x & (x-1) will clear the lowest set bit of x
x & ~(x-1) extracts the lowest set bit of x (all others are clear). Pretty patterns when applied to a linear sequencee.
x & (x + (1 << n)) = x, with the run of set bits (possibly length 0) starting at bit n cleared.
x & ~(x + (1 << n)) = the run of set bits (possibly length 0) in x, starting at bit n.
x | (x + 1) = x with the lowest cleared bit set.
x | ~(x + 1) = extracts the lowest cleared bit of x (all others are set).
x | (x - (1 << n)) = x, with the run of cleared bits (possibly length 0) starting at bit n set.
x | ~(x - (1 << n)) = the lowest run of cleared bits (possibly length 0) in x, starting at bit n are the only clear bits.