We describe LEGO, a new approach to optimizing data movement whereby code is expressed as a layout-independent computation and composed with layouts for data and computation. This code generator organization derives complex indexing expressions associated with hierarchical parallel code and data movement for GPUs. LEGO maps from layout specification to indexing expressions, and can be integrated into existing compilers and code templates. It facilitates the explo-ration of data layouts in combination with other optimizations. We demonstrate LEGO’s integration with the Triton and MLIR compilers, and with CUDA templates. We show that LEGO is capable of deriving performance competitive with Triton, and shows broad applicability for data and thread layout mapping optimizations in its integration with CUDA and MLIR.

Scheduling languages express to a compiler—or equivalently, a code generator—a sequence of optimizations to apply. Performance tools that support a scheduling language interface allow exploration of optimizations, i.e., exploratory compilers . While scheduling languages have become a common feature of tools for experts, the proliferation of these languages without unifying common features may be confusing to users. Moreover, we recognize a need to organize the compiler developer community around common exploratory compiler infrastructure, and future advances to address, for example, data layout and data movement. To support a broader set of users may require raising the level of abstraction. This article provides a chronology of scheduling languages, discussing their origins in iterative compilation and autotuning, noting the common features that are used in existing frameworks, and calling for changes to increase their utility and portability.