
    `static double` | `max(double a, double b)` Returns the greater of two `double` values.
    `static float` | `max(float a, float b)` Returns the greater of two `float` values.
    `static int` | `max(int a, int b)` Returns the greater of two `int` values.
    `static long` | `max(long a, long b)` Returns the greater of two `long` values.
    `static double` | `min(double a, double b)` Returns the smaller of two `double` values.
    `static float` | `min(float a, float b)` Returns the smaller of two `float` values.
    `static int` | `min(int a, int b)` Returns the smaller of two `int` values.
    `static long` | `min(long a, long b)` Returns the smaller of two `long` values.
    `static double` | `nextAfter(double start, double direction)` Returns the floating-point number adjacent to the first argument in the direction of the second argument.
    `static float` | `nextAfter(float start, double direction)` Returns the floating-point number adjacent to the first argument in the direction of the second argument.
    `static double` | `nextUp(double d)` Returns the floating-point value adjacent to `d` in the direction of positive infinity.
    `static float` | `nextUp(float f)` Returns the floating-point value adjacent to `f` in the direction of positive infinity.
    `static double` | `pow(double a, double b)` Returns the value of the first argument raised to the power of the second argument.
    `static double` | `random()` Returns a `double` value with a positive sign, greater than or equal to `0.0` and less than `1.0`.
    `static double` | `rint(double a)` Returns the `double` value that is closest in value to the argument and is equal to a mathematical integer.
    `static long` | `round(double a)` Returns the closest `long` to the argument, with ties rounding up.
    `static int` | `round(float a)` Returns the closest `int` to the argument, with ties rounding up.
    `static double` | `scalb(double d, int scaleFactor)` Return `d` × 2`scaleFactor` rounded as if performed by a single correctly rounded floating-point multiply to a member of the double value set.
    `static float` | `scalb(float f, int scaleFactor)` Return `f` × 2`scaleFactor` rounded as if performed by a single correctly rounded floating-point multiply to a member of the float value set.
    `static double` | `signum(double d)` 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.
    `static float` | `signum(float f)` 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.
    `static double` | `sin(double a)` Returns the trigonometric sine of an angle.
    `static double` | `sinh(double x)` Returns the hyperbolic sine of a `double` value.
    `static double` | `sqrt(double a)` Returns the correctly rounded positive square root of a `double` value.
    `static double` | `tan(double a)` Returns the trigonometric tangent of an angle.
    `static double` | `tanh(double x)` Returns the hyperbolic tangent of a `double` value.
    `static double` | `toDegrees(double angrad)` Converts an angle measured in radians to an approximately equivalent angle measured in degrees.
    `static double` | `toRadians(double angdeg)` Converts an angle measured in degrees to an approximately equivalent angle measured in radians.
    `static double` | `ulp(double d)` Returns the size of an ulp of the argument.
    `static float` | `ulp(float f)` Returns the size of an ulp of the argument.

    - ### Methods inherited from class java.lang.Object

      `clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait`

- - ### Field Detail

    - #### E

          public static final double E

      The `double` value that is closer than any other to e, the base of the natural logarithms.
      See Also:
        Constant Field Values

    - #### PI

          public static final double PI

      The `double` value that is closer than any other to pi, the ratio of the circumference of a circle to its diameter.
      See Also:
        Constant Field Values

  - ### Method Detail

    - #### sin

          public static double sin(double a)

      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.

      The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.

      Parameters:
        `a` - an angle, in radians.
      Returns:
        the sine of the argument.

    - #### cos

          public static double cos(double a)

      Returns the trigonometric cosine of an angle. Special cases:
      - If the argument is NaN or an infinity, then the result is NaN.

      The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.

      Parameters:
        `a` - an angle, in radians.
      Returns:
        the cosine of the argument.

    - #### tan

          public static double tan(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.

      The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.

      Parameters:
        `a` - an angle, in radians.
      Returns:
        the tangent of the argument.

    - #### asin

          public static double asin(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.

      The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.

