> ## Documentation Index
> Fetch the complete documentation index at: https://docs.dune.com/llms.txt
> Use this file to discover all available pages before exploring further.

# HyperLogLog functions

Trino implements the [`approx_distinct`](/query-engine/Functions-and-operators/aggregate#approximate-aggregate-functions) function using the [HyperLogLog](https://en.wikipedia.org/wiki/HyperLogLog) data structure.

### 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_type` implicitly casts to
`p4hyperloglog_type`, while one can
explicitly cast `HyperLogLog` to `P4HyperLogLog`:

```text theme={null}
    cast(hll AS P4HyperLogLog)
```

### 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:

```sql theme={null}
  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;
```

### Functions

#### 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()`.

#### cardinality()

**`cardinality(hll)`** → bigint

This will perform `approx_distinct` on
the data summarized by the `hll` HyperLogLog data sketch.

#### empty\_hll()

**`empty_hll()`** → HyperLogLog

Returns an empty `HyperLogLog`.

#### merge()

**`merge(hyperloglog)`** → HyperLogLog
Returns the `HyperLogLog` of the aggregate union of the individual `hll`
HyperLogLog structures.