Convert float to log space in python

Question

I am implementing the Viterbi algorithm (a dynamic algorithm) in Python, and I notice that for large input files, the probabilities keep getting multiplied and shrinking beyond the floating point precision. I need to store the numbers in log space.

Can anyone give a simple example Python code-snippet of how to convert, say, 0.0000003 to log-space? (I'm not sure if it needs to be natural log or some other log. I have only heard of "log-space" but don't really know about it.)

Thanks!

Answer 1

To move to log space, use log. To move back again use exp. The rules in log space are different - eg. to perform multiplication is to add in logspace.

>>> from math import log, exp
>>> log(0.0000003)
-15.01948336229021
>>> exp(-15.01948336229021)
3.0000000000000015e-07
>>> log(0.0000003) + log(0.0000003)
-30.03896672458042
>>> exp(-30.03896672458042)
9.000000000000011e-14 # 0.0000003 * 0.0000003 

Here is an example using some small probabilities

>>> probabilities = [0.0000003, 0.0000004, 0.0000005]
>>> exp(sum(log(p) for p in probabilities))
5.999999999999992e-20