Nimber arithmetic: Difference between revisions
→{{header|Julia}}
Line 372:
21508 * 42689 = 35202
</pre>
=={{header|Julia}}==
{{trans|FreeBASIC}}
<lang julia>""" highest power of 2 that divides a given number """
hpo2(n) = n & -n
""" base 2 logarithm of the highest power of 2 dividing a given number """
lhpo2(n) = begin q, m = 0, hpo2(n); while iseven(m) m >>= 1; q += 1 end; q end
""" nim-sum of two numbers """
nimsum(x, y) = x ⊻ y
""" nim-product of two numbers """
function nimprod(x, y)
(x < 2 || y < 2) && return x * y
h = hpo2(x)
(x > h) && return nimprod(h, y) ⊻ nimprod(x ⊻ h, y)
(hpo2(y) < y) && return nimprod(y, x)
xp, yp = lhpo2(x), lhpo2(y)
comp = xp & yp
comp == 0 && return x * y
h = hpo2(comp)
return nimprod(nimprod(x >> h, y >> h), 3 << (h - 1))
end
""" print a table of nim-sums or nim-products """
function printtable(n, op)
println(" $op |", prod([lpad(i, 3) for i in 0:n]), "\n--- -", "---"^(n + 1))
for j in 0:n
print(lpad(j, 2), " |")
for i in 0:n
print(lpad(op == '⊕' ? nimsum(i, j) : nimprod(i, j), 3))
end
print(j == n ? "\n\n" : "\n")
end
end
const a, b = 21508, 42689
printtable(15, '⊕')
printtable(15, '⊗')
println("nim-sum: $a ⊕ $b = $(nimsum(a, b))")
println("nim-product: $a ⊗ $b = $(nimprod(a, b))")
</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
nim-sum: 21508 ⊕ 42689 = 62149
nim-product: 21508 ⊗ 42689 = 35202
</pre>
=={{header|Phix}}==
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