# ROUNDing

> Date: Thu, 27 Jun 1991 18:50-0400
> From: barmar@Think.COM (Barry Margolin)

> However, I happened to pick up a copy of Knuth later in the afternoon,
> and found the section where he talks about rounding (Seminumerical
> Algorithms, section 4.2.2).  I couldn't find many details, but at one
> point he said that the "right" way to round a number that is exactly
> half-way between two units depends on the radix -- if it's even you
> round towards the even number, if it's odd you round towards the odd
> number.  Then he pointed out that all the commonly-used bases are even,
> so it's simplest to remember that rounding should be towards the even
> number.

I don't believe this, even if it's in Knuth.  Rounding is an issue
to do with numbers, not with numerals. If I ask you whether
(round 1/2) is 0 or 1, how can the answer depend on what
base I am using? What if I am using Roman Numerals? Or just

As far as I can see "round to an integer divisible by two" and
"round to an integer not divisible by two" are equally good rules
for rounding <integer> + 1/2. There may be a reason I don't see
for preferring even over odd, or maybe it's just convention. But
I can't believe that "round to a number whose last digit in your
preferred radix has the same parity as the radix" is as good a rule.

If you use an odd radix internally, evenp and oddp might be
expensive operations compared to last-digit-even-p and
last-digit-odd-p. If so, and you want round to be faster than
evenp and oddp, it might be that round-to-odd-last-digit
is better than round-to-even-last-digit if those are your choices,
but there's still nothing wrong with round-to-even.

Andy Latto
andy@chestnut.com

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• From: barmar@Think.COM (Barry Margolin)