Gauss-Legendre Algorithm in python

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()

Answers:

Thank you for visiting the Q&A section on Magenaut. Please note that all the answers may not help you solve the issue immediately. So please treat them as advisements. If you found the post helpful (or not), leave a comment & I’ll get back to you as soon as possible.

Method 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

Method 2

1. If you want to calculate PI to 1000 digits you need to use a data type that supports 1000 digits of precision (e.g., mxNumber)
2. You need to calculate a,b,t, and x until |a-b| < 10**-digits, not iterate digits times.
3. Calculate square and pi as @J.F. suggests.

Method 3

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

should be

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

All methods was sourced from stackoverflow.com or stackexchange.com, is licensed under cc by-sa 2.5, cc by-sa 3.0 and cc by-sa 4.0