# Quantile Digest Functions

CannerFlow implements the `approx_percentile` function with the quantile digest data structure. The underlying data structure, `qdigest <qdigest_type>`, is exposed as a data type in CannerFlow, and can be created, queried and stored separately from `approx_percentile`.

## Data Structures#

A quantile digest is a data sketch which stores approximate percentile information. The CannerFlow 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`(qdigest) -> qdigest#

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

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

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

#### `values_at_quantiles`(qdigest(T), quantiles) -> 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`(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.