/// <summary>
/// Calculates 'this'^power
/// </summary>
/// <param name="power"></param>
public void Power(BigInt power)
{
if (power.IsZero() || power.sign)
{
Zero();
digitArray[0] = 1;
return;
}
BigInt pow = new BigInt(power);
BigInt temp = new BigInt(this);
BigInt powTerm = new BigInt(this);
pow.Decrement();
for (; !pow.IsZero(); pow.RSH(1))
{
if ((pow.digitArray[0] & 1) == 1)
{
temp.Mul(powTerm);
}
powTerm.Square();
}
Assign(temp);
}
/// <summary>
/// Converts this to a string, in the specified base
/// </summary>
/// <param name="numberBase">the base to use (min 2, max 16)</param>
/// <returns>a string representation of the number</returns>
public string ToString(int numberBase)
{
char[] digitChars = { '0', '1', '2', '3', '4', '5', '6', '7', '8', '9', 'A', 'B', 'C', 'D', 'E', 'F' };
string output = "";
BigInt clone = new BigInt(this);
clone.sign = false;
int numDigits = 0;
while (!clone.IsZero())
{
BigInt div, mod;
DivMod(clone, (uint)numberBase, out div, out mod);
int iMod = (int)mod;
output = String.Concat(digitChars[(int)mod], output);
numDigits++;
clone = div;
}
if (output.Length == 0) output = "0";
if (sign) output = String.Concat("-", output);
return output;
}
/// <summary>
/// This function is used for floating-point division.
/// </summary>
/// <param name="n2"></param>
//Given two numbers:
// In floating point 1 <= a, b < 2, meaning that both numbers have their top bits set.
// To calculate a / b, maintaining precision, we:
// 1. Double the number of digits available to both numbers.
// 2. set a = a * 2^d (where d is the number of digits)
// 3. calculate the quotient a <- q: 2^(d-1) <= q < 2^(d+1)
// 4. if a >= 2^d, s = 1, else s = 0
// 6. shift a down by s, and undo the precision extension
// 7. return 1 - shift (change necessary to exponent)
public int DivAndShift(BigInt n2)
{
if (n2.IsZero()) return -1;
if (digitArray.Length != n2.digitArray.Length) MakeSafe(ref n2);
int oldLength = digitArray.Length;
//Double the number of digits, and shift a into the higher digits.
Pad();
n2.Extend();
//Do the divide (at double precision, ouch!)
Div(n2);
//Shift down if 'this' >= 2^d
int ret = 1;
if (digitArray[oldLength] != 0)
{
RSH(1);
ret--;
}
SetNumDigits(oldLength);
n2.SetNumDigits(oldLength);
return ret;
}
/// <summary>
/// True iff n2 (precision-adjusted to this) == n1
/// </summary>
/// <param name="n2"></param>
/// <returns></returns>
public bool Equals(BigInt n2)
{
if (IsZero() && n2.IsZero()) return true;
if (sign != n2.sign) return false;
int Length = digitArray.Length;
if (n2.digitArray.Length != Length) MakeSafe(ref n2);
for (int i = 0; i < Length; i++)
{
if (digitArray[i] != n2.digitArray[i]) return false;
}
return true;
}