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Custom Rounding and Truncation of Numbers in MDX

By Boyan Penev,

In some scenarios we need to be able to round or truncate decimals to achieve correct calculation results. In SQL we have ROUND, which can do either of these. It rounds like we are used to - 0.5 rounds up to 1, can round up or down and we rarely get a project where as a part of the requirements we are implementing our own rounding or truncation algorithm.

However, in MDX we have Round() which performs a "strange" operation - bankers' rounding, which our business users have usually not been exposed to, and if we decide to truncate to an integer number through casting with Int or cInt, we also get some strange results. To illustrate the problem with MDX please consider the value of these expressions:

Round(2.15, 1) = 2.2
Round(2.25, 1) = 2.2
Round(2.35, 1) = 2.4
Round(2.45, 1) = 2.4

Int(1.9) = 1
Int(-1.9) = -2
cInt(1.9) = 1
cInt(-1.9)= -2

These are usually considered wrong, because they are not the obvious results. Even though they are mathematically well founded, if we round 2.25 to 2.2, our users will come back at us with wrong numbers on their reports. Same goes for "trimming" -1.9 to -2.

To resolve the first problem with rounding, we can use our own math formula:

Ceiling((Fix(<value>*2*10^1)/2/10^1), Sqr(<value>^2)/<value>/10^1)

Here we are rounding <value> to the first decimal point. If we need to round to the second, we have to replace the 10^1s in the statement with 10^10s, and if we are rounding to whole - we can remove them, or change them to 10^0s.

As for the Int and cInt in MDX, we can use the Fix() VBA function to remove decimal places:

Fix(1.9) = 1
Fix(-1.9) = -1

Also, for truncation of values to a certain decimal point in MDX, we can use the following formula:

Fix(<value>*10^1)/10^1

All we need to adjust in order to change the decimal places is to replace 10^1 with another power of 10 - in example, to truncate 3.156 to 3.15 we can use: Fix(3.156*10^2)/10^2. To make things simpler, in all our formulas the power of 10 is what determines how many decimal paces we need to round to; negative powers will give us rounding to tens, thousands and so on. If we use ^0 we will round to whole numbers.

Using these we can avoid bankers' rounding and some strange results with converting to integers in MDX.

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Tags
bankers' rounding    
mdx    
round()    
 
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