/*************************/
/* interval arithmetics  */
/*     (c) R. Bart‡k     */
/*         1997          */
/*************************/

% module that implements interval arithmetics
%  functions: plus(+,+,?),minus(+,+,?),times(+,+,?)
%  example: ?-plus(1É5,3É7,X).

:-op(600,xfx,É).

plus(ALÉAU,BLÉBU,CLÉCU):-
  ((AL= -inf ; BL= -inf)
      -> CL= -inf
       ; CL is AL+BL),
  ((AU= +inf ; BU= +inf)
      -> CU= +inf
       ; CU is AU+BU).

minus(ALÉAU,BLÉBU,CLÉCU):-
  ((AL= -inf ; BU= +inf)
      -> CL= -inf
       ; CL is AL-BU),
  ((AU= +inf ; BL= -inf)
      -> CU= +inf
       ; CU is AU-BL).

times(ALÉAU,BLÉBU,CLÉCU):-
  num_times(AL,BL,T1),num_times(AL,BU,T2),num_times(AU,BL,T3),num_times(AU,BU,T4),
  min(T1,T2,L1),min(L1,T3,L2),min(L2,T4,CL),
  max(T1,T2,U1),max(U1,T3,U2),max(U2,T4,CU).
  
num_times(-inf,B,C):-!,
  (lt(0,B) -> C= -inf ;
   B=0     -> C=0 ;
              C= +inf).
num_times(+inf,B,C):-!,
  (lt(0,B) -> C= +inf ;
   B=0     -> C=0 ;
              C= -inf).
num_times(A,-inf,C):-!,
  (lt(0,A) -> C= -inf ;
   B=0     -> C=0 ;
              C= +inf).
num_times(A,+inf,C):-!,
  (lt(0,A) -> C= +inf ;
   B=0     -> C=0 ;
              C= -inf).
num_times(A,B,C):-
  C is A*B.

num_divide(LÉU,D,NLÉNU):-
  (L= -inf -> (D<0 -> A= +inf ; A= -inf)
            ; A is L/D),
  (U= +inf -> (D<0 -> B= -inf ; B= +inf)
            ; B is U/D),
  min(A,B,NL),max(A,B,NU).

join_inters(ALÉAU,BLÉBU,CLÉCU):-
  min(AL,BL,CL),
  max(AU,BU,CU),!.
intersection(ALÉAU,BLÉBU,CLÉCU):-
  max(AL,BL,CL),
  min(AU,BU,CU),!.

leq(-inf,B):-!.
leq(_,-inf):-!,fail.
leq(+inf,B):-!,B= +inf.
leq(A,+inf):-!.
leq(A,B):-A=<B.

lt(A,-inf):-!,fail.
lt(-inf,B):-!.
lt(+inf,B):-!,fail.
lt(A,+inf):-!.
lt(A,B):-A<B.

min(A,B,C):-
  lt(A,B) -> C=A ; C=B.
max(A,B,C):-
  lt(A,B) -> C=B ; C=A.