Tricks With Bits

• 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 sequence.
• 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.