///<summary>
///Returns the greatest common denominator between the value of this instance and the value of another instance
/// </summary>
/// <remarks>
/// X cannot be negative but can be zero; whereas y cannot be negative or zero
/// </remarks>
public Natural Gcd(Natural value)
{
BigInteger x = this.value, y = value.value, temp = 0;
try
{
if (x < 0 || y <= 0)
{
throw new ArgumentException("An invalid argument was detected.");
}
else if (y < x)
{
temp = x;
x = y;
y = temp;
}
while (y != 0)
{
temp = x % y;
x = y;
y = temp;
}
this.value = x;
return(this);
}
catch (ArgumentException e)
{
Console.WriteLine(e);
throw;
}
}
///<summary>
///Returns the next prime number greater than the value of this instance
/// </summary>
public Natural NextProbablePrime()
{
Natural n = new Natural(++this.value);
if (n.value < 0)
{
throw new ArgumentException("Number should be within the domain of natural numbers.");
}
bool PrimeCheck = n.IsPrime();
try
{
while (!PrimeCheck)
{
n.value++;
PrimeCheck = n.IsPrime();
if (PrimeCheck)
{
PrimeCheck = true;
return(n);
}
}
return(n);
}
catch (ArgumentException e)
{
Console.WriteLine(e);
throw;
}
}
///<summary>
///Return the value of the expression this raised to value % mod
/// </summary>
public Natural ModPow(Natural exponent, Natural mod)
{
BigInteger exp = exponent.value, m = mod.value;
this.value = this.Pow(exp).Modulo(mod).value;
return(this);
}
///<summary>
///Returns the least common multiple between the value of this instance and the value of another instance.
/// </summary>
/// <remarks>
/// Calls the result of GCD
/// </remarks>
public Natural Lcm(Natural value)
{
Natural temp = new Natural(this.value);
BigInteger gcd = temp.Gcd(value).value;
this.value = (this.value / gcd) * value.value;
return(this);
}
public BigInteger MODULO(BigInteger input, BigInteger input2)
{
Natural operand1 = new Natural(input);
Natural operand2 = new Natural(input2);
int result = operand1.Modulo(operand2).GetIntValue();
return(result);
}
public BigInteger MULTIPLICATION(BigInteger input, BigInteger input2)
{
Natural operand1 = new Natural(input);
Natural operand2 = new Natural(input2);
int result = operand1.Multiply(operand2).GetIntValue();
return(result);
}
public BigInteger DIVISION(BigInteger input, BigInteger input2)
{
Natural operand1 = new Natural(input);
Natural operand2 = new Natural(input2);
int result = operand1.Divide(operand2).GetIntValue();
return(result);
}
public BigInteger SUBTRACTION(BigInteger input, BigInteger input2)
{
Natural operand1 = new Natural(input);
Natural operand2 = new Natural(input2);
int result = operand1.Subtract(operand2).GetIntValue();
return(result);
}
public BigInteger ADDITION(BigInteger input, BigInteger input2)
{
Natural operand1 = new Natural(input);
Natural operand2 = new Natural(input2);
int result = operand1.Add(operand2).GetIntValue();
return(result);
}
public BigInteger COMPARE(BigInteger input, BigInteger input2)
{
Natural operand1 = new Natural(input);
Natural operand2 = new Natural(input2);
int result = operand1.CompareTo(operand2);
return(result);
}
public string STRINGBASE(BigInteger input, BigInteger input2)
{
Natural operand1 = new Natural(input);
Natural ibase = new Natural(input2);
string result = operand1.ToString(ibase.GetIntValue());
return(result);
}
public Natural[] DIVIDEREMAIN(BigInteger input, BigInteger input2)
{
Natural operand1 = new Natural(input);
Natural operand2 = new Natural(input2);
Natural[] result = operand1.DivideAndRemainder(operand2);
return(result);
}
public BigInteger POWER(BigInteger input, BigInteger input2)
{
Natural operand1 = new Natural(input);
BigInteger power = input2;
int result = operand1.Pow(power).GetIntValue();
return(result);
}
public BigInteger MODPOWER(BigInteger input, BigInteger input2, BigInteger input3)
{
Natural operand1 = new Natural(input);
Natural exponent = new Natural(input2);
Natural mod = new Natural(input3);
int result = operand1.ModPow(exponent, mod).GetIntValue();
return(result);
}
///<summary>
///This returns a string formatted representation of the division algorithm
/// </summary>
public String DivisionAlgorithm(Natural value)
{
Natural X = new Natural(this.value); Natural X2 = new Natural(this.value);
Natural Y = new Natural(value.value);
if (X.value <= 0 || Y.value <= 0)
{
throw new ArgumentException("Invalid arguments detected!");
}
BigInteger q = X.Divide(value).value, r = X2.Modulo(Y).value;
return(string.Format("{0} = {1} * {2} + {3}", X.value, Y.value, q, r));
}
///<summary>
///Divide the value of this instance by the value of another instance of Natural then return the remainder.
