Register allocation (mapping variables to processor registers or memory) and instruction scheduling (reordering instructions to increase instruction-level parallelism) are essential tasks for generating efficient assembly code in a compiler. In the last three decades, combinatorial optimization has emerged as an alternative to traditional, heuristic algorithms for these two tasks. Combinatorial optimization approaches can deliver optimal solutions according to a model, can precisely capture trade-offs between conflicting decisions, and are more flexible at the expense of increased compilation time.

This paper provides an exhaustive literature review and a classification of combinatorial optimization approaches to register allocation and instruction scheduling, with a focus on the techniques that are most applied in this context: integer programming, constraint programming, partitioned Boolean quadratic programming, and enumeration. Researchers in compilers and combinatorial optimization can benefit from identifying developments, trends, and challenges in the area; compiler practitioners may discern opportunities and grasp the potential benefit of applying combinatorial optimization.

This paper introduces a constraint model and solving techniques for code generation in a compiler back-end. It contributes a new model for global register allocation that combines several advanced aspects: multiple register banks (subsuming spilling to memory), coalescing, and packing. The model is extended to include instruction scheduling and bundling. The paper introduces a decomposition scheme exploiting the underlying program structure and exhibiting robust behavior for functions with thousands of instructions. Evaluation shows that code quality is on par with LLVM, a state-of-the-art compiler infrastructure.

The paper makes important contributions to the applicability of constraint programming as well as compiler construction: essential concepts are unified in a high-level model that can be solved by readily available modern solvers. This is a significant step towards basing code generation entirely on a high-level model and by this facilitates the construction of correct, simple, flexible, robust, and high-quality code generators.

This paper presents a novel combinatorial model that integrates global register allocation based on ultimate coalescing, spill code optimization, register packing, and multiple register banks with instruction scheduling (including VLIW). The model exploits alternative temporaries that hold the same value as a new concept for ultimate coalescing and spill code optimization. The paper presents Unison as a code generator based on the model and advanced solving techniques using constraint programming. Thorough experiments using MediaBench and a processor (Hexagon) that are typical for embedded systems demonstrate that Unison: is robust and scalable; generates faster code than LLVM (up to 4 1 % with a mean improvement of 7 %); possibly generates optimal code (for 2 9 % of the experiments); effortlessly supports different optimization criteria (code size on par with LLVM). Unison is significant as it addresses the same aspects as traditional code generation algorithms, yet is based on a simple integrated model and robustly can generate optimal code.

This paper introduces a combinatorial optimization approach to register allocation and instruction scheduling, two central compiler problems. Combinatorial optimization has the potential to solve these problems optimally and to exploit processor-specific features readily. Our approach is the first to leverage this potential in practice: it captures the complete set of program transformations used in state-of-the-art compilers, scales to medium-sized functions of up to 1000 instructions, and generates executable code. This level of practicality is reached by using constraint programming, a particularly suitable combinatorial optimization technique. Unison, the implementation of our approach, is open source, used in industry, and integrated with the LLVM toolchain.

An extensive evaluation of estimated speed, code size, and scalability confirms that Unison generates better code than LLVM while scaling to medium-sized functions. The evaluation uses systematically selected benchmarks from MediaBench and SPEC CPU2006 and different processor architectures (Hexagon, ARM, MIPS). Mean estimated speedup ranges from 1% to 9.3% and mean code size reduction ranges from 0.8% to 3.9% for the different architectures. Executing the generated code on Hexagon confirms that the estimated speedup indeed results in actual speedup. Given a fixed time limit, Unison solves optimally functions of up to 647 instructions, delivers improved solutions for functions of up to 874 instructions, and achieves more than 85% of the potential speed for 90% of the functions on Hexagon.

The results in this paper show that our combinatorial approach can be used in practice to trade compilation time for code quality beyond the usual compiler optimization levels, fully exploit processor-specific features, and identify improvement opportunities in existing heuristic algorithms.

This paper describes Unison, a simple, flexible, and potentially optimal software tool that performs register allocation and instruction scheduling in integration using combinatorial optimization. The tool can be used as an alternative or as a complement to traditional approaches, which are fast but complex and suboptimal. Unison is most suitable whenever high-quality code is required and longer compilation times can be tolerated (such as in embedded systems or library releases), or the targeted processors are so irregular that traditional compilers fail to generate satisfactory code.