Question

I was working on my advanced calculus homework today and we’re doing some iteration methods along the lines of newton’s method to find solutions to things like x^2=2. It got me thinking that I could write a function that would take two function pointers, one to the function itself and one to the derivative and automate the process. This wouldn’t be too challenging, then I started thinking could I have the user input a function and parse that input (yes I can do that). But can I then dynamically create a pointer to a one-variable function in c++. For instance if x^2+x, can I make a function double function(double x){ return x*x+x;} during run-time. Is this remotely feasible, or is it along the lines of self-modifying code?

Edit:

So I suppose how this could be done if you stored the information in an array and that had a function that evaluated the information stored in this array with a given input. Then you could create a class and initialize the array inside of that class and then use the function from there. Is there a better way?

Answer 1

You can’t dynamically create a function in the sense that you can generate raw machine code for it, but you can quite easily create mathematical expressions using polymorphism:

struct Expr
{
  virtual double eval(double x) = 0;
};

struct Sum : Expr
{
  Sum(Expr* a, Expr* b):a(a), b(b) {}
  virtual double eval(double x) {return a->eval(x) + b->eval(x);}
private:
  Expr *a, *b;
};

struct Product : Expr
{
  Product(Expr* a, Expr* b):a(a), b(b) {}
  virtual double eval(double x) {return a->eval(x) * b->eval(x);}
private:
  Expr *a, *b;
};

struct VarX : Expr
{
  virtual double eval(double x) {return x;}
};

struct Constant : Expr
{
  Constant(double c):c(c) {}
  virtual double eval(double x) {return c;}
private:
  double c;
};

You can then parse your expression into an Expr object at runtime. For example, x^2+x would be Expr* e = new Sum(new Product(new VarX(), new VarX()), new VarX()). You can then evaluate that for a given value of x by using e->eval(x).

Note: in the above code, I have ignored const-correctness for clarity — you should not 🙂