FA-324 / Floating-point arithmetic / Member archive

Large cancelling terms erase a small summand · case 04

A mathematically nonzero residual disappears when large positive and negative terms cancel.

Member previewVariant 4 · 3 implementations · 7 checks per implementation

Case contract

Sum a finite sequence of finite binary floating-point values using math.fsum semantics. These bounded fixtures have exactly representable expected residuals and do not overflow the final result.

Why this case matters

Mixed-sign measurements with a large dynamic range can expose weaknesses that positive-only sums do not. The experiment compares ordinary accumulation, Kahan accumulation, and standard-library accurate summation.

One recorded failure

Sample boundary fixture

This sample comes from the broken implementation of a controlled reproducer.

Boundary fixture	Actual	Expected	Outcome
small residual between cancelling large terms	`4.0`	`4.125`	Failed

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This record includes three runnable implementations, regression fixtures, execution results, and source hashes.

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