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Bloom filter sizing: probe count inverts the bits-per-item ratio · case 05

Filters use a single probe regardless of size, destroying the false-positive guarantee.

Member previewVariant 5 · 3 implementations · 10 checks per implementation

Case contract

Input {n, p}. Reject n <= 0 or p outside the open interval (0,1) with "invalid". Otherwise m = ceil(-n ln p / (ln 2)^2), k = max(1, round(m/n * ln 2)), bytes = ceil(m/8), and the predicted false-positive rate (1 - e^(-k n / m))^k rounded to 6 decimals. Return [m, k, bytes, fp].

Why this case matters

Capacity planning for a Bloom filter decides memory and probe count before any item is inserted; an undersized array silently exceeds the promised false-positive rate.

One recorded failure

Sample boundary fixture

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

Boundary fixture	Actual	Expected	Outcome
thousand items one percent	`[9921, 1, 1241, 0.099067]`	`[9921, 7, 1241, 0.010037]`	Failed

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