Imagine two bitmasks, I’ll just use 8 bits for simplicity:
01101010
10111011
The 2nd, 4th, and 6th bits are both 1. I want to pick one of those common “on” bits at random. But I want to do this in O(1).
The only way I’ve found to do this so far is pick a random “on” bit in one, then check the other to see if it’s also on, then repeat until I find a match. This is still O(n), and in my case the majority of the bits are off in both masks. I do of course & them together to initially check if there’s any common bits at all.
Is there a way to do this? If so, I can increase the speed of my function by around 6%. I’m using C# if that matters. Thanks!
Mike
If you are willing to have an O(lg n) solution, at the cost of a possibly nonuniform probability, recursively half split, i.e. and with the top half of the bits set and the bottom half set. If both are nonzero then chose one randomly, else choose the nonzero one. Then half split what remains, etc. This will take 10 comparisons for a 32 bit number, maybe not as few as you would like, but better than 32.
You can save a few ands by choosing to and with the high half or low half at random, and if there are no hits taking the other half, and if there are hits taking the half tested.
The random number only needs to be generated once, as you are only using one bit at each test, just shift the used bit out when you are done with it.
If you have lots of bits, this will be more efficient. I do not see how you can get this down to O(1) though.
For example, if you have a 32 bit number first and the anded combination with either 0xffff0000 or 0x0000ffff if the result is nonzero (say you anded with 0xffff0000) conitinue on with 0xff000000 of 0x00ff0000, and so on till you get to one bit. This ends up being a lot of tedious code. 32 bits takes 5 layers of code.