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 is 0
2. exponent is non-zero
pow(B,0,1).
pow(B,E,Result):- E2 is E - 1,
pow(B,E2,Result2),
Result is B*Result2.
How can I add another case where the power function can handle negative exponents?
First, one should consider how to define 00. Formally speaking it is indeterminate. It could be zero or it could be 1. As Wolfram's Mathworld says in its article on powers and in its article on zero:
00 (zero to the zeroth power) itself is undefined. The lack of a well-defined meaning for this quantity follows from the mutually contradictory facts that a0 is always 1, so 00 should equal 1, but 0a is always 0 (for a > 0), so 0a should equal 0. The choice of definition for 00 is usually defined to be indeterminate, although defining 00 = 1 allows some formulas to be expressed simply (Knuth 1992; Knuth 1997, p. 57).
So you should first choose how to define the special case of 00: Is it 0? Is it 1? Is it undefined?
I choose to look at it as being undefined.
That being said, you can look at a positive exponent as indicated repeated multiplication (e.g. 103 is 10*10*10, or 1,000), and you can look at a negative exponent as indicating repeated division (e.g, 10-3 is (((1/10)/10)/10), or 0.001). My inclination, partly because I like the symmetry of this approach and partly to avoid the cuts (since a cut is often a signal that you've not defined the solution properly), would be something like this:
% -----------------------------
% The external/public predicate
% -----------------------------
pow( 0 , 0 , _ ) :- ! , fail .
pow( X , N , R ) :-
pow( X , N , 1 , R )
.
% -----------------------------------
% the tail-recursive worker predicate
% -----------------------------------
pow( _ , 0 , R , R ).
pow( X , N , T , R ) :-
N > 0 ,
T1 is T * X ,
N1 is N-1 ,
pow( X , N1 , T1 , R )
.
pow( _ , 0 , R , R ) :-
N < 0 ,
T1 is T / X ,
N1 is N+1 ,
pow( X , N1 , T1 , R )
.
The other approach, as others have noted, is to define a positive exponent as indicating repeated multiplication, and a negative exponent as indicating the reciprocal of the positive exponent, so 103 is 10*10*10 or 1,000, and 10-3 is 1/(103), or 1/1,000 or 0.001. To use this definition, I'd again avoid the cuts and do something like this:
% -----------------------------
% the external/public predicate
% -----------------------------
pow( 0 , 0 , _ ) :- % 0^0 is indeterminate. Is it 1? Is it 0? Could be either.
! ,
fail
.
pow( X , N , R ) :-
N > 0 ,
pow( X , N , 1 , R )
.
pow( X , N , R ) :-
N < 0 ,
N1 = - N ,
pow( X , N1 , 1 , R1 ) ,
R is 1 / R1
.
% -----------------------------------
% The tail-recursive worker predicate
% -----------------------------------
pow( _ , 0 , R , R ).
pow( X , N , T , R ) :-
N > 0 ,
T1 is T * X ,
N1 is N-1 ,
pow( X , N1 , T1 , R )
.