std::abs(std::complex) too slow

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Why running std::abs over a big complex array is about 8 times slower than using sqrt and norm?

#include <ctime> #include <cmath> #include <vector> #include <complex> #include <iostream> using namespace std;  int main() {     typedef complex<double> compd;      vector<compd> arr(2e7);     for (compd& c : arr)     {         c.real(rand());         c.imag(rand());     }      double sm = 0;     clock_t tm = clock();     for (const compd& c : arr)     {         sm += abs(c);     }     cout << sm << ' ' << clock() - tm << endl; // 5.01554e+011 - 1640 ms      sm = 0;     tm = clock();     for (const compd& c : arr)     {         sm += sqrt(norm(c));     }     cout << sm << ' ' << clock() - tm << endl; // 5.01554e+011 - 154      sm = 0;     tm = clock();     for (const compd& c : arr)     {         sm += hypot(c.real(), c.imag());     }     cout << sm << ' ' << clock() - tm << endl; // 5.01554e+011 - 221 } 

 


I believe the two are not to be taken as identical in the strict sense.

From cppreference on std::abs(std::complex):

Errors and special cases are handled as if the function is implemented as std::hypot(std::real(z), std::imag(z))

Also from cppreference on std::norm(std::complex):

The norm calculated by this function is also known as field norm or absolute square.

The Euclidean norm of a complex number is provided by std::abs, which is more costly to compute. In some situations, it may be replaced by std::norm, for example, if abs(z1) > abs(z2) then norm(z1) > norm(z2).

In short, there are cases where a different result is obtained from each function. Some of these may be found in std::hypot. There the notes also mention the following:

std::hypot(x, y) is equivalent to std::abs(std::complex<double>(x,y))

In general the accuracy of the result may be different (due to the usual floating point mess), and it seems the functions were designed in such a way to be as accurate as possible.

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