t-digest extension

make installcheck

This PostgreSQL extension implements t-digest, a data structure for on-line accumulation of rank-based statistics such as quantiles and trimmed means. The algorithm is also very friendly to parallel programs.

The t-digest data structure was introduced by Ted Dunning in 2013, and more detailed description and example implementation is available in his github repository [1]. In particular, see the paper [2] explaining the idea. Some of the code was inspired by tdigestc [3] and tdigest [4] by ajwerner.

The accuracy of estimates produced by t-digests can be orders of magnitude more accurate than those produced by previous digest algorithms in spite of the fact that t-digests are much more compact when stored on disk.

Basic usage

For the basic use case the extension provides four aggregate functions. The tdigest_percentile ones can be seen as a replacement of the percentile_cont aggregate, while the tdigest_percentile_of ones perform the inverse operation (they answer what fraction of the data is below a given value):

  • tdigest_percentile(value double precision, compression int, quantile double precision)

  • tdigest_percentile(value double precision, compression int, quantiles double precision[])

  • tdigest_percentile_of(value double precision, compression int, hypothetical_value double precision)

  • tdigest_percentile_of(value double precision, compression int, hypothetical_values double precision[])

That is, instead of running

SELECT percentile_cont(0.95) WITHIN GROUP (ORDER BY a) FROM t

you might now run

SELECT tdigest_percentile(a, 100, 0.95) FROM t

and similarly for the variants with array of percentiles. This should run much faster, as the t-digest does not require sort of all the data and can be parallelized. Also, the memory usage is very limited, depending on the compression parameter.

Accuracy

All functions building the t-digest summaries accept an accuracy parameter (called compression in the function signatures) that determines how detailed the histogram approximating the CDF is. The value essentially limits the number of “buckets” (centroids) in the t-digest, so the higher the value the larger the digest. The accepted range is [10, 10000], and values outside this range are rejected with an error.

Each bucket is represented by a double precision mean and a 64-bit count (i.e. 16B per bucket), so the maximum of 10000 buckets means the largest possible t-digest is ~160kB. That is however before the transparent compression all varlena types go through, so the on-disk footprint may be much smaller.

It’s hard to say what is a good accuracy value, as it very much depends on the data set (how non-uniform the data distribution is, etc.), but given a t-digest with N buckets, the error is roughly 1/N. So t-digests build with accuracy set to 100 have roughly 1% error (with respect to the total range of data), which is more than enough for most use cases.

This however ignores that t-digests don’t have uniform bucket size. Buckets close to 0.0 and 1.0 are much smaller (thus providing more accurate results) while buckets close to the median are much bigger. That’s consistent with the purpose of the t-digest, i.e. estimating percentiles close to extremes.

Advanced usage

The extension also provides a tdigest data type, which makes it possible to precompute digests for subsets of data, and then quickly combine those “partial” digest into a digest representing the whole data set. The prebuilt digests should be much smaller compared to the original data set, allowing significantly faster response times.

To compute the t-digest use tdigest aggregate function. The digests can then be stored on disk and later summarized using the tdigest_percentile functions (with tdigest as the first argument).

  • tdigest(value double precision, compression int)

  • tdigest(digest tdigest)

  • tdigest_percentile(digest tdigest, quantile double precision)

  • tdigest_percentile(digest tdigest, quantiles double precision[])

  • tdigest_percentile_of(digest tdigest, hypothetical_value double precision)

  • tdigest_percentile_of(digest tdigest, hypothetical_values double precision[])

The tdigest(digest tdigest) variant is an aggregate merging multiple pre-computed digests into a single digest, which can be stored again.

So for example you may do this:

-- table with some random source data
CREATE TABLE t (a int, b int, c double precision);

INSERT INTO t SELECT 10 * random(), 10 * random(), random()
                FROM generate_series(1,10000000);

-- table with pre-aggregated digests into table "p"
CREATE TABLE p AS SELECT a, b, tdigest(c, 100) AS d FROM t GROUP BY a, b;

-- summarize the data from "p" (compute the 95-th percentile)
SELECT a, tdigest_percentile(d, 0.95) FROM p GROUP BY a ORDER BY a;

The pre-aggregated table is indeed much smaller:

db=# \d+
                         List of relations
 Schema | Name | Type  | Owner | Persistence |  Size  | Description 
--------+------+-------+-------+-------------+--------+-------------
 public | p    | table | user  | permanent   | 120 kB | 
 public | t    | table | user  | permanent   | 422 MB | 
(2 rows)

