Checking if an Integer is an Exact Binary Power

[Solomon E via Digitalmars-d]

On Monday, 25 April 2016 at 19:37:45 UTC, Andrei Alexandrescu 
wrote:
> On 04/25/2016 03:21 PM, Solomon E wrote:
>> I'm more concerned with getting the application
>> logic right when I program than optimizing for speed or bytes, 
>> until
>> something is noticeably pausing or taking extra megabytes.
>
> This is a luxury not available to library writers.

I agree.

>
>> bool isPow2D(T)(T x)
>> {
>>      return (x > 0) && !(x & (x - 1));
>> }
>
> This is worse than what we have now, which is easy to show is 
> correct.
>
>
> Andrei

I wasn't recommending isPow2D for the library, just for the 
luxury use case of writing cautiously to show the logic is 
correct.

It's easy to show that the current code for 
experimental.common.isPowerOf2 (the same logic as isPow2B) does 
wrong things when a signed type is forced into it.

I was hoping to suggest that if isPow2F isn't wrong, it might be 
used, because it has been proved and checked to be correct in 
this thread. However, I don't know if it actually is faster, and 
it would be difficult to test the speed up, if any, since the 
function variants are all so small, and isPow2F compiles to 
different instructions when used with different types. So it 
might not be worthwhile, unless there's an advantage of 
correctness or type-safety, which I'm not experienced enough in D 
to judge.

(The library's descriptions of std.math.nextPow2 are vastly 
oversimplified compared to what it does as shown in the examples, 
so attempting to use that for recognizing simple powers of 2 
would be a complexity mismatch.)