Eigen: coefficient-wise pow with small integer exponent slow - c++

Question

In Eigen,with
ArrayXXf a;
a = ArrayXXf::Random(1000, 10000);
doing
a = a.pow(4);
takes ~500ms on my pc, whereas doing
a = a.square().square();
takes only about 5ms. I'm compiling with a recent GCC in release.
Is this the expected behaviour or am I doing something wrong? I would expect, that at least for small integer (say < 20, if not using a cost function), an overload should exist that catches such cases.

Answer 1

After a whole day of debugging I realized this was the bottleneck in my code. On the documentation it says that there is no SIMD for a.pow(). For whatever reason, actually on my machine it appears a * a * a * a is faster for a 300 x 50 Eigen::ArrayXXd.
#include <iostream>
#include <chrono>
#include <Eigen/Dense>
int main() {
Eigen::ArrayXXd m = Eigen::ArrayXd::LinSpaced(300 * 50, 0, 300 * 50 - 1).reshaped(300, 50);
{
decltype(m) result; // prevent loop from being eliminated
auto start = std::chrono::steady_clock::now();
for (size_t i = 0; i < 100000; i++)
{
result = m.square().square();
}
auto end = std::chrono::steady_clock::now();
std::cout << "Per run(microsecond)=" << std::chrono::duration_cast<std::chrono::microseconds>(end - start).count() / 100000.0 << std::endl;
}
{
decltype(m) result; // prevent loop from being eliminated
auto start = std::chrono::steady_clock::now();
for (size_t i = 0; i < 100000; i++)
{
result = m * m * m * m;
}
auto end = std::chrono::steady_clock::now();
std::cout << "Per run(microsecond)=" << std::chrono::duration_cast<std::chrono::microseconds>(end - start).count() / 100000.0 << std::endl;
}
{
decltype(m) result; // prevent loop from being eliminated
auto start = std::chrono::steady_clock::now();
for (size_t i = 0; i < 10000; i++)
{
result = m.pow(4);
}
auto end = std::chrono::steady_clock::now();
std::cout << "Per run(microsecond)=" << std::chrono::duration_cast<std::chrono::microseconds>(end - start).count() / 10000.0 << std::endl;
}
return 0;
m.square().square();
Per run(microsecond)=17.9101
m * m * m * m;
Per run(microsecond)=10.3267
m.pow(4);
Per run(microsecond)=431.636

Answer 2

With C++17 if constexpr this could be possible, but otherwise it's not. So currently, a.pow(x) is equivalent to calling std::pow(a[i],x) for each i.