What Is Tail Call Optimization?

Question

Very simply, what is tail-call optimization? More specifically, Can anyone show some small code snippets where it could be applied, and where not, with an explanation of why?

Answer 1

TCO (Tail Call Optimization) is the process by which a smart compiler can make a call to a function and take no additional stack space. The only situation in which this happens is if the last instruction executed in a function f is a call to a function g (Note: g can be f). The key here is that f no longer needs stack space - it simply calls g and then returns whatever g would return. In this case the optimization can be made that g just runs and returns whatever value it would have to the thing that called f.

This optimization can make recursive calls take constant stack space, rather than explode.

Example: this factorial function is not TCOptimizable:

def fact(n):
    if n == 0:
        return 1
    return n * fact(n-1)

This function does things besides call another function in its return statement.

This below function is TCOptimizable:

def fact_h(n, acc):
    if n == 0:
        return acc
    return fact_h(n-1, acc*n)

def fact(n):
    return fact_h(n, 1)

This is because the last thing to happen in any of these functions is to call another function.

Answer 2

Tail-call optimization is where you are able to avoid allocating a new stack frame for a function because the calling function will simply return the value that it gets from the called function. The most common use is tail-recursion, where a recursive function written to take advantage of tail-call optimization can use constant stack space.

Scheme is one of the few programming languages that guarantee in the spec that any implementation must provide this optimization (JavaScript does also, starting with ES6), so here are two examples of the factorial function in Scheme:

(define (fact x)
  (if (= x 0) 1
      (* x (fact (- x 1)))))

(define (fact x)
  (define (fact-tail x accum)
    (if (= x 0) accum
        (fact-tail (- x 1) (* x accum))))
  (fact-tail x 1))

The first function is not tail recursive because when the recursive call is made, the function needs to keep track of the multiplication it needs to do with the result after the call returns. As such, the stack looks as follows:

(fact 3)
(* 3 (fact 2))
(* 3 (* 2 (fact 1)))
(* 3 (* 2 (* 1 (fact 0))))
(* 3 (* 2 (* 1 1)))
(* 3 (* 2 1))
(* 3 2)
6

In contrast, the stack trace for the tail recursive factorial looks as follows:

(fact 3)
(fact-tail 3 1)
(fact-tail 2 3)
(fact-tail 1 6)
(fact-tail 0 6)
6

As you can see, we only need to keep track of the same amount of data for every call to fact-tail because we are simply returning the value we get right through to the top. This means that even if I were to call (fact 1000000), I need only the same amount of space as (fact 3). This is not the case with the non-tail-recursive fact, and as such large values may cause a stack overflow.