Nimber arithmetic: Difference between revisions
Added XPL0 example.
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(Added XPL0 example.) |
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21508 + 42689 = 62149
21508 * 42689 = 35202
</pre>
=={{header|XPL0}}==
{{trans|FreeBASIC}}
<syntaxhighlight lang "XPL0">include xpllib; \for Print
function HPo2(N); \Highest power of 2 that divides a given number
integer N;
return N and -N;
function LHPo2(N);
\Base 2 logarithm of the highest power of 2 dividing a given number
integer N, Q, M;
[Q:= 0; M:= HPo2(N);
while (M and 1) = 0 do
[M:= M >> 1;
Q:= Q+1;
];
return Q;
];
function NimSum(X, Y); \Nim-sum of two numbers
integer X, Y;
return X xor Y;
function NimProd(X, Y); \Nim-product of two numbers
integer X, Y, H, XP, YP, Comp;
[if X < 2 or Y < 2 then return X*Y;
H:= HPo2(X);
\Recursively break X into its powers of 2
if X > H then return NimProd(H, Y) xor NimProd(X xor H, Y);
\Recursively break Y into its powers of 2 by flipping its operands
if HPo2(Y) < Y then return NimProd(Y, X);
\Now both X and Y are powers of two
XP:= LHPo2(X); YP:= LHPo2(Y); Comp:= XP and YP;
if Comp = 0 then return X*Y; \there is no Fermat power in common
H:= HPo2(Comp);
\A Fermat number square is its sequimultiple
return NimProd(NimProd(X>>H, Y>>H), 3<<(H-1));
];
integer A, B;
[Format(3, 0);
Print(" + |");
for A:= 0 to 15 do RlOut(0, float(A));
Print("\n --- -------------------------------------------------\n");
for B:= 0 to 15 do
[RlOut(0, float(B));
Print(" |");
for A:= 0 to 15 do
RlOut(0, float(NimSum(A,B)));
Print("\n");
];
Print("\n * |");
for A:= 0 to 15 do RlOut(0, float(A));
Print("\n --- -------------------------------------------------\n");
for B:= 0 to 15 do
[RlOut(0, float(B));
Print(" |");
for A:= 0 to 15 do
RlOut(0, float(NimProd(A,B)));
Print("\n");
];
A:= 21508;
B:= 42689;
Print("\n%5d + %5d = %10d\n", A, B, NimSum(A,B));
Print("%5d + %5d = %10d\n", A, B, NimProd(A,B));
]</syntaxhighlight>
{{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
21508 + 42689 = 35202
</pre>
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