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/*
* Portions Copyright IBM Corporation, 2001. All Rights Reserved.
*/
package java.math;
/**
* Specifies a <i>rounding behavior</i> 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 <i>discarded fraction</i> 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.
*
* <p>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
* {@code BigDecimal} number with the specified value, forming a
* {@link MathContext} object with the proper settings
* ({@code precision} set to {@code 1}, and the
* {@code roundingMode} set to the rounding mode in question), and
* calling {@link BigDecimal#round round} on this number with the
* proper {@code MathContext}. A summary table showing the results
* of these rounding operations for all rounding modes appears below.
*
*<table border>
* <caption><b>Summary of Rounding Operations Under Different Rounding Modes</b></caption>
* <tr><th></th><th colspan=8>Result of rounding input to one digit with the given
* rounding mode</th>
* <tr valign=top>
* <th>Input Number</th> <th>{@code UP}</th>
* <th>{@code DOWN}</th>
* <th>{@code CEILING}</th>
* <th>{@code FLOOR}</th>
* <th>{@code HALF_UP}</th>
* <th>{@code HALF_DOWN}</th>
* <th>{@code HALF_EVEN}</th>
* <th>{@code UNNECESSARY}</th>
*
* <tr align=right><td>5.5</td> <td>6</td> <td>5</td> <td>6</td> <td>5</td> <td>6</td> <td>5</td> <td>6</td> <td>throw {@code ArithmeticException}</td>
* <tr align=right><td>2.5</td> <td>3</td> <td>2</td> <td>3</td> <td>2</td> <td>3</td> <td>2</td> <td>2</td> <td>throw {@code ArithmeticException}</td>
* <tr align=right><td>1.6</td> <td>2</td> <td>1</td> <td>2</td> <td>1</td> <td>2</td> <td>2</td> <td>2</td> <td>throw {@code ArithmeticException}</td>
* <tr align=right><td>1.1</td> <td>2</td> <td>1</td> <td>2</td> <td>1</td> <td>1</td> <td>1</td> <td>1</td> <td>throw {@code ArithmeticException}</td>
* <tr align=right><td>1.0</td> <td>1</td> <td>1</td> <td>1</td> <td>1</td> <td>1</td> <td>1</td> <td>1</td> <td>1</td>
* <tr align=right><td>-1.0</td> <td>-1</td> <td>-1</td> <td>-1</td> <td>-1</td> <td>-1</td> <td>-1</td> <td>-1</td> <td>-1</td>
* <tr align=right><td>-1.1</td> <td>-2</td> <td>-1</td> <td>-1</td> <td>-2</td> <td>-1</td> <td>-1</td> <td>-1</td> <td>throw {@code ArithmeticException}</td>
* <tr align=right><td>-1.6</td> <td>-2</td> <td>-1</td> <td>-1</td> <td>-2</td> <td>-2</td> <td>-2</td> <td>-2</td> <td>throw {@code ArithmeticException}</td>
* <tr align=right><td>-2.5</td> <td>-3</td> <td>-2</td> <td>-2</td> <td>-3</td> <td>-3</td> <td>-2</td> <td>-2</td> <td>throw {@code ArithmeticException}</td>
* <tr align=right><td>-5.5</td> <td>-6</td> <td>-5</td> <td>-5</td> <td>-6</td> <td>-6</td> <td>-5</td> <td>-6</td> <td>throw {@code ArithmeticException}</td>
*</table>
*
*
* <p>This {@code enum} is intended to replace the integer-based
* enumeration of rounding mode constants in {@link BigDecimal}
* ({@link BigDecimal#ROUND_UP}, {@link BigDecimal#ROUND_DOWN},
* etc. ).
*
* @see BigDecimal
* @see MathContext
* @author Josh Bloch
* @author Mike Cowlishaw
* @author Joseph D. Darcy
* @since 1.5
*/
public enum RoundingMode {
/**
* 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.
