Re: probable bug of "ispower" function in GP: FALSE, apologies!

["Ruud H.G. van Tol" <rvtol@isolution.nl>]

On 2023-01-12 13:13, Karim Belabas wrote:
> * Vincent Lefevre [2023-01-12 12:40]:
> > On 2023-01-12 12:31:09 +0100, luis.gallardo@math.cnrs.fr wrote:
> > > I misunderstood the definition of "ispower"!
> > >
> > > I wanted a function that identify directly if some integer is a 
> > > power of 2
> > I suppose that you can use something like
> >
> > ispower(64,,&n)
> >
> > and check that n is 2. But I suppose that for large numbers, this may
> > be inefficient because ispower() will not just check for powers of 2.
> Use hammingweight(N) == 1.
>
> Or v = valuation(N,2); N >> v == 1 if you need the exact power. (Will be
> a little slower.)

Just meant for inspiration, not as effective implementations:

is_power_of1(n,p) = my(f=factor(n)); if(1==#f~, 
if(p==f[1,1],f[1,2],-oo), +oo)

is_power_of2(n,p)= my(r=valuation(n,p)); if(n==p^r,r,+oo)


? is_power_of1(32,2)
%= 5
? is_power_of2(32,2)
%= 5

? is_power_of1(27,2)
%= -oo  /* as 2 is not even a factor */
? is_power_of2(27,2)
%= +oo

? is_power_of1(54,2)
%= +oo
? is_power_of2(54,2)
%= +oo

? is_power_of1(1,10)
%= +oo  /* BUG */
? is_power_of2(1,10)
%= 0

-- Greetings, Ruud

xxx