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yap-6.3/pl/arith.yap
vsc 6662ca157e simplify module access 
git-svn-id: https://yap.svn.sf.net/svnroot/yap/trunk@981 b08c6af1-5177-4d33-ba66-4b1c6b8b522a
2004-02-12 12:37:12 +00:00

354 lines
11 KiB
Prolog
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/*************************************************************************
* *
* 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
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_in'(call(M:G),M,OUT).
'$do_c_built_in'(Mod:G, _, GN) :- !,
'$do_c_built_in'(G, Mod, GN0),
(GN0 = (_,_) -> GN = GN0 ; GN = Mod:GN0).
'$do_c_built_in'(\+ G, _, OUT) :-
nonvar(G),
G = (A = B),
!,
OUT = (A \= B).
'$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), M, OUT) :-
var(G), !,
'$do_c_built_metacall'(G, M, OUT).
'$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, ('$save_current_choice_point'(CP),NG,'$$cut_by'(CP))) :- !,
'$do_c_built_in'(G,M,NG).
'$do_c_built_in'(X is Y, _, P) :-
nonvar(Y), % Don't rewrite variables
!,
(
number(Y),
P = ( X = Y); % This case reduces to an unification
'$expand_expr'(Y, P0, X0),
'$drop_is'(X0, X, P1),
'$do_and'(P0, P1, P)
).
'$do_c_built_in'(Comp0, _, R) :- % now, do it for comparisons
'$compop'(Comp0, Op, E, F),
!,
'$compop'(Comp, Op, U, V),
'$expand_expr'(E, P, U),
'$expand_expr'(F, Q, V),
'$do_and'(P, Q, R0),
'$do_and'(R0, Comp, R).
'$do_c_built_in'(P, _, P).
'$do_c_built_metacall'(G1, Mod, call(Mod:G1)) :-
var(G1), var(Mod), !.
'$do_c_built_metacall'(G1, Mod, '$execute_in_mod'(G1,Mod)) :-
var(G1), atom(Mod), !.
'$do_c_built_metacall'(Mod:G1, _, call(Mod:G1)) :- !,
'$do_c_built_metacall'(G1, Mod, OUT).
'$do_c_built_metacall'(G1, Mod, '$execute_in_mod'(G1,Mod)) :-
atom(Mod), !.
'$do_c_built_metacall'(G1, Mod, call(Mod:G1)).
'$do_and'(true, P, P) :- !.
'$do_and'(P, true, P) :- !.
'$do_and'(P, Q, (P,Q)).
% V is the result of the simplification,
% X the result of the initial expression
% and the last argument is how we are writing this result
'$drop_is'(V, V, true) :- var(V), !. % usual case
'$drop_is'(V, X, X is V). % atoms
% Table of arithmetic comparisons
'$compop'(X < Y, < , X, Y).
'$compop'(X > Y, > , X, Y).
'$compop'(X=< Y,=< , X, Y).
'$compop'(X >=Y, >=, X, Y).
'$compop'(X=:=Y,=:=, X, Y).
'$compop'(X=\=Y,=\=, X, Y).
'$composed_built_in'(V) :- var(V), !,
fail.
'$composed_built_in'(('$save_current_choice_point'(_),NG,'$$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).
'$expand_expr'(A, true, A) :-
atomic(A), !.
'$expand_expr'(T, E, V) :-
'$unaryop'(T, O, A), !,
'$expand_expr'(A, Q, X),
'$expand_expr'(O, X, V, Q, E).
'$expand_expr'(T, E, V) :-
'$binaryop'(T, O, A, B), !,
'$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), integer(Y), \+ '$bignum'(Y), !,
Z is -Y,
'$do_and'(Q, '$plus'(X,Z,O), P).
'$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) :- !,
'$preprocess_args_for_non_commutative'(X, Y, X1, Y1, E),
'$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).
'$expand_expr'(<<, X, Y, O, Q, P) :- !,
'$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) :- !,
'$preprocess_args_for_non_commutative'(X, Y, X1, Y1, E),
'$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), \+ '$bignum'(Y), !.
'$preprocess_args_for_non_commutative'(X, Y, Z, W, E) :-
'$do_and'(Z = X, Y = W, E).
% These are the unary arithmetic operators
'$unaryop'(+X ,+ ,X).
'$unaryop'(-X ,- ,X).
'$unaryop'(\(X) ,\ ,X).
'$unaryop'(exp(X) ,exp ,X).
'$unaryop'(log(X) ,log ,X).
'$unaryop'(log10(X) ,log10 ,X).
'$unaryop'(sqrt(X) ,sqrt ,X).
'$unaryop'(sin(X) ,sin ,X).
'$unaryop'(cos(X) ,cos ,X).
'$unaryop'(tan(X) ,tan ,X).
'$unaryop'(asin(X) ,asin ,X).
'$unaryop'(acos(X) ,acos ,X).
'$unaryop'(atan(X) ,atan ,X).
