[ http://tools.oasis-open.org/issues/browse/OFFICE-2632?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=18398#action_18398 ]
Andreas Guelzow commented on OFFICE-2632:
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When I referred to SUM I wasn't talking about "simple rounding errors" but the problem that the order of addition of values with different magnitude may affect the result greatly.
> ODF 1.2 Part 2 CD01 5.18.72-5.18.75 STDEV* DANGEROUS EXTRA FORMULAS
> -------------------------------------------------------------------
>
> Key: OFFICE-2632
> URL: http://tools.oasis-open.org/issues/browse/OFFICE-2632
> Project: OASIS Open Document Format for Office Applications (OpenDocument) TC
> Issue Type: Bug
> Affects Versions: ODF 1.2 Part 2 CD 1
> Reporter: Dennis Hamilton
> Fix For: ODF 1.2 Part 2 CD 2
>
>
> For each of the STDEV, STDEVA, STDEVP, and STDEVPA, there is an extra formula in the definitiions.
> The first formula is a definition for s^2 or sigma^2 depending on whether we are talking about a sample or a set of equiprobable values. The second formula *is* mathematically equivalent but it is computationally worse. (It has the advantage that the mean does not have to be computed in advance. However, it is even worse as a computational method than the so-called "naive" mathematical definition. The second formula is equivalent to the formula 4.2.2(14) that Donald Knuth gives as an approach to be avoided because of its computational instability.)
> I recommend that the second form of the formula, the one that subtracts n X xbar^2, be stricken, because it raises more questions than it answer and we have no business even suggesting it.
> Furthermore, I would use the formulas to explain how the mathematical standard-deviation (or variance in the STDEVP and STDEVPA cases) is mathematically defined. I would say that the result is a computational approximation to the mathematical value, not that it returns the mathematical result.
> I would then add, perhaps,
> Note: Special computational methods are generally used to produce more-reliable results than achievable by direct implementation of the formula as a computational method.
> A non-normative reference to the treatment in the Art of Computer Programming might be useful here (and perhaps many other places).
> PS: These are also nice codefest challenges for assessing the ways that OpenFormula functions can be implemented reliably as computations from the specification and available expert materials.
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