ml_dtypes

ml_dtypes is a stand-alone implementation of several NumPy dtype extensions used in machine learning libraries, including:

bfloat16:
an alternative to the standard float16 format
8-bit floating point representations, parameterized by number of exponent and
mantissa bits, as well as the bias (if any) and representability of infinity,
NaN, and signed zero.
- float8_e3m4
- float8_e4m3
- float8_e4m3b11fnuz
- float8_e4m3fn
- float8_e4m3fnuz
- float8_e5m2
- float8_e5m2fnuz
- float8_e8m0fnu
Microscaling (MX) sub-byte floating point representations:
- float4_e2m1fn
- float6_e2m3fn
- float6_e3m2fn
Narrow integer encodings:
- int2
- int4
- uint2
- uint4

See below for specifications of these number formats.

Installation

The ml_dtypes package is tested with Python versions 3.9-3.12, and can be installed
with the following command:

pip install ml_dtypes

To test your installation, you can run the following:

pip install absl-py pytest
pytest --pyargs ml_dtypes

To build from source, clone the repository and run:

git submodule init
git submodule update
pip install .

Example Usage

>>> from ml_dtypes import bfloat16
>>> import numpy as np
>>> np.zeros(4, dtype=bfloat16)
array([0, 0, 0, 0], dtype=bfloat16)

Importing ml_dtypes also registers the data types with numpy, so that they may
be referred to by their string name:

>>> np.dtype('bfloat16')
dtype(bfloat16)
>>> np.dtype('float8_e5m2')
dtype(float8_e5m2)

Specifications of implemented floating point formats

`bfloat16`

A bfloat16 number is a single-precision float truncated at 16 bits.

Exponent: 8, Mantissa: 7, exponent bias: 127. IEEE 754, with NaN and inf.

`float4_e2m1fn`

Exponent: 2, Mantissa: 1, bias: 1.

Extended range: no inf, no NaN.

Microscaling format, 4 bits (encoding: 0bSEEM) using byte storage (higher 4
bits are unused). NaN representation is undefined.

Possible absolute values: [0, 0.5, 1, 1.5, 2, 3, 4, 6]

`float6_e2m3fn`

Exponent: 2, Mantissa: 3, bias: 1.

Extended range: no inf, no NaN.

Microscaling format, 6 bits (encoding: 0bSEEMMM) using byte storage (higher 2
bits are unused). NaN representation is undefined.

Possible values range: [-7.5; 7.5]

`float6_e3m2fn`

Exponent: 3, Mantissa: 2, bias: 3.

Extended range: no inf, no NaN.

Microscaling format, 4 bits (encoding: 0bSEEEMM) using byte storage (higher 2
bits are unused). NaN representation is undefined.

Possible values range: [-28; 28]

`float8_e3m4`

Exponent: 3, Mantissa: 4, bias: 3. IEEE 754, with NaN and inf.

`float8_e4m3`

Exponent: 4, Mantissa: 3, bias: 7. IEEE 754, with NaN and inf.

`float8_e4m3b11fnuz`

Exponent: 4, Mantissa: 3, bias: 11.

Extended range: no inf, NaN represented by 0b1000'0000.

`float8_e4m3fn`

Exponent: 4, Mantissa: 3, bias: 7.

Extended range: no inf, NaN represented by 0bS111'1111.

The fn suffix is for consistency with the corresponding LLVM/MLIR type, signaling this type is not consistent with IEEE-754. The f indicates it is finite values only. The n indicates it includes NaNs, but only at the outer range.

`float8_e4m3fnuz`

8-bit floating point with 3 bit mantissa.

An 8-bit floating point type with 1 sign bit, 4 bits exponent and 3 bits mantissa. The suffix fnuz is consistent with LLVM/MLIR naming and is derived from the differences to IEEE floating point conventions. F is for "finite" (no infinities), N for with special NaN encoding, UZ for unsigned zero.

This type has the following characteristics:

bit encoding: S1E4M3 - 0bSEEEEMMM
exponent bias: 8
infinities: Not supported
NaNs: Supported with sign bit set to 1, exponent bits and mantissa bits set to all 0s - 0b10000000
denormals when exponent is 0

`float8_e5m2`

Exponent: 5, Mantissa: 2, bias: 15. IEEE 754, with NaN and inf.

`float8_e5m2fnuz`

8-bit floating point with 2 bit mantissa.

An 8-bit floating point type with 1 sign bit, 5 bits exponent and 2 bits mantissa. The suffix fnuz is consistent with LLVM/MLIR naming and is derived from the differences to IEEE floating point conventions. F is for "finite" (no infinities), N for with special NaN encoding, UZ for unsigned zero.

This type has the following characteristics:

bit encoding: S1E5M2 - 0bSEEEEEMM
exponent bias: 16
infinities: Not supported
NaNs: Supported with sign bit set to 1, exponent bits and mantissa bits set to all 0s - 0b10000000
denormals when exponent is 0

`float8_e8m0fnu`

OpenCompute MX
scale format E8M0, which has the following properties:

Unsigned format
8 exponent bits
Exponent range from -127 to 127
No zero and infinity
Single NaN value (0xFF).

`int2`, `int4`, `uint2` and `uint4`

2 and 4-bit integer types, where each element is represented unpacked (i.e.,
padded up to a byte in memory).

NumPy does not support types smaller than a single byte: for example, the
distance between adjacent elements in an array (.strides) is expressed as
an integer number of bytes. Relaxing this restriction would be a considerable
engineering project. These types therefore use an unpacked representation, where
each element of the array is padded up to a byte in memory. The lower two or four
bits of each byte contain the representation of the number, whereas the remaining
upper bits are ignored.

Quirks of low-precision Arithmetic

If you're exploring the use of low-precision dtypes in your code, you should be
careful to anticipate when the precision loss might lead to surprising results.
One example is the behavior of aggregations like sum; consider this bfloat16
summation in NumPy (run with version 1.24.2):

>>> from ml_dtypes import bfloat16
>>> import numpy as np
>>> rng = np.random.default_rng(seed=0)
>>> vals = rng.uniform(size=10000).astype(bfloat16)
>>> vals.sum()
256

The true sum should be close to 5000, but numpy returns exactly 256: this is
because bfloat16 does not have the precision to increment 256 by values less than
1:

>>> bfloat16(256) + bfloat16(1)
256

After 256, the next representable value in bfloat16 is 258:

>>> np.nextafter(bfloat16(256), bfloat16(np.inf))
258

For better results you can specify that the accumulation should happen in a
higher-precision type like float32:

>>> vals.sum(dtype='float32').astype(bfloat16)
4992

In contrast to NumPy, projects like JAX which support
low-precision arithmetic more natively will often do these kinds of higher-precision
accumulations automatically:

>>> import jax.numpy as jnp
>>> jnp.array(vals).sum()
Array(4992, dtype=bfloat16)

License

This is not an officially supported Google product.

The ml_dtypes source code is licensed under the Apache 2.0 license
(see LICENSE). Pre-compiled wheels are built with the
EIGEN project, which is released under the
MPL 2.0 license (see LICENSE.eigen).

Dependency	Optional
numpy	false
absl-py	true
pyink	true
pylint	true
pytest	true
pytest-xdist	true

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