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Re: operation of 'round' function. Why does it matter?
From: |
David Kastrup |
Subject: |
Re: operation of 'round' function. Why does it matter? |
Date: |
09 Feb 2002 15:06:09 +0100 |
User-agent: |
Gnus/5.09 (Gnus v5.9.0) Emacs/21.1 |
address@hidden (Alan Mackenzie) writes:
> Deepak Goel <address@hidden> wrote on 08 Feb 2002 11:28:38 -0500:
> >>
> >> So, if it is 2.5, you round to 2, but, if it is 3.5, you round to 4??
>
>
> > well, yes. that's the convention i have seen more than any other.
> > if you have a large data of numbers to be rounded, this method ensures
> > that you do not change the mean..
>
> Of course you change the mean. What you mean, I think, is that the mean
> of the change of the mean is zero.
Yes. Unbiased.
> Why on earth does it matter? Any time you're doing rounding, truncating,
> flooring, or whatever, you're fudging the result and loosing
> accuracy.
"Losing", for heaven's sake, "losing". The art of numerics is to lose
as little accuracy as possible. Rounding to even in number bases
divisible by 2 but not by 4 rounds away from the next possible point
of ambiguity. That way, a subsequent rounding operation will in
several cases not continue to add error in the same direction in case
of another occuring ambiguity. This means, for example, that a+b-b =
a+b-b+b-b (bad enough that a+b-b = a does not hold). In case where
you are, say, approximating an integral by summing differences, not to
be sneezed at. If adding 10000 values already introduces a bias of
5000ulp...
There is a reason the IEEE mandates rounding to even. Now of course
you may feel free to point out that what a floating point processor
does with its least significant digits need not have any correlation
to what a function round() supposed to deliver whole numbers does.
But what and how numbers are used is probably not always easy to
discern.
--
David Kastrup, Kriemhildstr. 15, 44793 Bochum
Email: address@hidden
- Re: operation of 'round' function, (continued)
- Re: operation of 'round' function, Ronan Waide, 2002/02/07
- Re: operation of 'round' function, Francesco Potorti`, 2002/02/08
- Re: operation of 'round' function, Eli Zaretskii, 2002/02/08
- Re: operation of 'round' function, Francesco Potorti`, 2002/02/08
- Re: operation of 'round' function, David Kastrup, 2002/02/07
- Re: operation of 'round' function, Al Petrofsky, 2002/02/07
- Message not available
- Re: operation of 'round' function, Deepak Goel, 2002/02/07
- Re: operation of 'round' function, David Masterson, 2002/02/07
- Re: operation of 'round' function, Deepak Goel, 2002/02/08
- Re: operation of 'round' function. Why does it matter?, Alan Mackenzie, 2002/02/09
- Re: operation of 'round' function. Why does it matter?,
David Kastrup <=
- Re: operation of 'round' function. Why does it matter?, Alan Mackenzie, 2002/02/10
- Re: operation of 'round' function. Why does it matter?, David Kastrup, 2002/02/11
- Re: operation of 'round' function. Why does it matter?, Eli Zaretskii, 2002/02/12
- Re: operation of 'round' function, David Kastrup, 2002/02/07
- Re: operation of 'round' function, Francesco Potorti`, 2002/02/07
- Re: operation of 'round' function, maierh, 2002/02/07