Postponing sqrt computations

This section will show you how to use a proxy object in order to postpone, or even avoid, using the computationally heavy std::sqrt() function when comparing the length of two-dimensional vectors.

A simple two-dimensional vector class

Let's start with a simple two-dimensional vector class. It has x and y coordinates and a member function called length() that calculates the distance from the origin to the location (x, y). We will call the class Vec2D. Here follows the definition:

class Vec2D {
public:
  Vec2D(float x, float y) : x_{x}, y_{y} {}
  auto length() const {
    auto squared = x_*x_ + y_*y_;
    return std::sqrt(squared);
  }
private:
  float x_{};
  float y_{};
};

Here is an example of how clients can use Vec2D:

auto a = Vec2D{3, 4}; 
auto b = Vec2D{4, 4};
auto shortest = a.length() < b.length() ? a : b;
auto length = shortest.length();
std::cout << length; // Prints 5 

The example creates two vectors and...