Why does Java's RoundingMode HALF_UP round -2.5 to -3?

Question

RoundingMode allows the programmer to specify in what manner floating point numbers are to be rounded. This is great and all, but there is this one thing about it I found peculiar. Maybe I just misunderstood something fundamental at school.

But this rounding mode is described as the one I was taught at school, "Always round to the nearest number, and when dead in the center, always round up.", but why does it round -2.5 to -3?

I conclude as much that it rounds up in terms of absolute values, but -2 is, to me, certainly "up" from -2.5.

Answer 1

RoundingMode.UP is the rounding mode for "away from zero." RoundingMode.FLOOR is towards negative infinity, and CEILING is towards positive infinity. HALF_UP is consistent with UP when the fractional part is exactly 0.5.

They had to choose some term to mean "away from zero."

Answer 2

The rationale is outlined in the JavaDocs for RoundingMode.HALF_UP.

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.

The Wikipedia article about Rounding methods makes a different claim:

For example, by this rule the value 23.5 gets rounded to 24, but −23.5 gets rounded to −23.

This is one of two rules generally taught in US elementary mathematics classes.

Though a citation has been requested.