// Berechne die quadratwurzel aus q (Heronverfahren)
//
// 1 / q \
// xn+1 = --- * | xn + ---- |
// 2 \ xn /
// Each iteration about doubles the correct decimal places!
public static VeryLong Sqrt(VeryLong input, int numberOfDigits)
{
int additionalCalcDigits = 5;
int additionalLimitDigits = 0;
VeryLong limit = new VeryLong("0." + VeryLong.GetZeros(numberOfDigits + additionalLimitDigits) + "1"
+ VeryLong.GetZeros(additionalCalcDigits - additionalLimitDigits - 1));
VeryLong xnew;
VeryLong delta;
VeryLong xn = new VeryLong(input.ToString());
int i = 0;
while (true)
{
VeryLong summand2 = input.DivideBy(xn, numberOfDigits + additionalCalcDigits);
VeryLong factor = xn.Add(summand2);
xnew = new VeryLong("0.5").Multiply(factor);
delta = xnew.Subtract(xn);
Console.WriteLine("i " + i);
Console.WriteLine("Sqrt delta: " + delta.ToString());
Console.WriteLine("limit: " + limit.ToString());
Console.WriteLine("Sqrt: " + xnew.ToString());
xn = xnew;
i++;
if (!delta.Abs().IsLargerOrEqual(limit))
{
break;
}
}
xn.LimitPrecisionTo(numberOfDigits);
return(xn);
}
public static VeryLong AddSummands(List <string> summands)
{
VeryLong sum = new VeryLong(summands[0]);
for (int i = 1; i < summands.Count; i++)
{
sum = sum.Add(new VeryLong(summands[i]));
}
return(sum);
}
public static VeryLong GetPiTermDivisorEuler(int n)
{
// 1 --> 2*3*4
// 2 --> 4*5*6
// 3 --> 6*7*8
VeryLong factor1 = new VeryLong("2").Multiply(new VeryLong(n.ToString()));
VeryLong factor2 = new VeryLong(factor1.Add(new VeryLong("1")).ToString());
VeryLong factor3 = new VeryLong(factor2.Add(new VeryLong("1")).ToString());
return(factor1.Multiply(factor2).Multiply(factor3));
}
static void Main(string[] args)
{
for (int i = 0; i < 5; i++)
{
Console.WriteLine("Enter a calculation like '1+2' or enter 'pi'. Operations are + - * /. Numbers are integers of any size.");
string input = Console.ReadLine();
if (input == "pi")
{
Console.WriteLine("Enter the number of digits you want.");
string digitsString = Console.ReadLine();
int numberDigits = 0;
if (int.TryParse(digitsString, out numberDigits))
{
string pi = VeryLongMath.Pi(numberDigits).ToString();
Console.WriteLine("Pi is: " + pi.ToString());
}
else
{
Console.WriteLine("invalid number.");
}
continue;
}
if (input == "sqrt")
{
int numberDigits;
VeryLong number;
Console.WriteLine("Square root of?");
string numberString = Console.ReadLine();
Console.WriteLine("number of digits?");
string digitsString = Console.ReadLine();
if (int.TryParse(digitsString, out numberDigits))
{
number = new VeryLong(numberString);
string sqrt = VeryLongMath.Sqrt(number, numberDigits).ToString();
Console.WriteLine("Sqrt of " + numberString + " is: " + sqrt.ToString());
}
else
{
Console.WriteLine("invalid number.");
}
}
string[] parts = input.Split(new char[] { '+', '-', '*', '/' });
if (parts.Length != 2)
{
Console.WriteLine("invalid input.");
continue;
}
VeryLong number0 = new VeryLong(parts[0]);
VeryLong number1 = new VeryLong(parts[1]);
if (input.Contains('+'))
{
Console.WriteLine(number0.Add(number1).ToString());
}
else if (input.Contains('*'))
{
Console.WriteLine(number0.Multiply(number1).ToString());
}
else if (input.Contains('-'))
{
Console.WriteLine(number0.Subtract(number1).ToString());
}
else if (input.Contains('/'))
{
VeryLong remainder;
VeryLong quotient = number0.DivideBy(number1, out remainder);
Console.WriteLine(quotient.ToString() + " Remainder: " + remainder);
VeryLong quotientWithDecimal = number0.DivideBy(number1, 100);
Console.WriteLine(quotientWithDecimal.ToString());
}
else
{
Console.WriteLine("Please enter a valid operation...");
}
}
Console.ReadLine();
}