math - Inaccurate Logarithm in Python

Question

I work daily with Python 2.4 at my company. I used the versatile logarithm function 'log' from the standard math library, and when I entered log(2**31, 2) it returned 31.000000000000004, which struck me as a bit odd.

I did the same thing with other powers of 2, and it worked perfectly. I ran 'log10(2**31) / log10(2)' and I got a round 31.0

I tried running the same original function in Python 3.0.1, assuming that it was fixed in a more advanced version.

Why does this happen? Is it possible that there are some inaccuracies in mathematical functions in Python?

Answer 1

This is to be expected with computer arithmetic. It is following particular rules, such as IEEE 754, that probably don't match the math you learned in school.

If this actually matters, use Python's decimal type.

Example:

from decimal import Decimal, Context
ctx = Context(prec=20)
two = Decimal(2)
ctx.divide(ctx.power(two, Decimal(31)).ln(ctx), two.ln(ctx))