Leibniz_Pi.py

[Cousin Stanley]

Yesterday in the news group  comp.lang.java.help
I found a Java example of the  Leibniz Pi  approximation
and converted the Java code to Python ... 

The numerical results from either version 
using a  LARGE  number of terms as a program argument
provide approximations for the number  Pi   that seems correct ... 

Using  1 million  terms as an input argument,
the Java version is a bit faster, which I think
is expected ... 

   On a 250 MHz Win98 machine ... 
   
     Java SDK 1.4 .......  ~ 3-4   seconds
    Python 2.2.1 .........  ~ 9-10 seconds

Since I am fairly new to  BOTH  Java  AND  Python,
I'm wondering if there are any ... 

  obvious oversights        ???
  Python improvements ???

Python code follows ...

Cousin Stanley

----------------------------------------------------------------

''' 
    Leibniz_Pi.py

    Pi = 4 * ( 1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 + 1/13 - 1/15 ... )

    Using one million terms provides a good approximation ...

    Posted to the NewsGroup
    comp.lang.java.help           2002-10-10 
    By Jonas Lindström

    Converted to Python
    By Stanley C. Kitching
'''

import sys
print '\n    Approximate  Pi  via Leibniz Sequence '

def calculate_pi( nTerms ) :

    limit = ( 2 * nTerms ) - 1 

    if ( ( limit - 1 ) % 4 ) == 0 :  
           sign = +1.0 
    else : 
           sign = -1.0

    sum = 0.0

    for i in range( limit , 0 , -2 ) : 
        sum +=  sign / i
        sign = -sign

    return 4.0 * sum 

nTerms = int( sys.argv[ 1 ] ) 

Pi = calculate_pi( nTerms  )

print '\n    Terms : ' , nTerms
print '\n       Pi : ' , Pi