Python pi calculation?

It seems you are losing precision in this line:

pi = pi * Decimal(12)/Decimal(640320**(1.5))

Try using:

pi = pi * Decimal(12)/Decimal(640320**Decimal(1.5))

This happens because even though Python can handle arbitrary scale integers, it doesn't do so well with floats.

Bonus

A single line implementation using another algorithm (the BBP formula):

from decimal import Decimal, getcontextgetcontext().prec=100print sum(1/Decimal(16)**k *           (Decimal(4)/(8*k+1) -            Decimal(2)/(8*k+4) -            Decimal(1)/(8*k+5) -           Decimal(1)/(8*k+6)) for k in range(100))

For people who come here just to get a ready solution to get arbitrary precision of pi with Python (source with a couple of edits):

import decimaldef pi():    """    Compute Pi to the current precision.    Examples    --------    >>> print(pi())    3.141592653589793238462643383    Notes    -----    Taken from https://docs.python.org/3/library/decimal.html#recipes    """    decimal.getcontext().prec += 2  # extra digits for intermediate steps    three = decimal.Decimal(3)      # substitute "three=3.0" for regular floats    lasts, t, s, n, na, d, da = 0, three, 3, 1, 0, 0, 24    while s != lasts:        lasts = s        n, na = n + na, na + 8        d, da = d + da, da + 32        t = (t * n) / d        s += t    decimal.getcontext().prec -= 2    return +s               # unary plus applies the new precisiondecimal.getcontext().prec = 1000pi = pi()

from decimal import *#Sets decimal to 25 digits of precisiongetcontext().prec = 25def factorial(n):    if n<1:        return 1    else:        return n * factorial(n-1)def plouffBig(n): #http://en.wikipedia.org/wiki/Bailey%E2%80%93Borwein%E2%80%93Plouffe_formula    pi = Decimal(0)    k = 0    while k < n:        pi += (Decimal(1)/(16**k))*((Decimal(4)/(8*k+1))-(Decimal(2)/(8*k+4))-(Decimal(1)/(8*k+5))-(Decimal(1)/(8*k+6)))        k += 1    return pidef bellardBig(n): #http://en.wikipedia.org/wiki/Bellard%27s_formula    pi = Decimal(0)    k = 0    while k < n:        pi += (Decimal(-1)**k/(1024**k))*( Decimal(256)/(10*k+1) + Decimal(1)/(10*k+9) - Decimal(64)/(10*k+3) - Decimal(32)/(4*k+1) - Decimal(4)/(10*k+5) - Decimal(4)/(10*k+7) -Decimal(1)/(4*k+3))        k += 1    pi = pi * 1/(2**6)    return pidef chudnovskyBig(n): #http://en.wikipedia.org/wiki/Chudnovsky_algorithm    pi = Decimal(0)    k = 0    while k < n:        pi += (Decimal(-1)**k)*(Decimal(factorial(6*k))/((factorial(k)**3)*(factorial(3*k)))* (13591409+545140134*k)/(640320**(3*k)))        k += 1    pi = pi * Decimal(10005).sqrt()/4270934400    pi = pi**(-1)    return piprint "\t\t\t Plouff \t\t Bellard \t\t\t Chudnovsky"for i in xrange(1,20):    print "Iteration number ",i, " ", plouffBig(i), " " , bellardBig(i)," ", chudnovskyBig(i)