bignum operator*(const bignum& a, const bignum& b)
{
if (a.empty() or b.empty())
return bignum();
if (a.size() + b.size() < 19) {
long long x = a;
long long y = b;
return x*y;
}
const unsigned n = max(a.size(), b.size());
const unsigned h = n/2;
bignum w, x; // a = 10^h * w + x
bignum y, z; // b = 10^h * y + z
b_cit ha, hb;
ha = (h > a.size()) ? a.end() : a.begin()+h;
hb = (h > b.size()) ? b.end() : b.begin()+h;
x.assign(a.begin(), ha);
w.assign(ha, a.end());
x.clean();
w.clean();
z.assign(b.begin(), hb);
y.assign(hb, b.end());
z.clean();
y.clean();
bignum p = w*y;
bignum q = x*z;
bignum r = (w+x) * (y+z);
// result = 10^(2*h) * p + 10^h * (r-p-q) + q
bignum result;
result.resize(a.size() + b.size());
fill(result.begin(), result.begin()+2*h, 0);
copy(p.begin(), p.end(), result.begin() + 2*h);
result.clean();
r -= p+q;
// p = 10^h * r
p.resize(r.size() + h);
fill(p.begin(), p.begin()+h, 0);
copy(r.begin(), r.end(), p.begin()+h);
p.clean();
result += q;
result += p;
result.sign = a.sign != b.sign;
return result;
}
// a += b, ignoring signal
void add_inplace(bignum& a, const bignum& b)
{
a.resize( 1 + max(a.size(), b.size()) );
b_it i;
b_cit j;
Digit carry = 0;
for (i=a.begin(), j=b.begin();
i!=a.end();
++i) {
*i += (j!=b.end() ? *j++ : 0) + carry;
if (*i >= bignum::base) {
*i -= bignum::base;
carry = 1;
} else
carry = 0;
}
assert(carry == 0);
a.clean();
}
// a -= b, ignoring signal, assume a is larger than b
void subtract_inplace(bignum& a, const bignum& b)
{
bignum x=a, y=b;
b_it i;
b_cit j;
Digit borrow = 0;
for (i=a.begin(), j=b.begin();
i!=a.end();
++i) {
*i -= (j!=b.end() ? *j++ : 0) + borrow;
if (*i < 0) {
*i += bignum::base;
borrow = 1;
} else
borrow = 0;
}
assert(borrow == 0);
a.clean();
}
void doubleNum(bignum & num)
{
int carry = 0;
for(bignum::iterator p = num.begin(); p != num.end(); p++)
{
*p *= 2;
*p += carry;
carry = (*p >= 10) ? 1 : 0;
*p -= carry * 10;
}
if (carry != 0)
num.push_back(carry);
}
bool operator==(const bignum& a, const bignum& b)
{
return a.sign == b.sign and
a.size() == b.size() and
equal(a.begin(), a.end(), b.begin());
}