As I was reading, I was slowly understanding that N-bit division would require (in the worst case) an N + 1 bit magic number. How in the world could this be sol

As I was reading, I was slowly understanding that N-bit division would require (in the worst case) an N + 1 bit magic number. How in the world could this be solvable in the general case? My assumption was that we just did division for those numbers the "old-fashioned" way. But, at the end of the day, the actual solution -- ((n − q) ≫ 2) + q -- is ingenious, fantastic article!