// Returns a / b.
Integer Integer::divide(Integer& a, Integer& b) const
{
Integer q, row;
int asign = a.sign();
int bsign = b.sign();
int i;
q.set_size(a.size());
a.set_sign(PLUS);
b.set_sign(PLUS);
for (i = a.size() - 1; i >= 0; i--) {
row <<= 1;
row[0] = a[i];
q[i] = 0;
while (row >= b) {
q[i]++;
row -= b;
}
}
q.adjust();
if (q == ZERO)
q.set_sign(PLUS);
else
q.set_sign(asign * bsign);
a.set_sign(asign);
b.set_sign(bsign);
return q;
}
// Return a * b. This method is known as "Long Multiplication".
// Complexity: O(n^2)
Integer Integer::multiply(Integer& a, Integer& b) const
{
Integer ans;
unsigned int i, j, k, n, carry_mult, carry_sum;
for (i = 0; i < a.size(); i++) {
carry_mult = carry_sum = 0;
k = i; // Shifting
for (j = 0; j < b.size(); j++) {
n = a[i] * b[j] + carry_mult;
carry_mult = n / BASE;
n = ans[k] + n % BASE + carry_sum;
carry_sum = n / BASE;
ans[k] = n % BASE;
k++;
}
if (carry_sum > 0 || carry_mult > 0) {
ans[k++] = carry_sum + carry_mult;
}
ans.set_size(k);
}
if (ans == ZERO)
ans.set_sign(PLUS);
else
ans.set_sign(a.sign() * b.sign());
return ans;
}
// a and b are positive integers.
Integer Integer::subtract(Integer& a, Integer& b) const
{
Integer ans;
int borrow = 0, n;
// Three special cases:
// a - (-b) == a + b
// -a - b == -a + (-b)
// -a - (-b) == -a + b
if (a.sign() == MINUS || b.sign() == MINUS) {
b.set_sign(MINUS * b.sign());
ans = add(a, b);
b.set_sign(MINUS * b.sign());
return ans;
}
if (a == b) {
return ZERO;
}
if (a < b) {
ans = subtract(b, a);
ans.set_sign(MINUS);
return ans;
}
unsigned int i;
for (i = 0; i < a.size(); i++) {
n = a[i] - b[i] - borrow;
borrow = (n < 0) ? 1 : 0;
if (n < 0) {
n += BASE;
}
ans[i] = n;
}
ans.set_size(i);
ans.adjust();
ans.set_sign(PLUS);
return ans;
}
// Returns a new integer c = a + b
Integer Integer::add(Integer &a, Integer &b) const
{
Integer c;
int carry = 0, i;
if (a.sign() == b.sign()) {
c.set_sign(a.sign());
} else {
if (a.sign() == MINUS) {
a.set_sign(PLUS);
c = subtract(b, a);
a.set_sign(MINUS);
} else {
b.set_sign(PLUS);
c = subtract(a, b);
b.set_sign(MINUS);
}
return c;
}
int max = std::max(a.size(), b.size());
int n;
for (i = 0; i < max; i++) {
n = carry + a[i] + b[i];
c[i] = n % BASE;
carry = n / BASE;
}
if (carry > 0) {
c[i++] = carry;
}
c.set_size(i);
c.adjust();
return c;
}
// a and b are positive and a > b
void Integer::subtract(Integer& a, Integer& b, Integer& c) const
{
int n, borrow = 0;
unsigned int i;
for (i = 0; i < a.size(); i++) {
n = a[i] - b[i] - borrow;
if (n < 0) {
n += BASE;
}
borrow = (n < 0) ? 1 : 0;
c[i] = n;
}
c.set_size(i);
c.adjust();
c.set_sign(PLUS);
}
// Returns the absolute value of (*this).
Integer Integer::abs() const
{
Integer temp = *this;
temp.set_sign(temp.sign() * temp.sign());
return temp;
}