How can I calculate a factorial in C# using a library call?

Question

I need to calculate the factorial of numbers up to around 100! in order to determine if a series of coin flip-style data is random, as per this Wikipedia entry on Bayesian p

Answer 1

The following can calculate the factorial of 5000 in 1 second.

public class Number
{
    #region Fields
    private static long _valueDivision = 1000000000;
    private static int _valueDivisionDigitCount = 9;
    private static string _formatZeros = "000000000";
    List _value;
    #endregion

    #region Properties
    public int ValueCount { get { return _value.Count; } }
    public long ValueAsLong
    {
        get
        {
            return long.Parse(ToString());
        }
        set { SetValue(value.ToString()); }
    }
    #endregion

    #region Constructors
    public Number()
    {
        _value = new List();
    }
    public Number(long value)
        : this()
    {
        SetValue(value.ToString());
    }
    public Number(string value)
        : this()
    {
        SetValue(value);
    }
    private Number(List list)
    {
        _value = list;
    }
    #endregion

    #region Public Methods
    public void SetValue(string value)
    {
        _value.Clear();
        bool finished = false;
        while (!finished)
        {
            if (value.Length > _valueDivisionDigitCount)
            {
                _value.Add(long.Parse(value.Substring(value.Length - _valueDivisionDigitCount)));
                value = value.Remove(value.Length - _valueDivisionDigitCount, _valueDivisionDigitCount);
            }
            else
            {
                _value.Add(long.Parse(value));
                finished = true;
            }
        }
    }
    #endregion

    #region Static Methods
    public static Number operator +(Number c1, Number c2)
    {
        return Add(c1, c2);
    }
    public static Number operator *(Number c1, Number c2)
    {
        return Mul(c1, c2);
    }
    private static Number Add(Number value1, Number value2)
    {
        Number result = new Number();
        int count = Math.Max(value1._value.Count, value2._value.Count);
        long reminder = 0;
        long firstValue, secondValue;
        for (int i = 0; i < count; i++)
        {
            firstValue = 0;
            secondValue = 0;
            if (value1._value.Count > i)
            {
                firstValue = value1._value[i];
            }
            if (value2._value.Count > i)
            {
                secondValue = value2._value[i];
            }
            reminder += firstValue + secondValue;
            result._value.Add(reminder % _valueDivision);
            reminder /= _valueDivision;
        }
        while (reminder > 0)
        {
            result._value.Add(reminder % _valueDivision);
            reminder /= _valueDivision;
        }
        return result;
    }
    private static Number Mul(Number value1, Number value2)
    {
        List> values = new List>();
        for (int i = 0; i < value2._value.Count; i++)
        {
            values.Add(new List());
            long lastremain = 0;
            for (int j = 0; j < value1._value.Count; j++)
            {
                values[i].Add(((value1._value[j] * value2._value[i] + lastremain) % _valueDivision));
                lastremain = ((value1._value[j] * value2._value[i] + lastremain) / _valueDivision);
                //result.Add(();
            }
            while (lastremain > 0)
            {
                values[i].Add((lastremain % _valueDivision));
                lastremain /= _valueDivision;
            }
        }
        List result = new List();
        for (int i = 0; i < values.Count; i++)
        {
            for (int j = 0; j < i; j++)
            {
                values[i].Insert(0, 0);
            }
        }
        int count = values.Select(list => list.Count).Max();
        int index = 0;
        long lastRemain = 0;
        while (count > 0)
        {
            for (int i = 0; i < values.Count; i++)
            {
                if (values[i].Count > index)
                    lastRemain += values[i][index];
            }
            result.Add((lastRemain % _valueDivision));
            lastRemain /= _valueDivision;
            count -= 1;
            index += 1;
        }
        while (lastRemain > 0)
        {
            result.Add((lastRemain % _valueDivision));
            lastRemain /= _valueDivision;
        }
        return new Number(result);
    }
    #endregion

    #region Overriden Methods Of Object
    public override string ToString()
    {
        string result = string.Empty;
        for (int i = 0; i < _value.Count; i++)
        {
            result = _value[i].ToString(_formatZeros) + result;
        }
        return result.TrimStart('0');
    }
    #endregion
}

class Program
{
    static void Main(string[] args)
    {
        Number number1 = new Number(5000);
        DateTime dateTime = DateTime.Now;
        string s = Factorial(number1).ToString();
        TimeSpan timeSpan = DateTime.Now - dateTime;
        long sum = s.Select(c => (long) (c - '0')).Sum();
    }
    static Number Factorial(Number value)
    {
        if( value.ValueCount==1 && value.ValueAsLong==2)
        {
            return value;
        }
        return Factorial(new Number(value.ValueAsLong - 1)) * value;
    }
}