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Subroutines are essential building blocks in software design: users encapsulate common functionality in libraries and write applications by composing calls to subroutines. Unfortunately, performance may be lost at subroutine boundaries due to reduced locality and increased memory consumption. Operator fusion helps recover the performance lost at composition boundaries. Previous solutions fuse operators by manually rewriting code into monolithic fused subroutines, or by relying on heavy-weight compilers to generate code that performs fusion. Both approaches require a semantic understanding of the entire computation, breaking the decoupling necessary for modularity and reusability of subroutines. In this work, we attempt to identify the minimal ingredients required to fuse computations, enabling composition of subroutines without sacrificing performance or modularity. We find that, unlike previous approaches that require a semantic understanding of the computation, most opportunities for fusion require understanding only data production and consumption patterns.Exploiting this insight, we add fusion on top of black-box subroutines by proposing a lightweight enrichment of subroutine declarations to expose data-dependence patterns. We implement our approach in a system called Fern, and demonstrate Fern’s benefits by showing that it is competitive with state-of-the-art, high-performance libraries with manually fused operators, can fuse across library and domain boundaries for unforeseen workloads, and can deliver speedups of up to 5× over unfused code. 

Modern vector processors support a wide variety of instructions for fixed-point digital signal processing. These instructions support a proliferation of rounding, saturating, and type conversion modes, and are often fused combinations of more primitive operations. While these are common idioms in fixed-point signal processing, it is difficult to use these operations in portable code. It is challenging for programmers to write down portable integer arithmetic in a C-like language that corresponds exactly to one of these instructions, and even more challenging for compilers to recognize when these instructions can be used. Our system, Pitchfork, defines a portable fixed-point intermediate representation, FPIR, that captures common idioms in fixed-point code. FPIR can be used directly by programmers experienced with fixed-point, or Pitchfork can automatically lift from integer operations into FPIR using a term-rewriting system (TRS) composed of verified manual and automatically-synthesized rules. Pitchfork then lowers from FPIR into target-specific fixed-point instructions using a set of target-specific TRSs. We show that this approach improves runtime performance of portably-written fixed-point signal processing code in Halide, across a range of benchmarks, by geomean 1.31× on x86 with AVX2, 1.82× on ARM Neon, and 2.44× on Hexagon HVX compared to a standard LLVM-based compiler flow, while maintaining or improving existing compile times.