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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`.

#### 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\_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.

#### 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()

**`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()

**`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.