/// <summary>
/// Returns the Nth root of this instance plus the Remainder.
// The root must be greater than or equal to 1.
/// </summary>
public static BigInteger NthRoot(this BigInteger source, int root, out BigInteger remainder)
{
if (root < 1)
{
throw new Exception("Root must be greater than or equal to 1");
}
if (source.Sign == -1)
{
throw new Exception("Value must be a positive integer");
}
if (source == BigInteger.One)
{
remainder = 0;
return(BigInteger.One);
}
if (source == BigInteger.Zero)
{
remainder = 0;
return(BigInteger.Zero);
}
if (root == 1)
{
remainder = 0;
return(source.Clone());
}
BigInteger upperbound = source.Clone();
BigInteger lowerbound = new BigInteger(0);
while (true)
{
BigInteger nval = (upperbound + lowerbound) >> 1;
BigInteger tstsq = BigInteger.Pow(nval, root);
if (tstsq > source)
{
upperbound = nval;
}
if (tstsq < source)
{
lowerbound = nval;
}
if (tstsq == source)
{
lowerbound = nval;
break;
}
if (lowerbound == upperbound - 1)
{
break;
}
}
remainder = source - BigInteger.Pow(lowerbound, root);
return(lowerbound);
}
public PublicKeyEncSessionPacket(
long keyId,
PublicKeyAlgorithmTag algorithm,
BigInteger[] data)
{
this.version = 3;
this.keyId = keyId;
this.algorithm = algorithm;
this.data = (BigInteger[]) data.Clone();
}
/// <summary>
/// Returns the remainder of this instance modulus the specified number.
/// </summary>
public static BigInteger Mod(this BigInteger source, BigInteger mod)
{
if (mod.Equals(BigInteger.Zero))
{
throw new DivideByZeroException($"Parameter '{nameof(mod)}' must not be zero.");
}
BigInteger n = source.Clone();
BigInteger r = (n >= mod) ? n % mod : n;
return((r < 0) ? (r + mod) : r);
}
public static void Test_Clone()
{
BigInteger n1 = new BigInteger("12345");
Console.WriteLine("n1: {0}", n1);
BigInteger n2 = (BigInteger)n1.Clone();
Console.WriteLine("n2: {0}", n2);
Console.WriteLine("{0}", n1 == n2);
Console.WriteLine();
}
public T Inverse()
{
// Define our initial variables and give them their initial assignments.
BigInteger[] newt = new BigInteger[Degree + 1];
newt[0] = 1;
BigInteger[] t = new BigInteger[Degree + 1];
BigInteger[] newr = new BigInteger[Coefficients.Count + 1];
Coefficients.CopyTo(newr, 0);
BigInteger[] r = new BigInteger[ModulusCoefficients.Count + 1];
ModulusCoefficients.CopyTo(r, 0);
r[r.Length - 1] = 1;
// Loop while there are elements which are non-zero.
while (GetDegree(newr) != 0)
{
BigInteger[] quotient = DividePolynomialRounded(r, newr);
Array.Resize(ref quotient, Degree + 1);
BigInteger[] tempt = (BigInteger[])t.Clone();
BigInteger[] tempr = (BigInteger[])r.Clone();
for (int i = 0; i < Degree + 1; i++)
{
for (int j = 0; j < Degree + 1 - i; j++)
{
tempt[i + j] -= newt[i] * quotient[j];
tempr[i + j] -= newr[i] * quotient[j];
}
}
// Perform modulo on tempt
for (int i = 0; i < tempt.Length; i++)
{
tempt[i] = tempt[i].Mod(Bn128Curve.P);
}
// Perform modulo on tempr
for (int i = 0; i < tempr.Length; i++)
{
tempr[i] = tempr[i].Mod(Bn128Curve.P);
}
// Swap state for the next iteration.
(newt, newr, t, r) = (tempt, tempr, newt, newr);
}
// Resize the array to the degree size accordingly, divide and return.
Array.Resize(ref newt, Degree);
return(New(newt).Divide(newr[0]));
}
public static BigInteger Mod(this BigInteger n, BigInteger mod)
{
BigInteger r = (n >= mod) ? n % mod : n;
return((r < 0) ? BigInteger.Add(r, mod) : r.Clone());
}
public Term(BigInteger coefficient, Indeterminate[] variables)
{
CoEfficient = coefficient.Clone();
Variables = CloneHelper <Indeterminate> .CloneCollection(variables).ToArray();
}
/// <summary>
/// Initializes a new instance of the <see cref="Term"/> class with the specified coefficient and exponent.
/// </summary>
public Term(BigInteger coefficient, int exponent)
{
Exponent = exponent;
CoEfficient = coefficient.Clone();
}