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. ).

@version
1.x 01/xx/xx
@author
Josh Bloch
@author
Mike Cowlishaw
@author
Joseph D. Darcy
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

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

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

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

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

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

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

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

Compares this enum with the specified object for order. Returns a negative integer, zero, or a positive integer as this object is less than, equal to, or greater than the specified object. Enum constants are only comparable to other enum constants of the same enum type. The natural order implemented by this method is the order in which the constants are declared.
Returns true if the specified object is equal to this enum constant.
Parameters
 other the object to be compared for equality with this object.
Return
true if the specified object is equal to this enum constant.
Returns the runtime class of an object. That Class object is the object that is locked by static synchronized methods of the represented class.
Return
The `java.lang.Class` object that represents the runtime class of the object. The result is of type {@code Class} where X is the erasure of the static type of the expression on which `getClass` is called.
Returns the Class object corresponding to this enum constant's enum type. Two enum constants e1 and e2 are of the same enum type if and only if e1.getDeclaringClass() == e2.getDeclaringClass(). (The value returned by this method may differ from the one returned by the Object#getClass method for enum constants with constant-specific class bodies.)
Return
the Class object corresponding to this enum constant's enum type
Returns a hash code for this enum constant.
Return
a hash code for this enum constant.
Returns the name of this enum constant, exactly as declared in its enum declaration. Most programmers should use the #toString method in preference to this one, as the toString method may return a more user-friendly name. This method is designed primarily for use in specialized situations where correctness depends on getting the exact name, which will not vary from release to release.
Return
the name of this enum constant
Wakes up a single thread that is waiting on this object's monitor. If any threads are waiting on this object, one of them is chosen to be awakened. The choice is arbitrary and occurs at the discretion of the implementation. A thread waits on an object's monitor by calling one of the `wait` methods.

The awakened thread will not be able to proceed until the current thread relinquishes the lock on this object. The awakened thread will compete in the usual manner with any other threads that might be actively competing to synchronize on this object; for example, the awakened thread enjoys no reliable privilege or disadvantage in being the next thread to lock this object.

This method should only be called by a thread that is the owner of this object's monitor. A thread becomes the owner of the object's monitor in one of three ways:

• By executing a synchronized instance method of that object.
• By executing the body of a `synchronized` statement that synchronizes on the object.
• For objects of type `Class,` by executing a synchronized static method of that class.

Only one thread at a time can own an object's monitor.

Throws
 IllegalMonitorStateException if the current thread is not the owner of this object's monitor.
Wakes up all threads that are waiting on this object's monitor. A thread waits on an object's monitor by calling one of the `wait` methods.

The awakened threads will not be able to proceed until the current thread relinquishes the lock on this object. The awakened threads will compete in the usual manner with any other threads that might be actively competing to synchronize on this object; for example, the awakened threads enjoy no reliable privilege or disadvantage in being the next thread to lock this object.

This method should only be called by a thread that is the owner of this object's monitor. See the `notify` method for a description of the ways in which a thread can become the owner of a monitor.

Throws
 IllegalMonitorStateException if the current thread is not the owner of this object's monitor.
Returns the ordinal of this enumeration constant (its position in its enum declaration, where the initial constant is assigned an ordinal of zero). Most programmers will have no use for this method. It is designed for use by sophisticated enum-based data structures, such as java.util.EnumSet and java.util.EnumMap .
Return
the ordinal of this enumeration constant
Returns the name of this enum constant, as contained in the declaration. This method may be overridden, though it typically isn't necessary or desirable. An enum type should override this method when a more "programmer-friendly" string form exists.
Return
the name of this enum constant
Returns the enum constant of the specified enum type with the specified name. The name must match exactly an identifier used to declare an enum constant in this type. (Extraneous whitespace characters are not permitted.)
Parameters
 enumType the Class object of the enum type from which to return a constant name the name of the constant to return
Return
the enum constant of the specified enum type with the specified name
Throws
 IllegalArgumentException if the specified enum type has no constant with the specified name, or the specified class object does not represent an enum type NullPointerException if enumType or name is null
@since
1.5
Returns the RoundingMode object corresponding to a legacy integer rounding mode constant in BigDecimal .
Parameters
 rm legacy integer rounding mode to convert
Return
RoundingMode corresponding to the given integer.
Throws
 IllegalArgumentException integer is out of range
Causes current thread to wait until another thread invokes the method or the method for this object. In other words, this method behaves exactly as if it simply performs the call wait(0).

The current thread must own this object's monitor. The thread releases ownership of this monitor and waits until another thread notifies threads waiting on this object's monitor to wake up either through a call to the `notify` method or the `notifyAll` method. The thread then waits until it can re-obtain ownership of the monitor and resumes execution.

