Tenspiler: A Verified Lifting-Based Compiler for Translating Sequential Programs to Tensor Operations

Core Concepts

Tenspiler is a verified lifting-based compiler that uses program synthesis to translate sequential programs written in general-purpose programming languages into tensor operations, enabling developers to leverage powerful tensor processing infrastructures while preserving their current programming paradigm.

Abstract

Tenspiler is a verified lifting-based compiler that translates sequential programs written in general-purpose programming languages (e.g., C++ or Python) into tensor operations. It uses program synthesis to lift the input code into an intermediate representation called Tensir, which expresses tensor operations in a simple yet expressive way. Tensir enables efficient lifting, verification, and code generation.
The key aspects of Tenspiler's approach are:

Synthesis Phase: Tenspiler formulates the translation process as a syntax-guided synthesis problem, where it searches for a program expressed using Tensir operators that is semantically equivalent to the input code.

Verification Phase: Tenspiler uses a theorem prover to verify the functional equivalence of the synthesized Tensir program and the input code for all possible program states.

Code Generation: Tenspiler then translates the verified Tensir program into the concrete syntax of the target tensor processing DSL (e.g., NumPy, TensorFlow, PyTorch, MLX) using simple pattern-matching rules.

Tenspiler has been designed to be flexible and extensible. The Tensir IR is carefully crafted to capture the common tensor operations across various software frameworks and hardware accelerators, enabling Tenspiler to support a broad spectrum of tensor processing environments. Tenspiler also employs several optimization techniques, such as restricting the search space and leveraging expression trees, to make the synthesis process scalable.
Tenspiler has been evaluated on 10 real-world benchmark suites, including image processing kernels, deep learning models, and signal processing functions. The experimental results show that by translating the code to be executed on 6 different software frameworks and hardware devices, Tenspiler offers on average 105× kernel and 9.65× end-to-end execution time improvement over the fully-optimized sequential implementation of the same benchmarks.

Stats

The original sequential C++ programs compiled with gcc -O3 are on average 105x slower in kernel execution time and 9.65x slower in end-to-end execution time compared to the versions translated by Tenspiler and executed on various tensor processing software frameworks and hardware accelerators.

Quotes

"Tenspiler uses verified lifting [12] (VL), a technique using inductive program synthesis to infer provably equivalent program summaries expressed using a user-defined intermediate representation (IR), and generate executable code from the synthesized summary to the target DSL."
"Tensir is a small language based on tensor algebra that includes commonly used vector and matrix operations."
"Tenspiler formulates code translation as a search for a program expressed in Tensir that is provably semantic-equivalent to the input."

Key Insights Distilled From

Tenspiler: A Verified Lifting-Based Compiler for Tensor Operations

by Jie Qiu,Coli... at arxiv.org 04-30-2024

https://arxiv.org/pdf/2404.18249.pdf

Deeper Inquiries

How can Tenspiler be extended to support new tensor operations or target DSLs beyond the ones currently supported

Tenspiler can be extended to support new tensor operations or target DSLs beyond the ones currently supported by following a few key steps. Firstly, to add support for new tensor operations, the Tensir intermediate representation can be expanded by defining new operators that represent the functionalities of the desired tensor operations. These new operators should be carefully designed to align with the existing Tensir structure and maintain consistency in terms of syntax and semantics. Additionally, the grammar used in the synthesis phase can be updated to include rules for these new operators, allowing Tenspiler to generate code for the added tensor operations.
When it comes to supporting new target DSLs, the code generation phase of Tenspiler can be enhanced by incorporating translation rules specific to the syntax and features of the new DSLs. This involves defining mappings between Tensir expressions and the corresponding constructs in the new DSLs. By introducing these mappings and updating the code generation logic, Tenspiler can effectively generate executable code for the new target DSLs. Furthermore, the verification phase may need adjustments to ensure that the correctness of the translated code is maintained when targeting the new DSLs.
In summary, extending Tenspiler to support new tensor operations or target DSLs involves expanding the Tensir representation, updating the synthesis grammar, enhancing the code generation process, and adapting the verification mechanism to accommodate the additional functionalities and requirements of the new operations and DSLs.

What are the limitations of the current verification approach used in Tenspiler, and how could it be improved to handle more complex program semantics

The current verification approach used in Tenspiler, which involves checking the synthesized program summaries against verification conditions (VCs) using an SMT solver, has certain limitations that could be addressed for handling more complex program semantics. One limitation is the reliance on bounded synthesis, which restricts the verification to a finite set of program states. This limitation can be addressed by exploring techniques for unbounded synthesis, allowing for the verification of correctness across all possible program states.
Another limitation is the need for manually defined axioms to aid in the verification of certain operators in Tensir. To improve this aspect, automated methods for generating these axioms based on the semantics of the operators can be developed. By automating the axiom generation process, the verification phase can be made more robust and adaptable to a wider range of operators and program structures.
Furthermore, the verification process could benefit from enhanced support for reasoning about floating-point operations, as the current focus on integers and reals may not cover all scenarios, especially in domains where floating-point computations are prevalent. By expanding the verification capabilities to include floating-point arithmetic, Tenspiler can handle a broader range of program semantics and ensure the correctness of translated code in diverse contexts.

Could the techniques used in Tenspiler be applied to other domains beyond tensor processing, such as general-purpose program translation or optimization

The techniques used in Tenspiler, such as program synthesis, verified lifting, and code transpilation, can indeed be applied to other domains beyond tensor processing, such as general-purpose program translation or optimization. By adapting the Tenspiler framework to different programming paradigms and languages, it can serve as a versatile tool for automatically translating code written in one language or framework to another, optimizing it for performance and correctness in the process.
For general-purpose program translation, Tenspiler can be modified to support a wider range of programming languages and paradigms by adjusting the Tensir representation, synthesis algorithms, and code generation rules to accommodate the specific features and requirements of the target languages. This flexibility allows Tenspiler to be applied to various domains, including image processing, signal processing, machine learning, and more.
In terms of optimization, the techniques employed in Tenspiler can be leveraged to enhance the efficiency and performance of code in different contexts. By fine-tuning the synthesis process, optimizing the generated code, and verifying the correctness of translations, Tenspiler can be a valuable tool for automating program optimization tasks in diverse application areas. Overall, the principles and methodologies of Tenspiler can be adapted and extended to address a wide range of program translation and optimization challenges beyond tensor processing.