# test whether a number is a power of 2

Discussion in 'C Programming' started by Matt, Sep 28, 2003.

1. ### MattGuest

Give a one-line C expression to test whether a number is a power of 2.
No loops allowed.

Matt, Sep 28, 2003

2. ### Joona I PalasteGuest

Matt <> scribbled the following:
> Give a one-line C expression to test whether a number is a power of 2.
> No loops allowed.

((((x&&!(x&(x-!!x)))+x)-x)^x)^x

What do I win?

--
/-- Joona Palaste () ---------------------------\
| Kingpriest of "The Flying Lemon Tree" G++ FR FW+ M- #108 D+ ADA N+++|
| http://www.helsinki.fi/~palaste W++ B OP+ |
\----------------------------------------- Finland rules! ------------/
"Remember: There are only three kinds of people - those who can count and those
who can't."
- Vampyra

Joona I Palaste, Sep 28, 2003

3. ### Ivan VecerinaGuest

Ivan Vecerina, Sep 28, 2003
4. ### Keith ThompsonGuest

(Matt) writes:
> Give a one-line C expression to test whether a number is a power of 2.
> No loops allowed.

We're not here to do your homework for you.

--
Keith Thompson (The_Other_Keith) <http://www.ghoti.net/~kst>
San Diego Supercomputer Center <*> <http://www.sdsc.edu/~kst>
Schroedinger does Shakespeare: "To be *and* not to be"

Keith Thompson, Sep 28, 2003
5. ### jacob naviaGuest

> isPow2 = x && !( (x-1) & x );

Algorithm:
If x is a power of two, it doesn't have any bits in common with x-1, since it
consists of a single bit on. Any positive power of two is a single bit, using
binary integer representation.

This means that we test if x-1 and x doesn't share bits with the and operator.

Of course, if x is zero (not a power of two) this doesn't hold, so we add an
explicit test for zero with xx && expression.

Negative powers of two (0.5, 0.25, 0.125, etc) could share this same property
in a suitable fraction representation. 0.5 would be 0.1, 0.250 would be 0.01,
0.125 would be 0.001 etc.

jacob

jacob navia, Sep 28, 2003
6. ### AishwaryaGuest

Joona I Palaste <> wrote in message news:<bl79og\$2tv\$>...
> Matt <> scribbled the following:
> > Give a one-line C expression to test whether a number is a power of 2.
> > No loops allowed.

>
> ((((x&&!(x&(x-!!x)))+x)-x)^x)^x
>
> What do I win?

hi Joona,

i know this works because i just tested it .. but help me understand
the algoritm please ..

Thanks and Regards
A.

Aishwarya, Sep 29, 2003
7. ### Eric SosmanGuest

Matt wrote:
>
> Give a one-line C expression to test whether a number is a power of 2.
> No loops allowed.

true_or_false = a_number > 0;

(For example, 3.14159 ~= 2 ** 1.65149.)

--

Eric Sosman, Sep 29, 2003
8. ### Dan PopGuest

In <> Keith Thompson <> writes:

> (Matt) writes:
>> Give a one-line C expression to test whether a number is a power of 2.
>> No loops allowed.

>
>We're not here to do your homework for you.

OTOH, the solution is far too tricky for a homework assignment. It
requires a bit of knowledge that has precious little to do with C
programming.

Dan
--
Dan Pop
DESY Zeuthen, RZ group
Email:

Dan Pop, Sep 29, 2003
9. ### Dan PopGuest

In <> (Aishwarya) writes:

>Joona I Palaste <> wrote in message news:<bl79og\$2tv\$>...
>> Matt <> scribbled the following:
>> > Give a one-line C expression to test whether a number is a power of 2.
>> > No loops allowed.

>>
>> ((((x&&!(x&(x-!!x)))+x)-x)^x)^x

>
>i know this works because i just tested it .. but help me understand
>the algoritm please ..

Had you engaged your brain, you'd have easily noticed that one ^x cancels
the other and that -x cancels the +x, so you're left with

x&&!(x&(x-!!x))

Now, !!x is an obfuscated way of writing 1, when you know that x cannot
be zero (it was already tested), so, we're left with:

x&&!(x&(x-1))

The tricky bit is x&(x-1) which actually clears the least significant
bit that happens to be set. If the original number was a power of two,
it had only one bit set, so the result of x&(x-1) must be zero in such
cases.

The rest should be obvious.

Dan
--
Dan Pop
DESY Zeuthen, RZ group
Email:

Dan Pop, Sep 29, 2003
10. ### Jirka KlaueGuest

Aishwarya wrote:
> Joona I Palaste <> wrote in message news:<bl79og\$2tv\$>...

....
>>((((x&&!(x&(x-!!x)))+x)-x)^x)^x

>
> i know this works because i just tested it .. but help me understand
> the algoritm please ..

