Re: [FWP] Golf (7 strokes is par!)

[Jeff Helman <jhelman@wsb.com>]

Actually, there is still a bug in the $_&$_-1 logic.  Not only does it
work for positive powers of 2, it also (falsely) reports that 0 is a
power of 2 (i.e. 0&-1 == 0).

As to a formal proof, I don't know enough math to be able to state it in
all the proper terms, etc., but it seems to me that the only time that a
positive binary integer does not share any bits with its predecessor is
when, for lack of a better phrase, "the odometer rolls over" (e.g. from
00001111 to 0001000), and that only happens for a power of two.  Any
math guru want to put this in better terminology? :)

JH

Jeff Pinyan wrote:
> 
> On May 1, Jeff Helman said:
> 
> >>   if (YOUR CODE HERE) { print "$_ is a power of 2" }
> >     if (YOUR CODE HERE) { print "$_ is NOT a power of 2" }
> >
> >then $_&$_-1 would match your 7.  So I'll bite, what was your 7? (Of
> >course, you can send it to me privately if you don't want to spoil it
> >quite yet.)
> 
> Yes, I am a foolish stupid scum.  My mistake.  You are right with
> 
>   $_&$_-1
> 
> Do you happen to have the proof for why that is 0 for ONLY powers of 2? :)
> 
> -- japhy

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