Generating fast sparse matrix vector multiplication from a high level generic functional IR

Usage of high-level intermediate representations promises the generation of fast code from a high-level description, improving the productivity of developers while achieving the performance traditionally only reached with low-level programming approaches. High-level IRs come in two flavors: 1) domain-specific IRs designed to express only for a specific application area; or 2) generic high-level IRs that can be used to generate high-performance code across many domains. Developing generic IRs is more challenging but offers the advantage of reusing a common compiler infrastructure various applications. In this paper, we extend a generic high-level IR to enable efficient computation with sparse data structures. Crucially, we encode sparse representation using reusable dense building blocks already present in the high-level IR. We use a form of dependent types to model sparse matrices in CSR format by expressing the relationship between multiple dense arrays explicitly separately...采用高级中间表示（High-level Intermediate Representation, IR），可基于高级描述生成高效代码，在提升开发者开发效率的同时，达成传统上仅能通过低级编程手段实现的性能表现。 高级中间表示主要分为两类： 1） 领域特定型中间表示：仅针对特定应用领域设计的中间表示； 2） 通用型高级中间表示：可用于跨多领域生成高性能代码的中间表示。 开发通用型高级中间表示难度更高，但具备可复用通用编译器基础设施以适配各类应用的优势。 本文针对通用型高级中间表示进行扩展，使其可基于稀疏数据结构开展高效计算。 尤为关键的是，我们利用高级中间表示中已有的可复用稠密构建模块，对稀疏表示进行编码。 我们采用一类依赖类型，通过显式分别表述多个稠密数组间的关联关系，对压缩稀疏行格式（Compressed Sparse Row, CSR）的稀疏矩阵进行建模……