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Task/Balanced-ternary/Prolog/balanced-ternary-3.pro
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Task/Balanced-ternary/Prolog/balanced-ternary-3.pro
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:- module('bt_mult.pl', [op(850, xfx, btmult),
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btmult/2,
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multiplication/3
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]).
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:- use_module('bt_add.pl').
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:- op(850, xfx, btmult).
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A is B btmult C :-
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multiplication(B, C, A).
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neg(A, B) :-
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maplist(opp, A, B).
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opp(48, 48).
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opp(45, 43).
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opp(43, 45).
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% the multiplication (efficient)
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% multiplication(+BIn, +QIn, -AOut)
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% Aout is BIn * QIn
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% BIn, QIn, AOut are strings
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multiplication(BIn, QIn, AOut) :-
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string_to_list(BIn, B),
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string_to_list(QIn, Q),
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% We work with positive numbers
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( B = [45 | _] -> Pos0 = false, neg(B,BP) ; BP = B, Pos0 = true),
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( Q = [45 | _] -> neg(Q, QP), select(Pos0, [true, false], [Pos1]); QP = Q, Pos1 = Pos0),
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multiplication_(BP, QP, [48], A),
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( Pos1 = false -> neg(A, A1); A1 = A),
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string_to_list(AOut, A1).
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multiplication_(_B, [], A, A).
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multiplication_(B, [H | T], A, AF) :-
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multiplication_1(B, H, B1),
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append(A, [48], A1),
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bt_add1(B1, A1, A2),
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multiplication_(B, T, A2, AF).
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% by 1 (digit '+' code 43)
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multiplication_1(B, 43, B).
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% by 0 (digit '0' code 48)
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multiplication_1(_, 48, [48]).
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% by -1 (digit '-' code 45)
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multiplication_1(B, 45, B1) :- neg(B, B1).
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% the division (efficient)
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% division(+AIn, +BIn, -QOut, -ROut)
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%
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division(AIn, BIn, QOut, ROut) :-
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string_to_list(AIn, A),
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string_to_list(BIn, B),
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length(B, LB),
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length(A, LA),
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Len is LA - LB,
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( Len < 0 -> Q = [48], R = A
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; neg(B, NegB), division_(A, B, NegB, LB, Len, [], Q, R)),
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string_to_list(QOut, Q),
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string_to_list(ROut, R).
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division_(A, B, NegB, LenB, LenA, QC, QF, R) :-
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% if the remainder R is negative (last number A), we must decrease the quotient Q, annd add B to R
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( LenA = -1 -> (A = [45 | _] -> positive(A, B, QC, QF, R) ; QF = QC, A = R)
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; extract(LenA, _, A, AR, AF),
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length(AR, LR),
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( LR >= LenB -> ( AR = [43 | _] ->
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bt_add1(AR, NegB, S), Q0 = [43],
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% special case : R has the same length than B
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% and his first digit is + (1)
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% we must do another one substraction
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( (length(S, LenB), S = [43|_]) ->
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bt_add1(S, NegB, S1),
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bt_add1(QC, [43], QC1),
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Q00 = [45]
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; S1 = S, QC1 = QC, Q00 = Q0)
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; bt_add1(AR, B, S1), Q00 = [45], QC1 = QC),
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append(QC1, Q00, Q1),
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append(S1, AF, A1),
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strip_nombre(A1, A2, []),
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LenA1 is LenA - 1,
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division_(A2, B, NegB, LenB, LenA1, Q1, QF, R)
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; append(QC, [48], Q1), LenA1 is LenA - 1,
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division_(A, B, NegB, LenB, LenA1, Q1, QF, R))).
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% extract(+Len, ?N1, +L, -Head, -Tail)
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% remove last N digits from the list L
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% put them in Tail.
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extract(Len, Len, [], [], []).
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extract(Len, N1, [H|T], AR1, AF1) :-
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extract(Len, N, T, AR, AF),
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N1 is N-1,
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( N > 0 -> AR = AR1, AF1 = [H | AF]; AR1 = [H | AR], AF1 = AF).
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positive(R, _, Q, Q, R) :- R = [43 | _].
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positive(S, B, Q, QF, R ) :-
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bt_add1(S, B, S1),
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bt_add1(Q, [45], Q1),
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positive(S1, B, Q1, QF, R).
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% "euclidian" division (inefficient)
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% euclide(?A, +BIn, ?Q, ?R)
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% A = B * Q + R
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euclide(A, B, Q, R) :-
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mult(A, B, Q, R).
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mult(AIn, BIn, QIn, RIn) :-
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( nonvar(AIn) -> string_to_list(AIn, A); A = AIn),
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( nonvar(BIn) -> string_to_list(BIn, B); B = BIn),
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( nonvar(QIn) -> string_to_list(QIn, Q); Q = QIn),
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( nonvar(RIn) -> string_to_list(RIn, R); R = RIn),
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% we use positive numbers
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( B = [45 | _] -> Pos0 = false, neg(B,BP) ; BP = B, Pos0 = true),
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( (nonvar(Q), Q = [45 | _]) -> neg(Q, QP), select(Pos0, [true, false], [Pos1])
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; nonvar(Q) -> Q = QP , Pos1 = Pos0
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; Pos1 = Pos0),
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( (nonvar(A), A = [45 | _]) -> neg(A, AP)
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; nonvar(A) -> AP = A
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; true),
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% is R instancied ?
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( nonvar(R) -> R1 = R; true),
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% multiplication ? we add B to A and substract 1 (digit '-') to Q
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( nonvar(Q) -> BC = BP, Ajout = [45],
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( nonvar(R) -> bt_add1(BC, R, AP) ; AP = BC)
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% division ? we substract B to A and add 1 (digit '+') to Q
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; neg(BP, BC), Ajout = [43], QP = [48]),
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% do the real job
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mult_(BC, QP, AP, R1, Resultat, Ajout),
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( var(QIn) -> (Pos1 = false -> neg(Resultat, QT); Resultat = QT), string_to_list(QIn, QT)
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; true),
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( var(AIn) -> (Pos1 = false -> neg(Resultat, AT); Resultat = AT), string_to_list(AIn, AT)
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; true),
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( var(RIn) -> string_to_list(RIn, R1); true).
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% @arg1 : divisor
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% @arg2 : quotient
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% @arg3 : dividend
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% @arg4 : remainder
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% @arg5 : Result : receive either the dividend A
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% either the quotient Q
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mult_(B, Q, A, R, Resultat, Ajout) :-
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bt_add1(Q, Ajout, Q1),
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bt_add1(A, B, A1),
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( Q1 = [48] -> Resultat = A % a multiplication
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; ( A1 = [45 | _], Ajout = [43]) -> Resultat = Q, R = A % a division
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; mult_(B, Q1, A1, R, Resultat, Ajout)) .
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