I implemented the Madhava–Leibniz series to calculate pi in Python, and then in Cython to improve the speed. The Python version:

from __future__ import division
pi = 0
l = 1
x = True
while True:if x:pi += 4/lelse:pi -= 4/lx = not xl += 2print str(pi)

The Cython version:

cdef float pi = 0.0
cdef float l = 1.0
cdef unsigned short x = True
while True:if x:pi += 4.0/lelse:pi -= 4.0/lx = not xl += 2print str(pi)

When I stopped the Python version it had correctly calculated pi to 3.141592. The Cython version eventually ended up at 3.141597 with some more digits that I don't remember (my terminal crashed) but were incorrect. Why are the Cython version's calculations incorrect?

You are using float in the Cython version -- that's single precision! Use double instead, which corresponds to Python's float (funnily enough). The C type float only has about 8 significant decimal digits, whereas double or Python's float have about 16 digits.