Rule to calculate power of a number when the exponent is Negative in Prolog?

Question

I have a power function pow that attempts to calculate the value of B to the power of E. So far I handle the cases-
1. exponent i

Answer 1

To start, your second clause is non tail recursive (you can read about the subject here). It means that eventually, you will run out of call stack memory when running it. A good thing would be to use an accumulator to make it tail recursive. You can achieve that as follows :

% we add an accumulator to poW/3, making it pow/4.
pow(B, E, Result) :- pow(B, E, 1, Result).

% when we hit 0, our accumulator holds B^E so we unify it with result.
pow(_, 0, Accu, Accu) :- !.

% at each step, we multiply our accumulator by B
pow(B, E, Accu, Result) :-
    NewE is E - 1,
    NewAccu is Accu * B,
    pow(B, NewE, NewAccu, Result).

Then, you can simply handle the negative case by adding this clause on top of the others (it simply tells prolog that a negative power is the inverse of the positive one) :

pow(B, E, Result) :-
    E < 0,
    PositiveE is - E,
    pow(B, PositiveE, 1, R),
    !,
    Result is 1 / R.

Note that you can do it directly with your code :

pow(B, E, Result) :-
    E < 0,
    PositiveE is - E,
    pow(B, PositiveE, R),
    !,
    Result is 1 / R.

Plus, we now introduced a very red cut (see here for the meaning of red cut if necessary). So it'd be better to turn into a green cut with this modification :

pow(B, E, Result) :-
    E < 0,
    PositiveE is - E,
    pow(B, PositiveE, 1, R),
    !,
    Result is 1 / R.

% we add an accumulator to poW/3, making it pow/4.
pow(B, E, Result) :-
    E >= 0, %************* HERE *****************
    pow(B, E, 1, Result).

% when we hit 0, our accumulator holds B^E so we unify it with result.
pow(_, 0, Accu, Accu) :- !.

% at each step, we multiply our accumulator by B
pow(B, E, Accu, Result) :-
    NewE is E - 1,
    NewAccu is Accu * B,
    pow(B, NewE, NewAccu, Result).