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Nimber arithmetic: Difference between revisions
Added translation in python
(Added translation in python) |
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Line 1,210:
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|Python}}==
{{trans|Go}}
<lang python># Highest power of two that divides a given number.
def hpo2(n): return n & (-n)
# Base 2 logarithm of the highest power of 2 dividing a given number.
def lhpo2(n):
q = 0
m = hpo2(n)
while m%2 == 0:
m = m >> 1
q += 1
return q
def nimsum(x,y): return x ^ y
def nimprod(x,y):
if x < 2 or y < 2:
return x * y
h = hpo2(x)
if x > h:
return nimprod(h, y) ^ nimprod(x^h, y) # break x into powers of 2
if hpo2(y) < y:
return nimprod(y, x) # break y into powers of 2 by flipping operands
xp, yp = lhpo2(x), lhpo2(y)
comp = xp & yp
if comp == 0:
return x * y # no Fermat power in common
h = hpo2(comp)
# a Fermat number square is its sequimultiple
return nimprod(nimprod(x>>h, y>>h), 3<<(h-1))
if __name__ == '__main__':
for f, op in ((nimsum, '+'), (nimprod, '*')):
print(f" {op} |", end='')
for i in range(16):
print(f"{i:3d}", end='')
print("\n--- " + "-"*48)
for i in range(16):
print(f"{i:2d} |", end='')
for j in range(16):
print(f"{f(i,j):3d}", end='')
print()
print()
a, b = 21508, 42689
print(f"{a} + {b} = {nimsum(a,b)}")
print(f"{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
21508 + 42689 = 62149
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