Task: Arithmetic-geometric mean_Calculate Pi



C#: using System;
using System.Numerics;

class AgmPie
{
    static BigInteger IntSqRoot(BigInteger valu, BigInteger guess)
    {
        BigInteger term; do {
            term = valu / guess; if (BigInteger.Abs(term - guess) <= 1) break;
            guess += term; guess >>= 1;
        } while (true); return guess;
    }

    static BigInteger ISR(BigInteger term, BigInteger guess)
    {
        BigInteger valu = term * guess; do {
            if (BigInteger.Abs(term - guess) <= 1) break;
            guess += term; guess >>= 1; term = valu / guess;
        } while (true); return guess;
    }

    static BigInteger CalcAGM(BigInteger lam, BigInteger gm, ref BigInteger z,
                              BigInteger ep)
    {
        BigInteger am, zi; ulong n = 1; do {
            am = (lam + gm) >> 1; gm = ISR(lam, gm);
            BigInteger v = am - lam; if ((zi = v * v * n) < ep) break;
            z -= zi; n <<= 1; lam = am;
        } while (true); return am;
    }

    static BigInteger BIP(int exp, ulong man = 1) 
    {
        BigInteger rv = BigInteger.Pow(10, exp); return man == 1 ? rv : man * rv;
    }

    static void Main(string[] args)
    {
        int d = 25000;
        if (args.Length > 0)
        {
            int.TryParse(args[0], out d);
            if (d < 1 || d > 999999) d = 25000;
        }
        DateTime st = DateTime.Now;
        BigInteger am = BIP(d),
          gm = IntSqRoot(BIP(d + d - 1, 5),
                             BIP(d - 15, (ulong)(Math.Sqrt(0.5) * 1e+15))),
          z = BIP(d + d - 2, 25),
          agm = CalcAGM(am, gm, ref z, BIP(d + 1)),
          pi = agm * agm * BIP(d - 2) / z;
        Console.WriteLine("Computation time: {0:0.0000} seconds ",
                             (DateTime.Now - st).TotalMilliseconds / 1000);
        string s = pi.ToString();
        Console.WriteLine("{0}.{1}", s[0], s.Substring(1));
        if (System.Diagnostics.Debugger.IsAttached) Console.ReadKey();
    }
}






VB: Imports System, System.Numerics

Module Program
    Function IntSqRoot(ByVal valu As BigInteger, ByVal guess As BigInteger) As BigInteger
        Dim term As BigInteger : Do
            term = valu / guess
            If BigInteger.Abs(term - guess) <= 1 Then Exit Do
            guess += term : guess >>= 1
        Loop While True : Return guess
    End Function

    Function ISR(ByVal term As BigInteger, ByVal guess As BigInteger) As BigInteger
        Dim valu As BigInteger = term * guess : Do
            If BigInteger.Abs(term - guess) <= 1 Then Exit Do
            guess += term : guess >>= 1 : term = valu / guess
        Loop While True : Return guess
    End Function

    Function CalcAGM(ByVal lam As BigInteger, ByVal gm As BigInteger, ByRef z As BigInteger,
                     ByVal ep As BigInteger) As BigInteger
        Dim am, zi As BigInteger : Dim n As ULong = 1 : Do
            am = (lam + gm) >> 1 : gm = ISR(lam, gm)
            Dim v As BigInteger = am - lam
            zi = v * v * n : If zi < ep Then Exit Do
            z -= zi : n <<= 1 : lam = am
        Loop While True : Return am
    End Function

    Function BIP(ByVal exp As Integer, ByVal Optional man As ULong = 1) As BigInteger
        Dim rv As BigInteger = BigInteger.Pow(10, exp) : Return If(man = 1, rv, man * rv)
    End Function

    Sub Main(args As String())
        Dim d As Integer = 25000
        If args.Length > 0 Then
            Integer.TryParse(args(0), d)
            If d < 1 OrElse d > 999999 Then d = 25000
        End If
        Dim st As DateTime = DateTime.Now
        Dim am As BigInteger = BIP(d),
            gm As BigInteger = IntSqRoot(BIP(d + d - 1, 5),
                                         BIP(d - 15, Math.Sqrt(0.5) * 1.0E+15)),
             z As BigInteger = BIP(d + d - 2, 25),
             agm As BigInteger = CalcAGM(am, gm, z, BIP(d + 1)),
             pi As BigInteger = agm * agm * BIP(d - 2) / z
        Console.WriteLine("Computation time: {0:0.0000} seconds ",
                          (DateTime.Now - st).TotalMilliseconds / 1000)
        If args.Length > 1 OrElse d <= 1000 Then
            Dim s As String = pi.ToString()
            Console.WriteLine("{0}.{1}", s(0), s.Substring(1))
        End If
        If Diagnostics.Debugger.IsAttached Then Console.ReadKey()
    End Sub
End Module