/// </summary>
public Natural Modulo(Natural value)
{
try
{
if (value.value <= 0 || this.value <= 0)
{
throw new ArgumentException("You cannot divide by zero!");
}
this.value %= value.value;
return(this);
}
catch (ArgumentException e)
{
Console.WriteLine(e);
this.value = 0;
return(this);
}
}
///<summary>
///Divide the value of this instance by the value of another instance of Natural.
/// </summary>
public Natural Divide(Natural value)
{
try
{
if (this.value <= 0 || value.value <= 0)
{
throw new ArgumentException("You cannot divide by zero!");
}
else
{
this.value /= value.value;
return(this);
}
}
catch (Exception e)
{
Console.WriteLine(e);
throw;
}
}
///<summary>
///Subtract the value of this instance by the value of another instance of Natural.
///<para>
/// <see cref="Natural()"/> Post-condition: The methods may return negative numbers or 0.
/// </para>
/// </summary>
public Natural Subtract(Natural value)
{
try
{
if ((this.value - value.value) < 0)
{
throw new ArgumentException("Natural numbers cannot be negative");
}
else
{
this.value -= value.value;
}
return(this);
}
catch (ArgumentException e)
{
Console.WriteLine(e);
throw;
}
}
///<summary>
///Divide the value of this instance by the value of another instance of Natural then return the quotient and remainder as an array.
/// </summary>
/// <remarks>
/// Due to the nature of BigInteger, the decimal or floating point precision is omitted.
/// </remarks>
public Natural[] DivideAndRemainder(Natural value)
{
Natural[] divided = new Natural[2];
try
{
if (value.value <= 0 || this.value <= 0)
{
throw new ArgumentException("You cannot divide by zero!");
}
BigInteger quo = this.value / value.value;
BigInteger mod = this.value % value.value;
divided[0] = new Natural(quo);
divided[1] = new Natural(mod);
return(divided);
}
catch (ArgumentException e)
{
Console.WriteLine(e);
throw;
}
}
///<summary>
///Adds the value of this instance by the value of another instance of Natural.
/// </summary>
/// <remarks>
/// Due to the nature of BigInteger, System.OverflowException is not to be thrown.
/// </remarks>
public Natural Add(Natural value)
{
this.value += value.value;
return(this);
}
///<summary>
///Multiply the value of this instance by the value of another instance of Natural.
/// </summary>
public Natural Multiply(Natural value)
{
this.value *= value.value;
return(this);
}
///<summary>
///Returns a boolean check true or false, whether the gcd of two values is equal to 1.
/// </summary>
/// <returns>
/// @True: 1
/// </returns>
public Boolean IsRelativelyPrimeTo(Natural value)
{
return((this.Gcd(value).value == 1) ? true : false);
}
///<summary>
///Returns the maximum value between this instance and another instance.
/// </summary>
public Natural Max(Natural value)
{
return(this.value > value.value ? this : value);
}
///<summary>
///Returns the minimum value between this instance and another instance.
/// </summary>
public Natural Min(Natural value)
{
return(this.value < value.value ? this : value);
}
///<summary>
///Returns different values depending on the compared instance.
/// </summary>
/// <returns>
/// 1 if this instance value is greater than another instance
/// 0 if this instance value is equal to another instance value
///-1 if this instance value is less than another instance value
/// </returns>
public int CompareTo(Natural value)
{
return(this.value == value.value ? 0 : this.value < value.value ? -1 : 1);
}