*
*<p>Example:
*<table border>
* <caption><b>Rounding mode UP Examples</b></caption>
*<tr valign=top><th>Input Number</th>
* <th>Input rounded to one digit<br> with {@code UP} rounding
*<tr align=right><td>5.5</td> <td>6</td>
*<tr align=right><td>2.5</td> <td>3</td>
*<tr align=right><td>1.6</td> <td>2</td>
*<tr align=right><td>1.1</td> <td>2</td>
*<tr align=right><td>1.0</td> <td>1</td>
*<tr align=right><td>-1.0</td> <td>-1</td>
*<tr align=right><td>-1.1</td> <td>-2</td>
*<tr align=right><td>-1.6</td> <td>-2</td>
*<tr align=right><td>-2.5</td> <td>-3</td>
*<tr align=right><td>-5.5</td> <td>-6</td>
*</table>
*/
UP(BigDecimal.ROUND_UP),
/**
* 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.
*
*<p>Example:
*<table border>
* <caption><b>Rounding mode DOWN Examples</b></caption>
*<tr valign=top><th>Input Number</th>
* <th>Input rounded to one digit<br> with {@code DOWN} rounding
*<tr align=right><td>5.5</td> <td>5</td>
*<tr align=right><td>2.5</td> <td>2</td>
*<tr align=right><td>1.6</td> <td>1</td>
*<tr align=right><td>1.1</td> <td>1</td>
*<tr align=right><td>1.0</td> <td>1</td>
*<tr align=right><td>-1.0</td> <td>-1</td>
*<tr align=right><td>-1.1</td> <td>-1</td>
*<tr align=right><td>-1.6</td> <td>-1</td>
*<tr align=right><td>-2.5</td> <td>-2</td>
*<tr align=right><td>-5.5</td> <td>-5</td>
*</table>
*/
DOWN(BigDecimal.ROUND_DOWN),
/**
* Rounding mode to round towards positive infinity. If the
* result is positive, behaves as for {@code RoundingMode.UP};
* if negative, behaves as for {@code RoundingMode.DOWN}. Note
* that this rounding mode never decreases the calculated value.
*
*<p>Example:
*<table border>
* <caption><b>Rounding mode CEILING Examples</b></caption>
*<tr valign=top><th>Input Number</th>
* <th>Input rounded to one digit<br> with {@code CEILING} rounding
*<tr align=right><td>5.5</td> <td>6</td>
*<tr align=right><td>2.5</td> <td>3</td>
*<tr align=right><td>1.6</td> <td>2</td>
*<tr align=right><td>1.1</td> <td>2</td>
*<tr align=right><td>1.0</td> <td>1</td>
*<tr align=right><td>-1.0</td> <td>-1</td>
*<tr align=right><td>-1.1</td> <td>-1</td>
*<tr align=right><td>-1.6</td> <td>-1</td>
*<tr align=right><td>-2.5</td> <td>-2</td>
*<tr align=right><td>-5.5</td> <td>-5</td>
*</table>
*/
CEILING(BigDecimal.ROUND_CEILING),
/**
* Rounding mode to round towards negative infinity. If the
* result is positive, behave as for {@code RoundingMode.DOWN};
* if negative, behave as for {@code RoundingMode.UP}. Note that
* this rounding mode never increases the calculated value.
*
*<p>Example:
*<table border>
* <caption><b>Rounding mode FLOOR Examples</b></caption>
*<tr valign=top><th>Input Number</th>
* <th>Input rounded to one digit<br> with {@code FLOOR} rounding
*<tr align=right><td>5.5</td> <td>5</td>
*<tr align=right><td>2.5</td> <td>2</td>
*<tr align=right><td>1.6</td> <td>1</td>
*<tr align=right><td>1.1</td> <td>1</td>
*<tr align=right><td>1.0</td> <td>1</td>
*<tr align=right><td>-1.0</td> <td>-1</td>
*<tr align=right><td>-1.1</td> <td>-2</td>
*<tr align=right><td>-1.6</td> <td>-2</td>
*<tr align=right><td>-2.5</td> <td>-3</td>
*<tr align=right><td>-5.5</td> <td>-6</td>
*</table>
*/
FLOOR(BigDecimal.ROUND_FLOOR),
/**
* Rounding mode to round towards {@literal "nearest neighbor"}
* unless both neighbors are equidistant, in which case round up.
* Behaves as for {@code RoundingMode.UP} if the discarded
* fraction is ≥ 0.5; otherwise, behaves as for
* {@code RoundingMode.DOWN}. Note that this is the rounding
* mode commonly taught at school.
