Re: Rounding??

["Andreas J. Guelzow" <aguelzow math concordia ab ca>]

Kjetil Torgrim Homme wrote:

> Yes, it's conventional, but it introduces a bias.  Adding up the rounded
> numbers should ideally give the same result as rounding the sum of the
> full precision.
>
>   0.5 + 1.5 + 2.5 + 3.5 ==  8
>    0  +  2  +  2  +  4  ==  8
>    1  +  2  +  3  +  4  == 10
>
> The "round towards even" algorithm can perform as bad as "round up",
> but never worse, and usually much better.

That is incorrect:

round towards even:

0.4 + 2.5  == 2

round:

0.4 + 2.5 == 3

correct:

0.4 + 2.5 = 2.9

There is nothing better about `round towards even'.  (Which of course is
a completely unsupported statement as the above.)

Andreas

--
Prof. Dr. Andreas J. Guelzow                   
Chair of Science
Concordia University College of Alberta
aguelzow math concordia ab ca
http://www.math.concordia.ab.ca/aguelzow