      Parameters:
        `a` - the value whose arc sine is to be returned.
      Returns:
        the arc sine of the argument.

    - #### acos

          public static double acos(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.

      The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.

      Parameters:
        `a` - the value whose arc cosine is to be returned.
      Returns:
        the arc cosine of the argument.

    - #### atan

          public static double atan(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.

      The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.

      Parameters:
        `a` - the value whose arc tangent is to be returned.
      Returns:
        the arc tangent of the argument.

    - #### toRadians

          public static double toRadians(double angdeg)

      Converts an angle measured in degrees to an approximately equivalent angle measured in radians. The conversion from degrees to radians is generally inexact.
      Parameters:
        `angdeg` - an angle, in degrees
      Returns:
        the measurement of the angle `angdeg` in radians.
      Since:
        1.2

    - #### toDegrees

          public static double toDegrees(double angrad)

      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`.
      Parameters:
        `angrad` - an angle, in radians
      Returns:
        the measurement of the angle `angrad` in degrees.
      Since:
        1.2

    - #### exp

          public static double exp(double a)

      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.

      The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.

      Parameters:
        `a` - the exponent to raise e to.
      Returns:
        the value e`a`, where e is the base of the natural logarithms.

    - #### log

          public static double log(double 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.

      The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.

      Parameters:
        `a` - a value
      Returns:
        the value ln `a`, the natural logarithm of `a`.

    - #### log10

          public static double log10(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.

      The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.

      Parameters:
        `a` - a value
      Returns:
        the base 10 logarithm of `a`.
      Since:
        1.5

    - #### sqrt

          public static double sqrt(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.
      Parameters:
        `a` - a value.
      Returns:
        the positive square root of `a`. If the argument is NaN or less than zero, the result is NaN.

    - #### cbrt

          public static double cbrt(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.

      The computed result must be within 1 ulp of the exact result.

      Parameters:
        `a` - a value.
      Returns:
        the cube root of `a`.
      Since:
        1.5

    - #### IEEEremainder

          public static double IEEEremainder(double f1,
                             double f2)

      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.
      Parameters:
        `f1` - the dividend.
        `f2` - the divisor.
      Returns:
        the remainder when `f1` is divided by `f2`.

    - #### ceil

          public static double ceil(double a)

      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 `Math.ceil(x)` is exactly the value of `-Math.floor(-x)`.
      Parameters:
        `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.

    - #### floor

          public static double floor(double a)

      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.
      Parameters:
        `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.

    - #### rint

          public static double rint(double a)

      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, 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.
      Parameters:
        `a` - a `double` value.
      Returns:
        the closest floating-point value to `a` that is equal to a mathematical integer.

    - #### atan2

          public static double atan2(double y,
                     double x)

      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.

      The computed result must be within 2 ulps of the exact result. Results must be semi-monotonic.

      Parameters:
        `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.

    - #### pow

          public static double pow(double a,
                   double b)

      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.)

      The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.

      Parameters:
        `a` - the base.
        `b` - the exponent.
      Returns:
        the value `a``b`.

    - #### round

          public static int round(float a)

      Returns the closest `int` to the argument, with ties rounding up.

      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`.
      Parameters:
        `a` - a floating-point value to be rounded to an integer.
      Returns:
        the value of the argument rounded to the nearest `int` value.
      See Also:
        `Integer.MAX_VALUE`, `Integer.MIN_VALUE`

    - #### round

          public static long round(double a)

      Returns the closest `long` to the argument, with ties rounding up.

      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`.
      Parameters:
        `a` - a floating-point value to be rounded to a `long`.
      Returns:
        the value of the argument rounded to the nearest `long` value.
      See Also:
        `Long.MAX_VALUE`, `Long.MIN_VALUE`

    - #### random

          public static double 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.

      Returns:
        a pseudorandom `double` greater than or equal to `0.0` and less than `1.0`.
      See Also:
        `Random.nextDouble()`

    - #### abs

          public static int abs(int a)

      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.

      Parameters:
        `a` - the argument whose absolute value is to be determined
      Returns:
        the absolute value of the argument.

