# 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.

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LLMS index: [llms.txt](/llms.txt)

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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:

```sql {hl_lines=["3"]}
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.

```sql
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 \(1 - \frac{\Sigma x_iy_i}{\sqrt{\Sigma x_i^2 \Sigma y_i^2}}\).

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Backlinks:

- [pgvector vs. pgvecto.rs in 2024: A Comprehensive Comparison for Vector Search in PostgreSQL](/blog/post/pgvector-vs-pgvectors-in-2024-a-comprehensive-comparison-for-vector-search-in-postgresql/)
- [pgvecto.rs vs. pgvector](/docs/vectors/faqs/comparison-pgvector/)
- [Overview](/docs/vectors/getting-started/overview/)
- [Vector Types](/docs/vectors/reference/vector-types/)
- [Indexing](/docs/vectors/usage/indexing/)