c++ - meaning of (number) & (-number)

Question

What is the meaning of (number) & (-number)? I have searched it but was unable to find the meaning

I want to use i & (-i) in for loop like:

for (i = 0; i <= n; i += i & (-i))

Answer 1

Assuming 2's complement (or that i is unsigned), -i is equal to ~i+1.

i & (~i + 1) is a trick to extract the lowest set bit of i.

It works because what +1 actually does is to set the lowest clear bit, and clear all bits lower than that. So the only bit that is set in both i and ~i+1 is the lowest set bit from i (that is, the lowest clear bit in ~i). The bits lower than that are clear in ~i+1, and the bits higher than that are non-equal between i and ~i.

Using it in a loop seems odd unless the loop body modifies i, because i = i & (-i) is an idempotent operation: doing it twice gives the same result again.

[Edit: in a comment elsewhere you point out that the code is actually i += i & (-i). So what that does for non-zero i is to clear the lowest group of set bits of i, and set the next clear bit above that, for example 101100 -> 110000. For i with no clear bit higher than the lowest set bit (including i = 0), it sets i to 0. So if it weren't for the fact that i starts at 0, each loop would increase i by at least twice as much as the previous loop, sometimes more, until eventually it exceeds n and breaks or goes to 0 and loops forever.

It would normally be inexcusable to write code like this without a comment, but depending on the domain of the problem maybe this is an "obvious" sequence of values to loop over.]