Register Allocation, Instruction Selection, and Code Generation: Chaitin-Briggs Graph Coloring, Linear Scan, Tree-Pattern Matching, Peephole Superoptimizers, and SIMD Auto-Vectorization

Deep End Era. Engineering with Sankalp · Oct 29, 2026 · 1h 4m

Your SSA optimizer produced a function with 800 virtual registers, but your x86-64 CPU only has 16 integer registers. We trace how compiler backends bridge that gap: Chaitin-Briggs graph coloring, chordal SSA graphs, Linear Scan and LLVM's greedy allocator, DAG instruction selection, SMT superoptimizers, instruction scheduling, and SIMD auto-vectorization.

Chapters

00:00:00 Opening: Eight Hundred Virtual Variables, Sixteen Silicon Registers, and a Ten-Times Performance Cliff

00:04:11 Liveness Analysis and Gregory Chaitin's 1981 Reduction of Register Allocation to k-Graph Coloring

00:08:37…