Why do I get “OverflowError: (34, ‘Result too large’)” or “OverflowError: (34, ‘Numerical result out of range’)” from floating-point exponentiation?

Python floats are neither arbitary precision nor of unlimited size. When k = 349, 16.**k is much too large – that’s almost 2^1400. Fortunately, the decimal library allows arbitrary precision and can handle the size:

import decimal
decimal.getcontext().prec = 100
def pi():
    pi = decimal.Decimal(0)
    for k in range(350):
        pi += (decimal.Decimal(4)/(decimal.Decimal(8)*decimal.Decimal(k+1))...)