    - #### abs

          public static long abs(long 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.

      Parameters:
        `a` - the argument whose absolute value is to be determined
      Returns:
        the absolute value of the argument.

    - #### abs

          public static float abs(float 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.
      In other words, the result is the same as the value of the expression:

      `Float.intBitsToFloat(0x7fffffff & Float.floatToIntBits(a))`

      Parameters:
        `a` - the argument whose absolute value is to be determined
      Returns:
        the absolute value of the argument.

    - #### abs

          public static double abs(double 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.
      In other words, the result is the same as the value of the expression:

      `Double.longBitsToDouble((Double.doubleToLongBits(a)<<1)>>>1)`

      Parameters:
        `a` - the argument whose absolute value is to be determined
      Returns:
        the absolute value of the argument.

    - #### max

          public static int max(int a,
                int b)

      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.
      Parameters:
        `a` - an argument.
        `b` - another argument.
      Returns:
        the larger of `a` and `b`.

    - #### max

          public static long max(long a,
                 long 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.
      Parameters:
        `a` - an argument.
        `b` - another argument.
      Returns:
        the larger of `a` and `b`.

    - #### max

          public static float max(float a,
                  float 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.
      Parameters:
        `a` - an argument.
        `b` - another argument.
      Returns:
        the larger of `a` and `b`.

    - #### max

          public static double max(double a,
                   double 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.
      Parameters:
        `a` - an argument.
        `b` - another argument.
      Returns:
        the larger of `a` and `b`.

    - #### min

          public static int min(int a,
                int 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.
      Parameters:
        `a` - an argument.
        `b` - another argument.
      Returns:
        the smaller of `a` and `b`.

    - #### min

          public static long min(long a,
                 long 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.
      Parameters:
        `a` - an argument.
        `b` - another argument.
      Returns:
        the smaller of `a` and `b`.

    - #### min

          public static float min(float a,
                  float 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.
      Parameters:
        `a` - an argument.
        `b` - another argument.
      Returns:
        the smaller of `a` and `b`.

    - #### min

          public static double min(double a,
                   double 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.
      Parameters:
        `a` - an argument.
        `b` - another argument.
      Returns:
        the smaller of `a` and `b`.

    - #### ulp

          public static double ulp(double d)

      Returns the size of an ulp of the argument. An ulp 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.
      Parameters:
        `d` - the floating-point value whose ulp is to be returned
      Returns:
        the size of an ulp of the argument
      Since:
        1.5

    - #### ulp

          public static float ulp(float f)

      Returns the size of an ulp of the argument. An ulp 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.
      Parameters:
        `f` - the floating-point value whose ulp is to be returned
      Returns:
        the size of an ulp of the argument
      Since:
        1.5

    - #### signum

          public static double signum(double d)

      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.
      Parameters:
        `d` - the floating-point value whose signum is to be returned
      Returns:
        the signum function of the argument
      Since:
        1.5

    - #### signum

          public static float signum(float f)

      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.
      Parameters:
        `f` - the floating-point value whose signum is to be returned
      Returns:
        the signum function of the argument
      Since:
        1.5

    - #### sinh

          public static double sinh(double x)

      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.

      The computed result must be within 2.5 ulps of the exact result.

      Parameters:
        `x` - The number whose hyperbolic sine is to be returned.
      Returns:
        The hyperbolic sine of `x`.
      Since:
        1.5

    - #### cosh

          public static double cosh(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`.

      The computed result must be within 2.5 ulps of the exact result.

      Parameters:
        `x` - The number whose hyperbolic cosine is to be returned.
      Returns:
        The hyperbolic cosine of `x`.
      Since:
        1.5

    - #### tanh

          public static double tanh(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`.

      The computed result must be within 2.5 ulps of the exact result. The result of `tanh` for any finite input must have an absolute value less than or equal to 1. Note that once the exact result of tanh is within 1/2 of an ulp of the limit value of ±1, correctly signed ±`1.0` should be returned.

