Functional Programming in Erlang: 1.21 Tail recursion

tail.exs

-module(tail).
-export([fib/1, perfect/1]).

% Functional Programming in Erlang
% 1.21 Tail recursion

fib(0) -> 0;
fib(N) when N > 0 -> fib(N,0,1).
% fib(N,0,1) i.e."0,1"
% beginning of "0,1,1,2,3,5,..."

fib(0, BeforeLast, _) -> BeforeLast;
fib(1, _, Last) -> Last;
fib(N, BeforeLast, Last) ->
    fib(N-1, Last, BeforeLast+Last).

perfect(Num) when Num < 2 -> false;
perfect(Num) when is_integer(Num) ->
    Num == sum_divisors(1,2, trunc(math:sqrt(Num)), Num).

part_sum(Divisor, Num) ->
    Quotient = Num div Divisor,
    if Quotient == Divisor ->
            Divisor;
       true  ->
            Quotient + Divisor
    end.

sum_divisors(Sum, I, Limit, _Num) when I > Limit -> Sum;
sum_divisors(Sum, I, Limit, Num) when (Num rem I) == 0 ->
    sum_divisors(Sum + part_sum(I, Num), I + 1, Limit, Num);
sum_divisors(Sum, I, Limit, Num) ->
    sum_divisors(Sum, I + 1, Limit, Num).