And on my machine the last query takes ~1.5ms. Compare that to queries on the source data:

\timing on

-- exact results
SELECT a, percentile_cont(0.95) WITHIN GROUP (ORDER BY c)
  FROM t GROUP BY a ORDER BY a;
  ...
Time: 6956.566 ms (00:06.957)

-- tdigest estimate (no parallelism)
SET max_parallel_workers_per_gather = 0;
SELECT a, tdigest_percentile(c, 100, 0.95) FROM t GROUP BY a ORDER BY a;
  ...
Time: 2873.116 ms (00:02.873)

-- tdigest estimate (4 workers)
SET max_parallel_workers_per_gather = 4;
SELECT a, tdigest_percentile(c, 100, 0.95) FROM t GROUP BY a ORDER BY a;
  ...
Time: 893.538 ms

This shows how much more efficient the t-digest estimate is compared to the exact query with percentile_cont (the difference would increase for larger data sets, due to increased overhead for spilling to disk).

It also shows how effective the pre-aggregation can be. There are 121 rows in table p so with 120kB disk space that’s ~1kB per row, each representing about 80k values. With 8B per value, that’s ~640kB, i.e. a compression ratio of 640:1. As the digest size is not tied to the number of items, this will only improve for larger data set.

Pre-aggregated data

When dealing with data sets with a lot of redundancy (values repeating many times), it may be more efficient to partially pre-aggregate the data and use functions that allow specifying the number of occurrences for each value. This reduces the number of SQL-function calls.

There are seven such aggregate functions:

  • tdigest(value double precision, count bigint, compression int)

  • tdigest_percentile(value double precision, count bigint, compression int, quantile double precision)

  • tdigest_percentile(value double precision, count bigint, compression int, quantiles double precision[])

  • tdigest_percentile_of(value double precision, count bigint, compression int, hypothetical_value double precision)

  • tdigest_percentile_of(value double precision, count bigint, compression int, hypothetical_values double precision[])

  • tdigest_avg(value double precision, count bigint, compression int, low double precision, high double precision)

  • tdigest_sum(value double precision, count bigint, compression int, low double precision, high double precision)

The count has to be a positive value, and it determines how many times the value is added to the digest. See the “trimmed aggregates” section for more details about low and high parameters.

Incremental updates

An existing t-digest may be updated incrementally, either by adding a single value, or by merging-in a whole t-digest. The following examples use the table t with the pre-aggregated digests (in column d), built in the previous section.

For example, it’s possible to add 1000 random values to the t-digests like this:

DO LANGUAGE plpgsql $$
DECLARE
  r record;
BEGIN
  FOR r IN (SELECT random() AS v FROM generate_series(1,1000)) LOOP
    UPDATE t SET d = tdigest_add(d, r.v);
  END LOOP;
END $$;

The overhead of doing this is fairly high, though - the t-digest has to be deserialized and serialized over and over, for each value we’re adding. That overhead may be reduced by pre-aggregating data, either into an array or a t-digest.

DO LANGUAGE plpgsql $$
DECLARE
  vals double precision[];
BEGIN
  SELECT array_agg(random()) INTO vals FROM generate_series(1,1000);
  UPDATE t SET d = tdigest_add(d, vals);
END $$;

Alternatively, it’s possible to use pre-aggregated t-digest values instead of the arrays:

DO LANGUAGE plpgsql $$
DECLARE
  r record;
BEGIN
  FOR r IN (SELECT mod(i,3) AS a, tdigest(random(),100) AS d FROM generate_series(1,1000) s(i) GROUP BY mod(i,3)) LOOP
    UPDATE t SET d = tdigest_union(d, r.d);
  END LOOP;
END $$;

It may be undesirable to perform compaction after every incremental update (esp. when adding the values one by one). All functions in the incremental API allow disabling compaction by setting the compact parameter to false. The disadvantage is that without the compaction, the resulting digests may be somewhat larger (by a factor of 10). It’s advisable to use either the multi-value functions (with compaction after each batch) if possible, or force compaction, e.g. by re-aggregating the digest using the tdigest aggregate:

UPDATE p SET d = (SELECT tdigest(x) FROM (SELECT p.d) s(x));

Note that tdigest_add and tdigest_union simply return the other argument when one of the digests is NULL, so e.g. tdigest_union(NULL, d) does not compact the digest.

