* Warren D Smith <warren.wds@gmail.com> [Apr 07. 2014 07:22]:
Observe that 32 = 12 + 8 + 12.
1.Reverse all runs of 4 bits.
Two steps
2.Now reverse each of the 8, the 12, and the 12 by swapping their first with their last nybbles.
Two steps, as you can swap over a fixed distance only.
3.Finally swap the 12 & 12.
On step.
How's that do?
Five steps, just as the "well known" method whose steps come cheaper.
[Similarly 16=6+4+6 and 64=24+16+24.]
Hint: draw butterfly diagrams. Note that the technique I gave for words of length 2^k-1 gives a solution in "4 steps plus rotation by one". So you want "4 steps" (barely better than what we have for 64 bits!) or, ideally, "3 steps plus rotation". For the record, I do not know any solution (tried for about 3 hours). Best, jj
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