# 8.23. Quantile Digest Functions

Presto implements the approx_percentile function with the quantile digest data structure. The underlying data structure, qdigest, is exposed as a data type in Presto, 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 presto 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 qdigests 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.

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.

scale_qdigest(qdigest(T), scale_factor) -> qdigest(T)

Returns a qdigest whose distribution has been scaled by a factor specified by scale_factor.

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.