Nimber arithmetic: Difference between revisions
Added Prolog Solution
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14 | 0 14 7 9 5 11 2 12 10 4 13 3 15 1 8 6
15 | 0 15 5 10 1 14 4 11 2 13 7 8 3 12 6 9
21508 + 42689 = 62149
21508 * 42689 = 35202
</pre>
=={{header|Prolog}}==
{{trans|FreeBASIC}}
{{works with|SWI Prolog}}
<lang prolog>% highest power of 2 that divides a given number
hpo2(N, P):-
P is N /\ -N.
% base 2 logarithm of the highest power of 2 dividing a given number
lhpo2(N, Q):-
hpo2(N, M),
lhpo2_(M, 0, Q).
lhpo2_(M, Q, Q):-
1 is M mod 2,
!.
lhpo2_(M, Q1, Q):-
M1 is M >> 1,
Q2 is Q1 + 1,
lhpo2_(M1, Q2, Q).
% nim-sum of two numbers
nimsum(X, Y, Sum):-
Sum is X xor Y.
% nim-product of twp numbers
nimprod(X, Y, Product):-
(X < 2 ; Y < 2),
!,
Product is X * Y.
nimprod(X, Y, Product):-
hpo2(X, H),
X > H,
!,
nimprod(H, Y, P1),
X1 is X xor H,
nimprod(X1, Y, P2),
Product is P1 xor P2.
nimprod(X, Y, Product):-
hpo2(Y, H),
H < Y,
!,
nimprod(Y, X, Product).
nimprod(X, Y, Product):-
lhpo2(X, Xp),
lhpo2(Y, Yp),
Comp is Xp /\ Yp,
(Comp == 0 ->
Product is X * Y
;
hpo2(Comp, H),
X1 is X >> H,
Y1 is Y >> H,
Z is 3 << (H - 1),
nimprod(X1, Y1, P),
nimprod(P, Z, Product)
).
print_row(N, B, Function):-
writef('%3r |', [B]),
Goal =.. [Function, A, B, C],
forall(between(0, N, A), (call(Goal), writef('%3r', [C]))),
nl.
print_table(N, Operator, Function):-
writef(' %w |', [Operator]),
forall(between(0, N, A), writef('%3r', [A])),
writef('\n --- -', []),
forall(between(0, N, _), writef('---', [])),
nl,
forall(between(0, N, A), print_row(N, A, Function)).
main:-
print_table(15, '+', nimsum),
nl,
print_table(15, '*', nimprod),
nl,
A = 21508, B = 42689,
nimsum(A, B, Sum),
nimprod(A, B, Product),
writef('%w + %w = %w\n', [A, B, Sum]),
writef('%w * %w = %w\n', [A, B, Product]).</lang>
{{out}}
<pre>
+ | 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
--- -------------------------------------------------
0 | 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
1 | 1 0 3 2 5 4 7 6 9 8 11 10 13 12 15 14
2 | 2 3 0 1 6 7 4 5 10 11 8 9 14 15 12 13
3 | 3 2 1 0 7 6 5 4 11 10 9 8 15 14 13 12
4 | 4 5 6 7 0 1 2 3 12 13 14 15 8 9 10 11
5 | 5 4 7 6 1 0 3 2 13 12 15 14 9 8 11 10
6 | 6 7 4 5 2 3 0 1 14 15 12 13 10 11 8 9
7 | 7 6 5 4 3 2 1 0 15 14 13 12 11 10 9 8
8 | 8 9 10 11 12 13 14 15 0 1 2 3 4 5 6 7
9 | 9 8 11 10 13 12 15 14 1 0 3 2 5 4 7 6
10 | 10 11 8 9 14 15 12 13 2 3 0 1 6 7 4 5
11 | 11 10 9 8 15 14 13 12 3 2 1 0 7 6 5 4
12 | 12 13 14 15 8 9 10 11 4 5 6 7 0 1 2 3
13 | 13 12 15 14 9 8 11 10 5 4 7 6 1 0 3 2
14 | 14 15 12 13 10 11 8 9 6 7 4 5 2 3 0 1
15 | 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0
* | 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
--- -------------------------------------------------
0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 | 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
2 | 0 2 3 1 8 10 11 9 12 14 15 13 4 6 7 5
3 | 0 3 1 2 12 15 13 14 4 7 5 6 8 11 9 10
4 | 0 4 8 12 6 2 14 10 11 15 3 7 13 9 5 1
5 | 0 5 10 15 2 7 8 13 3 6 9 12 1 4 11 14
6 | 0 6 11 13 14 8 5 3 7 1 12 10 9 15 2 4
7 | 0 7 9 14 10 13 3 4 15 8 6 1 5 2 12 11
8 | 0 8 12 4 11 3 7 15 13 5 1 9 6 14 10 2
9 | 0 9 14 7 15 6 1 8 5 12 11 2 10 3 4 13
10 | 0 10 15 5 3 9 12 6 1 11 14 4 2 8 13 7
11 | 0 11 13 6 7 12 10 1 9 2 4 15 14 5 3 8
12 | 0 12 4 8 13 1 9 5 6 10 2 14 11 7 15 3
13 | 0 13 6 11 9 4 15 2 14 3 8 5 7 10 1 12
14 | 0 14 7 9 5 11 2 12 10 4 13 3 15 1 8 6
15 | 0 15 5 10 1 14 4 11 2 13 7 8 3 12 6 9
21508 + 42689 = 62149
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