I have a bad tendency to not write things. So I tend to forget some nice tricks. I will use this gist to list some of them as I remember/learn them

isPowerOfTwo

We will assume for all the following examples that x > 0 (IMPORTANT !)
This little formula  will determine if the number is power of two :
(x & -x) == x
How does it works ?
First, let's try to formulate what it means in english :
The only bits that x and -x have set to 1 in common, are the bits
set to 1 in x.
In fact, it's based on a simple observation. Let examine the number 4 :
4  = 00000100b
-4 = ~00000100b + 1b
   = 11111011b + 1b
   = 11111100b
thus : 4 & -4 = 00000100b & 11111100b = 00000100b = 4

This is not possible if the number is not a power of two. Indeed, if the power is
not a power of two, then more than one bit in the number is equal to one. Thus, the
negative representation of this number could not have all the 1 bit in the
positive number set to 1 (because the two's complement only add 1b)
For example, take the number 5:
5  = 00000101b
-5 = ~00000101b + 1b
   = 11111010b + 1b
   = 11111011b

We can also use x & (x-1) == 0.

oddOrEven

There's a nice trick (that modern compilers do automatically) to check if a number is odd or even.
The canonical way of checking if a number x is even for example, is :
x % 2 == 0
But we can use the fact that if x is even, the the LSB is 0. Of course, the LSB always represent 1,
and if it is 1, then the number can not be even. To understand it a bit better, it's worth to consider
mathematical representation of even and odd numbers :
For all natural numbers n, then 2n is even, and 2n + 1 is odd.
So, we just need to apply this fact to our problem, and we got that x is even if and only if :
x & 1 == 0

Similarly, to check if a number is odd :
x & 1 != 0

This trick is usually unecessary when working with modern compiler, but when dealing with assembly,
or other things like this, it could be useful.