Splitting math sums with python -

this simple question has been bothering me while now.

i attempting rewrite code parallel, , in process need split sum done on multiple nodes , add small sums together. piece working this:

def pia(n, i):         k = 0         lsum = 0         while k < n:                 p = (n-k)                 ld = (8.0*k+i)                 ln = pow(16.0, p, ld)                 lsum += (ln/ld)                 k += 1         return lsum 

where n limit , i integer. have hints on how split , same result in end?

edit: asking, i'm not using pow() custom version efficiently floating point:

def ssp(b, n, m):     ssp = 1     while n>0:             if n % 2 == 1:                     ssp = (b*ssp) % m             b = (b**2) % m             n = n // 2     return ssp 

since variable that's used 1 pass next k, , k increments 1 each time, it's easy split calculation.

if pass k pia, you'll have both definable starting , ending points, , can split many pieces want, , @ end, add results together. like:

# instead of pia(20000, i), use pia(n, i, k) , run result = pia(20000, i, 10000) + pia(10000, i, 0) 

also, since n used both set limits , in calculation directly, these 2 uses need split.

from math import pow  def pia(nlimit, ncalc, i, k):         lsum = 0         while k < nlimit:                 p = ncalc-k                 ld = 8.0*k+i                 ln = ssp(16., p, ld)                 lsum += ln/ld                 k += 1         return lsum  if __name__=="__main__":     i, ncalc = 5, 10     print pia(10, ncalc, i, 0)     print pia(5, ncalc, i, 0) + pia(10, ncalc, i, 5)