/*************************************************************************
*									 *
*	 YAP Prolog 							 *
*									 *
*	Yap Prolog was developed at NCCUP - Universidade do Porto	 *
*									 *
* Copyright L.Damas, V.S.Costa and Universidade do Porto 1985-1997	 *
*									 *
**************************************************************************
*									 *
* File:		arith.yap						 *
* Last rev:								 *
* mods:									 *
* comments:	arithmetical optimization				 *
*									 *
*************************************************************************/

% the default mode is on

:- system_module( '$_arith', [compile_expressions/0,
        expand_exprs/2,
        plus/3,
        succ/2], ['$c_built_in'/3]).

:- private( [do_c_built_in/3,
	     do_c_built_metacall/3,
	     expand_expr/3,
	     expand_expr/5,
	     expand_expr/6] ).
		   

:- use_system_module( '$_errors', ['$do_error'/2]).

:- use_system_module( '$_modules', ['$clean_cuts'/2]).

expand_exprs(Old,New) :-
	(get_value('$c_arith',true) ->
			Old = on ;
			Old = off ),
	'$set_arith_expan'(New).

'$set_arith_expan'(on) :- set_value('$c_arith',true).
'$set_arith_expan'(off) :- set_value('$c_arith',[]).

compile_expressions :- set_value('$c_arith',true).

do_not_compile_expressions :- set_value('$c_arith',[]).

'$c_built_in'(IN, M, OUT) :-
	get_value('$c_arith',true), !,
	do_c_built_in(IN, M, OUT).
'$c_built_in'(IN, _, IN).


do_c_built_in(G, M, OUT) :- var(G), !,
	do_c_built_metacall(G, M, OUT).
do_c_built_in(Mod:G, _, OUT) :- 
	strip_module(Mod:G, M, G1),
	( var(G1) -> M = M2, G1 = G2 ; G1 = M2:G2), !, 
	do_c_built_metacall(G2, M2, OUT).
do_c_built_in(\+ G, _, OUT) :-
	nonvar(G),
	G = (A = B),
	!,
	OUT = (A \= B).
do_c_built_in(call(G), _, OUT) :-
	nonvar(G),
	G = (Mod:G1), !,
	do_c_built_metacall(G1, Mod, OUT).
do_c_built_in(call(G), Mod, OUT) :-
	var(G), !,
	do_c_built_metacall(G, Mod, OUT).
do_c_built_in(depth_bound_call(G,D), M, OUT) :- !,
	do_c_built_in(G, M, NG),
	% make sure we don't have something like (A,B) -> $depth_next(D), A, B.
	( '$composed_built_in'(NG) ->
	    OUT = depth_bound_call(NG,D)
	;
	    OUT = ('$set_depth_limit_for_next_call'(D),NG)
	).
do_c_built_in(once(G), M, (yap_hacks:current_choice_point(CP),NG,'$$cut_by'(CP))) :- !,
	do_c_built_in(G,M,NG0),
	'$clean_cuts'(NG0, NG).
do_c_built_in(forall(Cond,Action), M, \+((NCond, \+(NAction)))) :- !,
	do_c_built_in(Cond,M,ICond),
	do_c_built_in(Action,M,IAction),
	'$clean_cuts'(ICond, NCond),
	'$clean_cuts'(IAction, NAction).
do_c_built_in(ignore(Goal), M, (NGoal -> true ; true)) :- !,
	do_c_built_in(Goal,M,IGoal),
	'$clean_cuts'(IGoal, NGoal).
do_c_built_in(if(G,A,B), M, (yap_hacks:current_choicepoint(DCP),NG,yap_hacks:cut_at(DCP),NA; NB)) :- !,
	do_c_built_in(G,M,NG0),
	'$clean_cuts'(NG0, NG),
	do_c_built_in(A,M,NA),
	do_c_built_in(B,M,NB).
do_c_built_in((G*->A;B), M, (yap_hacks:current_choicepoint(DCP),NG,yap_hacks:cut_at(DCP),NA; NB)) :- !,
	do_c_built_in(G,M,NG0),
	'$clean_cuts'(NG0, NG),
	do_c_built_in(A,M,NA),
	do_c_built_in(B,M,NB).
do_c_built_in((G*->A), M, (NG,NA)) :- !,
	do_c_built_in(G,M,NG0),
	'$clean_cuts'(NG0, NG),
	do_c_built_in(A,M,NA).
do_c_built_in('C'(A,B,C), _, (A=[B|C])) :- !.
do_c_built_in(X is Y, M, P) :-
        primitive(X), !,
	do_c_built_in(X =:= Y, M, P).
do_c_built_in(X is Y, M, (P,A=X)) :-
	nonvar(X), !,
	do_c_built_in(A is Y, M, P).
do_c_built_in(X is Y, _, P) :-
	nonvar(Y),		% Don't rewrite variables
	!,
	(
		number(Y) ->
		P = ( X = Y); % This case reduces to an unification
		expand_expr(Y, P0, X0),
		'$drop_is'(X0, X, P0, P)
	).
do_c_built_in(Comp0, _, R) :-		% now, do it for comparisons
	'$compop'(Comp0, Op, E, F),
	!,
	'$compop'(Comp,  Op, U, V),
	expand_expr(E, P, U),
	expand_expr(F, Q, V),
	'$do_and'(P, Q, R0),
	'$do_and'(R0, Comp, R).
do_c_built_in(P, _, P).

