| Name | ml-dtypes JSON |
| Version |
0.5.0
JSON |
| download |
| home_page | None |
| Summary | None |
| upload_time | 2024-09-14 21:50:53 |
| maintainer | None |
| docs_url | None |
| author | None |
| requires_python | >=3.9 |
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# ml_dtypes
[](https://github.com/jax-ml/ml_dtypes/actions/workflows/test.yml)
[](https://github.com/jax-ml/ml_dtypes/actions/workflows/wheels.yml)
[](https://badge.fury.io/py/ml_dtypes)
`ml_dtypes` is a stand-alone implementation of several NumPy dtype extensions used in machine learning libraries, including:
- [`bfloat16`](https://en.wikipedia.org/wiki/Bfloat16_floating-point_format):
an alternative to the standard [`float16`](https://en.wikipedia.org/wiki/Half-precision_floating-point_format) format
- `float8_*`: several experimental 8-bit floating point representations
including:
* `float8_e3m4`
* `float8_e4m3`
* `float8_e4m3b11fnuz`
* `float8_e4m3fn`
* `float8_e4m3fnuz`
* `float8_e5m2`
* `float8_e5m2fnuz`
- Microscaling (MX) sub-byte floating point representations including:
* `float4_e2m1fn`
* `float6_e2m3fn`
* `float6_e3m2fn`
- `int2`, `int4`, `uint2` and `uint4`: low precision integer types.
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
```python
>>> 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:
```python
>>> 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](https://www.opencompute.org/documents/ocp-microscaling-formats-mx-v1-0-spec-final-pdf)
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):
```python
>>> 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`:
```python
>>> bfloat16(256) + bfloat16(1)
256
```
After 256, the next representable value in bfloat16 is 258:
```python
>>> 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`:
```python
>>> vals.sum(dtype='float32').astype(bfloat16)
4992
```
In contrast to NumPy, projects like [JAX](http://jax.readthedocs.io/) which support
low-precision arithmetic more natively will often do these kinds of higher-precision
accumulations automatically:
```python
>>> 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](LICENSE)). Pre-compiled wheels are built with the
[EIGEN](https://eigen.tuxfamily.org/) project, which is released under the
MPL 2.0 license (see [LICENSE.eigen](LICENSE.eigen)).
Raw data
{
"_id": null,
"home_page": null,
"name": "ml-dtypes",
"maintainer": null,
"docs_url": null,
"requires_python": ">=3.9",
"maintainer_email": null,
"keywords": null,
"author": null,
"author_email": "ml_dtypes authors <ml_dtypes@google.com>",
"download_url": "https://files.pythonhosted.org/packages/ab/79/717c5e22ad25d63ce3acdfe8ff8d64bdedec18914256c59b838218708b16/ml_dtypes-0.5.0.tar.gz",
"platform": null,
"description": "# ml_dtypes\n\n[](https://github.com/jax-ml/ml_dtypes/actions/workflows/test.yml)\n[](https://github.com/jax-ml/ml_dtypes/actions/workflows/wheels.yml)\n[](https://badge.fury.io/py/ml_dtypes)\n\n`ml_dtypes` is a stand-alone implementation of several NumPy dtype extensions used in machine learning libraries, including:\n\n- [`bfloat16`](https://en.wikipedia.org/wiki/Bfloat16_floating-point_format):\n an alternative to the standard [`float16`](https://en.wikipedia.org/wiki/Half-precision_floating-point_format) format\n- `float8_*`: several experimental 8-bit floating point representations\n including:\n * `float8_e3m4`\n * `float8_e4m3`\n * `float8_e4m3b11fnuz`\n * `float8_e4m3fn`\n * `float8_e4m3fnuz`\n * `float8_e5m2`\n * `float8_e5m2fnuz`\n- Microscaling (MX) sub-byte floating point representations including:\n * `float4_e2m1fn`\n * `float6_e2m3fn`\n * `float6_e3m2fn`\n- `int2`, `int4`, `uint2` and `uint4`: low precision integer types.\n\nSee below for specifications of these number formats.\n\n## Installation\n\nThe `ml_dtypes` package is tested with Python versions 3.9-3.12, and can be installed\nwith the following command:\n```\npip install ml_dtypes\n```\nTo test your installation, you can run the following:\n```\npip install absl-py pytest\npytest --pyargs ml_dtypes\n```\nTo build from source, clone the repository and run:\n```\ngit submodule init\ngit submodule update\npip install .\n```\n\n## Example Usage\n\n```python\n>>> from ml_dtypes import bfloat16\n>>> import numpy as np\n>>> np.zeros(4, dtype=bfloat16)\narray([0, 0, 0, 0], dtype=bfloat16)\n```\nImporting `ml_dtypes` also registers the data types with numpy, so that they may\nbe referred to by their string name:\n\n```python\n>>> np.dtype('bfloat16')\ndtype(bfloat16)\n>>> np.dtype('float8_e5m2')\ndtype(float8_e5m2)\n```\n\n## Specifications of implemented floating point formats\n\n### `bfloat16`\n\nA `bfloat16` number is a single-precision float truncated at 16 bits.\n\nExponent: 8, Mantissa: 7, exponent bias: 127. IEEE 754, with NaN and inf.\n\n### `float4_e2m1fn`\n\nExponent: 2, Mantissa: 1, bias: 1.\n\nExtended range: no inf, no NaN.\n\nMicroscaling format, 4 bits (encoding: `0bSEEM`) using byte storage (higher 4\nbits are unused). NaN representation is undefined.\n\nPossible absolute values: [`0`, `0.5`, `1`, `1.5`, `2`, `3`, `4`, `6`]\n\n### `float6_e2m3fn`\n\nExponent: 2, Mantissa: 3, bias: 1.\n\nExtended range: no inf, no NaN.