T fast_power_0(T a, I n, Op op)
{
assert(!is_negative(n));
T result = identity_element(op);
while (!is_zero(n)) {
if (is_odd(n)) result = op(result, a);
a = op(a, a);
halve_non_negative(n);
}
return result;
}
TR fast_power_0(TR tr, IN in, OP op)
{
assert(!is_negative(in));
TR result = identity_element(op);
while (!is_zero(in))
{
if (is_odd(in)) result = op(result, tr);
tr = op(tr, tr);
halve_non_negative(in);
}
return result;
}
friend
matrix operator*(const matrix& x, const matrix& y) {
matrix result;
Multiply mult = Multiply{};
Plus plus = Plus{};
for (std::size_t i = 0; i < N; ++i) {
for (std::size_t j = 0; j < N; ++j) {
result.data[i][j] = identity_element(plus);
for (std::size_t k = 0; k < N; ++k) {
result.data[i][j] = plus(result.data[i][j],
mult(x.data[i][k], y.data[k][j]));
}
}
}
return result;
}
T power(T x, N n, O op) {
if (n == 0) {
return identity_element(op);
}
while ((n & 1) == 0) {
n >>= 1;
x = op(x, x);
}
T result = x;
n >>= 1;
while (n != 0) {
x = op(x, x);
if ((n & 1) != 0) {
result = op(result, x);
}
n >>= 1;
}
return result;
}