Nimber arithmetic: Difference between revisions

{{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>

=={{header|Swift}}==

{{trans|Rust}}

<lang swift>import Foundation

// highest power of 2 that divides a given number

func hpo2(_ n: Int) -> Int {

n & -n

}

// base 2 logarithm of the highest power of 2 dividing a given number

func lhpo2(_ n: Int) -> Int {

var q: Int = 0

var m: Int = hpo2(n)

while m % 2 == 0 {

m >>= 1

q += 1

}

return q

}

// nim-sum of two numbers

func nimSum(x: Int, y: Int) -> Int {

x ^ y

}

// nim-product of two numbers

func nimProduct(x: Int, y: Int) -> Int {

if x < 2 || y < 2 {

return x * y

}

var h = hpo2(x);

if x > h {

return nimProduct(x: h, y: y) ^ nimProduct(x: x ^ h, y: y)

}

if hpo2(y) < y {

return nimProduct(x: y, y: x)

}

let xp = lhpo2(x)

let yp = lhpo2(y)

let comp = xp & yp

if comp == 0 {

return x * y

}

h = hpo2(comp)

return nimProduct(x: nimProduct(x: x >> h, y: y >> h), y: 3 << (h - 1))

}

func printTable(n: Int, op: Character, function: (Int, Int) -> Int) {

print(" \(op) |", terminator: "")

for a in 0...n {

print(String(format: "%3d", a), terminator: "")

}

print("\n--- -", terminator: "")

for _ in 0...n {

print("---", terminator: "")

}

print()

for b in 0...n {

print("\(String(format: "%2d", b)) |", terminator: "")

for a in 0...n {

print(String(format: "%3d", function(a, b)), terminator: "")

}

print()

}

}

printTable(n: 15, op: "+", function: nimSum)

print()

printTable(n: 15, op: "*", function: nimProduct)

let a: Int = 21508

let b: Int = 42689

print("\n\(a) + \(b) = \(nimSum(x: a, y: b))")

print("\(a) * \(b) = \(nimProduct(x: a, y: b))")</lang>