// 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 VeryLong DivideBy(VeryLong divisor, int numberOfDigits)
{
int numberDecimalPlacesDivisor = divisor.GetDecimalPlaces();
divisor = RemoveDecimalPlaces(divisor);
FillUpDecimalPlacesWithZero(numberOfDigits + numberDecimalPlacesDivisor);
string dividendString = "";
string divisorString = divisor.ToString();
string quotientDigit = "";
string quotient = "";
string mult = "";
string diff = "";
for (int i = 0; i < Length(); i++)
{
if (GetFirstDigit(i) == ".")
{
quotient += ".";
continue;
}
dividendString += GetFirstDigit(i);
dividendString = VeryLong.RemoveLeadingZeros(dividendString);
quotientDigit = DivideSimple(dividendString, divisorString);
quotient += quotientDigit;
mult = (new VeryLong(quotientDigit).Multiply(new VeryLong(divisorString))).ToString();
diff = (new VeryLong(dividendString).Subtract(new VeryLong(mult))).ToString();
dividendString = diff;
}
VeryLong quotientResult = new VeryLong(quotient);
int resultDecimalPlaces = quotientResult.GetDecimalPlaces();
quotientResult = RemoveDecimalPlaces(quotientResult);
quotientResult.SetDecimalPlaces(resultDecimalPlaces - numberDecimalPlacesDivisor);
quotientResult.RemoveLeadingZeros();
quotientResult.LimitPrecisionTo(numberOfDigits);
return(quotientResult);
}
// 1 / 4 2 1 1 \
//------ * |----- - ------ - ------ - ------ |
// 16^n \ 8n+1 8n+4 8n+5 8n+6 /
public static VeryLong GetPiTermBBP(int n, int numberOfDigits, ref VeryLong factor)
{
VeryLong factor16 = new VeryLong(16.ToString());
factor = factor.DivideBy(factor16, numberOfDigits);
VeryLong summand1 = new VeryLong(4.ToString());
VeryLong divisor1 = new VeryLong(8.ToString());
divisor1 = divisor1.Multiply(new VeryLong(n.ToString())).Add(new VeryLong(1.ToString()));
summand1 = summand1.DivideBy(divisor1, numberOfDigits);
VeryLong subtrahend2 = new VeryLong(2.ToString());
VeryLong divisor2 = new VeryLong(8.ToString());
divisor2 = divisor2.Multiply(new VeryLong(n.ToString())).Add(new VeryLong(4.ToString()));
subtrahend2 = subtrahend2.DivideBy(divisor2, numberOfDigits);
VeryLong subtrahend3 = new VeryLong(1.ToString());
VeryLong divisor3 = new VeryLong(8.ToString());
divisor3 = divisor3.Multiply(new VeryLong(n.ToString())).Add(new VeryLong(5.ToString()));
subtrahend3 = subtrahend3.DivideBy(divisor3, numberOfDigits);
VeryLong subtrahend4 = new VeryLong(1.ToString());
VeryLong divisor4 = new VeryLong(8.ToString());
divisor4 = divisor4.Multiply(new VeryLong(n.ToString())).Add(new VeryLong(6.ToString()));
subtrahend4 = subtrahend4.DivideBy(divisor4, numberOfDigits);
VeryLong sum = summand1.Subtract(subtrahend2).Subtract(subtrahend3).Subtract(subtrahend4);
VeryLong term = sum.Multiply(factor);
term.LimitPrecisionTo(numberOfDigits);
return(term);
}