*
*<p>Example:
*<table border>
* <caption><b>Rounding mode HALF_UP Examples</b></caption>
*<tr valign=top><th>Input Number</th>
* <th>Input rounded to one digit<br> with {@code HALF_UP} rounding
*<tr align=right><td>5.5</td> <td>6</td>
*<tr align=right><td>2.5</td> <td>3</td>
*<tr align=right><td>1.6</td> <td>2</td>
*<tr align=right><td>1.1</td> <td>1</td>
*<tr align=right><td>1.0</td> <td>1</td>
*<tr align=right><td>-1.0</td> <td>-1</td>
*<tr align=right><td>-1.1</td> <td>-1</td>
*<tr align=right><td>-1.6</td> <td>-2</td>
*<tr align=right><td>-2.5</td> <td>-3</td>
*<tr align=right><td>-5.5</td> <td>-6</td>
*</table>
*/
HALF_UP(BigDecimal.ROUND_HALF_UP),
/**
* Rounding mode to round towards {@literal "nearest neighbor"}
* unless both neighbors are equidistant, in which case round
* down. Behaves as for {@code RoundingMode.UP} if the discarded
* fraction is > 0.5; otherwise, behaves as for
* {@code RoundingMode.DOWN}.
*
*<p>Example:
*<table border>
* <caption><b>Rounding mode HALF_DOWN Examples</b></caption>
*<tr valign=top><th>Input Number</th>
* <th>Input rounded to one digit<br> with {@code HALF_DOWN} rounding
*<tr align=right><td>5.5</td> <td>5</td>
*<tr align=right><td>2.5</td> <td>2</td>
*<tr align=right><td>1.6</td> <td>2</td>
*<tr align=right><td>1.1</td> <td>1</td>
*<tr align=right><td>1.0</td> <td>1</td>
*<tr align=right><td>-1.0</td> <td>-1</td>
*<tr align=right><td>-1.1</td> <td>-1</td>
*<tr align=right><td>-1.6</td> <td>-2</td>
*<tr align=right><td>-2.5</td> <td>-2</td>
*<tr align=right><td>-5.5</td> <td>-5</td>
*</table>
*/
HALF_DOWN(BigDecimal.ROUND_HALF_DOWN),
/**
* Rounding mode to round towards the {@literal "nearest neighbor"}
* unless both neighbors are equidistant, in which case, round
* towards the even neighbor. Behaves as for
* {@code RoundingMode.HALF_UP} if the digit to the left of the
* discarded fraction is odd; behaves as for
* {@code 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 {@literal "Banker's rounding,"} and is
* chiefly used in the USA. This rounding mode is analogous to
* the rounding policy used for {@code float} and {@code double}
* arithmetic in Java.
*
*<p>Example:
*<table border>
* <caption><b>Rounding mode HALF_EVEN Examples</b></caption>
*<tr valign=top><th>Input Number</th>
* <th>Input rounded to one digit<br> with {@code HALF_EVEN} rounding
*<tr align=right><td>5.5</td> <td>6</td>
*<tr align=right><td>2.5</td> <td>2</td>
*<tr align=right><td>1.6</td> <td>2</td>
*<tr align=right><td>1.1</td> <td>1</td>
*<tr align=right><td>1.0</td> <td>1</td>
*<tr align=right><td>-1.0</td> <td>-1</td>
*<tr align=right><td>-1.1</td> <td>-1</td>
*<tr align=right><td>-1.6</td> <td>-2</td>
*<tr align=right><td>-2.5</td> <td>-2</td>
*<tr align=right><td>-5.5</td> <td>-6</td>
*</table>
*/
HALF_EVEN(BigDecimal.ROUND_HALF_EVEN),
/**
* 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
* {@code ArithmeticException} is thrown.
*<p>Example:
*<table border>
* <caption><b>Rounding mode UNNECESSARY Examples</b></caption>
*<tr valign=top><th>Input Number</th>
* <th>Input rounded to one digit<br> with {@code UNNECESSARY} rounding
*<tr align=right><td>5.5</td> <td>throw {@code ArithmeticException}</td>
*<tr align=right><td>2.5</td> <td>throw {@code ArithmeticException}</td>
*<tr align=right><td>1.6</td> <td>throw {@code ArithmeticException}</td>
*<tr align=right><td>1.1</td> <td>throw {@code ArithmeticException}</td>
*<tr align=right><td>1.0</td> <td>1</td>
*<tr align=right><td>-1.0</td> <td>-1</td>
*<tr align=right><td>-1.1</td> <td>throw {@code ArithmeticException}</td>
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