Nimber arithmetic: Difference between revisions

=={{header|Nim}}==

{{trans|FreeBASIC}}

<lang Nim>import bitops, strutils

type Nimber = Natural

func hpo2(n: Nimber): Nimber =

## Return the highest power of 2 that divides a given number.

n and -n

func lhpo2(n: Nimber): Nimber =

## Return the base 2 logarithm of the highest power of 2 dividing a given number.

fastLog2(hpo2(n))

func ⊕(x, y: Nimber): Nimber =

## Return the nim-sum of two nimbers.

x xor y

func ⊗(x, y: Nimber): Nimber =

## Return the nim-product of two nimbers.

if x < 2 and y < 2: return x * y

var h = hpo2(x)

if x > h:

return ⊗(h, y) xor ⊗(x xor h, y) # Recursively break "x" into its powers of 2.

if hpo2(y) < y:

return ⊗(y, x) # Recursively break "y" into its powers of 2 by flipping the operands.

# Now both "x" and "y" are powers of two.

let comp = lhpo2(x) * lhpo2(y)

if comp == 0: return x * y # No Fermat number in common.

h = hpo2(comp)

# A fermat number square is its sequimultiple.

result = ⊗(⊗(x div (1 shl h), y div (1 shl h)), 3 * (1 shl (h - 1)))

when isMainModule:

for (opname, op) in [("⊕", ⊕), ("⊗", ⊗)]:

stdout.write ' ', opname, " |"

for i in 0..15: stdout.write ($i).align(3)

stdout.write "\n--- -", repeat('-', 48), '\n'

for b in 0..15:

stdout.write ($b).align(2), " |"

for a in 0..15:

stdout.write ($op(a, b)).align(3)

stdout.write '\n'

echo ""

const A = 21508

const B = 42689

echo "$1 ⊕ $2 = $3".format(A, B, ⊕(A, B))

echo "$1 ⊗ $2 = $3".format(A, B, ⊗(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</pre>