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

On 2023-01-12 13:13, Karim Belabas wrote:
> * Vincent Lefevre [2023-01-12 12:40]:
>> On 2023-01-12 12:31:09 +0100, [email protected] 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