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# Quantile digest functions

## Data structures

A quantile digest is a data sketch which stores approximate percentile
information.  The Trino type for this data structure is called `qdigest`,
and it takes a parameter which must be one of `bigint`, `double` or
`real` which represent the set of numbers that may be ingested by the
`qdigest`.  They may be merged without losing precision, and for storage
and retrieval they may be cast to/from `VARBINARY`.

## Functions

### merge

```
merge(qdigest) -> qdigest
```

Merges all input `qdigest`s into a single `qdigest`.

### value\_at\_quantile

```
value_at_quantile(qdigest(T), quantile) -> T
```

Returns the approximate percentile value from the quantile digest given
the number `quantile` between 0 and 1.

### quantile\_at\_value

```
quantile_at_value(qdigest(T), T) -> quantile
```

Returns the approximate `quantile` number between 0 and 1 from the
quantile digest given an input value. Null is returned if the quantile digest
is empty or the input value is outside of the range of the quantile digest.

### values\_at\_quantiles

```
values_at_quantiles(qdigest(T), quantiles) -> array(T)
```

Returns the approximate percentile values as an array given the input
quantile digest and array of values between 0 and 1 which
represent the quantiles to return.

### qdigest\_agg

```
qdigest_agg(x) -> qdigest([same as x])
```

Returns the `qdigest` which is composed of  all input values of `x`.

```
qdigest_agg(x, w) -> qdigest([same as x])
```

Returns the `qdigest` which is composed of  all input values of `x` using
the per-item weight `w`.

```
qdigest_agg(x, w, accuracy) -> qdigest([same as x])
```

Returns the `qdigest` which is composed of  all input values of `x` using
the per-item weight `w` and maximum error of `accuracy`. `accuracy`
must be a value greater than zero and less than one, and it must be constant
for all input rows.