tail recursive function and wrapper function

Ok so it program a tail-recursive function to calculate A. and i need to add a wrapper function..

A=1-(1/2)+(1/3)-(1/4)+(1/5)-(1/6).... A is calculated when the last item is smaller than 10^-3

Answer 1

[Ramon Villamangca]

The question is not about whether Matlab supports tail recursion. The question is to make a tail recursive function and wrapper function that presumably would enable to tail recursion support. Can we do that?

Lets see the tail recursive function first:

function a = asum(lim)
    a = arec(lim-1,0,1);
end

function a = arec(lim,acc,cur)
    if cur > lim
        a = acc;
    elseif mod(cur,2)
        a = arec(lim,acc+1/cur,cur+1);
    else
        a = arec(lim,acc-1/cur,cur+1);
    end
end

Now, the limit given (1/10^3) is so small that the above function will work without any wrapper function:

>> asum(10^3)

ans =

    0.6936

But if we increase the limit to say, 1/10^6, we will run to "out of memory" error:

>> asum(1000000)
Out of memory. The likely cause is an infinite recursion within the program.

Error in asum>arec (line 9)
        a = arec(lim,acc+1/cur,cur+1);

For this we need a wrapper function. One way is to use a "trampoline" wrapper. We need to modify the recursive function as follows:

function a = asum(lim)
    a = trampoline(arec(lim-1,0,1));
end

function a = arec(lim,acc,cur)
    if cur > lim
        a = acc;
    elseif mod(cur,2)
        a = @() arec(lim,acc+1/cur,cur+1);
    else
        a = @() arec(lim,acc-1/cur,cur+1);
    end
end

With this one we will not run out of memory:

>> asum(1000000)

ans =

    0.6931

The trampoline wrapper function looks like this:

function t = trampoline(f)
%TRAMPOLINE wrapper function to convert tail-recursive functions to loops
%   Usage: trampoline(f), where f is a tail-recursive function

    while isa(f,'function_handle')
        f = f();
    end
    t = f;
end

Answer 2

[Walter Roberson]

MATLAB has no special support for tail recursion, just for recursion.