'$unaryop'(atan2(X) ,atan2 ,X).
'$unaryop'(sinh(X) ,sinh ,X).
'$unaryop'(cosh(X) ,cosh ,X).
'$unaryop'(tanh(X) ,tanh ,X).
'$unaryop'(asinh(X) ,asinh ,X).
'$unaryop'(acosh(X) ,acosh ,X).
'$unaryop'(atanh(X) ,atanh ,X).
'$unaryop'(floor(X) ,floor ,X).
'$unaryop'(abs(X) ,abs ,X).
'$unaryop'(float(X) ,float ,X).
'$unaryop'(+(X) ,+ ,X).
'$unaryop'(integer(X) ,integer,X).
'$unaryop'(truncate(X) ,truncate,X).
'$unaryop'(round(X) ,round ,X).
'$unaryop'(ceiling(X) ,ceiling,X).
'$unaryop'(msb(X) ,msb ,X).
'$unaryop'(sign(X) ,sign ,X).
% These are the binary arithmetic operators
'$binaryop'(X+Y ,+ ,X,Y).
'$binaryop'(X-Y ,- ,X,Y).
'$binaryop'(X*Y ,* ,X,Y).
'$binaryop'(X/Y ,/ ,X,Y).
'$binaryop'(X mod Y ,mod ,X,Y).
'$binaryop'(X//Y ,// ,X,Y).
'$binaryop'(X/\Y ,/\ ,X,Y).
'$binaryop'(X\/Y ,\/ ,X,Y).
'$binaryop'(X#Y ,'#' ,X,Y).
'$binaryop'(X<<Y ,<< ,X,Y).
'$binaryop'(X>>Y ,>> ,X,Y).
'$binaryop'(X^Y ,^ ,X,Y).
'$binaryop'(X**Y ,^ ,X,Y).
'$binaryop'(exp(X,Y) ,^ ,X,Y).
'$binaryop'(max(X,Y) ,max ,X,Y).
'$binaryop'(min(X,Y) ,min ,X,Y).
'$binaryop'(gcd(X,Y) ,gcd ,X,Y).
'$binaryop'(gcdmult(X,Y),gcdmult,X,Y).
% The table number for each operation is given here
% Depends on eval.c
'$unary_op_as_integer'(+,0).
'$unary_op_as_integer'(-,1).
'$unary_op_as_integer'(\,2).
'$unary_op_as_integer'(exp,3).
'$unary_op_as_integer'(log,4).
'$unary_op_as_integer'(log10,5).
'$unary_op_as_integer'(sqrt,6).
'$unary_op_as_integer'(sin,7).
'$unary_op_as_integer'(cos,8).
'$unary_op_as_integer'(tan,9).
'$unary_op_as_integer'(sinh,10).
'$unary_op_as_integer'(cosh,11).
'$unary_op_as_integer'(tanh,12).
'$unary_op_as_integer'(asin,13).
'$unary_op_as_integer'(acos,14).
'$unary_op_as_integer'(atan,15).
'$unary_op_as_integer'(asinh,16).
'$unary_op_as_integer'(acosh,17).
'$unary_op_as_integer'(atanh,18).
'$unary_op_as_integer'(floor,19).
'$unary_op_as_integer'(ceiling,20).
'$unary_op_as_integer'(round,21).
'$unary_op_as_integer'(truncate,22).
'$unary_op_as_integer'(integer,23).
'$unary_op_as_integer'(float,24).
'$unary_op_as_integer'(abs,25).
'$unary_op_as_integer'(msb,26).
'$unary_op_as_integer'(float_fractional_part,27).
'$unary_op_as_integer'(float_integer_part,28).
'$unary_op_as_integer'(sign,29).
'$binary_op_as_integer'(+,0).
'$binary_op_as_integer'(-,1).
'$binary_op_as_integer'(*,2).
'$binary_op_as_integer'(/,3).
'$binary_op_as_integer'(mod,4).
'$binary_op_as_integer'(rem,5).
'$binary_op_as_integer'(//,6).
'$binary_op_as_integer'(<<,7).
'$binary_op_as_integer'(>>,8).
'$binary_op_as_integer'(/\,9).
'$binary_op_as_integer'(\/,10).
'$binary_op_as_integer'('#',11).
'$binary_op_as_integer'(atan2,12).
'$binary_op_as_integer'(^,13).
'$binary_op_as_integer'('**',14).
'$binary_op_as_integer'(exp,15).
'$binary_op_as_integer'(gcd,16).
'$binary_op_as_integer'(min,17).
'$binary_op_as_integer'(max,18).
%'$binary_op_as_integer'(gcdmult,28).
/* Arithmetics */
% M and N nonnegative integers, N is the successor of M
succ(M,N) :- integer(M), !, '$plus'(M,1,N).
succ(M,N) :- integer(N), !, N > 0, '$plus'(N,-1,M).
succ(0,1).
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