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 standardfloat16format- 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_e3m4float8_e4m3float8_e4m3b11fnuzfloat8_e4m3fnfloat8_e4m3fnuzfloat8_e5m2float8_e5m2fnuzfloat8_e8m0fnu
- Microscaling (MX) sub-byte floating point representations:
float4_e2m1fnfloat6_e2m3fnfloat6_e3m2fn
- Narrow integer encodings:
int1int2int4uint1uint2uint4
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).
int1, uint1, int2, int4, uint2 and uint4
1, 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).
2 maintainers
Release files for ml-dtypes 0.6.0
For a detailed explanation of source distributions (sdists) and built distributions (wheels), please see the package formats documentation.
Source distribution (sdist)
| File | Size | Uploaded | |
|---|---|---|---|
| ml_dtypes-0.6.0.tar.gz | 3.0 MB | Details |
Built distributions (wheels)
| File | Reset | |||
|---|---|---|---|---|
| ml_dtypes-0.6.0-cp315-cp315t-win_arm64.whl | CPython 3.15 | CPython 3.15 free-threading | Windows ARM64 | Details |
| ml_dtypes-0.6.0-cp315-cp315t-win_amd64.whl | CPython 3.15 | CPython 3.15 free-threading | Windows x86-64 | Details |
| ml_dtypes-0.6.0-cp315-cp315t-manylinux_2_27_x86_64.manylinux_2_28_x86_64.whl | CPython 3.15 | CPython 3.15 free-threading | Linux glibc 2.28+ x86-64, Linux glibc 2.27+ x86-64 | Details |
| ml_dtypes-0.6.0-cp315-cp315t-manylinux_2_27_aarch64.manylinux_2_28_aarch64.whl | CPython 3.15 | CPython 3.15 free-threading | Linux glibc 2.28+ ARM64, Linux glibc 2.27+ ARM64 | Details |
| ml_dtypes-0.6.0-cp315-cp315t-macosx_10_15_universal2.whl | CPython 3.15 | CPython 3.15 free-threading | macOS 10.15+ universal2 (ARM64, x86-64) | Details |
| ml_dtypes-0.6.0-cp315-cp315-win_arm64.whl | CPython 3.15 | CPython 3.15 | Windows ARM64 | Details |
| ml_dtypes-0.6.0-cp315-cp315-win_amd64.whl | CPython 3.15 | CPython 3.15 | Windows x86-64 | Details |
| ml_dtypes-0.6.0-cp315-cp315-manylinux_2_27_x86_64.manylinux_2_28_x86_64.whl | CPython 3.15 | CPython 3.15 | Linux glibc 2.27+ x86-64, Linux glibc 2.28+ x86-64 | Details |
| ml_dtypes-0.6.0-cp315-cp315-manylinux_2_27_aarch64.manylinux_2_28_aarch64.whl | CPython 3.15 | CPython 3.15 | Linux glibc 2.27+ ARM64, Linux glibc 2.28+ ARM64 | Details |
| ml_dtypes-0.6.0-cp315-cp315-macosx_10_15_universal2.whl | CPython 3.15 | CPython 3.15 | macOS 10.15+ universal2 (ARM64, x86-64) | Details |
| ml_dtypes-0.6.0-cp314-cp314t-win_arm64.whl | CPython 3.14 | CPython 3.14 free-threading | Windows ARM64 | Details |
| ml_dtypes-0.6.0-cp314-cp314t-win_amd64.whl | CPython 3.14 | CPython 3.14 free-threading | Windows x86-64 | Details |
| ml_dtypes-0.6.0-cp314-cp314t-manylinux_2_27_x86_64.manylinux_2_28_x86_64.whl | CPython 3.14 | CPython 3.14 free-threading | Linux glibc 2.28+ x86-64, Linux glibc 2.27+ x86-64 | Details |
| ml_dtypes-0.6.0-cp314-cp314t-manylinux_2_27_aarch64.manylinux_2_28_aarch64.whl | CPython 3.14 | CPython 3.14 free-threading | Linux glibc 2.28+ ARM64, Linux glibc 2.27+ ARM64 | Details |
| ml_dtypes-0.6.0-cp314-cp314t-macosx_10_15_universal2.whl | CPython 3.14 | CPython 3.14 free-threading | macOS 10.15+ universal2 (ARM64, x86-64) | Details |
| ml_dtypes-0.6.0-cp314-cp314-win_arm64.whl | CPython 3.14 | CPython 3.14 | Windows ARM64 | Details |
