sketch_tuple.nx

sketch_tuple.nx -- Tuple sketch (Theta + per-hash auxiliary data). Extends the Theta sketch family by attaching a SCALAR value to each hash slot. Use cases (matching DataSketches Tuple docs): - sum-of-revenue across distinct users (one (hash, revenue) per user) - max-recency across distinct items - count-of-events-per-distinct-user Multiple inserts of the same hash combine via a CALLER-CHOSEN reducer: NX_TUPLE_RED_SUM — add (default for revenue / counts) NX_TUPLE_RED_MAX — keep larger (for recency / peak) NX_TUPLE_RED_MIN — keep smaller (for first-seen / earliest) NX_TUPLE_RED_REPLACE— overwrite (last-write-wins) THETA + AGGREGATE ESTIMATOR: E[sum_over_set] ≈ (sum_over_sample) * HASH_MAX / theta where the sum_over_sample is over the values < theta currently stored. Theta-corrected like Theta cardinality estimator. MERGE (capability beyond DataSketches Tuple-merge spec): - theta_out = min(theta_a, theta_b) - hashes_out = K smallest across union, filtered to < theta_out - value_out for each surviving hash = reducer(a.val, b.val) if both have it, else whichever side had it.