# ROUNDing

```    Date: Fri, 28 Jun 1991 11:30 EDT
From: andy@chestnut.com (Andy Latto)

> 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

The context of Knuth's discussion was in rounding floating point
numbers after a computation.  I think the point was that extra digits
are used internally during the computation (e.g. multiplying floats with
24-bit fractions results in a 48-bit fraction in the temporary), and
then the result has to be rounded to the precision of the regular
representation.

barmar

```

• References:
• ROUNDing
• From: andy@chestnut.com (Andy Latto)