Re: Classic RW (was: Rounding errors

"Robert Wagner" <robert@wagner.net.yourmammaharvests> wrote in message
 news:o7b3j01nfgsr6b72q0h3hmnnn8kkejicqc@
4ax.com...
> On Sun, 29 Aug 2004 04:42:10 GMT, "William M. Klein"
> <wmklein@nospam.netcom.com> wrote:
> 
[snip] 
>
> How about the prize for Numerancy. If you don't understand that
> fixed-point numbers are integers, you're innumerate.

Mr Wagner, it is my understanding that fixed-point numbers are
scaled-integers, not mere integers, and that fixed-point numbers
consist of an integer value and an implied operator and integer
scale factor.

Perhaps I am innumerate, nonetheless, because I cannot count
the number of times you have introduced an inaccuaracy and
defended it as correct. <g>

Mr Wagner, your allegation was, as I recall, that COBOL
rounding was wrong because the sum of rounded numbers
was too high for a contrived sequence of numbers. This
cannot be the case because the COBOL rounding rule
applies to only single calculations not their sum.

The method I learned (and have not practiced since) was, as
I recall, 'Round to even numbers'. This may be implemented,
for positive numbers, (untested) as:

if (function rem (my-number 1) = 0.5
if (function mod (function integer (my-number) 2)) = 0
subtract 0.5 from my-number giving rounded-number
end-if
else
add 0 my-number giving rounded-number rounded
end-if

1.5+2.5+3.5+4.5=12 becomes
2+2+4+4=12

but 1.5+3.5+5.5+7.5=18 becomes
2+4+6+8=20

and 2.5+4.5+6.5+8.5=22 becomes
2+4+6+8=20

thus, as shown here, the accuracy of the sum of rounded
numbers depends upon the distribution, between even and
odd, of the integer part of the numbers. Furthermore, the
accuracy of the sum of rounded numbers also depends
on the distribution, relative to 0.5, of the fractional part.
The COBOL rounding rule does not define, nor control,
such distributions.

The point being that a rounding rule that applies to only
single calculations cannot, properly, be blamed for the
inaccuracy of the sum. This includes the rule 'Round to
even numbers'.