/* 

  Crypt benchmark in Picat v3. 
  
  From bench/crypt.pl (for Picat v3)
  https://github.com/SWI-Prolog/bench

  Changes: I had to rename odd -> oddx and even -> evenx 
  since they are defined in Picat standard module.
  (Got a weird error: error(instantiation_error,mod/2) before renaming)

  This Picat model was created by Hakan Kjellerstrand, hakank@gmail.com
  See also my Picat page: http://www.hakank.org/picat/

*/


% import util.
% import cp.


main => go.


go ?=>
	oddx(A),
        evenx(B), evenx(C),
	evenx(E),
	mult([C,B,A], E, [I,H,G,F|X]),
	lefteven(F), oddx(G), evenx(H), evenx(I), zero(X),
	lefteven(D),
	mult([C,B,A], D, [L,K,J|Y]),
	lefteven(J), oddx(K), evenx(L), zero(Y),
	sum([I,H,G,F], [0,L,K,J], [P,O,N,M|Z]),
	oddx(M), oddx(N), evenx(O), evenx(P), zero(Z),
        print(' '), print(A), print(B), print(C), nl,
	print('  '), print(D), print(E), nl,
	print(F), print(G), print(H), print(I), nl,
	print(J), print(K), print(L), nl,
       	print(M), print(N), print(O), print(P),
        nl,
        fail,
        nl.

go => true.


% Cryptomultiplication:
% Find the unique answer to:
%	OEE
%	 EE
% 	---
%      EOEE
%      EOE
%      ----
%      OOEE
%
% where E=even, O=odd.
% This program generalizes easily to any such problem.
% Written by Peter Van Roy

top:-
	oddx(A),
        evenx(B), evenx(C),
	evenx(E),
	mult([C,B,A], E, [I,H,G,F|X]),
	lefteven(F), oddx(G), evenx(H), evenx(I), zero(X),
	lefteven(D),
	mult([C,B,A], D, [L,K,J|Y]),
	lefteven(J), oddx(K), evenx(L), zero(Y),
	sum([I,H,G,F], [0,L,K,J], [P,O,N,M|Z]),
	oddx(M), oddx(N), evenx(O), evenx(P), zero(Z),
        % print(' '), print(A), print(B), print(C), nl,
	% print('  '), print(D), print(E), nl,
	% print(F), print(G), print(H), print(I), nl,
	% print(J), print(K), print(L), nl,
       	% print(M), print(N), print(O), print(P),
        % nl,
        fail,
        nl.

top.

% Addition of two numbers
sum(AL, BL, CL) :- sum(AL, BL, 0, CL).

sum([A|AL], [B|BL], Carry, [C|CL]) :- !,
	X is (A+B+Carry),
	C is X mod 10,
	NewCarry is X // 10,
	sum(AL, BL, NewCarry, CL).
sum([], BL, 0, BL) :- !.
sum(AL, [], 0, AL) :- !.
sum([], [B|BL], Carry, [C|CL]) :- !,
	X is B+Carry,
	NewCarry is X // 10,
	C is X mod 10,
	sum([], BL, NewCarry, CL).
sum([A|AL], [], Carry, [C|CL]) :- !,
	X is A+Carry,
	NewCarry is X // 10,
	C is X mod 10,
	sum([], AL, NewCarry, CL).
sum([], [], Carry, [Carry]).

% Multiplication
mult(AL, D, BL) :- mult(AL, D, 0, BL).

mult([A|AL], D, Carry, [B|BL] ) :-
	X is A*D+Carry,
	B is X mod 10,
	NewCarry is X // 10,
	mult(AL, D, NewCarry, BL).
mult([], _, Carry, [C,Cend]) :-
	C is Carry mod 10,
	Cend is Carry // 10.

zero([]).
zero([0|L]) :- zero(L).


oddx(1).
oddx(3).
oddx(5).
oddx(7).
oddx(9).

evenx(0).
evenx(2).
evenx(4).
evenx(6).
evenx(8).

lefteven(2).
lefteven(4).
lefteven(6).
lefteven(8).