So the norm specifies you should represent the number immediately before the real one, which leaves you with 0,39999.9997346 (or whatever the tail is). there is no finite decomposition of 0.4 in binary weights. Try attaining 1,4 with this representation, and you hit the precision wall. The pertinent issue is Base=2 which makes "x" in "1,x" to be a finite-precision (53bits of it) fractional binary.
Excel vba examples 2007 full#
There's an exponent and a sign, which makes the full representation in Base 2. The choice becomes where you stop resolving and accept the inherent inaccuracy as being "good enough" for the problem you're solving/modeling.ĭouble representation follows a fixed point notation, where the mantissa is a number "1,x" with "1" being implicit. 2 -3 (.125) is too big, but 2 -4 (.0625) is too small.so you keep going to smaller powers of two, realizing you'll never quite represent the number precisely. If you're representing exactly those numbers, all is good. *įor a very simple example that illustrates this issue in a trivial case, consider a situation in which decimals are represented as sums of inverse powers of two, eg 2 -1, 2 -2, 2 -3, and so on. * Edit: Just a minor bit of extra info for detail. In VBA a normal variable can store only one value at a time. An example would be storing a list of countries or a list of weekly totals. The Primer has been written for those who are new to VBA programming and the Excel object model. At all times, the VBA language is presented in the context of Excel, not just as a general application programming language. There is a very decent treatment of the subject of IEEE representation at this location. It is used to store lists of data of the same type. This book is aimed squarely at Excel users who want to harness the power of the VBA language in their Excel applications. The fundamental problem lies with the inherent inaccuracy in the representation of fractional numbers in binary, and how at least some effort to mitigate that inaccuracy was made with IEEE floating point representations. The core VBA system is largely unchanged despite the migration into later versions, hence the same kinds of accuracy gremlins that plague older VBA macros will persist. The explanation for the problem from Office 97 and VBA is equally applicable going forward into Excel 2007.
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