Avoiding expensive calculations in Python IRC bot

It looks like the float() cast was the solution after all.

First of all, the inverse trigonometric functions don't take values outside of their domain, so they're completely safe and the exception can be caught.

>>> acos(5e100)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
ValueError: math domain error

The same thing happens with the fmod() function.

The "normal" trigonometric functions don't seem to have any problem with big values unless they're really big, which makes the function return ValueError again.

The rounding functions (ceil(), floor() and round()) work fine and return inf if the value is too big. The same goes for the degrees(), log(), log10(), pow(), sqrt(), fabs(), hypot() and radians() functions.

The hyperbolic trigonometric functions and the exp() function throw OverflowErrors or return inf.

The atan2() function works perfectly fine with big values.

For simple arithmetic operations, the float cast makes the function throw an OverflowError (or an inf) instead of doing the calculation.

>>> float(10) ** float(100) ** float(100) ** float(1000)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
OverflowError: (34, 'Numerical result out of range')
>>> float(5e500) * float(4e1000)
inf

Lastly, the problematic factorial() function. All I had to do was redefining the function in an iterative way and adding it to safe_dict.

import sys

def factorial(n):
    fact = 1
    while (n > 0):
        fact = float(fact) * float(n)
        n -= float(1)
        if float(fact) > sys.float_info.max:
            return "Too big"
    return str(fact)

print factorial(50e500)

While this is a very ugly and grossly inefficient way of calculating a factorial, it's enough for my needs. In fact, I think I added a lot of unnecessary float()s.

Now I need to figure out how to put float()s around all the terms in an expression so this happens automatically.