java.math

## Enum RoundingMode

- java.lang.Object
- - java.lang.Enum<RoundingMode>
  - - java.math.RoundingMode

- All Implemented Interfaces:
    Serializable, Comparable<RoundingMode>

      public enum RoundingMode
      extends Enum<RoundingMode>

  Specifies a rounding behavior for numerical operations capable of discarding precision. Each rounding mode indicates how the least significant returned digit of a rounded result is to be calculated. If fewer digits are returned than the digits needed to represent the exact numerical result, the discarded digits will be referred to as the discarded fraction regardless the digits' contribution to the value of the number. In other words, considered as a numerical value, the discarded fraction could have an absolute value greater than one.

  Each rounding mode description includes a table listing how different two-digit decimal values would round to a one digit decimal value under the rounding mode in question. The result column in the tables could be gotten by creating a `BigDecimal` number with the specified value, forming a `MathContext` object with the proper settings (`precision` set to `1`, and the `roundingMode` set to the rounding mode in question), and calling `round` on this number with the proper `MathContext`. A summary table showing the results of these rounding operations for all rounding modes appears below.

  Summary of Rounding Operations Under Different Rounding Modes
  | Result of rounding input to one digit with the given rounding mode
  --- | ---
  Input Number | `UP` | `DOWN` | `CEILING` | `FLOOR` | `HALF_UP` | `HALF_DOWN` | `HALF_EVEN` | `UNNECESSARY`
  5.5 | 6 | 5 | 6 | 5 | 6 | 5 | 6 | throw `ArithmeticException`
  2.5 | 3 | 2 | 3 | 2 | 3 | 2 | 2 | throw `ArithmeticException`
  1.6 | 2 | 1 | 2 | 1 | 2 | 2 | 2 | throw `ArithmeticException`
  1.1 | 2 | 1 | 2 | 1 | 1 | 1 | 1 | throw `ArithmeticException`
  1.0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1
  -1.0 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1
  -1.1 | -2 | -1 | -1 | -2 | -1 | -1 | -1 | throw `ArithmeticException`
  -1.6 | -2 | -1 | -1 | -2 | -2 | -2 | -2 | throw `ArithmeticException`
  -2.5 | -3 | -2 | -2 | -3 | -3 | -2 | -2 | throw `ArithmeticException`
  -5.5 | -6 | -5 | -5 | -6 | -6 | -5 | -6 | throw `ArithmeticException`

  This `enum` is intended to replace the integer-based enumeration of rounding mode constants in `BigDecimal` (`BigDecimal.ROUND_UP`, `BigDecimal.ROUND_DOWN`, etc. ).

  Since:
    1.5
  Author:
    Josh Bloch, Mike Cowlishaw, Joseph D. Darcy
  See Also:
    `BigDecimal`, `MathContext`

- - ### Enum Constant Summary

    Enum Constants
    Enum Constant and Description
    `CEILING` Rounding mode to round towards positive infinity.
    `DOWN` Rounding mode to round towards zero.
    `FLOOR` Rounding mode to round towards negative infinity.
    `HALF_DOWN` Rounding mode to round towards "nearest neighbor" unless both neighbors are equidistant, in which case round down.
    `HALF_EVEN` Rounding mode to round towards the "nearest neighbor" unless both neighbors are equidistant, in which case, round towards the even neighbor.
    `HALF_UP` Rounding mode to round towards "nearest neighbor" unless both neighbors are equidistant, in which case round up.
    `UNNECESSARY` Rounding mode to assert that the requested operation has an exact result, hence no rounding is necessary.
    `UP` Rounding mode to round away from zero.

  - ### Method Summary

    All Methods Static Methods Concrete Methods
    Modifier and Type | Method and Description
    --- | ---
    `static RoundingMode` | `valueOf(int rm)` Returns the `RoundingMode` object corresponding to a legacy integer rounding mode constant in `BigDecimal`.
    `static RoundingMode` | `valueOf(String name)` Returns the enum constant of this type with the specified name.
    `static RoundingMode[]` | `values()` Returns an array containing the constants of this enum type, in the order they are declared.

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

      `clone, compareTo, equals, finalize, getDeclaringClass, hashCode, name, ordinal, toString, valueOf`

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

      `getClass, notify, notifyAll, wait, wait, wait`

- - ### Enum Constant Detail

    - #### UP

          public static final RoundingMode UP

      Rounding mode to round away from zero. Always increments the digit prior to a non-zero discarded fraction. Note that this rounding mode never decreases the magnitude of the calculated value.

      Example:

      Input Number | Input rounded to one digit with `UP` rounding
      --- | ---
      5.5 | 6
      2.5 | 3
      1.6 | 2
      1.1 | 2
      1.0 | 1
      -1.0 | -1
      -1.1 | -2
      -1.6 | -2
      -2.5 | -3
      -5.5 | -6

    - #### DOWN

          public static final RoundingMode DOWN

      Rounding mode to round towards zero. Never increments the digit prior to a discarded fraction (i.e., truncates). Note that this rounding mode never increases the magnitude of the calculated value.

      Example:

      Input Number | Input rounded to one digit with `DOWN` rounding
      --- | ---
      5.5 | 5
      2.5 | 2
      1.6 | 1
      1.1 | 1
      1.0 | 1
      -1.0 | -1
      -1.1 | -1
      -1.6 | -1
      -2.5 | -2
      -5.5 | -5

    - #### CEILING

          public static final RoundingMode CEILING

      Rounding mode to round towards positive infinity. If the result is positive, behaves as for `RoundingMode.UP`; if negative, behaves as for `RoundingMode.DOWN`. Note that this rounding mode never decreases the calculated value.

