Towards Optimized Arithmetic Circuits with MLIR
Résumé
Numerical programs are typically conceived with real numbers in mind. However, programming languages operate at a lower abstraction level with fixed-width machine arithmetic. This abstraction gap limits the scope of legal arithmetic optimizations in compilers, in particular when targetting hardware.
This work introduces a set of MLIR dialects that explicitly separate concerns between real-valued computation and low-level arithmetic representation. The RealArith dialect captures mathematical intent, enabling algebraic rewrites and approximationaware transformations. The FixedPointArith dialect expresses quantized arithmetic with fine-grained control over bit widths. This separation enables arithmetic optimizations beyond those supported by conventional compilers. An example end-to-end lowering flow performs polynomial approximation, then generates fixed-point Horner-form architectures tailored for hardware synthesis. Early hardware results on signal processing benchmarks demonstrate the potential of this approach.
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