Question

I need some help calculating Pi. I am trying to write a python program that will calculate Pi to X digits. I have tried several from the python mailing list, and it is to slow for my use. I have read about the Gauss-Legendre Algorithm, and I have tried porting it to Python with no success.

I am reading from Here, and I would appreciate any input as to where I am going wrong!

It outputs: 0.163991276262

from __future__ import division import math def square(x):return x*x a = 1 b = 1/math.sqrt(2) t = 1/4 x = 1 for i in range(1000):     y = a     a = (a+b)/2     b = math.sqrt(b*y)     t = t - x * square((y-a))     x = 2* x  pi = (square((a+b)))/4*t print pi raw_input() 

Answer 1

1. You forgot parentheses around 4*t:

   pi = (a+b)**2 / (4*t) 

2. You can use decimal to perform calculation with higher precision.

   #!/usr/bin/env python from __future__ import with_statement import decimal  def pi_gauss_legendre():     D = decimal.Decimal     with decimal.localcontext() as ctx:         ctx.prec += 2                         a, b, t, p = 1, 1/D(2).sqrt(), 1/D(4), 1                         pi = None         while 1:             an    = (a + b) / 2             b     = (a * b).sqrt()             t    -= p * (a - an) * (a - an)             a, p  = an, 2*p             piold = pi             pi    = (a + b) * (a + b) / (4 * t)             if pi == piold:  # equal within given precision                 break     return +pi  decimal.getcontext().prec = 100 print pi_gauss_legendre() 

Output:

3.141592653589793238462643383279502884197169399375105820974944592307816406286208\     998628034825342117068