// 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 Pi(int numberOfDigits)
{
VeryLong factor = new VeryLong(1.ToString());
int additionalCalcDigits = 10;
int additionalLimitDigits = 0;
VeryLong pi = new VeryLong("0");
if (_piAlgorithm == PiAlgorithm.BBP)
{
pi = GetStartValueBBP(numberOfDigits + additionalCalcDigits); // BBP
}
else if (_piAlgorithm == PiAlgorithm.Euler)
{
pi = new VeryLong("3"); // Euler
}
VeryLong limit = new VeryLong("0." + VeryLong.GetZeros(numberOfDigits + additionalLimitDigits) + "1"
+ VeryLong.GetZeros(additionalCalcDigits - additionalLimitDigits - 1));
int i = 0;
StartTime();
while (true)
{
i++;
VeryLong term = new VeryLong("0");
if (_piAlgorithm == PiAlgorithm.BBP)
{
term = GetPiTermBBP(i, numberOfDigits + additionalCalcDigits, ref factor);
}
else if (_piAlgorithm == PiAlgorithm.Euler)
{
term = GetPiTermEuler(i, numberOfDigits + additionalCalcDigits);
}
if (!term.IsLargerOrEqual(limit))
{
Console.WriteLine("limit reached:");
Console.WriteLine("Term: " + term.ToString());
Console.WriteLine("limit: " + limit.ToString());
PrintTime();
break;
}
if (_piAlgorithm == PiAlgorithm.BBP) // BBP
{
pi = pi.Add(term);
}
else if (_piAlgorithm == PiAlgorithm.Euler)
{
if (i % 2 == 1)
{
pi = pi.Add(term);
}
else
{
pi = pi.Subtract(term);
}
}
if (i % 10 == 0)
{
Console.WriteLine();
Console.WriteLine("Term " + i);
Console.WriteLine("Pi: " + pi.ToString());
Console.WriteLine("Term: " + term.ToString());
Console.WriteLine("limit: " + limit.ToString());
PrintTime();
}
else if (i % 1 == 0)
{
Console.Write(".");
}
}
VeryLong piCorrectDigits = new VeryLong(pi.ToString().Remove(numberOfDigits + 2));
return(piCorrectDigits);
}