# 15.14. Aggregate Functions

Aggregate functions operate on a set of values to compute a single result.

Except for `count()`, `count_if()`, `max_by()`, `min_by()` and `approx_distinct()`, all of these aggregate functions ignore null values and return null for no input rows or when all values are null. For example, `sum()` returns null rather than zero and `avg()` does not include null values in the count. The `coalesce` function can be used to convert null into zero.

## General Aggregate Functions

`arbitrary`(x) → [same as input]

Returns an arbitrary non-null value of `x`, if one exists.

`array_agg`(x) → array<[same as input]>

Returns an array created from the input `x` elements.

`avg`(x) → double

Returns the average (arithmetic mean) of all input values.

`bool_and`(boolean) → boolean

Returns `TRUE` if every input value is `TRUE`, otherwise `FALSE`.

`bool_or`(boolean) → boolean

Returns `TRUE` if any input value is `TRUE`, otherwise `FALSE`.

`checksum`(x) → varbinary

Returns an order-insensitive checksum of the given values.

`count`(*) → bigint

Returns the number of input rows.

`count`(x) → bigint

Returns the number of non-null input values.

`count_if`(x) → bigint

Returns the number of `TRUE` input values. This function is equivalent to `count(CASE WHEN x THEN 1 END)`.

`every`(boolean) → boolean

This is an alias for `bool_and()`.

`geometric_mean`(x) → double

Returns the geometric mean of all input values.

`grouping`(col1, ..., colN) → integer

Returns a bit set converted to decimal, indicating which columns are present in a grouping. The function must be used in conjunction with `GROUPING SETS`, `ROLLUP`, `CUBE` or `GROUP BY` and its arguments must match exactly the columns referenced in the corresponding `GROUPING SETS`, `ROLLUP`, `CUBE` or `GROUP BY` clause.

To compute the resulting bit set for a particular row, bits are assigned to the argument columns with the rightmost column being the least significant bit. For a given grouping, a bit is set to 0 if the corresponding column is included in the grouping and to 1 otherwise. For example, consider the query below:

```SELECT origin_state, origin_zip, destination_state, sum(package_weight), grouping(origin_state, origin_zip, destination_state)
FROM shipping
GROUP BY GROUPING SETS (
(origin_state),
(origin_state, origin_zip),
(destination_state));
```
```origin_state | origin_zip | destination_state | _col3 | _col4
--------------+------------+-------------------+-------+-------
California   | NULL       | NULL              |  1397 |     3
New Jersey   | NULL       | NULL              |   225 |     3
New York     | NULL       | NULL              |     3 |     3
California   |      94131 | NULL              |    60 |     1
New Jersey   |       7081 | NULL              |   225 |     1
California   |      90210 | NULL              |  1337 |     1
New York     |      10002 | NULL              |     3 |     1
NULL         | NULL       | New Jersey        |    58 |     6
NULL         | NULL       | Connecticut       |  1562 |     6
NULL         | NULL       | Colorado          |     5 |     6
(10 rows)
```

The first grouping in the above result only includes the `origin_state` column and excludes the `origin_zip` and `destination_state` columns. The bit set constructed for that grouping is `011` where the most significant bit represents `origin_state`.

`max_by`(x, y) → [same as x]

Returns the value of `x` associated with the maximum value of `y` over all input values.

`max_by`(x, y, n) → array<[same as x]>

Returns `n` values of `x` associated with the `n` largest of all input values of `y` in descending order of `y`.

`min_by`(x, y) → [same as x]

Returns the value of `x` associated with the minimum value of `y` over all input values.

`min_by`(x, y, n) → array<[same as x]>

Returns `n` values of `x` associated with the `n` smallest of all input values of `y` in ascending order of `y`.

`max`(x) → [same as input]

Returns the maximum value of all input values.

`max`(x, n) → array<[same as x]>

Returns `n` largest values of all input values of `x`.

`min`(x) → [same as input]

Returns the minimum value of all input values.

`min`(x, n) → array<[same as x]>

Returns `n` smallest values of all input values of `x`.

`sum`(x) → [same as input]

Returns the sum of all input values.

## Bitwise Aggregate Functions

`bitwise_and_agg`(x) → bigint

Returns the bitwise AND of all input values in 2’s complement representation.

`bitwise_or_agg`(x) → bigint

Returns the bitwise OR of all input values in 2’s complement representation.

