Exponential of very small number in python

Question

I am trying to calculate the exponential of -1200 in python (it's an example, I don't need -1200 in particular but a collection of numbers that are around -1200).

>>> math.exp(-1200)
0.0

It is giving me an underflow; How may I go around this problem?

Thanks for any help :)

Answer 1

In the standard library, you can look at the decimal module:

>>> import decimal
>>> decimal.Decimal(-1200)
Decimal('-1200')
>>> decimal.Decimal(-1200).exp()
Decimal('7.024601888177132554529322758E-522')

If you need more functions than decimal supports, you could look at the library mpmath, which I use and like a lot:

>>> import mpmath
>>> mpmath.exp(-1200)
mpf('7.0246018881771323e-522')
>>> mpmath.mp.dps = 200
>>> mpmath.exp(-1200)
mpf('7.0246018881771325545293227583680003334372949620241053728126200964731446389957280922886658181655138626308272350874157946618434229308939128146439669946631241632494494046687627223476088395986988628688095132e-522')

but if possible, you should see if you can recast your equations to work entirely in the log space.

Answer 2

Try calculating in logarithmic domain as long as possible. I.e. avoid calculating the exact value but keep working with exponents.

exp(-1200) IS a very very small number (just as exp(1200) is a very very big one), so maybe the exact value is not really what you are interested in. If you only need to compare these numbers then logarithmic space should be enough.