private static void SingleDivide(BigInteger leftSide, BigInteger rightSide, out BigInteger quotient, out BigInteger remainder)
{
if (rightSide.IsZero)
{
throw new DivideByZeroException();
}
DigitsArray remainderDigits = new DigitsArray(leftSide.m_digits);
remainderDigits.ResetDataUsed();
int pos = remainderDigits.DataUsed - 1;
ulong divisor = (ulong)rightSide.m_digits[0];
ulong dividend = (ulong)remainderDigits[pos];
DType[] result = new DType[leftSide.m_digits.Count];
leftSide.m_digits.CopyTo(result, 0, result.Length);
int resultPos = 0;
if (dividend >= divisor)
{
result[resultPos++] = (DType)(dividend / divisor);
remainderDigits[pos] = (DType)(dividend % divisor);
}
pos--;
while (pos >= 0)
{
dividend = ((ulong)(remainderDigits[pos + 1]) << DigitsArray.DataSizeBits) + (ulong)remainderDigits[pos];
result[resultPos++] = (DType)(dividend / divisor);
remainderDigits[pos + 1] = 0;
remainderDigits[pos--] = (DType)(dividend % divisor);
}
remainder = new BigInteger(remainderDigits);
DigitsArray quotientDigits = new DigitsArray(resultPos + 1, resultPos);
int j = 0;
for (int i = quotientDigits.DataUsed - 1; i >= 0; i--, j++)
{
quotientDigits[j] = result[i];
}
quotient = new BigInteger(quotientDigits);
}
/// <summary>
/// Multiply two BigIntegers returning the result.
/// </summary>
/// <remarks>
/// See Knuth.
/// </remarks>
/// <param name="leftSide">A BigInteger.</param>
/// <param name="rightSide">A BigInteger</param>
/// <returns></returns>
public static BigInteger operator *(BigInteger leftSide, BigInteger rightSide)
{
if (object.ReferenceEquals(leftSide, null))
{
throw new ArgumentNullException("leftSide");
}
if (object.ReferenceEquals(rightSide, null))
{
throw new ArgumentNullException("rightSide");
}
bool leftSideNeg = leftSide.IsNegative;
bool rightSideNeg = rightSide.IsNegative;
leftSide = Abs(leftSide);
rightSide = Abs(rightSide);
DigitsArray da = new DigitsArray(leftSide.m_digits.DataUsed + rightSide.m_digits.DataUsed);
da.DataUsed = da.Count;
for (int i = 0; i < leftSide.m_digits.DataUsed; i++)
{
ulong carry = 0;
for (int j = 0, k = i; j < rightSide.m_digits.DataUsed; j++, k++)
{
ulong val = ((ulong)leftSide.m_digits[i] * (ulong)rightSide.m_digits[j]) + (ulong)da[k] + carry;
da[k] = (DType)(val & DigitsArray.AllBits);
carry = (val >> DigitsArray.DataSizeBits);
}
if (carry != 0)
{
da[i + rightSide.m_digits.DataUsed] = (DType)carry;
}
}
//da.ResetDataUsed();
BigInteger result = new BigInteger(da);
return (leftSideNeg != rightSideNeg ? -result : result);
}
private static void MultiDivide(BigInteger leftSide, BigInteger rightSide, out BigInteger quotient, out BigInteger remainder)
{
if (rightSide.IsZero)
{
throw new DivideByZeroException();
}
DType val = rightSide.m_digits[rightSide.m_digits.DataUsed - 1];
int d = 0;
for (uint mask = DigitsArray.HiBitSet; mask != 0 && (val & mask) == 0; mask >>= 1)
{
d++;
}
int remainderLen = leftSide.m_digits.DataUsed + 1;
DType[] remainderDat = new DType[remainderLen];
leftSide.m_digits.CopyTo(remainderDat, 0, leftSide.m_digits.DataUsed);
DigitsArray.ShiftLeft(remainderDat, d);
rightSide = rightSide << d;
ulong firstDivisor = rightSide.m_digits[rightSide.m_digits.DataUsed - 1];
ulong secondDivisor = (rightSide.m_digits.DataUsed < 2 ? (DType)0 : rightSide.m_digits[rightSide.m_digits.DataUsed - 2]);
int divisorLen = rightSide.m_digits.DataUsed + 1;
DigitsArray dividendPart = new DigitsArray(divisorLen, divisorLen);
DType[] result = new DType[leftSide.m_digits.Count + 1];
int resultPos = 0;
ulong carryBit = (ulong)0x1 << DigitsArray.DataSizeBits; // 0x100000000
for (int j = remainderLen - rightSide.m_digits.DataUsed, pos = remainderLen - 1; j > 0; j--, pos--)
{
ulong dividend = ((ulong)remainderDat[pos] << DigitsArray.DataSizeBits) + (ulong)remainderDat[pos - 1];
ulong qHat = (dividend / firstDivisor);
ulong rHat = (dividend % firstDivisor);
while (pos >= 2)
{
if (qHat == carryBit || (qHat * secondDivisor) > ((rHat << DigitsArray.DataSizeBits) + remainderDat[pos - 2]))
{
qHat--;
rHat += firstDivisor;
if (rHat < carryBit)
{
continue;
}
}
break;
}
for (int h = 0; h < divisorLen; h++)
{
dividendPart[divisorLen - h - 1] = remainderDat[pos - h];
}
BigInteger dTemp = new BigInteger(dividendPart);
BigInteger rTemp = rightSide * (long)qHat;
while (rTemp > dTemp)
{
qHat--;
rTemp -= rightSide;
}
rTemp = dTemp - rTemp;
for (int h = 0; h < divisorLen; h++)
{
remainderDat[pos - h] = rTemp.m_digits[rightSide.m_digits.DataUsed - h];
}
result[resultPos++] = (DType)qHat;
}
Array.Reverse(result, 0, resultPos);
quotient = new BigInteger(new DigitsArray(result));
int n = DigitsArray.ShiftRight(remainderDat, d);
DigitsArray rDA = new DigitsArray(n, n);
rDA.CopyFrom(remainderDat, 0, 0, rDA.DataUsed);
remainder = new BigInteger(rDA);
}
/// <summary>
/// Substracts two BigIntegers and returns a new BigInteger that represents the sum.
