VEC_DISTANCE_COSINE fails cosine identities for an accepted tiny nonzero vector

I get failed cosine-distance checks for an accepted nonzero vector containing 1e-30 on MariaDB 12.3.3. The vector has a nonzero encoding and positive Euclidean distance from zero, but VEC_DISTANCE_COSINE fails both self-distance and same-direction comparisons. The same self-distance check also fails through a prepared statement, while a unit-vector control passes.

This occurs when cosine distance is calculated for an accepted vector whose components are small enough for their products to underflow.

The following single-session SQL reproduces the problem:

SET @small = VEC_FROMTEXT('[1e-30]');

SET @unit = VEC_FROMTEXT('[1]');

SELECT 'inputs' AS check_name,

       @small IS NOT NULL AS valid_ok,

       HEX(@small) <> '00000000' AS nonzero_ok,

       VEC_DISTANCE_EUCLIDEAN(@small, VEC_FROMTEXT('[0]')) > 0 AS euclidean_ok;

SELECT 'direct' AS check_name,

       COALESCE(ABS(VEC_DISTANCE_COSINE(@unit, @unit)) < 1e-6, 0) AS control_ok,

       COALESCE(ABS(VEC_DISTANCE_COSINE(@small, @small)) < 1e-6, 0) AS small_self_ok,

       COALESCE(ABS(VEC_DISTANCE_COSINE(@small, @unit)) < 1e-6, 0) AS same_direction_ok;

SHOW WARNINGS;

PREPARE cosine_stmt FROM

  'SELECT ''prepared'' AS check_name,

          COALESCE(ABS(VEC_DISTANCE_COSINE(?, ?)) < 1e-6, 0) AS cosine_ok';

EXECUTE cosine_stmt USING @small, @small;

DEALLOCATE PREPARE cosine_stmt;

SET @small = NULL, @unit = NULL;

The recorded semantic rows were:

check_name  valid_ok  nonzero_ok  euclidean_ok

inputs      1         1           1

check_name  control_ok  small_self_ok  same_direction_ok

direct      1           0              0

check_name  cosine_ok

prepared    0

No warnings or errors were produced by this confirmation case.

For a nonzero vector, cosine distance from itself must be zero. The vectors [1e-30] and [1] also have the same positive direction, so their cosine distance must be zero. All three tested comparisons should therefore evaluate to 1 within the supplied 1e-6 tolerance, and direct and prepared execution should agree. Instead, the unit-vector control evaluates to 1 while both tiny-vector checks and the prepared check evaluate to 0.

The observed result is consistent with the component products underflowing before they are accumulated at wider precision, causing a valid nonzero vector to be treated as having a zero norm during cosine-distance calculation.