Trimmed aggregates

The extension provides aggregate functions allowing to calculate trimmed (truncated) sum and average, either directly from the values or from a pre-computed digest:

  • tdigest_sum(value double precision, compression int, low double precision, high double precision)

  • tdigest_sum(value double precision, count bigint, compression int, low double precision, high double precision)

  • tdigest_sum(digest tdigest, low double precision, high double precision)

  • tdigest_avg(value double precision, compression int, low double precision, high double precision)

  • tdigest_avg(value double precision, count bigint, compression int, low double precision, high double precision)

  • tdigest_avg(digest tdigest, low double precision, high double precision)

The low and high parameters specify where to truncate the data. They are percentiles (not values), so both have to be in [0.0, 1.0] with low <= high, otherwise an error is raised. For example low = 0.1 and high = 0.9 means the lowest and highest 10% of the values are discarded.

There are also two non-aggregate functions, calculating the trimmed sum and average for a single tdigest value:

  • tdigest_digest_sum(digest tdigest, low double precision DEFAULT 0.0, high double precision DEFAULT 1.0)

  • tdigest_digest_avg(digest tdigest, low double precision DEFAULT 0.0, high double precision DEFAULT 1.0)

The difference between tdigest_sum(digest, low, high) and tdigest_digest_sum(digest, low, high) is that the former is an aggregate (combining all the digests in a group first), while the latter is a plain function processing a single digest value (and thus may be combined with other columns without a GROUP BY clause).

Functions

The following list covers the complete SQL API. The accuracy parameter is the compression used when building the t-digest, as described in the Accuracy section.

The tdigest, tdigest_percentile, tdigest_percentile_of, tdigest_avg and tdigest_sum functions are aggregates (all of them parallel safe), while tdigest_count, tdigest_add, tdigest_union, tdigest_json, tdigest_double_array, tdigest_digest_sum and tdigest_digest_avg are plain functions operating on a single tdigest value.

The examples use a table t with the values in column c, and - for the variants with a count parameter - the number of occurrences of each value in column a. The counts have to be positive, otherwise an error is raised.

tdigest_percentile(value, accuracy, percentile)

Computes a requested percentile from the data, using a t-digest with the specified accuracy.

Synopsis

SELECT tdigest_percentile(t.c, 100, 0.95) FROM t

Parameters

  • value - values to aggregate
  • accuracy - accuracy of the t-digest
  • percentile - value in [0, 1] specifying the percentile

tdigest_percentile(value, count, accuracy, percentile)

Computes a requested percentile from the data, using a t-digest with the specified accuracy.

Synopsis

SELECT tdigest_percentile(t.c, t.a, 100, 0.95) FROM t

Parameters

  • value - values to aggregate
  • count - number of occurrences of the value
  • accuracy - accuracy of the t-digest
  • percentile - value in [0, 1] specifying the percentile

tdigest_percentile(value, accuracy, percentile[])

Computes requested percentiles from the data, using a t-digest with the specified accuracy.

Synopsis

SELECT tdigest_percentile(t.c, 100, ARRAY[0.95, 0.99]) FROM t

Parameters

  • value - values to aggregate
  • accuracy - accuracy of the t-digest
  • percentile[] - array of values in [0, 1] specifying the percentiles

tdigest_percentile(value, count, accuracy, percentile[])

Computes requested percentiles from the data, using a t-digest with the specified accuracy.

Synopsis

SELECT tdigest_percentile(t.c, t.a, 100, ARRAY[0.95, 0.99]) FROM t

Parameters

  • value - values to aggregate
  • count - number of occurrences of the value
  • accuracy - accuracy of the t-digest
  • percentile[] - array of values in [0, 1] specifying the percentiles

tdigest_percentile_of(value, accuracy, hypothetical_value)

Computes relative rank of a hypothetical value, using a t-digest with the specified accuracy.

Synopsis

SELECT tdigest_percentile_of(t.c, 100, 139832.3) FROM t

Parameters

  • value - values to aggregate
  • accuracy - accuracy of the t-digest
  • hypothetical_value - hypothetical value

tdigest_percentile_of(value, count, accuracy, hypothetical_value)

Computes relative rank of a hypothetical value, using a t-digest with the specified accuracy.

Synopsis

SELECT tdigest_percentile_of(t.c, t.a, 100, 139832.3) FROM t

Parameters

  • value - values to aggregate
  • count - number of occurrences of the value
  • accuracy - accuracy of the t-digest
  • hypothetical_value - hypothetical value

tdigest_percentile_of(value, accuracy, hypothetical_value[])

Computes relative ranks of a hypothetical values, using a t-digest with the specified accuracy.