      Example:

      Input Number | Input rounded to one digit with `CEILING` rounding
      --- | ---
      5.5 | 6
      2.5 | 3
      1.6 | 2
      1.1 | 2
      1.0 | 1
      -1.0 | -1
      -1.1 | -1
      -1.6 | -1
      -2.5 | -2
      -5.5 | -5

    - #### FLOOR

          public static final RoundingMode FLOOR

      Rounding mode to round towards negative infinity. If the result is positive, behave as for `RoundingMode.DOWN`; if negative, behave as for `RoundingMode.UP`. Note that this rounding mode never increases the calculated value.

      Example:

      Input Number | Input rounded to one digit with `FLOOR` rounding
      --- | ---
      5.5 | 5
      2.5 | 2
      1.6 | 1
      1.1 | 1
      1.0 | 1
      -1.0 | -1
      -1.1 | -2
      -1.6 | -2
      -2.5 | -3
      -5.5 | -6

    - #### HALF_UP

          public static final RoundingMode HALF_UP

      Rounding mode to round towards "nearest neighbor" unless both neighbors are equidistant, in which case round up. Behaves as for `RoundingMode.UP` if the discarded fraction is ≥ 0.5; otherwise, behaves as for `RoundingMode.DOWN`. Note that this is the rounding mode commonly taught at school.

      Example:

      Input Number | Input rounded to one digit with `HALF_UP` rounding
      --- | ---
      5.5 | 6
      2.5 | 3
      1.6 | 2
      1.1 | 1
      1.0 | 1
      -1.0 | -1
      -1.1 | -1
      -1.6 | -2
      -2.5 | -3
      -5.5 | -6

    - #### HALF_DOWN

          public static final RoundingMode HALF_DOWN

      Rounding mode to round towards "nearest neighbor" unless both neighbors are equidistant, in which case round down. Behaves as for `RoundingMode.UP` if the discarded fraction is > 0.5; otherwise, behaves as for `RoundingMode.DOWN`.

      Example:

      Input Number | Input rounded to one digit with `HALF_DOWN` rounding
      --- | ---
      5.5 | 5
      2.5 | 2
      1.6 | 2
      1.1 | 1
      1.0 | 1
      -1.0 | -1
      -1.1 | -1
      -1.6 | -2
      -2.5 | -2
      -5.5 | -5

    - #### HALF_EVEN

          public static final RoundingMode HALF_EVEN

      Rounding mode to round towards the "nearest neighbor" unless both neighbors are equidistant, in which case, round towards the even neighbor. Behaves as for `RoundingMode.HALF_UP` if the digit to the left of the discarded fraction is odd; behaves as for `RoundingMode.HALF_DOWN` if it's even. Note that this is the rounding mode that statistically minimizes cumulative error when applied repeatedly over a sequence of calculations. It is sometimes known as "Banker's rounding," and is chiefly used in the USA. This rounding mode is analogous to the rounding policy used for `float` and `double` arithmetic in Java.

      Example:

      Input Number | Input rounded to one digit with `HALF_EVEN` rounding
      --- | ---
      5.5 | 6
      2.5 | 2
      1.6 | 2
      1.1 | 1
      1.0 | 1
      -1.0 | -1
      -1.1 | -1
      -1.6 | -2
      -2.5 | -2
      -5.5 | -6

    - #### UNNECESSARY

          public static final RoundingMode UNNECESSARY

      Rounding mode to assert that the requested operation has an exact result, hence no rounding is necessary. If this rounding mode is specified on an operation that yields an inexact result, an `ArithmeticException` is thrown.

      Example:

      Input Number | Input rounded to one digit with `UNNECESSARY` rounding
      --- | ---
      5.5 | throw `ArithmeticException`
      2.5 | throw `ArithmeticException`
      1.6 | throw `ArithmeticException`
      1.1 | throw `ArithmeticException`
      1.0 | 1
      -1.0 | -1
      -1.1 | throw `ArithmeticException`
      -1.6 | throw `ArithmeticException`
      -2.5 | throw `ArithmeticException`
      -5.5 | throw `ArithmeticException`

  - ### Method Detail

    - #### values

          public static RoundingMode[] values()

      Returns an array containing the constants of this enum type, in the order they are declared. This method may be used to iterate over the constants as follows:

          for (RoundingMode c : RoundingMode.values())
              System.out.println(c);

      Returns:
        an array containing the constants of this enum type, in the order they are declared

    - #### valueOf

          public static RoundingMode valueOf(String name)

      Returns the enum constant of this type with the specified name. The string must match exactly an identifier used to declare an enum constant in this type. (Extraneous whitespace characters are not permitted.)
      Parameters:
        `name` - the name of the enum constant to be returned.
      Returns:
        the enum constant with the specified name
      Throws:
        `IllegalArgumentException` - if this enum type has no constant with the specified name
        `NullPointerException` - if the argument is null

    - #### valueOf

          public static RoundingMode valueOf(int rm)

      Returns the `RoundingMode` object corresponding to a legacy integer rounding mode constant in `BigDecimal`.
      Parameters:
        `rm` - legacy integer rounding mode to convert
      Returns:
        `RoundingMode` corresponding to the given integer.
      Throws:
        `IllegalArgumentException` - integer is out of range

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