C++ & Swap/Copy applied to a Point struct

Question

I have written a Point struct I am using to model the n-body problem. I have found it difficult to fully understand and implement the copy & swap idiom and adapting it to my needs, which are mainly speed. Am I doing this correctly? Would it be different in C++17?

#pragma once
#include <algorithm>

struct Point
{
  double x, y, z;

  explicit Point(double X = 0, double Y = 0, double Z = 0) : x(X), y(Y), z(Z) {}
  void swap(Point&, Point&);

  inline bool operator==(Point b) const { return (x == b.x && y == b.y && z == b.z); }
  inline bool operator!=(Point b) const { return (x != b.x || y != b.y || z != b.z); }

  Point& operator=(Point&);
  Point& operator+(Point&) const;
  Point& operator-(Point&) const;
  inline double operator*(Point& b) const { return b.x*x + b.y*y + b.z*z; } // Dot product
  Point& operator%(Point&) const; // % = Cross product

  inline Point& operator+=(Point& b) { return *this = *this + b; }
  inline Point& operator-=(Point& b) { return *this = *this - b; }
  inline Point& operator%=(Point& b) { return *this = *this % b; }

  Point& operator*(double) const;
  Point& operator/(double) const;

  inline Point& operator*=(double k) { return *this = *this * k; }
  inline Point& operator/=(double k) { return *this = *this / k; }
};

std::ostream &operator<<(std::ostream &os, const Point& a) {
   os << "("  << a.x << ", " << a.y << ", " << a.z << ")";
   return os;
}

void Point::swap(Point& a, Point& b) {
    std::swap(a.x, b.x);
    std::swap(a.y, b.y);
    std::swap(a.z, b.z);
}

Point& Point::operator=(Point& b) {
  swap(*this, b);
  return *this;
}

Point& Point::operator+(Point& b) const {
  Point *p = new Point(x + b.x, y + b.y, z + b.z);
  return *p;
}

Point& Point::operator-(Point& b) const {
  Point *p = new Point(x - b.x, y - b.y, z - b.z);
  return *p;
}

Point& Point::operator%(Point& b) const {
  Point *p = new Point(
      y*b.z - z*b.y,
      z*b.x - x*b.z,
      x*b.y - y*b.x
  );

  return *p;
}

Point& Point::operator*(double k) const {
  Point *p = new Point(k*x, k*y, k*z);
  return *p;
}

Point& Point::operator/(double k) const {
  Point *p = new Point(x/k, y/k, z/k);
  return *p;
}

Answer 1

The copy/swap-ideom actually copies and swap()s the values. Your "adaptation" merely swap()s. A correct use of the copy/swap-ideom would look, e.g., like this:

Point& Point::operator= (Point other) { // note: by value, i.e., already copied
    this->swap(other);
    return *this;
}

(of course, this also assumes that your swap() function is a member taking just one additional argument: there is already an object to swap with).

If speed is your primary concern, the copy/swap-ideom is probably not particular suitable for the case of Point: the copy operation is essentially trivial. Swapping values is quite reasonable compared to relatively involved operations like copying an array old by a std::vector where the swap operation just amounts to a few pointer swaps in addition to copying probably multiple values and some allocation operations. That is, your Point assignment is probably best off to just assign all members:

Point& Point::operator= (Point const& other) { // note: no copy...
    this->x = other.x;
    this->y = other.y;
    this->z = other.z;
    return *this;
}

As was pointed out in comments, you should also not allocate new Point objects with new: C++ isn't Java or C#! You can just create an object on the stack it doesn't need to come from the heap, e.g.:

Point Point::operator+ (Point const& other) const {
    return Point(this->x + other.x, this->y + other.y, this->z + other.z);
}