Synopsis

SELECT tdigest_percentile_of(t.c, 100, ARRAY[6343.43, 139832.3]) FROM t

Parameters

  • value - values to aggregate
  • accuracy - accuracy of the t-digest
  • hypothetical_value - hypothetical values

tdigest_percentile_of(value, count, accuracy, hypothetical_value[])

Computes relative ranks of a hypothetical values, using a t-digest with the specified accuracy.

Synopsis

SELECT tdigest_percentile_of(t.c, t.a, 100, ARRAY[6343.43, 139832.3]) FROM t

Parameters

  • value - values to aggregate
  • count - number of occurrences of the value
  • accuracy - accuracy of the t-digest
  • hypothetical_value - hypothetical values

tdigest(value, accuracy)

Computes t-digest with the specified accuracy.

Synopsis

SELECT tdigest(t.c, 100) FROM t

Parameters

  • value - values to aggregate
  • accuracy - accuracy of the t-digest

tdigest(value, count, accuracy)

Computes t-digest with the specified accuracy. The values are added with as many occurrences as determined by the count parameter.

Synopsis

SELECT tdigest(t.c, t.a, 100) FROM t

Parameters

  • value - values to aggregate
  • count - number of occurrences for each value
  • accuracy - accuracy of the t-digest

tdigest(digest)

Merges pre-computed t-digests into a single t-digest. This is also the way to force compaction of a digest built with compact = false.

Synopsis

SELECT tdigest(d) FROM (
    SELECT tdigest(t.c, 100) AS d FROM t GROUP BY t.a
) foo

Parameters

  • digest - t-digests to merge

tdigest_count(tdigest)

Returns number of items represented by the t-digest. This is a plain function, not an aggregate.

Synopsis

SELECT tdigest_count(d) FROM (
    SELECT tdigest(t.c, 100) AS d FROM t
) foo

Parameters

  • tdigest - t-digest to inspect

tdigest_percentile(tdigest, percentile)

Computes requested percentile from the pre-computed t-digests.

Synopsis

SELECT tdigest_percentile(d, 0.99) FROM (
    SELECT tdigest(t.c, 100) AS d FROM t
) foo

Parameters

  • tdigest - t-digest to aggregate and process
  • percentile - value in [0, 1] specifying the percentile

tdigest_percentile(tdigest, percentile[])

Computes requested percentiles from the pre-computed t-digests.

Synopsis

SELECT tdigest_percentile(d, ARRAY[0.95, 0.99]) FROM (
    SELECT tdigest(t.c, 100) AS d FROM t
) foo

Parameters

  • tdigest - t-digest to aggregate and process
  • percentile - values in [0, 1] specifying the percentiles

tdigest_percentile_of(tdigest, hypothetical_value)

Computes relative rank of a hypothetical value, using a pre-computed t-digest.

Synopsis

SELECT tdigest_percentile_of(d, 349834.1) FROM (
    SELECT tdigest(t.c, 100) AS d FROM t
) foo

Parameters

  • tdigest - t-digest to aggregate and process
  • hypothetical_value - hypothetical value

tdigest_percentile_of(tdigest, hypothetical_value[])

Computes relative ranks of hypothetical values, using a pre-computed t-digest.

Synopsis

SELECT tdigest_percentile_of(d, ARRAY[438.256, 349834.1]) FROM (
    SELECT tdigest(t.c, 100) AS d FROM t
) foo

Parameters

  • tdigest - t-digest to aggregate and process
  • hypothetical_value - hypothetical values

tdigest_add(tdigest, double precision)

Performs incremental update of the t-digest by adding a single value.

Synopsis

UPDATE t SET d = tdigest_add(d, random());

Parameters

  • tdigest - t-digest to update (may be NULL)
  • element - value to add to the digest
  • compression - compression to use (required when the t-digest is NULL, ignored otherwise; default: NULL)
  • compact - force compaction (default: true)

tdigest_add(tdigest, double precision[])

Performs incremental update of the t-digest by adding values from an array.

Synopsis

UPDATE t SET d = tdigest_add(d, ARRAY[random(), random(), random()]);

Parameters

  • tdigest - t-digest to update (may be NULL)
  • elements - array of values to add to the digest
  • compression - compression to use (required when the t-digest is NULL, ignored otherwise; default: NULL)
  • compact - force compaction (default: true)

tdigest_union(tdigest, tdigest)

Performs incremental update of the t-digest by merging-in another digest. When either of the digests is NULL, the other one is returned unchanged (without compaction).

