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Bloom filter sizing: bit formula divides by ln 2 instead of its square · case 03

Filters are sized far smaller than required for the requested false-positive rate.

Member previewVariant 3 · 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	`[6784, 5, 848, 0.041354]`	`[9787, 7, 1224, 0.010036]`	Failed

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