// binary arithmetic operators
BigInteger operator+ (const BigInteger& a, const BigInteger& b)
{
// handle sign and change operation
if (a.Sign() != b.Sign())
return (a.Sign()) ? a - b.Abs() : b - a.Abs();
// allocate array
int length = (a.Cardinality() >= b.Cardinality()) ?
a.Cardinality() + 1 :
b.Cardinality() + 1;
int* digits = new int[length];
// add numbers digit per digit
int carry = 0;
for (int i = 0; i < length; i++)
{
if (i < a.Cardinality())
carry += a[i];
if (i < b.Cardinality())
carry += b[i];
digits[i] = carry % 10;
carry /= 10;
}
BigInteger tmp (a.Sign(), digits, length);
tmp.RemoveLeadingZeros();
return tmp;
}
BigInteger operator/ (const BigInteger& a, const BigInteger& b)
{
BigInteger remainder;
char* result = new char[1];
result[0] = '\0';
// need positive divisor
BigInteger bAbs = b.Abs();
int pos = a.Cardinality() - 1;
while (pos >= 0)
{
// append next digit from dividend to temporary divisor
int len = (remainder.IsNull()) ? 1 : remainder.Cardinality() + 1;
int* digits = new int[len];
// copy old digits
for (int k = 0; k < len - 1; k++)
digits[k + 1] = remainder.m_digits[k];
// fetch digit from dividend
digits[0] = a.m_digits[pos];
remainder = BigInteger(true, digits, len); // TODO: Ob len hier stimmt, ist OFFEN
// divide current dividend with divisor
int n = 0;
while (bAbs <= remainder)
{
n++;
remainder -= bAbs;
}
// append digit to result string
int slen = strlen(result);
char* tmp = new char[slen + 2];
strcpy_s (tmp, slen + 2, result);
tmp[slen] = '0' + n;
tmp[slen + 1] = '\0';
delete[] result;
result = tmp;
// fetch next digit from divisor
pos--;
}
BigInteger tmp (result);
tmp.m_sign = (a.Sign() == b.Sign()) ? true : false;
tmp.RemoveLeadingZeros();
return tmp;
}
BigInteger operator- (const BigInteger& a, const BigInteger& b)
{
// handle sign and change operation
if (a.Sign() != b.Sign())
return (a.Sign()) ? a + b.Abs() : -(a.Abs() + b);
if (a.Abs() < b.Abs())
return (a.Sign()) ? -(b - a) : b.Abs() - a.Abs();
// create copy of minuend
BigInteger tmp (a);
// traverse digits of subtrahend
for (int i = 0; i < b.Cardinality(); i++)
{
if (tmp[i] < b[i])
{
if (tmp[i + 1] != 0)
{
tmp[i + 1]--;
tmp[i] += 10;
}
else
{
// preceding digit is zero, cannot borrow directly
int pos = i + 1;
while (tmp[pos] == 0)
pos++;
// borrow indirectly
for (int k = pos; k >= i + 1; k--)
{
tmp[k]--;
tmp[k - 1] += 10;
}
}
}
// subtract current subtrahend digit from minuend digit
tmp[i] -= b[i];
}
tmp.RemoveLeadingZeros();
return tmp;
}
