Peter Eisentraut <peter_e@gmx.net> writes:
> Tom Lane writes:
>> It's correct, if the underlying float arithmetic is IEEE-compliant.
>> Rounding for exact half-integral values is supposed to be "round to
>> nearest even". So 42.5 goes to 42, but 43.5 goes to 44.
>>
>> I notice our NUMERIC rounding code does not do that ... perhaps it
>> should.
> More precisely, an IEEE-compliant system would offer the choice of
> rounding up, rounding down, rounding toward zero, or rounding toward even.
> I would guess that the default is merely the potentially best performing.
Hmm. Round-toward-even is preferred by numerical analysts on the theory
that it introduces less systematic bias than simpler rounding rules.
(If you always round half-integral values in the same direction, then
your results are slightly biased, just as if you'd set the up/down split
point at say 0.4 instead of 0.5.) However this theory only holds if you
assume an imprecise starting value. That's a reasonable assumption for
float arithmetic, but not so reasonable for type numeric.
> We could offer these options (much more easily) for the numeric case, but
> since numeric is very often used for business type applications, the
> customary rounding method (up) should be preferred.
You're probably right, we shouldn't change it.
regards, tom lane