/// </summary>
/// <param name="leftSide">A BigInteger</param>
/// <param name="rightSide">A BigInteger</param>
/// <returns>The BigInteger result of substracting <paramref name="leftSide" /> and <paramref name="rightSide" />.</returns>
public static BigInteger operator -(BigInteger leftSide, BigInteger rightSide)
{
int size = System.Math.Max(leftSide.m_digits.DataUsed, rightSide.m_digits.DataUsed) + 1;
DigitsArray da = new DigitsArray(size);
long carry = 0;
for (int i = 0; i < da.Count; i++)
{
long diff = (long)leftSide.m_digits[i] - (long)rightSide.m_digits[i] - carry;
da[i] = (DType)(diff & DigitsArray.AllBits);
da.DataUsed++;
carry = ((diff < 0) ? 1 : 0);
}
return new BigInteger(da);
}
/// <summary>
/// Negates the BigInteger, that is, if the BigInteger is negative return a positive BigInteger, and if the
/// BigInteger is negative return the postive.
/// </summary>
/// <param name="leftSide">A BigInteger operand.</param>
/// <returns>The value of the <paramref name="this" /> negated.</returns>
public static BigInteger operator -(BigInteger leftSide)
{
if (object.ReferenceEquals(leftSide, null))
{
throw new ArgumentNullException("leftSide");
}
if (leftSide.IsZero)
{
return new BigInteger(0);
}
DigitsArray da = new DigitsArray(leftSide.m_digits.DataUsed + 1, leftSide.m_digits.DataUsed + 1);
for (int i = 0; i < da.Count; i++)
{
da[i] = (DType)(~(leftSide.m_digits[i]));
}
// add one to result (1's complement + 1)
bool carry = true;
int index = 0;
while (carry && index < da.Count)
{
long val = (long)da[index] + 1;
da[index] = (DType)(val & DigitsArray.AllBits);
carry = ((val >> DigitsArray.DataSizeBits) > 0);
index++;
}
return new BigInteger(da);
}
/// <summary>
/// Copy constructor, doesn't copy the digits parameter, assumes <code>this</code> owns the DigitsArray.
/// </summary>
/// <remarks>The <paramef name="digits" /> parameter is saved and reset.</remarks>
/// <param name="digits"></param>
private BigInteger(DigitsArray digits)
{
digits.ResetDataUsed();
this.m_digits = digits;
}
/// <summary>
/// Adds two BigIntegers and returns a new BigInteger that represents the sum.
/// </summary>
/// <param name="leftSide">A BigInteger</param>
/// <param name="rightSide">A BigInteger</param>
/// <returns>The BigInteger result of adding <paramref name="leftSide" /> and <paramref name="rightSide" />.</returns>
public static BigInteger operator +(BigInteger leftSide, BigInteger rightSide)
{
int size = System.Math.Max(leftSide.m_digits.DataUsed, rightSide.m_digits.DataUsed);
DigitsArray da = new DigitsArray(size + 1);
long carry = 0;
for (int i = 0; i < da.Count; i++)
{
long sum = (long)leftSide.m_digits[i] + (long)rightSide.m_digits[i] + carry;
carry = (long)(sum >> DigitsArray.DataSizeBits);
da[i] = (DType)(sum & DigitsArray.AllBits);
}
return new BigInteger(da);
}
private void ConstructFrom(byte[] array, int offset, int length)
{
if (array == null)
{
throw new ArgumentNullException("array");
}
if (offset > array.Length || length > array.Length)
{
throw new ArgumentOutOfRangeException("offset");
}
if (length > array.Length || (offset + length) > array.Length)
{
throw new ArgumentOutOfRangeException("length");
}
int estSize = length / 4;
int leftOver = length & 3;
if (leftOver != 0)
{
++estSize;
}
m_digits = new DigitsArray(estSize + 1, 0); // alloc one extra since we can't init -'s from here.
