Hacker’s Delight, Second Edition

Chapter 3. Power-of-2 Boundaries

3–1 Rounding Up/Down to a Multiple of a Known Power of 2

Rounding an unsigned integer x down to, for example, the next smaller multiple of 8 is trivial: x & −8 does it. An alternative is . These work for signed integers as well, provided “round down” means to round in the negative direction (e.g., (−37) & (−8) = −40).

Rounding up is almost as easy. For example, an unsigned integer x can be rounded up to the next greater multiple of 8 with either of

These expressions are correct for signed integers as well, provided ...