\n\nMicroscaling format, 6 bits (encoding: `0bSEEMMM`) using byte storage (higher 2\nbits are unused). NaN representation is undefined.\n\nPossible values range: [`-7.5`; `7.5`]\n\n### `float6_e3m2fn`\n\nExponent: 3, Mantissa: 2, bias: 3.\n\nExtended range: no inf, no NaN.\n\nMicroscaling format, 4 bits (encoding: `0bSEEEMM`) using byte storage (higher 2\nbits are unused). NaN representation is undefined.\n\nPossible values range: [`-28`; `28`]\n\n### `float8_e3m4`\n\nExponent: 3, Mantissa: 4, bias: 3. IEEE 754, with NaN and inf.\n\n### `float8_e4m3`\n\nExponent: 4, Mantissa: 3, bias: 7. IEEE 754, with NaN and inf.\n\n### `float8_e4m3b11fnuz`\n\nExponent: 4, Mantissa: 3, bias: 11.\n\nExtended range: no inf, NaN represented by 0b1000'0000.\n\n### `float8_e4m3fn`\n\nExponent: 4, Mantissa: 3, bias: 7.\n\nExtended range: no inf, NaN represented by 0bS111'1111.\n\nThe `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.\n\n### `float8_e4m3fnuz`\n\n8-bit floating point with 3 bit mantissa.\n\nAn 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.\n\nThis type has the following characteristics:\n * bit encoding: S1E4M3 - `0bSEEEEMMM`\n * exponent bias: 8\n * infinities: Not supported\n * NaNs: Supported with sign bit set to 1, exponent bits and mantissa bits set to all 0s - `0b10000000`\n * denormals when exponent is 0\n\n### `float8_e5m2`\n\nExponent: 5, Mantissa: 2, bias: 15. IEEE 754, with NaN and inf.\n\n### `float8_e5m2fnuz`\n\n8-bit floating point with 2 bit mantissa.\n\nAn 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.\n\nThis type has the following characteristics:\n * bit encoding: S1E5M2 - `0bSEEEEEMM`\n * exponent bias: 16\n * infinities: Not supported\n * NaNs: Supported with sign bit set to 1, exponent bits and mantissa bits set to all 0s - `0b10000000`\n * denormals when exponent is 0\n\n### `float8_e8m0fnu`\n\n[OpenCompute MX](https://www.opencompute.org/documents/ocp-microscaling-formats-mx-v1-0-spec-final-pdf)\nscale format E8M0, which has the following properties:\n * Unsigned format\n * 8 exponent bits\n * Exponent range from -127 to 127\n * No zero and infinity\n * Single NaN value (0xFF).\n\n## `int2`, `int4`, `uint2` and `uint4`\n\n2 and 4-bit integer types, where each element is represented unpacked (i.e.,\npadded up to a byte in memory).\n\nNumPy does not support types smaller than a single byte: for example, the\ndistance between adjacent elements in an array (`.strides`) is expressed as\nan integer number of bytes. Relaxing this restriction would be a considerable\nengineering project. These types therefore use an unpacked representation, where\neach element of the array is padded up to a byte in memory. The lower two or four\nbits of each byte contain the representation of the number, whereas the remaining\nupper bits are ignored.\n\n## Quirks of low-precision Arithmetic\n\nIf you're exploring the use of low-precision dtypes in your code, you should be\ncareful to anticipate when the precision loss might lead to surprising results.\nOne example is the behavior of aggregations like `sum`; consider this `bfloat16`\nsummation in NumPy (run with version 1.24.2):\n\n```python\n>>> from ml_dtypes import bfloat16\n>>> import numpy as np\n>>> rng = np.random.default_rng(seed=0)\n>>> vals = rng.uniform(size=10000).astype(bfloat16)\n>>> vals.sum()\n256\n```\nThe true sum should be close to 5000, but numpy returns exactly 256: this is\nbecause `bfloat16` does not have the precision to increment `256` by values less than\n`1`:\n\n```python\n>>> bfloat16(256) + bfloat16(1)\n256\n```\nAfter 256, the next representable value in bfloat16 is 258:\n\n```python\n>>> np.nextafter(bfloat16(256), bfloat16(np.inf))\n258\n```\nFor better results you can specify that the accumulation should happen in a\nhigher-precision type like `float32`:\n\n```python\n>>> vals.sum(dtype='float32').astype(bfloat16)\n4992\n```\nIn contrast to NumPy, projects like [JAX](http://jax.readthedocs.io/) which support\nlow-precision arithmetic more natively will often do these kinds of higher-precision\naccumulations automatically:\n\n```python\n>>> import jax.numpy as jnp\n>>> jnp.array(vals).sum()\nArray(4992, dtype=bfloat16)\n```\n\n## License\n\n*This is not an officially supported Google product.*\n\nThe `ml_dtypes` source code is licensed under the Apache 2.0 license\n(see [LICENSE](LICENSE)). Pre-compiled wheels are built with the\n[EIGEN](https://eigen.tuxfamily.org/) project, which is released under the\nMPL 2.0 license (see [LICENSE.eigen](LICENSE.eigen)).\n",
"bugtrack_url": null,
"license": " Apache License Version 2.0, January 2004 http://www.apache.org/licenses/ TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION 1. Definitions. \"License\" shall mean the terms and conditions for use, reproduction, and distribution as defined by Sections 1 through 9 of this document. \"Licensor\" shall mean the copyright owner or entity authorized by the copyright owner that is granting the License. \"Legal Entity\" shall mean the union of the acting entity and all other entities that control, are controlled by, or are under common control with that entity. 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