On Thu, 19 Mar 2009, Oded Ben-Tal wrote:
I am getting a negative number occasionally.
Ok, i isolated an example: [metro 100] | [100000] | [variance 10] | converges to -281.6 and then changing 100000 to 0 makes the result converge to -691.2.actually, afaik, [variance] doesn't have a bug by itself. The bug is in [mean_n], which displays similar behaviour in default mode.
The bug is because of algebraic assumptions that don't work with floats. With real numbers, a+b-a-b = 0, but with floats, a+b-a-b is only guaranteed to be a "small" number, that is, less than 2^24 times smaller than abs(a)+abs(b), or something like that. But 100000*100000 = 10000000000, and if you divide that by 2^24 = 16777216, you get about 596, which is an upper bound for the amount of error: so, the error is surely between -596 and +596.
Then [mean_n] boosts this error to the max by adding it all together. Statistically, that error could diverge.
So, the shortcut of keeping a total of a list of length N and only add the new element to it and subtract the oldest element from it, is not something that works with all floats. It's a trick that works with an int type, but with floats, it only works sometimes.
_ _ __ ___ _____ ________ _____________ _____________________ ... | Mathieu Bouchard - tél:+1.514.383.3801, Montréal, Québec
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