Implementing the Tak function using tail recursion - c++

Question

Is it possible to implement the Tak function:
tail recursively in C/C++ in a way so that gcc/g++ can perform tail-recursion optimization?
I'm not sure if the nested recursive function calls will confuse the compiler.

Answer 1

Tail recursion optimization in C++ requires that there only be 1 recursive call (which basically allows it to be converted to a loop) and that recursive call is the last operation in the function:
Example:
unsigned int f( unsigned int a )
{
if ( a == 0 )
{
return a;
}
return f( a - 1 ); // tail recursion
}
Since the Tak function requires 4 recursive calls per "iteration":
int tak(int x, int y, int z)
{
if (x >= y)
{
return z;
}
else
{
return tak(tak(x-1, y, z), tak(y-1, z, x), tak(z-1, x, y)); // this is why it cannot happen
}
}
As you can see, the last call is recursive, but it has 3 recursive calls inside it. This prevents tail-recursion optimization (and there is no logical method for converting this into a non-recursive-loop - which is required to obtain tail-recursion optimization).
Another way it can be implemented is:
int tak(int x, int y, int z)
{
while (x > y)
{
int oldx = x, oldy = y;
x = tak(x - 1, y, z);
y = tak(y - 1, z, oldx);
if (x <= y)
break;
z = tak(z - 1, oldx, oldy);
}
return z;
}
Which again shows that even in a loop form, it is still recursive, preventing tail-recursion optimization.

Answer 2

Going straight from your math definition, we can just write the function as:
int tak(int x, int y, int z){
if(x>y)
return tak(tak(1-x,y,z), tak(y-1,z,x), tak(z-1,x,y));
else
return z;
}
However you can't do it with tail-recrusion as it cannot be converted into a loop. Since there is more than one recrusion call.