As in the one argument version, interrupts and spurious wakeups are possible, and this method should always be used in a loop:

```     synchronized (obj) {
while (<condition does not hold>)
obj.wait();
... // Perform action appropriate to condition
}
```
This method should only be called by a thread that is the owner of this object's monitor. See the `notify` method for a description of the ways in which a thread can become the owner of a monitor.
Throws
 IllegalMonitorStateException if the current thread is not the owner of the object's monitor. InterruptedException if another thread interrupted the current thread before or while the current thread was waiting for a notification. The interrupted status of the current thread is cleared when this exception is thrown.
Causes current thread to wait until either another thread invokes the method or the method for this object, or a specified amount of time has elapsed.

The current thread must own this object's monitor.

This method causes the current thread (call it T) to place itself in the wait set for this object and then to relinquish any and all synchronization claims on this object. Thread T becomes disabled for thread scheduling purposes and lies dormant until one of four things happens:

• Some other thread invokes the notify method for this object and thread T happens to be arbitrarily chosen as the thread to be awakened.
• Some other thread invokes the notifyAll method for this object.
• The specified amount of real time has elapsed, more or less. If timeout is zero, however, then real time is not taken into consideration and the thread simply waits until notified.
The thread T is then removed from the wait set for this object and re-enabled for thread scheduling. It then competes in the usual manner with other threads for the right to synchronize on the object; once it has gained control of the object, all its synchronization claims on the object are restored to the status quo ante - that is, to the situation as of the time that the wait method was invoked. Thread T then returns from the invocation of the wait method. Thus, on return from the wait method, the synchronization state of the object and of thread T is exactly as it was when the wait method was invoked.

A thread can also wake up without being notified, interrupted, or timing out, a so-called spurious wakeup. While this will rarely occur in practice, applications must guard against it by testing for the condition that should have caused the thread to be awakened, and continuing to wait if the condition is not satisfied. In other words, waits should always occur in loops, like this one:

```     synchronized (obj) {
while (<condition does not hold>)
obj.wait(timeout);
... // Perform action appropriate to condition
}
```
(For more information on this topic, see Section 3.2.3 in Doug Lea's "Concurrent Programming in Java (Second Edition)" (Addison-Wesley, 2000), or Item 50 in Joshua Bloch's "Effective Java Programming Language Guide" (Addison-Wesley, 2001).

If the current thread is interrupted by another thread while it is waiting, then an InterruptedException is thrown. This exception is not thrown until the lock status of this object has been restored as described above.

Note that the wait method, as it places the current thread into the wait set for this object, unlocks only this object; any other objects on which the current thread may be synchronized remain locked while the thread waits.

This method should only be called by a thread that is the owner of this object's monitor. See the `notify` method for a description of the ways in which a thread can become the owner of a monitor.

Parameters
 timeout the maximum time to wait in milliseconds.
Throws
 IllegalArgumentException if the value of timeout is negative. IllegalMonitorStateException if the current thread is not the owner of the object's monitor. InterruptedException if another thread interrupted the current thread before or while the current thread was waiting for a notification. The interrupted status of the current thread is cleared when this exception is thrown.
Causes current thread to wait until another thread invokes the method or the method for this object, or some other thread interrupts the current thread, or a certain amount of real time has elapsed.

This method is similar to the `wait` method of one argument, but it allows finer control over the amount of time to wait for a notification before giving up. The amount of real time, measured in nanoseconds, is given by:

` 1000000*timeout+nanos`

In all other respects, this method does the same thing as the method of one argument. In particular, wait(0, 0) means the same thing as wait(0).

The current thread must own this object's monitor. The thread releases ownership of this monitor and waits until either of the following two conditions has occurred:

• Another thread notifies threads waiting on this object's monitor to wake up either through a call to the `notify` method or the `notifyAll` method.
• The timeout period, specified by `timeout` milliseconds plus `nanos` nanoseconds arguments, has elapsed.

The thread then waits until it can re-obtain ownership of the monitor and resumes execution.

As in the one argument version, interrupts and spurious wakeups are possible, and this method should always be used in a loop:

```     synchronized (obj) {
while (<condition does not hold>)
obj.wait(timeout, nanos);
... // Perform action appropriate to condition
}
```
This method should only be called by a thread that is the owner of this object's monitor. See the `notify` method for a description of the ways in which a thread can become the owner of a monitor.
Parameters
 timeout the maximum time to wait in milliseconds. nanos additional time, in nanoseconds range 0-999999.
Throws
 IllegalArgumentException if the value of timeout is negative or the value of nanos is not in the range 0-999999. IllegalMonitorStateException if the current thread is not the owner of this object's monitor. InterruptedException if another thread interrupted the current thread before or while the current thread was waiting for a notification. The interrupted status of the current thread is cleared when this exception is thrown.