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Racer: Hunting GPU Kernel Bugs with Symbolic Equivalence Checking

Vu Tuan Truong, Cheng Tan · 2026 · arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.28429 · cited by 0 works (OpenAlex) · open-access PDF

Chinese

每一个重写都必须保留由它取代的实现计算的函数,今天,这种义务几乎完全取决于差异测试:运行新的内核和随机采样的紧张器的可信参考,然后在一个宽度内比较它们的输出。这种方法有额外的测试案例无法消除的盲点。例如,一个逻辑错误可能产生一个错误,小于对应正确的优化内核所需的宽度。我们提出了象征性等同性检查,它执行一个内核和它的象征性输入参考,将每个细胞输出转化为一个准确的算法表达,然后检查以前的符号是否一致表达在所有bugputs中。 因为这些符号检查器的确切值是41号,因此(2)在生产中确切检查预定值(3)与C

Machine translation (Meta M2M100); the English original follows.

Abstract

GPU kernels are critical to the performance of today's AI services, yet the same operators are rewritten repeatedly: for each GPU generation, numeric format, serving regime, and kernel language. Every rewrite must preserve the function computed by the implementation it replaces. Today, this obligation depends almost entirely on differential testing: run the new kernel and a trusted reference on randomly sampled tensors, then compare their outputs within a tolerance. This approach has blind spots that additional test cases cannot eliminate. For example, a logical bug may produce an error smaller than the tolerance required to accommodate a correct optimized kernel. We propose symbolic equivalence checking, which executes a kernel and its reference on symbolic inputs, turning each output cell into an exact algebraic expression, and then checks whether the paired expressions agree for all inputs. Because these expressions are exact, symbolic equivalence checking distinguishes floating-point error from logical bugs, while a single check covers the entire input space. We implement Racer, a PTX-level symbolic equivalence checking engine, with three techniques that make this approach practical for production kernels: (1) Shape Reduction to control checking cost, (2) a lockstep CTA scheduler to handle concurrency, and (3) idiom templates with exact numeric refutation for otherwise inconclusive results. Across 2,408 production kernels from 41 collection targets, Racer found 82 real bugs in 23 libraries, including 76 previously unknown bugs and 41 confirmed so far.

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Topics: Symbolic trajectory evaluation, Computer science, Symbolic execution, Equivalence (formal languages), Model checking, Kernel (algebra)

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