do_c_built_metacall(G1, Mod, '$execute_wo_mod'(G1,Mod)) :- 
	var(Mod), !.
do_c_built_metacall(G1, Mod, '$execute_in_mod'(G1,Mod)) :- 
	var(G1), atom(Mod), !.
do_c_built_metacall(Mod:G1, _, OUT) :-  !,
	do_c_built_metacall(G1, Mod, OUT).
do_c_built_metacall(G1, Mod, '$execute_in_mod'(G1,Mod)) :-
	atom(Mod), !.
do_c_built_metacall(G1, Mod, call(Mod:G1)).

'$do_and'(true, P, P) :- !.
'$do_and'(P, true, P) :- !.
'$do_and'(P, Q, (P,Q)).

% V is the result of the simplification,
% X the result of the initial expression
% and the last argument is how we are writing this result
'$drop_is'(V, V1, P0, G) :- var(V), !,		% usual case
        V = V1, P0 = G.
'$drop_is'(V, X, P0, P) :-			% atoms
        '$do_and'(P1, X is V, P).


% Table of arithmetic comparisons
'$compop'(X < Y, < , X, Y).
'$compop'(X > Y, > , X, Y).
'$compop'(X=< Y,=< , X, Y).
'$compop'(X >=Y, >=, X, Y).
'$compop'(X=:=Y,=:=, X, Y).
'$compop'(X=\=Y,=\=, X, Y).

'$composed_built_in'(V) :- var(V), !,
	fail.
'$composed_built_in'((yap_hacks:current_choice_point(_),NG,'$$cut_by'(_))) :- !,
	'$composed_built_in'(NG).
'$composed_built_in'((_,_)).
'$composed_built_in'((_;_)).
'$composed_built_in'((_|_)).
'$composed_built_in'((_->_)).
'$composed_built_in'(_:G) :-
	'$composed_built_in'(G).
'$composed_built_in'(\+G) :-
	'$composed_built_in'(G).
'$composed_built_in'(not(G)) :-
	'$composed_built_in'(G).
	
% expanding an expression:
% first argument is the expression not expanded,
% second argument the expanded expression
% third argument unifies with the result from the expression
expand_expr(V, true, V) :-
	var(V), !.
expand_expr([T], E, V) :- !,
	expand_expr(T, E, V).
expand_expr(String, _E, V) :-
	string( String ), !,
	string_codes(String, [V]).
expand_expr(A, true, A) :-
	atomic(A), !.
expand_expr(T, E, V) :-
	T =.. [O, A], !,
	expand_expr(A, Q, X),
	expand_expr(O, X, V, Q, E).
expand_expr(T, E, V) :-
	T =.. [O, A, B], !,
	expand_expr(A, Q, X),
	expand_expr(B, R, Y),
	expand_expr(O, X, Y, V, Q, S),
	'$do_and'(R, S, E).

% expanding an expression of the form:
%	O is Op(X),
%	after having expanded into Q
%	and giving as result P (the last argument)
expand_expr(Op, X, O, Q, Q) :-
	number(X), !,
	is( O, Op, X).
expand_expr(Op, X, O, Q, P) :-
	'$unary_op_as_integer'(Op,IOp),
	'$do_and'(Q, is( O, IOp, X), P).

