Trino implements the approx_distinct function using the HyperLogLog data structure.

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Data structures

Trino implements HyperLogLog data sketches as a set of 32-bit buckets which store a maximum hash. They can be stored sparsely (as a map from bucket ID to bucket), or densely (as a contiguous memory block). The HyperLogLog data structure starts as the sparse representation, switching to dense when it is more efficient. The P4HyperLogLog structure is initialized densely and remains dense for its lifetime. HyperLogLog implicitly casts to P4HyperLogLog, while one can explicitly cast HyperLogLog to P4HyperLogLog: 
cast(hll AS P4HyperLogLog)

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Serialization

Data sketches can be serialized to and deserialized from varbinary. This allows them to be stored for later use. Combined with the ability to merge multiple sketches, this allows one to calculate approx_distinct of the elements of a partition of a query, then for the entirety of a query with very little cost. For example, calculating the HyperLogLog for daily unique users will allow weekly or monthly unique users to be calculated incrementally by combining the dailies. This is similar to computing weekly revenue by summing daily revenue. Uses of approx_distinct with GROUPING SETS can be converted to use HyperLogLog. Examples: 
CREATE TABLE visit_summaries (
  visit_date date,
  hll varbinary
);

INSERT INTO visit_summaries
SELECT visit_date, cast(approx_set(user_id) AS varbinary)
FROM user_visits
GROUP BY visit_date;

SELECT cardinality(merge(cast(hll AS HyperLogLog))) AS weekly_unique_users
FROM visit_summaries
WHERE visit_date >= current_date - interval '7' day;

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Functions

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approx_set

  approx_set(x) -> HyperLogLog
Returns the HyperLogLog sketch of the input data set of x. This data sketch underlies approx_distinct and can be stored and used later by calling cardinality().

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cardinality

cardinality(hll) -> bigint
This will perform approx_distinct on the data summarized by the hll HyperLogLog data sketch.

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empty_approx_set

empty_approx_set() -> HyperLogLog
Returns an empty HyperLogLog.

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merge

merge(HyperLogLog) -> HyperLogLog
Returns the HyperLogLog of the aggregate union of the individual hll HyperLogLog structures.