[Moshe Zadka]
> If we had an affine operation, instead of a linear one, we could have
> [0, 2**n). I won't repeat the proof here but changing
>
> def f(i):
> i <<= 1
> i^=1 # This is the line I added
> if i >= 2**N:
> i ^= MAGIC_CONSTANT_DEPENDING_ON_N
> return i
>
> Makes you waltz all over [0, 2**n) if the original made you comple
> (0, 2**n).
[Tim]
> But, Moshe! The proof would have been the most interesting part <wink>.
Turns out the proof would have been intensely interesting, as you can see by
running the attached with and without the new line commented out.
don't-ever-trust-a-theoretician<wink>-ly y'rs - tim
N = 2
MAGIC_CONSTANT_DEPENDING_ON_N = 7
def f(i):
i <<= 1
# i^=1 # This is the line I added
if i >= 2**N:
i ^= MAGIC_CONSTANT_DEPENDING_ON_N
return i
i = 1
for nothing in range(4):
print i,
i = f(i)
print i
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