How to compute huge numbers with python?

Question

I\'m currently trying to find the value of x,

x = (math.log(X) - math.log(math.fabs(p))/math.log(g))

with :

X = 53710695204         


        

Answer 1

The "machine epsilon" for the numpy float64 dtype is about 2.2e-16. This means that you should only expect the first 16 significant digits in your result to be accurate unless you are doing something extremely tricky (like rolling your own custom data type).

Dietrich suggested using sympy and setting a high internal precision, but the sympy documentation confirms that this does not escape the machine epsilon issue.

some Python floats are only accurate to about 15 digits as inputs, while others (those that have a denominator that is a power of 2, like .125 = 1/4) are exact.

In other words, be extremely wary of the results you get working with numbers as large as yours, because only the first 16 significant digits will be meaningful as long as you are using 64 bit floats to do your math.