User-schedulable languages (USLs) help programmers productively optimize programs by providing safe means of transforming them. Current USLs are designed to give programmers exactly the control they want, while automating all other concerns. However, there is no universal answer for what performance-conscious programmers want to control, how they want to control it, and what they want to automate, even in relatively narrow domains. We claim that USLs should, instead, be designed to grow. We present Exo 2, a scheduling language that enables users to define new scheduling operations externally to the compiler. By composing a set of trusted, fine-grained primitives, users can safely write their own scheduling library to build up desired automation. We identify actions (ways of modifying code), inspection (ways of interrogating code), and references (ways of pointing to code) as essential for any user-extensible USL. We fuse these ideas into a new mechanism called Cursors that enables the creation of scheduling libraries in user code. We demonstrate libraries that amortize scheduling effort across more than 80 high-performance kernels, reducing total scheduling code by an order of magnitude and delivering performance competitive with state-of-the-art implementations on three different platforms.

The proliferation of RISC-V platforms and their use in a wide variety of scientific applications, including deep learning scenarios, has dramatically increased the interest to generate optimized code for them. In the field of HPC (High Performance Computing), the RISCV ISA (Instruction Set Architecture) has been adopted by a wide variety of designs with different micro-architecture; as a result, performance portability of existing codes is a major endeavor. Code generators and compilers such as Apache TVM, MLIR, or EXO provide a hardware abstraction for implementing optimized hardware-aware codes, thus reducing development time and potential errors. These generators can handle the full software stack, from basic micro-kernels to complex operations. In this work, we focus on the optimization of GEMM (general matrix-matrix multiplication), a key operation on top of which dense linear algebra libraries and deep learning frameworks are built. Specifically, we present an EXO-based GEMM microkernel generator for the RISC-V ISA with RVV vector extensions that addresses the lack of high-performance and portable GEMM micro-kernels. Our results demonstrate that, by generating a wide range of micro-kernels, one can obtain GEMM realizations that outperform those in the state-of-the-art high performance libraries.

The optimization of the matrix multiplication (or GEMM) has been a need during the last decades. This operation is considered the flagship of current linear algebra libraries such as BLIS, OpenBLAS, or Intel OneAPI because of its widespread use in a large variety of scientific applications. The GEMM is usually implemented following the GotoBLAS philosophy, which tiles the GEMM operands and uses a series of nested loops for performance improvement. These approaches extract the maximum computational power of the architectures through small pieces of hardware-oriented, high-performance code called micro-kernel. However, this approach forces developers to generate, with a nonnegligible effort, a dedicated micro-kernel for each new hardware. In this work, we present a step-by-step procedure for generating micro-kernels with the Exo compiler that perform close to (or even better than) manually developed microkernels written with intrinsic functions or assembly language. Our solution also improves the portability of the generated code, since a hardware target is fully specified by a concise library-based description of its instructions.

Programming low-level controls for knitting machines is a meticulous, time-consuming task that demands specialized expertise. Recently, there has been a shift towards automatically generating low-level knitting machine programs from high-level knit representations that describe knit objects in a more intuitive, user-friendly way. Current high-level systems trade off expressivity for ease-of-use, requiring ad-hoc trapdoors to access the full space of machine capabilities, or eschewing completeness in the name of utility. Thus, advanced techniques either require ad-hoc extensions from domain experts, or are entirely unsupported. Furthermore, errors may emerge during the compilation from knit object representations to machine instructions. While the generated program may describe a valid machine control sequence, the fabricated object is topologically different from the specified input, with little recourse for understanding and fixing the issue. To address these limitations, we introduce instruction graphs , an intermediate representation capable of capturing the full range of machine knitting programs. We define a semantic mapping from instruction graphs to fenced tangles, which make them compatible with the established formal semantics for machine knitting instructions. We establish a semantics-preserving bijection between machine knittable instruction graphs and knit programs that proves three properties - upward, forward, and ordered (UFO) - are both necessary and sufficient to ensure the existence of a machine knitting program that can fabricate the fenced tangle denoted by the graph. As a proof-of-concept, we implement an instruction graph editor and compiler that allows a user to transform an instruction graph into UFO presentation and then compile it to a machine program, all while maintaining semantic equivalence. In addition, we use the UFO properties to more precisely characterize the limitations of existing compilers. This work lays the groundwork for more expressive and reliable automated knitting machine programming systems by providing a formal characterization of machine knittability.

Machine knitting is a well-established fabrication technique for complex soft objects, and both companies and researchers have developed tools for generating machine knitting patterns. However, existing representations for machine knitted objects are incomplete (do not cover the complete domain of machine knittable objects) or overly specific (do not account for symmetries and equivalences among knitting instruction sequences). This makes it difficult to define correctness in machine knitting, let alone verify the correctness of a given program or program transformation. The major contribution of this work is a formal semantics for knitout, a low-level Domain Specific Language for knitting machines. We accomplish this by using what we call the fenced tangle , which extends concepts from knot theory to allow for a mathematical definition of knitting program equivalence that matches the intuition behind knit objects. Finally, using this formal representation, we prove the correctness of a sequence of rewrite rules; and demonstrate how these rewrite rules can form the foundation for higher-level tasks such as compiling a program for a specific machine and optimizing for time/reliability, all while provably generating the same knit object under our proposed semantics. By establishing formal definitions of correctness, this work provides a strong foundation for compiling and optimizing knit programs.

High-performance kernel libraries are critical to exploiting accelerators and specialized instructions in many applications. Because compilers are difficult to extend to support diverse and rapidly-evolving hardware targets, and automatic optimization is often insufficient to guarantee state-of-the-art performance, these libraries are commonly still coded and optimized by hand, at great expense, in low-level C and assembly. To better support development of high-performance libraries for specialized hardware, we propose a new programming language, Exo, based on the principle of exocompilation: externalizing target-specific code generation support and optimization policies to user-level code. Exo allows custom hardware instructions, specialized memories, and accelerator configuration state to be defined in user libraries. It builds on the idea of user scheduling to externalize hardware mapping and optimization decisions. Schedules are defined as composable rewrites within the language, and we develop a set of effect analyses which guarantee program equivalence and memory safety through these transformations. We show that Exo enables rapid development of state-of-the-art matrix-matrix multiply and convolutional neural network kernels, for both an embedded neural accelerator and x86 with AVX-512 extensions, in a few dozen lines of code each.

Writing high-performance image processing code is challenging and labor-intensive. To address this, we propose a programming support method called “guided optimization.” Guided optimization provides programmers a set of valid optimization options and interactive feedback about their current choices, which enables them to comprehend and efficiently optimize image processing code without the time-consuming trial-and-error process of traditional text editors. We implemented a proof-of-concept system, Roly-poly, which integrates guided optimization, program visualization, and schedule cost estimation to support the comprehension and development of efficient image processing code. We conducted a user study with novice Halide programmers and confirmed that Roly-poly and its guided optimization was informative, increased productivity, and resulted in higher-performing schedules in less time.