舍入算法

策略

Directed Rounding to an integer

• 定向舍入

  原始值x到舍入值y的舍入方向是固定的：指向或远离限制值（0 或 +-无穷大）

  y=f(x)

Round up

up 有两种解释

toward positive infinity

向正无穷取整

JS Math.ceil

23.5 gets rounded to 24, and −23.5 gets rounded to −23

away from zero

远离零取整（向无穷取整）

23.2 gets rounded to 24, and −23.2 gets rounded to −24

Big.roundUp

Round down

down 有两种解释

toward negative infinity

向负无穷取整

JS Math.floor

23.5 gets rounded to 23, and −23.5 gets rounded to −24

towards zero

向零取整

23.7 gets rounded to 23, and −23.7 gets rounded to −23

Big.roundDown

Rounding to the nearest integer

四舍六入五判断方向

• 小数部分是0.5时，不同的策略有不同的舍入方向
• 通常说的四舍五入采用的策略应该是 Round half up toward positive infinity

Round half up

有两种不同的解释

toward positive infinity

如果距离两个整数的距离相等，则向正无穷方向取整

23.5 gets rounded to 24, and −23.5 gets rounded to −24.

JS Math.round

JS中的 Math.round 采用该策略

Math.round(-Infinity); // -Infinity
Math.round(-20.51); // -21
Math.round(-20.5); // -20
Math.round(-0.1); // -0
Math.round(0); // 0
Math.round(20.49); // 20
Math.round(20.5); // 21
Math.round(42); // 42
Math.round(Infinity); // Infinity

away from zero

Rounds towards nearest neighbour. If equidistant, rounds away from zero

Big.roundHalfUp

> big(-23.5).round().toString()
'-24'
> Math.round(-23.5)
-23

PG numeric#round

d72=# select round(-23.5::numeric);
 round 
-------
   -24
(1 行记录)

Round half down

Round half to odd

如果距离两个整数的距离相等，则取奇数

+23.5 becomes +23, as does +22.5

−23.5 becomes −23, as does −22.5

Round half to even

Rounds towards nearest neighbour. If equidistant, rounds towards even neighbour.

如果距离两个整数的距离相等，则取偶数

0.245 舍入为 0.24

+23.5 becomes +24, as does +24.5; −23.5 becomes −24, as does −24.5.

银行家舍入法 Banker’s round

• 四舍六入五取偶

  0.5 rounds down to 0; 1.5 rounds up to 2

• IEEE 754标准规定的小数舍入标准

• 取最接近的整数，如果有两个最接近的整数，取偶数

  舍入位的数值小于5时舍去

  舍入位的数值大于6时进一

  舍入位的数值等于5时，前位数为奇数，则进一得偶数，前位数为偶数，则舍去留偶数

PG real/double precision#round

d72=# select round(-24.5::real);
 round 
-------
   -24
(1 行记录)

d72=# select round(-23.5::real);
 round 
-------
   -24
(1 行记录)

d72=# select round(-24.5::double precision);
 round 
-------
   -24
(1 行记录)

d72=# select round(-23.5::double precision);
 round 
-------
   -24
(1 行记录)