| ml_dtypes-0.6.0-cp314-cp314-win_amd64.whl | CPython 3.14 | CPython 3.14 | Windows x86-64 | Details |
| ml_dtypes-0.6.0-cp314-cp314-manylinux_2_27_x86_64.manylinux_2_28_x86_64.whl | CPython 3.14 | CPython 3.14 | Linux glibc 2.27+ x86-64, Linux glibc 2.28+ x86-64 | Details |
| ml_dtypes-0.6.0-cp314-cp314-manylinux_2_27_aarch64.manylinux_2_28_aarch64.whl | CPython 3.14 | CPython 3.14 | Linux glibc 2.27+ ARM64, Linux glibc 2.28+ ARM64 | Details |
| ml_dtypes-0.6.0-cp314-cp314-macosx_10_15_universal2.whl | CPython 3.14 | CPython 3.14 | macOS 10.15+ universal2 (ARM64, x86-64) | Details |
| ml_dtypes-0.6.0-cp313-cp313-win_arm64.whl | CPython 3.13 | CPython 3.13 | Windows ARM64 | Details |
| ml_dtypes-0.6.0-cp313-cp313-win_amd64.whl | CPython 3.13 | CPython 3.13 | Windows x86-64 | Details |
| ml_dtypes-0.6.0-cp313-cp313-manylinux_2_27_x86_64.manylinux_2_28_x86_64.whl | CPython 3.13 | CPython 3.13 | Linux glibc 2.28+ x86-64, Linux glibc 2.27+ x86-64 | Details |
| ml_dtypes-0.6.0-cp313-cp313-manylinux_2_27_aarch64.manylinux_2_28_aarch64.whl | CPython 3.13 | CPython 3.13 | Linux glibc 2.28+ ARM64, Linux glibc 2.27+ ARM64 | Details |
| ml_dtypes-0.6.0-cp313-cp313-macosx_10_13_universal2.whl | CPython 3.13 | CPython 3.13 | macOS 10.13+ universal2 (ARM64, x86-64) | Details |
| ml_dtypes-0.6.0-cp312-cp312-win_arm64.whl | CPython 3.12 | CPython 3.12 | Windows ARM64 | Details |
| ml_dtypes-0.6.0-cp312-cp312-win_amd64.whl | CPython 3.12 | CPython 3.12 | Windows x86-64 | Details |
| ml_dtypes-0.6.0-cp312-cp312-manylinux_2_27_x86_64.manylinux_2_28_x86_64.whl | CPython 3.12 | CPython 3.12 | Linux glibc 2.27+ x86-64, Linux glibc 2.28+ x86-64 | Details |
| ml_dtypes-0.6.0-cp312-cp312-manylinux_2_27_aarch64.manylinux_2_28_aarch64.whl | CPython 3.12 | CPython 3.12 | Linux glibc 2.28+ ARM64, Linux glibc 2.27+ ARM64 | Details |
| ml_dtypes-0.6.0-cp312-cp312-macosx_10_13_universal2.whl | CPython 3.12 | CPython 3.12 | macOS 10.13+ universal2 (ARM64, x86-64) | Details |
| ml_dtypes-0.6.0-cp311-cp311-win_arm64.whl | CPython 3.11 | CPython 3.11 | Windows ARM64 | Details |
| ml_dtypes-0.6.0-cp311-cp311-win_amd64.whl | CPython 3.11 | CPython 3.11 | Windows x86-64 | Details |
| ml_dtypes-0.6.0-cp311-cp311-manylinux_2_27_x86_64.manylinux_2_28_x86_64.whl | CPython 3.11 | CPython 3.11 | Linux glibc 2.27+ x86-64, Linux glibc 2.28+ x86-64 | Details |
| ml_dtypes-0.6.0-cp311-cp311-manylinux_2_27_aarch64.manylinux_2_28_aarch64.whl | CPython 3.11 | CPython 3.11 | Linux glibc 2.27+ ARM64, Linux glibc 2.28+ ARM64 | Details |
| ml_dtypes-0.6.0-cp311-cp311-macosx_10_9_universal2.whl | CPython 3.11 | CPython 3.11 | macOS 10.9+ universal2 (ARM64, x86-64) | Details |
| ml_dtypes-0.6.0-cp310-cp310-win_amd64.whl | CPython 3.10 | CPython 3.10 | Windows x86-64 | Details |
| ml_dtypes-0.6.0-cp310-cp310-manylinux_2_27_x86_64.manylinux_2_28_x86_64.whl | CPython 3.10 | CPython 3.10 | Linux glibc 2.28+ x86-64, Linux glibc 2.27+ x86-64 | Details |
| ml_dtypes-0.6.0-cp310-cp310-manylinux_2_27_aarch64.manylinux_2_28_aarch64.whl | CPython 3.10 | CPython 3.10 | Linux glibc 2.28+ ARM64, Linux glibc 2.27+ ARM64 | Details |
| ml_dtypes-0.6.0-cp310-cp310-macosx_10_9_universal2.whl | CPython 3.10 | CPython 3.10 | macOS 10.9+ universal2 (ARM64, x86-64) | Details |
Total release size: 21.3 MB
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