How to calculate pi to N number of places in C# using loops

Question

How might I go about calculating PI in C# to a certain number of decimal places?

I want to be able to pass a number into a method and get back PI calculated to that number of decimal places.

public decimal CalculatePi(int places)
{
    // magic
    return pi;
}

Console.WriteLine(CalculatePi(5)); // Would print 3.14159

Console.WriteLine(CalculatePi(10)); // Would print 3.1415926535

etc...

I don't care about the speed of the program. I just want it to be as simple and easy to understand as it can be. Thanks in advance for the help.

Answer 1

Same algorithm as nicholas but uses yield for lazy evaluation

    static public IEnumerable<uint> Pi()
    {
        uint[] x = new uint[short.MaxValue];
        uint[] r = new uint[short.MaxValue];

        for (int j = 0; j < short.MaxValue; j++)
            x[j] = 20;

        for (int i = 0; i < short.MaxValue; i++)
        {
            uint carry = 0;
            for (int j = 0; j < x.Length; j++)
            {
                uint num = (uint)(x.Length - j - 1);
                uint dem = num * 2 + 1;

                x[j] += carry;

                uint q = x[j] / dem;
                r[j] = x[j] % dem;

                carry = q * num;
            }

            yield return (x[x.Length - 1] / 10);

            r[x.Length - 1] = x[x.Length - 1] % 10; ;
            for (int j = 0; j < x.Length; j++)
            {
                x[j] = r[j] * 10;
            }                    
        }
    }

I used short.MaxValue as the upper bound for the number of places but that is because my machine is low on virtual memory. A better machine should be able to accommodate up to int.MaxValue.

The function can be called like so:

 class Program
{
    static void Main(string[] args)
    {
        foreach (uint digit in Calculator.Pi().Take(100))
        {
            Console.WriteLine(digit);
        }

        Console.Read();
    }
}