Recursive Grid Indexing for Fast Non‐Uniform Quantization Without Binary Search

Purpose To present Recursive Grid Indexing (RGI), a practical software technique for accelerating non‐uniform quantization and predecessor queries without relying on binary search at any stage. Design/Methodology/Approach RGI replaces conventional logarithmic binary search with a recursive, low‐branching grid structure. The method constructs a hierarchy of uniform auxiliary grids over the boundary range. Each query descends through a small number of grid levels and terminates in a leaf containing at most (T) candidate boundaries, resolved via a fixed‐size comparison sequence. Binary search is entirely eliminated by bounded recursive refinement. Findings RGI was implemented in portable C and evaluated on ARM and x86 platforms using both synthetic boundary distributions and real‐world (μ)‐law audio data. Across the evaluated workloads, the method achieved approximately (1.8)–(5.1×) speedup over classical binary search while maintaining stable performance, small memory footprint, and architecture‐independent behavior. Originality/Value The work introduces an exact recursive alternative to binary search for predecessor‐style lookup in non‐uniform quantization. Unlike earlier two‐level approaches, it uses bounded recursive refinement throughout the lookup path and avoids binary‐search fallback entirely.