Half-Precision Vector: `vecf16`

Stored as a half-precision number format, vecf16 takes advantage of the 16-bit float, which uses half the memory and bandwidth compared to vector.

Here’s an example of creating a table with a vecf16 column and inserting values:

CREATE TABLE items (
  id bigserial PRIMARY KEY,
  embedding vecf16(3) NOT NULL
);

INSERT INTO items (embedding) VALUES ('[0.1, 0.2, 0]'), ('[0, 0.1, 0.2]');

Index can be created on vecf16 type as well.

CREATE INDEX your_index_name ON items USING vectors (embedding vecf16_l2_ops);

SELECT * FROM items ORDER BY embedding <-> '[0.3,0.2,0.1]' LIMIT 1;

We support three operators to calculate the distance between two vecf16 values.

• <-> (vecf16_l2_ops): squared Euclidean distance, defined as $\Sigma (x_i - y_i) ^ 2$.
• <#> (vecf16_dot_ops): negative dot product, defined as $- \Sigma x_iy_i$.
• <=> (vecf16_cos_ops): cosine distance, defined as $1 - \frac{\Sigma x_iy_i}{\sqrt{\Sigma x_i^2 \Sigma y_i^2}}$.