+x -x does nothing, ^x ^x does nothing.

remains:
x && !(x & (x - !!x))

!!x ist alway 1, because x can't be 0 at this point.

remains:
x && !(x & (x - 1))

Jirka

Jirka Klaue, Sep 29, 2003
11. ### Ed MortonGuest

On 9/28/2003 1:21 PM, Matt wrote:
> Give a one-line C expression to test whether a number is a power of 2.
> No loops allowed.

if (!(x%2)) {
puts("x is a power of 2");
}

Regards,

Ed.

Ed Morton, Sep 29, 2003
12. ### Jirka KlaueGuest

Ed Morton wrote:
> On 9/28/2003 1:21 PM, Matt wrote:
>
>>Give a one-line C expression to test whether a number is a power of 2.
>>No loops allowed.

>
> if (!(x%2)) {
> puts("x is a power of 2");
> }

Are you implying that 42 is a power of 2 and 43 is not?
BTW: It's a three-liner and no C expression at all. ;-)

Jirka

Jirka Klaue, Sep 29, 2003
13. ### Ed MortonGuest

On 9/29/2003 10:44 AM, Jirka Klaue wrote:
> Ed Morton wrote:
>
>>On 9/28/2003 1:21 PM, Matt wrote:
>>
>>
>>>Give a one-line C expression to test whether a number is a power of 2.
>>>No loops allowed.

>>
>>if (!(x%2)) {
>> puts("x is a power of 2");
>>}

>
>
> Are you implying that 42 is a power of 2 and 43 is not?
> BTW: It's a three-liner and no C expression at all. ;-)
>
> Jirka
>

I had intended !(x%2) to be the expression, the rest was demonstrating using it.
I'll go back to sleep now.... wake me next time you want to know if a number is
a multiple of 2 rather than a power of 2. Sorry 'bout that.

Ed.

Ed Morton, Sep 29, 2003
14. ### Guest

Joona I Palaste <> wrote:
>
> ((((x&&!(x&(x-!!x)))+x)-x)^x)^x
>
> What do I win?

Nothing. What if x is negative? What if it's not an integer? What if
the original poster provided a complete specification of the problem?

-Larry Jones

I kind of resent the manufacturer's implicit assumption
that this would amuse me. -- Calvin

, Sep 29, 2003
15. ### Peter NilssonGuest

Eric Sosman <> wrote in message news:<>...
> Matt wrote:
> >
> > Give a one-line C expression to test whether a number is a power of 2.
> > No loops allowed.

>
> true_or_false = a_number > 0;
> (For example, 3.14159 ~= 2 ** 1.65149.)

Why stop there? C99 has complex types.

--
Peter

Peter Nilsson, Sep 29, 2003
16. ### CBFalconerGuest

Ed Morton wrote:
> On 9/28/2003 1:21 PM, Matt wrote:
>
> > Give a one-line C expression to test whether a number is a
> > power of 2. No loops allowed.

>
> if (!(x%2)) {
> puts("x is a power of 2");
> }

^^^^^^^^^^^^
even

--
Chuck F () ()
Available for consulting/temporary embedded and systems.
<http://cbfalconer.home.att.net> USE worldnet address!

CBFalconer, Sep 30, 2003
17. ### AishwaryaGuest

(Dan Pop) wrote in message news:<bl9hsv\$368\$>...
...

> Now, !!x is an obfuscated way of writing 1, when you know that x cannot
> be zero (it was already tested)

this is exactly what i got stuck in i should have guessed it ...
thanks for the explanation though

Aishwarya, Sep 30, 2003
18. ### R. Rajesh Jeba AnbiahGuest

"jacob navia" <> wrote in message news:<bl7kgo\$d5e\$>...
> > isPow2 = x && !( (x-1) & x );

>
> Algorithm:
> If x is a power of two, it doesn't have any bits in common with x-1, since it
> consists of a single bit on. Any positive power of two is a single bit, using
> binary integer representation.
>
> This means that we test if x-1 and x doesn't share bits with the and operator.
>
> Of course, if x is zero (not a power of two) this doesn't hold, so we add an
> explicit test for zero with xx && expression.

Few Mathematicians say any positive integer raised to the power minus
infinity is 0. That is,
n (pow) (-infinity) = 0

IOW, 2 (pow) 3 = 8, 2 (pow) 2 = 4, 2 (pow) 1 = 2, 2 (pow) 0 = 1,
and, 2 (pow) (-infinity) = 0.

Because of this religious reason, I would just write my macro as
(without 0 check)
#define ISPOWOF2( n ) ( ! ( n & (n-1) ) )

But, someone here in CLC told me that the above macro won't work all
the time. I know, it won't work for float; I know the necessity of
additional paranthesis for n. But, I couldn't see any other reasons.
Anybody have any good comments? TIA

---
"Silence is the only right answer for many wrong questions" --
G.K.Moopanaar, Indian Politician
http://guideme.itgo.com/atozofc/ - "A to Z of C" Project
Email: rrjanbiah-at-Y!com

R. Rajesh Jeba Anbiah, Oct 1, 2003

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