numerical-stability

I understand how mathematically-equivalent arithmentic operations can result in different results due to numerical errors (e.g. summing floats in different orders). However, it surprises me that adding zeros to sum can change the result. I thought that this always holds for floats, no matter what: x + 0. == x . Here's an example. I expected all the lines to be exactly zero. Can anybody please explain why this happens? M = 4 # number of random values Z = 4 # number of additional zeros for i in range(20): a = np.random.rand(M) b = np.zeros(M+Z) b[:M] = a print a.sum() - b.sum() -4.4408920985e-16

I have translated the experimental C# "float" version of Clipper library to javascript. In the newest sandbox version there is a function IsAlmostEqual which seems to be hard to translate. Double equality cannot be compared using == operator due to numerical stability issues, so this function is needed to handle those issues. -9223372036854775808 - aInt and -9223372036854775808 - bInt are easy to calculate using e.g. BigInteger library, but BitConverter.DoubleToInt64Bits is harder. Any idea how to translate IsAlmostEqual function to javascript? Or specifically how to implement BitConverter

I have a Bayesian Classifier programmed in Python, the problem is that when I multiply the features probabilities I get VERY small float values like 2.5e-320 or something like that, and suddenly it turns into 0.0. The 0.0 is obviously of no use to me since I must find the "best" class based on which class returns the MAX value (greater value). What would be the best way to deal with this? I thought about finding the exponential portion of the number (-320) and, if it goes too low, multiplying the value by 1e20 or some value like that. But maybe there is a better way? Muhammad Alkarouri What