Nimber arithmetic: Difference between revisions
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(Added translation in python) |
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14 | 0 14 7 9 5 11 2 12 10 4 13 3 15 1 8 6 |
14 | 0 14 7 9 5 11 2 12 10 4 13 3 15 1 8 6 |
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15 | 0 15 5 10 1 14 4 11 2 13 7 8 3 12 6 9 |
15 | 0 15 5 10 1 14 4 11 2 13 7 8 3 12 6 9 |
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21508 + 42689 = 62149 |
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21508 * 42689 = 35202 |
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</pre> |
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=={{header|Python}}== |
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{{trans|Go}} |
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<lang python># Highest power of two that divides a given number. |
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def hpo2(n): return n & (-n) |
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# Base 2 logarithm of the highest power of 2 dividing a given number. |
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def lhpo2(n): |
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q = 0 |
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m = hpo2(n) |
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while m%2 == 0: |
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m = m >> 1 |
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q += 1 |
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return q |
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def nimsum(x,y): return x ^ y |
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def nimprod(x,y): |
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if x < 2 or y < 2: |
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return x * y |
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h = hpo2(x) |
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if x > h: |
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return nimprod(h, y) ^ nimprod(x^h, y) # break x into powers of 2 |
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if hpo2(y) < y: |
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return nimprod(y, x) # break y into powers of 2 by flipping operands |
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xp, yp = lhpo2(x), lhpo2(y) |
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comp = xp & yp |
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if comp == 0: |
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return x * y # no Fermat power in common |
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h = hpo2(comp) |
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# a Fermat number square is its sequimultiple |
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return nimprod(nimprod(x>>h, y>>h), 3<<(h-1)) |
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if __name__ == '__main__': |
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for f, op in ((nimsum, '+'), (nimprod, '*')): |
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print(f" {op} |", end='') |
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for i in range(16): |
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print(f"{i:3d}", end='') |
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print("\n--- " + "-"*48) |
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for i in range(16): |
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print(f"{i:2d} |", end='') |
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for j in range(16): |
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print(f"{f(i,j):3d}", end='') |
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print() |
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print() |
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a, b = 21508, 42689 |
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print(f"{a} + {b} = {nimsum(a,b)}") |
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print(f"{a} * {b} = {nimprod(a,b)}")</lang> |
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{{out}} |
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<pre> |
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+ | 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 |
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--- ------------------------------------------------ |
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0 | 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 |
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1 | 1 0 3 2 5 4 7 6 9 8 11 10 13 12 15 14 |
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2 | 2 3 0 1 6 7 4 5 10 11 8 9 14 15 12 13 |
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3 | 3 2 1 0 7 6 5 4 11 10 9 8 15 14 13 12 |
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4 | 4 5 6 7 0 1 2 3 12 13 14 15 8 9 10 11 |
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5 | 5 4 7 6 1 0 3 2 13 12 15 14 9 8 11 10 |
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6 | 6 7 4 5 2 3 0 1 14 15 12 13 10 11 8 9 |
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7 | 7 6 5 4 3 2 1 0 15 14 13 12 11 10 9 8 |
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8 | 8 9 10 11 12 13 14 15 0 1 2 3 4 5 6 7 |
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9 | 9 8 11 10 13 12 15 14 1 0 3 2 5 4 7 6 |
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10 | 10 11 8 9 14 15 12 13 2 3 0 1 6 7 4 5 |
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11 | 11 10 9 8 15 14 13 12 3 2 1 0 7 6 5 4 |
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12 | 12 13 14 15 8 9 10 11 4 5 6 7 0 1 2 3 |
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13 | 13 12 15 14 9 8 11 10 5 4 7 6 1 0 3 2 |
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14 | 14 15 12 13 10 11 8 9 6 7 4 5 2 3 0 1 |
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15 | 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 |
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* | 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 |
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--- ------------------------------------------------ |
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0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
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1 | 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 |
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2 | 0 2 3 1 8 10 11 9 12 14 15 13 4 6 7 5 |
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3 | 0 3 1 2 12 15 13 14 4 7 5 6 8 11 9 10 |
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4 | 0 4 8 12 6 2 14 10 11 15 3 7 13 9 5 1 |
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5 | 0 5 10 15 2 7 8 13 3 6 9 12 1 4 11 14 |
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6 | 0 6 11 13 14 8 5 3 7 1 12 10 9 15 2 4 |
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7 | 0 7 9 14 10 13 3 4 15 8 6 1 5 2 12 11 |
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8 | 0 8 12 4 11 3 7 15 13 5 1 9 6 14 10 2 |
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9 | 0 9 14 7 15 6 1 8 5 12 11 2 10 3 4 13 |
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10 | 0 10 15 5 3 9 12 6 1 11 14 4 2 8 13 7 |
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11 | 0 11 13 6 7 12 10 1 9 2 4 15 14 5 3 8 |
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12 | 0 12 4 8 13 1 9 5 6 10 2 14 11 7 15 3 |
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13 | 0 13 6 11 9 4 15 2 14 3 8 5 7 10 1 12 |
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14 | 0 14 7 9 5 11 2 12 10 4 13 3 15 1 8 6 |
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15 | 0 15 5 10 1 14 4 11 2 13 7 8 3 12 6 9 |
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21508 + 42689 = 62149 |
21508 + 42689 = 62149 |