table.md

IEEE 754 starndart

WIKI

Roundings to nearest

• Round to nearest, ties to even – rounds to the nearest value; if the number falls midway, it is rounded to the nearest value with an even least significant digit; this is the default for binary floating point and the recommended default for decimal.
• Round to nearest, ties away from zero – rounds to the nearest value; if the number falls midway, it is rounded to the nearest value above (for positive numbers) or below (for negative numbers); this is intended as an option for decimal floating point.

Directed roundings Round toward 0 – directed rounding towards zero (also known as truncation). Round toward +∞ – directed rounding towards positive infinity (also known as rounding up or ceiling). Round toward −∞ – directed rounding towards negative infinity (also known as rounding down or floor).

Mode / Example Value	+11.5	+12.5	−11.5	−12.5
to nearest, ties to even	+12.0	+12.0	−12.0	−12.0
to nearest, ties away from zero	+12.0	+13.0	-12.0	-13.0
toward 0	+11.0	+12.0	-11.0	-12.0
toward +∞	+12.0	+13.0	−11.0	-12.0
toward −∞	+11.0	+12.0	−12.0	−13.0

EASYMONEY

HALF_EVEN aka (Banker's Rounding)

+5.0	+5.1	+5.4	+5.5	+5.6	+5.9	+6.0	+6.1	+6.4	+6.5	+6.6	+6.9	+7.0
+5	+5	+5	+6	+6	+6	6	+6	+6	+6	+7	+7	+7
			-->			center			<--

-7.0	-6.9	-6.6	-6.5	-6.4	-6.1	-6.0	-5.9	-5.6	-5.5	-5.4	-5.1	-5.0
-7	-7	-7	-6	-6	-6	-6	-6	-6	-6	-5	-5	-5
			-->			center			<--

HALF_UP aka arithmetic rounding | half up with symmetric implementation (like in Java, PHP or Python)

+5.0	+5.1	+5.4	+5.5	+5.6	+5.9	+6.0
+5	+5	+5	+6	+6	+6	6
<—	<—	<—	—>	—>	—>	<—

-7.0	-6.9	-6.6	-6.5	-6.4	-6.1	-6.0	-5.9	-5.6	-5.5	-5.4	-5.1	-5.0
-7	-7	-7	-7	-6	-6	-6	-6	-6	-6	-5	-5	-5
			<—						<—

HALF_DOWN aka arithmetic rounding | half down with symmetric implementation

+5.0	+5.1	+5.4	+5.5	+5.6	+5.9	+6.0
+5	+5	+5	+5	+6	+6	6
<—	<—	<—	<—	—>	—>	<—

-7.0	-6.9	-6.6	-6.5	-6.4	-6.1	-6.0	-5.9	-5.6	-5.5	-5.4	-5.1	-5.0
-7	-7	-7	-6	-6	-6	-6	-6	-6	-5	-5	-5	-5
			-->						—>

FLOOR TOWARD negative infinity

+5.0	+5.1	+5.4	+5.5	+5.6	+5.9	+6.0
+5	+5	+5	+5	+5	+5	6
<—	<—	<—	<—	<—	<—	<—

-6.0	-5.9	-5.6	-5.5	-5.4	-5.2	-5.0
-6	-6	-6	-6	-6	-6	-5
—>	<—	<—	<—	<—	<—	—>

CEILING toward positive infinity

+5.0	+5.1	+5.4	+5.5	+5.6	+5.9	+6.0
+5	+6	+6	+6	+6	+6	6
<—	—>	—>	—>	—>	—>	<—

-6.0	-5.9	-5.6	-5.5	-5.4	-5.2	-5.0
-6	-5	-5	-5	-5	-5	-5
—>	—>	—>	—>	—>	—>	—>

TOWARD_ZERO

+5.0	+5.1	+5.4	+5.5	+5.6	+5.9	+6.0
+5	+5	+5	+5	+5	+5	+6
<—	<—	<—	<—	<—	<—	<—

-6.0	-5.9	-5.6	-5.5	-5.4	-5.2	-5.0
-6	-5	-5	-5	-5	-5	-5
—>	—>	—>	—>	—>	—>	—>

AWAY_FROM_ZERO

+5.0	+5.1	+5.4	+5.5	+5.6	+5.9	+6.0
+5	+6	+6	+6	+6	+6	+6
<—	—>	—>	—>	—>	—>	<—

-6.0	-5.9	-5.6	-5.5	-5.4	-5.2	-5.0
-6	-6	-6	-6	-6	-6	-5
—>	<—	<—	<—	<—	<—	—>

SUMMARY TABLE

easymoney	HALF_EVEN	HALF_UP	HALF_DOWN	FLOOR	CEILING	TOWARDS_ZERO	AWAY_FROM_ZERO
JAVA	HALF_EVEN	HALF_UP	HALF_DOWN	FLOOR	CEILING	DOWN	UP
PHP
IEEE 754	Ties to even	—	—	Round toward -∞	Round toward +∞	Round toward 0	Round to nearest, ties away from zero
5.5	6	6	5	5	6	5	6
2.5	2	3	2	2	3	2	3
1.6	2	2	2	1	2	1	2
1.1	1	1	1	1	2	1	2
1.0	1	1	1	1	1	1	1
-1.0	-1	-1	-1	-1	-1	-1	-1
-1.1	-1	-1	-1	-2	-1	-1	-2
-1.6	-2	-2	-2	-2	-1	-1	-2
-2.5	-3	-3	-2	-3	-2	-2	-3
-5.5	-6	-6	-5	-6	-5	-5	-6