float4_e2m1fn data type

Defines a 4-bit floating point representation with:

• 1 sign bit
• 2 exponent bits, with bias of 1
• 1 mantissa bit
• Extended range: no infinity, no NaN.
• Subnormal numbers when biased exponent is 0.

Data type name

The data type is specified as "float4_e2m1fn".

Configuration

None.

Fill value representation

The fill value is specified in the same way as the core IEEE 754 floating point numbers: https://zarr-specs.readthedocs.io/en/latest/v3/core/v3.0.html#fill-value

• The constants "Infinity", "-Infinity", and "NaN" are not supported since there is no corresponding representation.

Codec compatibility

bytes

Encoded as a 1-byte value 0bXXXXSEEM. The "endian" parameter has no effect. The upper XXXX bits are ignored.

packbits

Encoded as a 4-bit value 0bSEEM.

See also

• Specified as the E2M1 format by OpenCompute MX.
• Python implementation available at https://pypi.org/project/ml-dtypes/
• Implemented in LLVM/MLIR as Float4E2M1FN.

Current maintainers

• Jeremy Maitin-Shepard (@jbms), Google