Nimber arithmetic: Difference between revisions

</pre>

=={{header|Wren}}==

{{trans|FreeBASIC}}

{{libheader|Wren-fmt}}

<lang ecmascript>import "/fmt" for Fmt

// Highest power of two that divides a given number.

var hpo2 = Fn.new { |n| n & (-n) }

// Base 2 logarithm of the highest power of 2 dividing a given number.

var lhpo2 = Fn.new { |n|

var q = 0

var m = hpo2.call(n)

while (m%2 == 0) {

m = m >> 1

q = q + 1

}

return q

}

// nim-sum of two numbers.

var nimsum = Fn.new { |x, y| x ^ y }

// nim-product of two numbers.

var nimprod // recursive

nimprod = Fn.new { |x, y|

if (x < 2 || y < 2) return x * y

var h = hpo2.call(x)

System.write("") // fixes VM recursion bug

if (x > h) return nimprod.call(h, y) ^ nimprod.call(x ^ h, y) // break x into powers of 2

if (hpo2.call(y) < y) return nimprod.call(y, x) // break y into powers of 2

var xp = lhpo2.call(x)

var yp = lhpo2.call(y)

var comp = xp & yp

if (comp == 0) return x * y // no Fermat power in common

h = hpo2.call(comp)

// a Fermat number square is its sequimultiple

return nimprod.call(nimprod.call(x >> h, y >> h), 3 << (h-1))

}

var fns = [[nimsum, "+"], [nimprod, "*"]]

for (fn in fns) {

System.write(" %(fn[1]) |")

for (i in 0..15) System.write(Fmt.d(3, i))

System.print("\n--- %("-" * 48)")

for (i in 0..15) {

System.write("%(Fmt.d(2, i)) |")

for (j in 0..15) System.write(Fmt.d(3, fn[0].call(i, j)))

System.print()

}

System.print()

}

var a = 21508

var b = 42689

System.print("%(a) + %(b) = %(nimsum.call(a, b))")

System.print("%(a) * %(b) = %(nimprod.call(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

21508 + 42689 = 62149

21508 * 42689 = 35202