Modern parallel hardware promises unprecedented performance, for the gifted few experts who can program it correctly. Code generators from high-level languages provide an attractive alternative, promising to deliver high performance automatically. Existing projects such as Accelerate, Futhark, Halide, or Lift show that this approach is feasible. Unfortunately, existing efforts focus on computations over tensors: regularly shaped higher dimensional arrays. This limits the expressiveness of these approaches and excludes many interesting data structures that are commonly encoded manually in memory, such as trees or triangular matrices.This paper presents an extended array type that lifts this restriction. For multidimensional arrays, the size of a nested array might depend on its position in the surrounding arrays, which enables the expression of computations over less regularly shaped data structures. However, these positiondependent arrays bring new challenges for high-performance code generation, as determining the position of the elements in memory becomes more challenging.This paper shows how these challenges are addressed by extending the existing Lift type system and compiler. The experimental results show that this approach enables the efficient code generation of triangular matrix-vector multiplication, with performance improvements over cuBLAS on an Nvidia GPU by up to 2×. Furthermore, we show a use case for a low-level optimization for avoiding unnecessary out-ofbound checks in stencils, leading to up to 3× improvements over already optimized generated stencil codes.

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 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 across 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 storing the length of rows, the column indices, and the non-zero values of the matrix.We achieve high-performance compared to sparse lowlevel library code using our extended generic high-level code generator. On an Nvidia GPU, we outperform the highly tuned Nvidia cuSparse implementation of SpMV (Sparsematrix vector multiplication) multiplication across 28 sparse matrices of varying sparsity on average by 1.7×.• Software and its engineering → Parallel programming languages; Compilers.

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