% expanding an expression of the form:
%	O is Op(X,Y),
%	after having expanded into Q
%	and giving as result P (the last argument)
%	included is some optimization for:
%		incrementing and decrementing,
%		the elementar arithmetic operations [+,-,*,//]
expand_expr(Op, X, Y, O, Q, Q) :-
	number(X), number(Y), !,
	is( O, Op, X, Y).
expand_expr(+, X, Y, O, Q, P) :- !,
	'$preprocess_args_for_commutative'(X, Y, X1, Y1, E),
	'$do_and'(E, '$plus'(X1,Y1,O), F),
	'$do_and'(Q, F, P).
expand_expr(-, X, Y, O, Q, P) :-
	var(X), number(Y),
	Z is -Y, !,
	expand_expr(+, Z, X, O, Q, P).
expand_expr(-, X, Y, O, Q, P) :- !,
	'$preprocess_args_for_non_commutative'(X, Y, X1, Y1, E),
	'$do_and'(E, '$minus'(X1,Y1,O), F),
	'$do_and'(Q, F, P).
expand_expr(*, X, Y, O, Q, P) :- !,
	'$preprocess_args_for_commutative'(X, Y, X1, Y1, E),
	'$do_and'(E, '$times'(X1,Y1,O), F),
	'$do_and'(Q, F, P).
expand_expr(//, X, Y, O, Q, P) :-
	nonvar(Y), Y == 0, !,
	'$binary_op_as_integer'(//,IOp),
	'$do_and'(Q, is(O,IOp,X,Y), P).
expand_expr(//, X, Y, O, Q, P) :- !,
	'$preprocess_args_for_non_commutative'(X, Y, X1, Y1, E),
	'$do_and'(E, '$div'(X1,Y1,O), F),
	'$do_and'(Q, F, P).
expand_expr(/\, X, Y, O, Q, P) :- !,
	'$preprocess_args_for_commutative'(X, Y, X1, Y1, E),
	'$do_and'(E, '$and'(X1,Y1,O), F),
	'$do_and'(Q, F, P).
expand_expr(\/, X, Y, O, Q, P) :- !,
	'$preprocess_args_for_commutative'(X, Y, X1, Y1, E),
	'$do_and'(E, '$or'(X1,Y1,O), F),
	'$do_and'(Q, F, P).
expand_expr(<<, X, Y, O, Q, P) :-
	var(X), number(Y), Y < 0,
	Z is -Y, !,
	expand_expr(>>, X, Z, O, Q, P).
expand_expr(<<, X, Y, O, Q, P) :- !,
	'$preprocess_args_for_non_commutative'(X, Y, X1, Y1, E),
	'$do_and'(E, '$sll'(X1,Y1,O), F),
	'$do_and'(Q, F, P).
expand_expr(>>, X, Y, O, Q, P) :-
	var(X), number(Y), Y < 0,
	Z is -Y, !,
	expand_expr(<<, X, Z, O, Q, P).
expand_expr(>>, X, Y, O, Q, P) :- !,
	'$preprocess_args_for_non_commutative'(X, Y, X1, Y1, E),
	'$do_and'(E, '$slr'(X1,Y1,O), F),
	'$do_and'(Q, F, P).
expand_expr(Op, X, Y, O, Q, P) :-
	'$binary_op_as_integer'(Op,IOp),
	'$do_and'(Q, is(O,IOp,X,Y), P).

'$preprocess_args_for_commutative'(X, Y, X, Y, true) :-
	var(X), var(Y), !.
'$preprocess_args_for_commutative'(X, Y, X, Y, true) :-
	var(X), integer(Y), \+ '$bignum'(Y), !.
'$preprocess_args_for_commutative'(X, Y, X, Z, Z = Y) :-
	var(X), !.
'$preprocess_args_for_commutative'(X, Y, Y, X, true) :-
	integer(X), \+ '$bignum'(X), var(Y), !.
'$preprocess_args_for_commutative'(X, Y, Z, X, Z = Y) :-
	integer(X), \+ '$bignum'(X), !.
'$preprocess_args_for_commutative'(X, Y, Z, W, E) :-
	'$do_and'(Z = X, Y = W, E).

'$preprocess_args_for_non_commutative'(X, Y, X, Y, true) :-
	var(X), var(Y), !.
'$preprocess_args_for_non_commutative'(X, Y, X, Y, true) :-
	var(X), integer(Y), \+ '$bignum'(Y), !.
'$preprocess_args_for_non_commutative'(X, Y, X, Z, Z = Y) :-
	var(X), !.
'$preprocess_args_for_non_commutative'(X, Y, X, Y, true) :-
	integer(X), \+ '$bignum'(X), var(Y), !.
'$preprocess_args_for_non_commutative'(X, Y, X, Z, Z = Y) :-
	integer(X), \+ '$bignum'(X), !.
'$preprocess_args_for_non_commutative'(X, Y, Z, W, E) :-
	'$do_and'(Z = X, Y = W, E).