Java BigDecimal中的RoundingMode

BigDecimal有八种RoundingMode，其中最基本的有两种，它们是：

ROUND_UP：Always increments the digit prior to a nonzero discarded fraction. 总是将要丢掉的数字前一位的数字加1.

例如：

Rounding mode UP Examples

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

比方说5.5的scale是1，那么需要丢掉的数字的0.5, 将0.5丢掉，然后给5加1，就变成6了；

需要注意的是-5.5，这里的负号是不参加运算的，将它当成5.5，先进行Round up，然后将负号加上；

ROUND_DOWN：Never increments the digit prior to a discarded fraction (i.e., truncates).将要丢掉的数字直接丢掉。

Rounding mode DOWN Examples

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

比方说5.5的scale是1，那么需要丢掉的数字的0.5, 直接将0.5丢掉就可以了；

需要注意的是-5.5，这里的负号是不参加运算的，将它当成5.5，先进行Round Down，然后将负号加上；

然后其它五中都是根据Round Down/Up来推出来的；

例如：

ROUND_CEILING：If the result is positive, behaves as for RoundingMode.UP; if negative, behaves as forRoundingMode.DOWN.如果参数是正数，使用UP规则，如果参数是负数，使用DOWN规则；

Rounding mode CEILING Examples

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

ROUND_FLOOR：If the result is positive, behave as for RoundingMode.DOWN; if negative, behave as forRoundingMode.UP.如果参数是正数，使用DOWN规则，如果参数是负数，使用UP规则；

Rounding mode FLOOR Examples

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

ROUND_HALF_UP: Behaves as for RoundingMode.UP if the discarded fraction is ≥ 0.5; otherwise, behaves as for RoundingMode.DOWN. 如果要丢掉的数字大于等于0.5，使用UP规则；否则使用DOWN规则；

Rounding mode HALF_UP Examples

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

ROUND_HALF_DOWN: Behaves as for RoundingMode.UP if the discarded fraction is > 0.5; otherwise, behaves as for RoundingMode.DOWN. 如果要丢掉的数字大于0.5，使用UP规则；否则使用DOWN规则；

Rounding mode HALF_DOWN Examples

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

ROUND_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. 如果要丢掉的数字不是5的话，需要看这个数字前面的数字的奇偶性，如果是奇数，使用HALF_UP规则；如果是偶数使用HALF_DOWN规则；如果要丢掉的数字是5的话，round到它的偶数邻居上；

Rounding mode HALF_EVEN Examples

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

ROUND_UNNECESSARY：不需要ROUND

最后来一张总表，

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

refs：

http://stackoverflow.com/questions/792237/why-and-how-does-round-half-even-minimize-cumulative-error-when-applied-repeated

jdk document

http://en.wikipedia.org/wiki/Floor_and_ceiling_functions

http://www.opentaps.org/docs/index.php/How_to_Use_Java_BigDecimal:_A_Tutorial