## Map Aggregate Functions

`histogram`(x) → map<K,bigint>

Returns a map containing the count of the number of times each input value occurs.

`map_agg`(key, value) → map<K,V>

Returns a map created from the input `key` / `value` pairs.

`map_union`(x<K, V>) → map<K,V>

Returns the union of all the input maps. If a key is found in multiple input maps, that key’s value in the resulting map comes from an arbitrary input map.

`multimap_agg`(key, value) → map<K,array<V>>

Returns a multimap created from the input `key` / `value` pairs. Each key can be associated with multiple values.

## Approximate Aggregate Functions

`approx_distinct`(x) → bigint

Returns the approximate number of distinct input values. This function provides an approximation of `count(DISTINCT x)`. Zero is returned if all input values are null.

This function should produce a standard error of 2.3%, which is the standard deviation of the (approximately normal) error distribution over all possible sets. It does not guarantee an upper bound on the error for any specific input set.

`approx_distinct`(x, e) → bigint

Returns the approximate number of distinct input values. This function provides an approximation of `count(DISTINCT x)`. Zero is returned if all input values are null.

This function should produce a standard error of no more than `e`, which is the standard deviation of the (approximately normal) error distribution over all possible sets. It does not guarantee an upper bound on the error for any specific input set. The current implementation of this function requires that `e` be in the range: [0.01150, 0.26000].

`approx_percentile`(x, percentage) → [same as x]

Returns the approximate percentile for all input values of `x` at the given `percentage`. The value of `percentage` must be between zero and one and must be constant for all input rows.

`approx_percentile`(x, percentages) → array<[same as x]>

Returns the approximate percentile for all input values of `x` at each of the specified percentages. Each element of the `percentages` array must be between zero and one, and the array must be constant for all input rows.

`approx_percentile`(x, w, percentage) → [same as x]

Returns the approximate weighed percentile for all input values of `x` using the per-item weight `w` at the percentage `p`. The weight must be an integer value of at least one. It is effectively a replication count for the value `x` in the percentile set. The value of `p` must be between zero and one and must be constant for all input rows.

`approx_percentile`(x, w, percentage, accuracy) → [same as x]

Returns the approximate weighed percentile for all input values of `x` using the per-item weight `w` at the percentage `p`, with a maximum rank error of `accuracy`. The weight must be an integer value of at least one. It is effectively a replication count for the value `x` in the percentile set. The value of `p` must be between zero and one and must be constant for all input rows. `accuracy` must be a value greater than zero and less than one, and it must be constant for all input rows.

`approx_percentile`(x, w, percentages) → array<[same as x]>

Returns the approximate weighed percentile for all input values of `x` using the per-item weight `w` at each of the given percentages specified in the array. The weight must be an integer value of at least one. It is effectively a replication count for the value `x` in the percentile set. Each element of the array must be between zero and one, and the array must be constant for all input rows.

`numeric_histogram`(buckets, value, weight) → map<double, double>

Computes an approximate histogram with up to `buckets` number of buckets for all `value`s with a per-item weight of `weight`. The algorithm is based loosely on:

```Yael Ben-Haim and Elad Tom-Tov, "A streaming parallel decision tree algorithm",
J. Machine Learning Research 11 (2010), pp. 849--872.
```

`buckets` must be a `bigint`. `value` and `weight` must be numeric.

`numeric_histogram`(buckets, value) → map<double, double>

Computes an approximate histogram with up to `buckets` number of buckets for all `value`s. This function is equivalent to the variant of `numeric_histogram()` that takes a `weight`, with a per-item weight of `1`.

## Statistical Aggregate Functions

`corr`(y, x) → double

Returns correlation coefficient of input values.

`covar_pop`(y, x) → double

Returns the population covariance of input values.

`covar_samp`(y, x) → double

Returns the sample covariance of input values.

`regr_intercept`(y, x) → double

Returns linear regression intercept of input values. `y` is the dependent value. `x` is the independent value.

`regr_slope`(y, x) → double

Returns linear regression slope of input values. `y` is the dependent value. `x` is the independent value.

`stddev`(x) → double

This is an alias for `stddev_samp()`.

`stddev_pop`(x) → double

Returns the population standard deviation of all input values.

`stddev_samp`(x) → double

Returns the sample standard deviation of all input values.

`variance`(x) → double

This is an alias for `var_samp()`.

`var_pop`(x) → double

Returns the population variance of all input values.

`var_samp`(x) → double

Returns the sample variance of all input values.