Other implementation of x at power n in Prolog

Question

Hi does anyone know other implementation to compute X at power N in Prolog beside this one:

predicates
power(real, integer, real)

clauses

power(_,0,1).

power(X,N,R):-
      N<0,
      N1 = -N,
      X1 = 1/X,
      power(X1,N1,R).

power(X,N,R):-
    N1=N-1,
    power(X,N1,R1),
    R=R1*X.

You can use the built-in arithmetic operator for it, or, you can use one of the "short-cuts", see this question: http://stackoverflow.com/questions/15283482/transforming-recursion-into-tail-recursion — , Jan 10 '14 at 10:53

score 1 · Answer 1 · answered Jan 10 '14 at 14:43

In any case, I would treat the negative exponent with a predicate, as already given in the problem post, which is:

power(Base, N, P) :-
    N < 0,
    N1 is -N,
    power(Base, N1, P1),
    P is 1/P1.

So the following assume non-negative exponents.

This algorithm multiples the base N times:

power1(Base, N, P) :-
    N > 0,
    N1 is N - 1,
    power1(Base, N1, P1),
    P is P1 * Base.
power1(Base, N, P) :-
    N < 0,
    N1 is N + 1,
    power1(Base, N1, P1),
    P is P1 / Base.
power1( _Base, 0, 1 ).

This algorithm multiples the base N times using tail recursion:

power1t(Base, N, P) :-
    N >= 0,
    power1t(Base, N, 1, P).
power1t(Base, N, A, P) :-
    N > 0,
    A1 is A * Base,
    N1 is N - 1,
    power1t(Base, N1, A1, P).
power1t(_, 0, P, P).

This version uses the "power of 2" method, minimizing the multiplications:

power2(_, 0, 1).
power2(Base, N, P) :-
    N > 0,
    N1 is N div 2,
    power2(Base, N1, P1),
    (   0 is N /\ 1
    ->  P is P1 * P1
    ;   P is P1 * P1 * Base
    ).

This version uses a "power of 2" method, minimizing multiplications, but is tail recursive. It's a little different than the one Boris linked:

power2t(Base, N, P) :-
    N >= 0,
    power2t(Base, N, Base, 1, P).
power2t(Base, N, B, A, P) :-
    N > 0,
    (  1 is N /\ 1
    -> A1 is B * A
    ;  A1 = A
    ),
    N1 is N div 2,
    B1 is B * B,
    power2t(Base, N1, B1, A1, P).
power2t(_, 0, _, P, P).

Other implementation of x at power n in Prolog

1 Answers1