Synopsis

WITH x AS (SELECT tdigest(random(), 100) AS d FROM generate_series(1,1000))
UPDATE t SET d = tdigest_union(p.d, x.d) FROM x;

Parameters

  • digest1 - t-digest to update
  • digest2 - t-digest to merge into digest1
  • compact - force compaction (default: true)

tdigest_json(tdigest)

Returns the t-digest as a JSON value. The function is also exposed as a cast from tdigest to json.

Synopsis

SELECT tdigest_json(d) FROM (
    SELECT tdigest(t.c, 100) AS d FROM t
) foo;

SELECT CAST(d AS json) FROM (
    SELECT tdigest(t.c, 100) AS d FROM t
) foo;

Parameters

  • tdigest - t-digest to cast to a json value

tdigest_double_array(tdigest)

Returns the t-digest as a double precision[] array. The function is also exposed as a cast from tdigest to double precision[]. The array contains the flags, the total number of items, the compression and the number of centroids, followed by a (mean, count) pair for each centroid.

Synopsis

SELECT tdigest_double_array(d) FROM (
    SELECT tdigest(t.c, 100) AS d FROM t
) foo;

SELECT CAST(d AS double precision[]) FROM (
    SELECT tdigest(t.c, 100) AS d FROM t
) foo;

Parameters

  • tdigest - t-digest to cast to a double precision[] value

tdigest_avg(value, accuracy, low, high)

Computes trimmed mean of values, discarding values at the low and high end. The low and high values are percentiles in [0, 1] (with low <= high) specifying which part of the sample should be included in the mean, so e.g. low = 0.1 and high = 0.9 means 10% low and high values will be discarded.

Synopsis

SELECT tdigest_avg(t.c, 100, 0.1, 0.9) FROM t

Parameters

  • value - values to aggregate
  • accuracy - accuracy of the t-digest
  • low - low threshold percentile (values below are discarded)
  • high - high threshold percentile (values above are discarded)

tdigest_avg(value, count, accuracy, low, high)

Computes trimmed mean of values, discarding values at the low and high end. The low and high values are percentiles in [0, 1] (with low <= high) specifying which part of the sample should be included in the mean, so e.g. low = 0.1 and high = 0.9 means 10% low and high values will be discarded.

Synopsis

SELECT tdigest_avg(t.c, t.a, 100, 0.1, 0.9) FROM t

Parameters

  • value - values to aggregate
  • count - number of occurrences of the value
  • accuracy - accuracy of the t-digest
  • low - low threshold percentile (values below are discarded)
  • high - high threshold percentile (values above are discarded)

tdigest_avg(tdigest, low, high)

Computes trimmed mean of values, discarding values at the low and high end. The low and high values are percentiles in [0, 1] (with low <= high) specifying which part of the sample should be included in the mean, so e.g. low = 0.1 and high = 0.9 means 10% low and high values will be discarded.

Synopsis

SELECT tdigest_avg(d, 0.05, 0.95) FROM (
    SELECT tdigest(t.c, 100) AS d FROM t
) foo;

Parameters

  • tdigest - tdigest to calculate mean from
  • low - low threshold percentile (values below are discarded)
  • high - high threshold percentile (values above are discarded)

tdigest_sum(value, accuracy, low, high)

Computes trimmed sum of values, discarding values at the low and high end. The low and high values are percentiles in [0, 1] (with low <= high) specifying which part of the sample should be included in the sum, so e.g. low = 0.1 and high = 0.9 means 10% low and high values will be discarded.

Synopsis

SELECT tdigest_sum(t.c, 100, 0.1, 0.9) FROM t

Parameters

  • value - values to aggregate
  • accuracy - accuracy of the t-digest
  • low - low threshold percentile (values below are discarded)
  • high - high threshold percentile (values above are discarded)

tdigest_sum(value, count, accuracy, low, high)

Computes trimmed sum of values, discarding values at the low and high end. The low and high values are percentiles in [0, 1] (with low <= high) specifying which part of the sample should be included in the sum, so e.g. low = 0.1 and high = 0.9 means 10% low and high values will be discarded.

