Why architecture matters here

HLL failures come from wrong precision + confusion about accuracy at small cardinalities. Architecture matters because register width + merge shape guarantees.

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The architecture: every piece explained

The top strip is the algorithm. Element x. Bucket b. Leading zeros. Register M[b].

The middle row is guarantees. Estimate. Error bound. Merge. Sparse to dense.

The lower rows are practice. Use cases. Variants. Ops — precision + rollups + correlation.

HyperLogLog — cardinality estimation + registers + accuracy + mergescount distinct with tiny memoryElement xhash to bitsBucket btop bitsLeading zerosin remaining bitsRegister M[b]max leading zerosEstimateharmonic mean of MError bound~1.04/sqrt(m)Merge two HLLselementwise maxSparse to denseadaptiveUse casesunique users / IPs / clicksVariantsHLL++ + tuned biasOps — precision choice + rollups + correlationaverageknowcombineadaptapplyimproveimproveoperateoperate
HyperLogLog cardinality estimation + merge.
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End-to-end flow

End-to-end: analytics job counts unique users. Each event hashes → bucket + leading zeros. Per-shard HLL sketches produced; central HLL merges them elementwise. Estimate cardinality with ~1% error at 8KB memory. HLL++ variant fixes small-cardinality bias.