October 6, 2009 at 12:11 am
Comments posted to this topic are about the item Custom Rounding and Truncation of Numbers in MDX
October 6, 2009 at 1:49 am
This article http://en.wikipedia.org/wiki/Rounding explains various rounding techniques.
After reading the Wiki article, my guess is that MDX uses it because it is the only deterministic method which is essentially non-biased, also in presence of a predominant sign among samples.
Or simply because it is the .NET default.
Thank you for the article, it opened my eyes to looking closely at current implementation of rounding every time I encounter a new environment or revisit a supposedly familiar one after a while. Assume nothing.
October 6, 2009 at 2:48 am
Nice article Boyan, - I found it extermely interesting.
October 6, 2009 at 4:05 am
I tend to use standard rounding via a user function ROUNDIT(RawVal,DecPl,RoundVal) which uses a similar approach to the example:-
FIX(RawVal * 10^DecPl + (SGN(RawVal) * RoundVal))/ 10 ^ DecPl
where
RawVal is the value to be rounded
DecPl is the number of decimal places required
RoundVal is the rounding factor
This ensures that negative values get rounded DOWN e.g. -1.5 gets rounded to -2.0:cool:
(Useful where a value is contra'd out so that sum of 1.25 and -1.25 returns zero) - if this is not required then change the function to:-
FIX(RawVal * 10^DecPl + RoundVal)/ 10 ^ DecPl
If rounding OFF is required (surplus dec places removed) then RoundVal should be passed as 0.
Trainee Novice:w00t:
October 6, 2009 at 10:34 am
There's a reason why it's called "Banker's Rounding". Summating a column of numbers that are all rounded using arithmetic rounding may introduce a rounding error that produces a higher total than summating the same column of numbers without rounding then rounding the total. Bankers rounding mitigates this rounding error. It's not wrong, it's mearly different. As long as you're aware, you can use the proper method for your application.
October 6, 2009 at 3:49 pm
Heh,
After SQL Server Central published the article, I found this really good reference on Custom Rounding:
http://support.microsoft.com/kb/196652
In the end of the page there are examples, and the SymArith function does exaclty what my rounding function does, just that it avoids a Div by 0 on a 0 number, and additionally, does not require the Excel functions to be available on the server. The actual code in MDX is:
Fix([Measures].[???] * Factor + 0.5 * Sgn([Measures].[???])) / Factor
Where Factor is the rounding factor - 1 for 0 decimal places, 10 for 1 and so on (defined by 1/Factor).
Of course, Factor of 0 will give us Div by 0 error and for truncation we can just use the truncation function in my article.
Furthermore, Chris Webb advises that if you have the Excel libraries installed on your server, you can just use Excel!Round() instead of the function I've provided (it requires Excel to be installed, as it uses Ceiling).
It is kind of bad that I did not include all this in the main article and I will ask SQL Server Central admins to include it as it is a definite miss.
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