ROUNDing

[barmar@Think.COM (Barry Margolin)]

    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
    tally marks, instead of radix notation?

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