Last week I wrote a post on hiding cryptographic keys in decks of cards. I wrote some code for that post that shouldn’t work, but before fixing I noticed that it in fact did work.
The code computes logarithms for integers larger than the largest representable float. For example, the largest float is on the order of 10308, and yet the following code works.
>>> import math >>> math.log10(10**400) 400.0
The log, log2, and log10 functions have some code inside that handles large integers specially. It doesn’t simply convert the integers to floats before taking the logarithm. If it did, it would overflow.
While playing around with this I also noticed that you can define floats larger than the largest float without warnings.
>>> math.log(1e308) 709.1962086421661 >>> math.log(1e309) inf
This isn’t a feature of math.log but of how Python handles scientific notation. The expression 1e308 is the floating point representation of 10308. It is a float, not an int.
>>> type(1e308) <class 'float'>
The expression 1e309 is also a float. But since it’s larger than is possible for a float, Python interprets it as inf. The code
math.log(1e309)
returns inf based on the reasoning that log(∞) = ∞.
That explains the following behavior:
>>> 1e309 == 1e310 True
The expressions 1e309 and 1e310 are equal because both are alternate ways of writing inf.