A long division story
Summary
This article recounts a decades-old bug in Knuth's Algorithm D for long division, how the author discovered it while implementing multiprecision arithmetic, and how it led to a formal theorem correction (Theorem B) and an errata. It also examines the LLVM APInt implementation and discusses historical division approaches, normalisation, and the practical implications for cryptographic and numeric libraries. The post blends deep theory with practical code insights and a narrative about how such issues surface in real-world software.