Standard library - higher-precision floating point?

Question

So, I'm having some precision issues in Python.

I would like to calculate functions like this:

P(x,y) = exp(-x)/(exp(-x) + exp(-y))

Where x and y might be >1000. Python's math.exp(-1000) (in 2.6 at least!) doesn't have enough floating point precision to handle this.

1. this form looks like logistic / logit / log-odds, but it's not, right? Is there some algebraic simplification I'm missing here?
2. I know about Decimal, but am not sure if it applies here
3. looks like homework, but it's not, I promise!

(Also, I'm open to titles! I couldn't think of a good one for this question!)

Answer 1

I think you are looking for the bigfloat package for arbitrary precision floating-point reliable arithmetic.

Answer 2

you could divide the top and bottom by exp(-x)

P(x,y) = 1/(1 + exp(x-y))

Answer 3

P(x,y) = exp(-x)/(exp(-x) + exp(-y))

is equivalent to:

P(x,y) = 1 / (1 + exp(x-y))

Perhaps the second one works without the use of more precision.

Answer 4

>>> import decimal
>>> decimal.Decimal(-1000).exp()
Decimal('5.075958897549456765291809480E-435')
>>> decimal.getcontext().prec = 60
>>> decimal.Decimal(-1000).exp()
Decimal('5.07595889754945676529180947957433691930559928289283736183239E-435')