Signed ceiling and parity remainder
Abstract
Signed ceiling and parity remainder
The signed integer ceiling works for negative numerators as well as positive ones. Choosing M=Dceil((K-B+L)/(DL))-1 places the second remainder in [0,D*L), and a dyadic D makes all low bits available. Parity adjustment chooses j in the required congruence class and proves the exact first remainder before converting integers to natural masks.