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

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.

First, assuming you want some arbitrary number of digits of pi, and we do not want to be confined with the precision of any of the various floating point numbers out there, let us define a Pi function as a string rather than any number type.

One of the coolest algorithms I found while searching for this technique is the Stanley Rabinowitz and Stan Wagon - Spigot Algorithm. It requires no floating point math, and is mostly an iterative method. It does require some memory for storing integer arrays in the intermediate calculations.

Without taking the time to streamline or clean the code here is an implementation of the algorithm (note the result does not add the decimal point).

Please be sure to cite the algorithm and this site if you intend to use this code for anything other than personal use.

C# Code
public static string CalculatePi(int digits)
{   
    digits++;

    uint[] x = new uint[digits*10/3+2];
    uint[] r = new uint[digits*10/3+2];

    uint[] pi = new uint[digits];

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

    for (int i = 0; i < digits; 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;
        }


        pi[i] = (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;
    }

    var result = "";

    uint c = 0;

    for(int i = pi.Length - 1; i >=0; i--)
    {
        pi[i] += c;
        c = pi[i] / 10;

        result = (pi[i] % 10).ToString() + result;
    }

    return result;
}
Update

I finally got around to fixing the "carry error" that happens after 35 digits. Page 6 of the linked document, in fact, specifically talks about what is going on here. I have tested the final version good to 1000 digits.

How do I calculate PI in C#?, Isaac Newton (you may have heard of him before ;) ) came up with this trick. which is good to several decimal places (at least three or four, I think). 355/113 is an old Chinese estimate, and I believe it pre-dates 22/7 by many years. but tail recursion allows an algorithm to be expressed recursively,  Programming Challenge 6.19: Calculating Value of Pi using While Loops Calculate the value of Pi from the infinite series. Display a table that shows the value of Pi approximated by computing one

Math.Round(Math.PI, places)

If you need more precision you will have trouble using the double data type as it supports a certain max. precision (which is provided by Math.PI).

PI Calculator, Interview Challenge, then you can work on the PI itself and use it for the actual calculation which Here, we have a simple "Are you capable of writing a loop" question Now if you need a certain number of digits of precision, you first compute the number of int N=100; // number of values to include double PI=2*acos(0.0); // to  Estimating the value of pi using a summation through creation of an m.file by using a loop.

After much searching I found this little snippet:

public static class BigMath
{
    // digits = number of digits to calculate;
    // iterations = accuracy (higher the number the more accurate it will be and the longer it will take.)
    public static BigInteger GetPi(int digits, int iterations)
    {
        return 16 * ArcTan1OverX(5, digits).ElementAt(iterations)
            - 4 * ArcTan1OverX(239, digits).ElementAt(iterations);
    }

    //arctan(x) = x - x^3/3 + x^5/5 - x^7/7 + x^9/9 - ...
    public static IEnumerable<BigInteger> ArcTan1OverX(int x, int digits)
    {
        var mag = BigInteger.Pow(10, digits);
        var sum = BigInteger.Zero;
        bool sign = true;
        for (int i = 1; true; i += 2)
        {
            var cur = mag / (BigInteger.Pow(x, i) * i);
            if (sign)
            {
                sum += cur;
            }
            else
            {
                sum -= cur;
            }
            yield return sum;
            sign = !sign;
        }
    }
}

It is working like a charm so far. You just have to add the System.Numerics library from the GAC to resolve the BigInteger type.

Calculating Pi in C# with series algorithms, Google took me to a post discussing using recursion to calculate Pi. as the name suggests, there stop if I've reached my target number of digits. out of the loop if I've done far too many iterations (which I keep track of in the  Introduction. Introducing the number PI with their first 50 decimal places: 3.1415926535897932384626433832795028841971693993751 It is an irrational and transcendental number. Its decimal part is an infinite succession of numbers and their calculation became a classical problem of computational mathematics.

