The Arithmetic Jump is a deterministic arithmetic method for direct inversion of row major linear indices into 3D coordinates without nested loops, branches, or iterative traversal. The method relies only on integer division and modulo operations, which enables constant time coordinate reconstruction and uniform GPU execution behavior.
- Gagniuc, P.A. The Arithmetic Jump: A Branch-Free Index Inversion for 3D Arrays. Algorithms 2026, 19, 375.