Re: vector search support

Attached is a proof-of-concept/work-in-progress patch set that adds
functions for "vectors" repreѕented with one-dimensional float8 arrays.
These functions may be used in a variety of applications, but I am
proposing them with the AI/ML use-cases in mind.  I am posting this early
in the v17 cycle in hopes of gathering feedback prior to PGCon.

With the accessibility of AI/ML tools such as large language models (LLMs),
there has been a demand for storing and manipulating high-dimensional
vectors in PostgreSQL, particularly around nearest-neighbor queries.  Many
of these vectors have more than 1500 dimensions.  The cube extension [0]
provides some of the distance functionality (e.g., taxicab, Euclidean, and
Chebyshev), but it is missing some popular functions (e.g., cosine
similarity, dot product), and it is limited to 100 dimensions.  We could
extend cube to support more dimensions, but this would require reworking
its indexing code and filling in gaps between the cube data type and the
array types.  For some previous discussion about using the cube extension
for this kind of data, see [1].

float8[] is well-supported and allows for effectively unlimited dimensions
of data.  float8 matches the common output format of many AI embeddings,
and it allows us or extensions to implement indexing methods around these
functions.  This patch set does not yet contain indexing support, but we
are exploring using GiST or GIN for the use-cases in question.  It might
also be desirable to add support for other linear algebra operations (e.g.,
operations on matrices).  The attached patches likely only scratch the
surface of the "vector search" use-case.

The patch set is broken up as follows:

 * 0001 does some minor refactoring of dsqrt() in preparation for 0002.
 * 0002 adds several vector-related functions, including distance functions
   and a kmeans++ implementation.
 * 0003 adds support for optionally using the OpenBLAS library, which is an
   implementation of the Basic Linear Algebra Subprograms [2]
   specification.  Basic testing with this library showed a small
   performance boost, although perhaps not enough to justify giving this
   patch serious consideration.

Of course, there are many open questions.  For example, should PostgreSQL
support this stuff out-of-the-box in the first place?  And should we
introduce a vector data type or SQL domains for treating float8[] as
vectors?  IMHO these vector search use-cases are an exciting opportunity
for the PostgreSQL project, so I am eager to hear what folks think.

[0] https://www.postgresql.org/docs/current/cube.html
[1] https://postgr.es/m/2271927.1593097400%40sss.pgh.pa.us
[2] https://en.wikipedia.org/wiki/Basic_Linear_Algebra_Subprograms

--
Nathan Bossart
Amazon Web Services: https://aws.amazon.com