// 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 Subtract(VeryLong subtrahend)
{
int minuendDecimalPlaces = GetDecimalPlaces();
int subtrahendDecimalPlaces = subtrahend.GetDecimalPlaces();
int decimalPlaces = Math.Max(minuendDecimalPlaces, subtrahendDecimalPlaces);
FillUpDecimalPlacesWithZero(decimalPlaces);
subtrahend.FillUpDecimalPlacesWithZero(decimalPlaces);
string result = "";
int diff = 0;
int borrow = 0;
int currentLastDigit = 0;
int currentLastDigitSubtrahend = 0;
int i = 0;
if (!IsLargerOrEqual(subtrahend))
{
// swap: minuend is smaller than subtrahend --> result is negative
VeryLong newMinuend = subtrahend;
VeryLong newSubtrahend = new VeryLong(ToString());
VeryLong difference = newMinuend.Subtract(newSubtrahend);
return(new VeryLong("-" + difference.ToString()));
}
while (Length() > i || subtrahend.Length() > i || borrow != 0)
{
if (GetLastDigit(i) == ".")
{
result = result.Insert(0, ".");
i++;
continue;
}
currentLastDigit = int.Parse(GetLastDigit(i));
currentLastDigitSubtrahend = int.Parse(subtrahend.GetLastDigit(i));
diff = currentLastDigit - currentLastDigitSubtrahend - borrow;
if (diff < 0)
{
borrow = 1;
diff += 10;
}
else
{
borrow = 0;
}
result = result.Insert(0, diff.ToString());
i++;
}
result = RemoveLeadingZeros(result);
return(new VeryLong(result));
}
// 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);
}
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();
}