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();
    }
}

Pi, with Ada.Text_IO; use Ada.Text_IO; with Ada.Integer_Text_IO; use Ada. 8400) of Integer; procedure Dec(n : in out Integer) is begin n := n - 1; end Dec; end loop; while c > 0 loop d := 0; g := c*2; b := c; while b > 0 loop d := d + f(b) * a; Dec(​g); f(b) := d BAS 'Prints PI to number of decimal places desired. An approximate value of pi can be calculated using the series given below: pi = 4 * [ 1 - 1/3 + 1/5 - 1/7 + 1/9 … + ((-1)^n)/(2n + 1) ] write a C++ program to calculate the approximate value of

If you are satisfied with the number of digits provided by the native math library, then it is simple; just round to the desired number of digits. If you need more digits (dozens, or hundreds, or thousands), you need a spigot algorithm that spits out the digits one at a time. Jeremy Gibbons gives an algorithm which I implement twice at my blog, where you will find code in Scheme, C, Python, Haskell, Perl and Forth (but not C#, sorry).

Calculate digits of pi, Lower and Upper Bound Theory · Analysis of Loops · Solving Recurrences · Amortized Given a number N(where N <= 50), the task is to find the value of Pi (​Π) up to N decimals places. The value of Π is calculated using acos() function which returns a numeric value between [-Π, Π]. C# program to calculate the. If yes, we increment the number of points that appears inside the circle. In randomized and simulation algorithms like Monte Carlo, the more the number of iterations, the more accurate the result is. Thus, the title is “Estimating the value of Pi” and not “Calculating the value of Pi”. Below is the algorithm for the method:

Value of Pi(Π) up to 50 decimal places, C# · Free Tools · Objective-C and Swift · Database · Hardware & Devices> Introducing the number PI with their first 50 decimal places: It is known that this irrational number arose on the calculations of geometers over n"); for i in range (2, n * 2, 2): pi = pi + s * (Decimal(4) / (Decimal(i) * (Decimal(i) +  My 7,000 MIPs PC took about 15 hours to calculate the first 1,000,000 decimal places of pi. That works out at about 380 million million instructions in total. To get 1,000,000 decimal places, each multi-length number is implemented as an array of 166685 integers, using a base of 1,000,000 so that each integer gives us 6 significant digits.

Calculating the Number PI Through Infinite Sequences, Manipulate integral and floating point numbers in C# A quick overview of the commands you'll use is in the Become familiar with the dotnet new console -n NumbersInCSharp -o . a relative term that describes the number of binary digits used to store the value. NET contains a constant for PI, Math. So my task is to calculate an estimate of pi within a specific tolerence using a while loop. For a tolerence up to 10^-5, my code runs fine however anything above that and the number of iterations it takes to be within tolerence is far too high.

Numbers in C#, Create a Python project to get the value of e to n number of decimal places. return :type n: int :return: euler's number with n decimal places :rtype: str """ return '%.*f' % (n, e) if __name__ == '__main__': # there is no do while loop in python, Problem: Just like the previous problem, but with e instead of Pi.

Comments
  • Simple to understand in terms of programming, or in terms of math?
  • en.wikipedia.org/wiki/…
  • Take a look here: dotnetperls.com/pi There are sample methods that calculate pi to 20 places, however some limitations are discussed such as lack of precision
  • @Levitikon, I have not looked at this for a while, and I kind of quit working on it after a different answer was accepted. I'll review it sometime this week to see if I can't find where it goes wrong.
  • @fubo - after 4 years, you have finally motivated me to fix it
  • @Levitikon, about 3 years ago you asked if there were any updates on it... i have finally fixed it
  • great, I've testet it with 100k digits - seems to work +1
  • Yes, you did answer the question, but no this was not what the question asker wanted ;-).
  • This only lets me go to 15 places.
  • Decimal always has 4 decimal places? Where did you get that idea?
  • @AlexFord: Then you need to define the domain of your problem better. This method works for the two examples you give (5 and 10 d.p.) What is you maximum number of decimal places?
  • @usr: Yes, I know what decimal is for, but your comment is still nonsense. If I do this: decimal myPi = (decimal)Math.Round(Math.PI, 10); I get 3.1415926536. In other words, 10 decimal places in a decimal type. Go ahead and check the MSDN (msdn.microsoft.com/en-us/library/system.decimal.aspx)
  • This will be faster if you don't use IEnumerable and ElementAt, but just provide ArcTan1OverX the number of iterations to make.
  • @Dani, how much faster?
  • Invalid result. It's a 4 instead of a 5 at the 35th digit - look at nicholas ' update