An ode to livelyness analysis; SSA to registers

The piece explains liveness analysis as the first step in register allocation for Purple Garden, a language with both a register-based bytecode VM and an x86 JIT compiler. Register allocation maps the compiler’s unlimited virtual registers to the limited physical registers and stack storage available on a machine. The example function is lowered to SSA-form intermediate representation: each value is assigned once, and control-flow between blocks passes values through block parameters and terminators rather than phi nodes. Annotating this IR with each value’s first and last use shows which values may share storage because their lifetimes do not overlap.

The implementation represents each value’s lifetime as a pair of positions in a linearized function. It walks blocks, records terminator uses, scans instructions backward to observe their uses and definitions, then records block parameters. Helper functions enumerate definitions and every operand used by each instruction or terminator, including branch conditions and values passed along control-flow edges. The Rust code reuses an output vector and assigns positions based on block parameters, instructions, and terminators. The remaining sections describe connecting this analysis to bytecode register allocation, including preparation and instruction lowering, and point toward using it for the JIT as well. The emphasis is on a compact, practical implementation and on making lifetime information visible enough to support and inspect allocation decisions.