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About this paper
David Monniaux
A detailed analysis of floating-point computations in real-world systems demonstrates their complex and often non-deterministic behavior, highlighting how factors like hardware, compilers, and libraries challenge assumptions about IEEE 754 compliance and complicate program verification.
Key insights
- "IEEE 754 compliance" at the hardware level does not guarantee deterministic or reproducible program behavior due to interactions with compilers, libraries, and runtime environments.
- The Intel x87 FPU's extended 80-bit precision registers are a primary source of non-determinism, as temporary value spilling to memory can alter computation results.
- Optimizing compilers frequently apply algebraic transformations (e.g., associativity) that are mathematically unsound for floating-point numbers, sometimes ignoring C99 standard pragmas.
Summary by alphaXiv.
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