GoKawiilDeveloper uses brute-force superoptimization to simplify FPU bit-twiddling function
A developer building a floating-point library needed a function returning the lowest set bit of a float's mantissa, but the straightforward bitwise algorithm failed on powers of two, requiring a slow conditional branch. Unable to find a branch-free formula by hand, they built a brute-force search that tests short sequences of integer operations against representative test cases, adding counterexamples when a candidate formula fails.
GoKawiil's interpretation of the reporting above, not reported fact.
The approach suggests that for small, well-defined numerical kernels, exhaustive search over short instruction sequences can outperform both manual derivation and automated compiler optimization, since compilers struggle with non-obvious algorithmic leaps. It also illustrates a practical alternative to formal verification: iterative counterexample testing rather than full correctness proofs, which could appeal to other low-level library authors facing similar branch-elimination problems.
- A branchy bit-twiddling algorithm for extracting a float's lowest set bit motivated a search for a branch-free alternative.
- The author built a brute-force tool to enumerate short instruction sequences and test them against sample cases rather than proving correctness formally.
- The method relies on iteratively adding counterexamples when a discovered formula fails, rather than exhaustive formal verification.
Source: purplesyringa.moe, 2026-10-16
Published there as: “Superoptimizing an FPU Emulator”
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