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DuckDB Extensions All extensions Lindel

Morton (Z-order) functions in the Lindel DuckDB extension

Function category

Morton (Z-order)

2 functions

Morton-curve encoding (also known as Z-order). Faster to compute, slightly weaker locality. The classic Z-Order optimization that Delta Lake popularized.

morton_decode

Scalar function Morton (Z-order)
Signature
morton_decode( encoded_value: <numeric>, num_elements: UTINYINT, return_float: BOOLEAN, return_unsigned: BOOLEAN ) → ANY[ANY]
Arguments (Positional)
Argument encoded_value Type <numeric>
5 concrete types
UBIGINTUHUGEINTUINTEGERUSMALLINTUTINYINT
Mode Positional Description
Argument num_elements Type UTINYINT Mode Positional Description
Argument return_float Type BOOLEAN Mode Positional Description
Argument return_unsigned Type BOOLEAN Mode Positional Description
Description

Recover component values from a Morton-encoded key. Supply the original dimension count; use (return_float, return_unsigned) = (false, true) for unsigned integers, (false, false) for signed integers, or (true, false) for floats. Preserve the encoded key’s SQL type. Community build 6435106 rejects one-dimensional signed-integer decoding; v1.5 source commit a92ec61 (extension version 2026100701) fixes it. Older community binaries may still be affected.

1 Round-trip an encoded integer back to its components (num_elements, return_float, return_unsigned) 
SELECT morton_decode(morton_encode([10, 20]::UINTEGER[2]), 2, false, true) AS roundtrip;
2 Round-trip signed integer coordinates with return_unsigned = false 
SELECT morton_decode(morton_encode([-10, 20]::INTEGER[2]), 2, false, false) AS roundtrip;
3 Round-trip floating-point values with return_float = true 
SELECT morton_decode(morton_encode([-1.5, 2.25]::DOUBLE[2]), 2, true, false) AS roundtrip;
Related functions

morton_encode

Scalar function Morton (Z-order)
Signature
morton_encode(values: ANY[ANY]) → ANY
Arguments (Positional)
Argument values Type ANY[ANY] Mode Positional Description
Description

Encode a fixed-size numeric array into an unsigned integer by interleaving its coordinate bits (Morton / Z-order). Accepts the same types and dimensions as hilbert_encode. Signed and floating-point values are encoded by their bit patterns without normalizing numeric distance.

1 Order points by the Morton (Z-order) curve 
SELECT x, y, morton_encode([x, y]::UINTEGER[2]) AS morton
FROM (VALUES (1, 1), (1, 2), (2, 1), (6, 7), (7, 6)) AS t(x, y)
ORDER BY morton;
Related functions