\set ECHO none
NOTICE:  Inverse ranks increase at a centroid boundary
NOTICE:  Scalar and array inverse percentiles agree
NOTICE:  Inverse ranks increase at a centroid boundary
NOTICE:  Scalar and array inverse percentiles agree
NOTICE:  Inverse ranks increase at a centroid boundary
NOTICE:  Scalar and array inverse percentiles agree
NOTICE:  Inverse ranks increase at a centroid boundary
NOTICE:  Scalar and array inverse percentiles agree
NOTICE:  Equal-mean ranks follow the half-weight convention
SET extra_float_digits = 2;
-- The CDF used to decrease from 0.375 to 0.37499999999999994 just above 1.
-- Both equal-mean centroids survive compaction at this compression.
WITH ranks AS (
    SELECT tdigest_percentile_of(d, 1::double precision) AS at_mean,
           tdigest_percentile_of(d, 1.0000000000000002::double precision) AS above_mean,
           tdigest_percentile_of(d, ARRAY[1, 1.0000000000000002]::double precision[]) AS array_ranks
    FROM (VALUES (
        'flags 1 count 36028797018963981 compression 10000 centroids 4 (0, 9007199254740995) (1, 2) (1, 9007199254740993) (10, 18014398509481991)'::tdigest
    )) AS input(d)
)
SELECT at_mean, above_mean, array_ranks,
       at_mean <= above_mean AS monotone,
       array_ranks = ARRAY[at_mean, above_mean] AS scalar_array_agree
FROM ranks;
       at_mean       | above_mean |         array_ranks         | monotone | scalar_array_agree 
---------------------+------------+-----------------------------+----------+--------------------
 0.37499999999999994 |      0.375 | {0.37499999999999994,0.375} | t        | t
(1 row)

-- Preserve half-items without rounding the integer part and half separately.
-- In particular, (double) (18014398509481987 / 2) + 0.5 double-rounds.
WITH counts(n) AS (
    VALUES (1::bigint), (3), (18014398509481987), (9223372036854775807)
)
SELECT n, tdigest_percentile_of(
           format('flags 1 count %s compression 10000 centroids 1 (1, %s)', n, n)::tdigest,
           1::double precision) AS rank
FROM counts
GROUP BY n
ORDER BY n;
          n          | rank 
---------------------+------
                   1 |  0.5
                   3 |  0.5
   18014398509481987 |  0.5
 9223372036854775807 |  0.5
(4 rows)