      Parameters:
        `x` - The number whose hyperbolic tangent is to be returned.
      Returns:
        The hyperbolic tangent of `x`.
      Since:
        1.5

    - #### hypot

          public static double hypot(double x,
                     double y)

      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.

      The computed result must be within 1 ulp of the exact result. If one parameter is held constant, the results must be semi-monotonic in the other parameter.

      Parameters:
        `x` - a value
        `y` - a value
      Returns:
        sqrt(x2 +y2) without intermediate overflow or underflow
      Since:
        1.5

    - #### expm1

          public static double expm1(double x)

      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.

      The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic. The result of `expm1` for any finite input must be greater than or equal to `-1.0`. Note that once the exact result of e`x` - 1 is within 1/2 ulp of the limit value -1, `-1.0` should be returned.

      Parameters:
        `x` - the exponent to raise e to in the computation of e`x` -1.
      Returns:
        the value e`x` - 1.
      Since:
        1.5

    - #### log1p

          public static double log1p(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.

      The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.

      Parameters:
        `x` - a value
      Returns:
        the value ln(`x` + 1), the natural log of `x` + 1
      Since:
        1.5

    - #### copySign

          public static double copySign(double magnitude,
                        double sign)

      Returns the first floating-point argument with the sign of the second floating-point argument. Note that unlike the `StrictMath.copySign` method, this method does not require NaN `sign` arguments to be treated as positive values; implementations are permitted to treat some NaN arguments as positive and other NaN arguments as negative to allow greater performance.
      Parameters:
        `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

    - #### copySign

          public static float copySign(float magnitude,
                       float sign)

      Returns the first floating-point argument with the sign of the second floating-point argument. Note that unlike the `StrictMath.copySign` method, this method does not require NaN `sign` arguments to be treated as positive values; implementations are permitted to treat some NaN arguments as positive and other NaN arguments as negative to allow greater performance.
      Parameters:
        `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

    - #### getExponent

          public static int getExponent(float f)

      Returns the unbiased exponent used in the representation of a `float`. Special cases:
      - If the argument is NaN or infinite, then the result is `Float.MAX_EXPONENT` + 1.
      - If the argument is zero or subnormal, then the result is `Float.MIN_EXPONENT` -1.
      Parameters:
        `f` - a `float` value
      Returns:
        the unbiased exponent of the argument
      Since:
        1.6

    - #### getExponent

          public static int getExponent(double d)

      Returns the unbiased exponent used in the representation of a `double`. Special cases:
      - If the argument is NaN or infinite, then the result is `Double.MAX_EXPONENT` + 1.
      - If the argument is zero or subnormal, then the result is `Double.MIN_EXPONENT` -1.
      Parameters:
        `d` - a `double` value
      Returns:
        the unbiased exponent of the argument
      Since:
        1.6

    - #### nextAfter

          public static double nextAfter(double start,
                         double direction)

      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.
      Parameters:
        `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

    - #### nextAfter

          public static float nextAfter(float start,
                        double 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.
      Parameters:
        `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

    - #### nextUp

          public static double nextUp(double d)

      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`
      Parameters:
        `d` - starting floating-point value
      Returns:
        The adjacent floating-point value closer to positive infinity.
      Since:
        1.6

    - #### nextUp

          public static float nextUp(float f)

      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`
      Parameters:
        `f` - starting floating-point value
      Returns:
        The adjacent floating-point value closer to positive infinity.
      Since:
        1.6

    - #### scalb

          public static double scalb(double d,
                     int scaleFactor)

      Return `d` × 2`scaleFactor` 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.
      Parameters:
        `d` - number to be scaled by a power of two.
        `scaleFactor` - power of 2 used to scale `d`
      Returns:
        `d` × 2`scaleFactor`
      Since:
        1.6

    - #### scalb

          public static float scalb(float f,
                    int scaleFactor)

      Return `f` × 2`scaleFactor` 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.
      Parameters:
        `f` - number to be scaled by a power of two.
        `scaleFactor` - power of 2 used to scale `f`
      Returns:
        `f` × 2`scaleFactor`
      Since:
        1.6

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