Getting ready

We will use the Eigen C++ template library for linear algebra and show how to set up compiler flags to enable vectorization. The source code for this recipe the linear-algebra.cpp file:

#include <chrono>
#include <iostream>

#include <Eigen/Dense>

EIGEN_DONT_INLINE
double simple_function(Eigen::VectorXd &va, Eigen::VectorXd &vb) {
  // this simple function computes the dot product of two vectors
  // of course it could be expressed more compactly
  double d = va.dot(vb);
  return d;
}

int main() {
  int len = 1000000;
  int num_repetitions = 100;

  // generate two random vectors
  Eigen::VectorXd va = Eigen::VectorXd::Random(len);
  Eigen::VectorXd vb = Eigen::VectorXd::Random(len);

  double result;
  auto start = std::chrono::system_clock::now();
  for (auto i = 0; i < num_repetitions; i++) {
    result = simple_function(va, vb);
  }
  auto end = std::chrono::system_clock::now();
  auto elapsed_seconds = end - start;

  std::cout << "result: " << result << std::endl;
  std::cout << "elapsed seconds: " << elapsed_seconds.count() << std::endl;
}

We expect vectorization to speed up the execution of the dot product operation in simple_function.