What is tail recursion?

Question

Whilst starting to learn lisp, I\'ve come across the term tail-recursive. What does it mean exactly?

Answer 1

In short, a tail recursion has the recursive call as the last statement in the function so that it doesn't have to wait for the recursive call.

So this is a tail recursion i.e. N(x - 1, p * x) is the last statement in the function where the compiler is clever to figure out that it can be optimised to a for-loop (factorial). The second parameter p carries the intermediate product value.

function N(x, p) {
   return x == 1 ? p : N(x - 1, p * x);
}

This is the non-tail-recursive way of writing the above factorial function (although some C++ compilers may be able to optimise it anyway).

function N(x) {
   return x == 1 ? 1 : x * N(x - 1);
}

but this is not:

function F(x) {
  if (x == 1) return 0;
  if (x == 2) return 1;
  return F(x - 1) + F(x - 2);
}

I did write a long post titled "Understanding Tail Recursion – Visual Studio C++ – Assembly View"