pythonpi

Why isn't my function giving the desired number of decimal digits for PI?

I have been trying to make a function that calculates pi to n digits using the Leibniz' formula. I am using the decimal module to be able to set how many decimal points I wish to output, but for some reason I always get the same number of points.

def my_leibniz(k,n):
    
    pi_over_four = 0
    getcontext().prec = n
    
    for num in range(k):
        pi_over_four += (-1.0)**num/(2.0*num + 1.0)

    pie = 4*pi_over_four
    
    return f'Your value of pi to {n} decimal spaces is ' + str(Decimal(pie))

The output is always in the form: 'Your value of pi to 3 decimal spaces is 3.140592653839794134995599961257539689540863037109375'

The value of Pi does change as I change k, but the number of decimal points is the same for whatever integer greater than 0 I put in for n.

I have looked through other code that uses the Decimal class to create this program using a difference method to calculate Pi, and can't see why my one is not working as expected.

Solution

  • The problem is that you're doing all of your math in floats, and only converting to Decimal at the very end.

    Replace the line:

    pi_over_four += (-1.0)**num/(2.0*num + 1.0)

    with

    pi_over_four += Decimal(-1)**num / (Decimal(2)*num + Decimal(1))

    Which is the most direct equivalent, replacing each float literal with a Decimal constructor call.

    (Technically, you only need one of the Decimal constructor calls, and then the ints will automatically be promoted to Decimal during mixed arithmetic.)