for (int i = offset + length - 1, j = 0; (i - offset) >= 3; i -= 4, j++)
{
m_digits[j] = (DType)((array[i - 3] << 24) + (array[i - 2] << 16) + (array[i - 1] << 8) + array[i]);
m_digits.DataUsed++;
}
DType accumulator = 0;
for (int i = leftOver; i > 0; i--)
{
DType digit = array[offset + leftOver - i];
digit = (digit << ((i - 1) * 8));
accumulator |= digit;
}
m_digits[m_digits.DataUsed] = accumulator;
m_digits.ResetDataUsed();
}
private void Construct(string digits, int radix)
{
if (digits == null)
{
throw new ArgumentNullException("digits");
}
BigInteger multiplier = new BigInteger(1);
BigInteger result = new BigInteger();
digits = digits.ToUpper(System.Globalization.CultureInfo.CurrentCulture).Trim();
int nDigits = (digits[0] == '-' ? 1 : 0);
for (int idx = digits.Length - 1; idx >= nDigits; idx--)
{
int d = (int)digits[idx];
if (d >= '0' && d <= '9')
{
d -= '0';
}
else if (d >= 'A' && d <= 'Z')
{
d = (d - 'A') + 10;
}
else
{
throw new ArgumentOutOfRangeException("digits");
}
if (d >= radix)
{
throw new ArgumentOutOfRangeException("digits");
}
result += (multiplier * d);
multiplier *= radix;
}
if (digits[0] == '-')
{
result = -result;
}
this.m_digits = result.m_digits;
}
/// <summary>
/// Create a BigInteger with an integer value of 0.
/// </summary>
public BigInteger()
{
m_digits = new DigitsArray(1, 1);
}
/// <summary>
/// Creates a BigInteger with the value of the operand. Can never be negative.
/// </summary>
/// <param name="number">A unsigned long.</param>
public BigInteger(ulong number)
{
m_digits = new DigitsArray((8 / DigitsArray.DataSizeOf) + 1, 0);
while (number != 0 && m_digits.DataUsed < m_digits.Count)
{
m_digits[m_digits.DataUsed] = (DType)(number & DigitsArray.AllBits);
number >>= DigitsArray.DataSizeBits;
m_digits.DataUsed++;
}
m_digits.ResetDataUsed();
}
internal DigitsArray(DigitsArray copyFrom)
{
Allocate(copyFrom.Count, copyFrom.DataUsed);
Array.Copy(copyFrom.m_data, 0, m_data, 0, copyFrom.Count);
}
public static BigInteger operator >>(BigInteger leftSide, int shiftCount)
{
if (leftSide == null)
{
throw new ArgumentNullException("leftSide");
}
DigitsArray da = new DigitsArray(leftSide.m_digits);
da.DataUsed = da.ShiftRight(shiftCount);
if (leftSide.IsNegative)
{
for (int i = da.Count - 1; i >= da.DataUsed; i--)
{
da[i] = DigitsArray.AllBits;
}
DType mask = DigitsArray.HiBitSet;
for (int i = 0; i < DigitsArray.DataSizeBits; i++)
{
if ((da[da.DataUsed - 1] & mask) == DigitsArray.HiBitSet)
{
break;
}
da[da.DataUsed - 1] |= mask;
mask >>= 1;
}
da.DataUsed = da.Count;
}
return new BigInteger(da);
}
public static BigInteger operator <<(BigInteger leftSide, int shiftCount)
{
if (leftSide == null)
{
throw new ArgumentNullException("leftSide");
}
DigitsArray da = new DigitsArray(leftSide.m_digits);
da.DataUsed = da.ShiftLeftWithoutOverflow(shiftCount);
return new BigInteger(da);
}
public static BigInteger operator ~(BigInteger leftSide)
{
DigitsArray da = new DigitsArray(leftSide.m_digits.Count);
for (int idx = 0; idx < da.Count; idx++)
{
da[idx] = (DType)(~(leftSide.m_digits[idx]));
}
return new BigInteger(da);
}
public static BigInteger operator ^(BigInteger leftSide, BigInteger rightSide)
{
int len = System.Math.Max(leftSide.m_digits.DataUsed, rightSide.m_digits.DataUsed);
DigitsArray da = new DigitsArray(len, len);
for (int idx = 0; idx < len; idx++)
{
da[idx] = (DType)(leftSide.m_digits[idx] ^ rightSide.m_digits[idx]);
}
return new BigInteger(da);
}
