Towards Semantics Lifting for Scientific Computing: A Case Study on FFT

TL;DR

This paper presents a semantics lifting approach using symbolic execution and theorem proving to verify the correctness of LLM-generated scientific kernels, demonstrated on FFT code.

Contribution

It introduces a stepwise semantics lifting method with an extended SPIRAL framework for verifying code correctness from LLM outputs.

Findings

Successfully lifted GPT-generated FFT code to high-level specifications.

Demonstrated feasibility of semantics lifting for scientific computing kernels.

Provides a structured verification pathway for automated code generation tools.

Abstract

The rise of automated code generation tools, such as large language models (LLMs), has introduced new challenges in ensuring the correctness and efficiency of scientific software, particularly in complex kernels, where numerical stability, domain-specific optimizations, and precise floating-point arithmetic are critical. We propose a stepwise semantics lifting approach using an extended SPIRAL framework with symbolic execution and theorem proving to statically derive high-level code semantics from LLM-generated kernels. This method establishes a structured path for verifying the source code's correctness via a step-by-step lifting procedure to high-level specification. We conducted preliminary tests on the feasibility of this approach by successfully lifting GPT-generated fast Fourier transform code to high-level specifications.