Synopsis

SELECT tdigest_sum(t.c, t.a, 100, 0.1, 0.9) FROM t

Parameters

  • value - values to aggregate
  • count - number of occurrences of the value
  • accuracy - accuracy of the t-digest
  • low - low threshold percentile (values below are discarded)
  • high - high threshold percentile (values above are discarded)

tdigest_sum(tdigest, low, high)

Computes trimmed sum of values, discarding values at the low and high end. The low and high values are percentiles in [0, 1] (with low <= high) specifying which part of the sample should be included in the sum, so e.g. low = 0.1 and high = 0.9 means 10% low and high values will be discarded.

Synopsis

SELECT tdigest_sum(d, 0.05, 0.95) FROM (
    SELECT tdigest(t.c, 100) AS d FROM t
) foo;

Parameters

  • tdigest - tdigest to calculate sum from
  • low - low threshold percentile (values below are discarded)
  • high - high threshold percentile (values above are discarded)

tdigest_digest_avg(tdigest, low, high)

Calculates trimmed mean for a single t-digest value. Unlike tdigest_avg, this is a plain function, not an aggregate.

Synopsis

SELECT tdigest_digest_avg(d, 0.25, 0.75) FROM (
    SELECT tdigest(t.c, 100) AS d FROM t
) foo;

Parameters

  • tdigest - t-digest to calculate the mean for
  • low - low threshold percentile (values below are discarded, default: 0.0)
  • high - high threshold percentile (values above are discarded, default: 1.0)

tdigest_digest_sum(tdigest, low, high)

Calculates trimmed sum for a single t-digest value. Unlike tdigest_sum, this is a plain function, not an aggregate.

Synopsis

SELECT tdigest_digest_sum(d, 0.25, 0.75) FROM (
    SELECT tdigest(t.c, 100) AS d FROM t
) foo;

Parameters

  • tdigest - t-digest to calculate the sum for
  • low - low threshold percentile (values below are discarded, default: 0.0)
  • high - high threshold percentile (values above are discarded, default: 1.0)

tdigest_is_valid(tdigest)

Checks the t-digest is valid, i.e. that it passes the same sanity checks as the input functions (parsing the text or binary representation). Returns true for valid digests, false otherwise.

Digests produced by the extension are always valid, and it’s not possible to construct an invalid one through the input functions. But digests stored by older versions of the extension (which did not have all the checks) may be broken in various ways, and the values are not re-validated when read back. This function makes it possible to find such digests.

Synopsis

SELECT id FROM t WHERE NOT tdigest_is_valid(t.d);

Parameters

  • tdigest - t-digest to check

Notes

At the moment, the extension only supports double precision values, but it should not be very difficult to extend it to other numeric types (both integer and/or floating point, including numeric). Ultimately, it could support any data type with a concept of ordering and mean.

The estimates do depend on the order of incoming data, and so may differ between runs. This applies especially to parallel queries, for which the workers generally see different subsets of data for each run (and build different digests, which are then combined together).

Known issues

incorrect alignment

The SQL data type is defined without specifying the ALIGNMENT parameter, so it’s left set to 4, the default value. This means the on-disk data may be misaligned, as it contains double fields and so the correct alignment would be 8. On amd64/arm64 this is mostly harmless (except for some minor performance penalty), but on on platforms with strict alignment it may cause SIGBUS crashes.

It’s not clear how to best fix this. One option would be to change the CREATE TYPE, and only use the correct alignment for new installations. But maybe that’d be a problem with binary upgrades? The other option is to simply copy the data into the correct alignment before accessing the double/int64 fields (on platforms with strict alignment).

In fact, detoasted values are already aligned properly, because that allocates a new buffer - which is guaranteed to be aligned. But values with 4B header, while stored inline, still have the issue. This makes the price for extra copy much lower, we’re already paying it anyway.

FINALFUNC_MODIFY = READ_ONLY

The final functions are mutating the state (by sorting and compacting it), which means the FINALFUNC_MODIFY should not be READ_ONLY. This means the aggregates will give incorrect results when used as window functions.

OTOH the mutation is sorting and compaction of the aggregate state, which can introduce some differences, but it’s within the bounds of what we expect from an estimate. In fact, most final functions probably should not do compaction at all, just sort. Which would eliminate the differences.

License

This software is distributed under the terms of PostgreSQL license. See LICENSE or http://www.opensource.org/licenses/bsd-license.php for more details.

[1] https://github.com/tdunning/t-digest

[2] https://github.com/tdunning/t-digest/blob/master/docs/t-digest-paper/histo.pdf

[3] https://github.com/ajwerner/tdigestc

[4] https://github.com/ajwerner/tdigest