ml-dtypes


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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. For the purposes of this definition, "control" means (i) the power, direct or indirect, to cause the direction or management of such entity, whether by contract or otherwise, or (ii) ownership of fifty percent (50%) or more of the outstanding shares, or (iii) beneficial ownership of such entity. "You" (or "Your") shall mean an individual or Legal Entity exercising permissions granted by this License. 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Subject to the terms and conditions of this License, each Contributor hereby grants to You a perpetual, worldwide, non-exclusive, no-charge, royalty-free, irrevocable copyright license to reproduce, prepare Derivative Works of, publicly display, publicly perform, sublicense, and distribute the Work and such Derivative Works in Source or Object form. 3. Grant of Patent License. Subject to the terms and conditions of this License, each Contributor hereby grants to You a perpetual, worldwide, non-exclusive, no-charge, royalty-free, irrevocable (except as stated in this section) patent license to make, have made, use, offer to sell, sell, import, and otherwise transfer the Work, where such license applies only to those patent claims licensable by such Contributor that are necessarily infringed by their Contribution(s) alone or by combination of their Contribution(s) with the Work to which such Contribution(s) was submitted. 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            # ml_dtypes

[![Unittests](https://github.com/jax-ml/ml_dtypes/actions/workflows/test.yml/badge.svg)](https://github.com/jax-ml/ml_dtypes/actions/workflows/test.yml)
[![Wheel Build](https://github.com/jax-ml/ml_dtypes/actions/workflows/wheels.yml/badge.svg)](https://github.com/jax-ml/ml_dtypes/actions/workflows/wheels.yml)
[![PyPI version](https://badge.fury.io/py/ml_dtypes.svg)](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_e4m3b11fnuz`
  * `float8_e4m3fn`
  * `float8_e4m3fnuz`
  * `float8_e5m2`
  * `float8_e5m2fnuz`
- `int4` 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.

### `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

## `int4` and `uint4`

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 in
bytes. Relaxing this restriction would be a considerable engineering project.
The `int4` and `uint4` types therefore use an unpacked representation, where
each element of the array is padded up to a byte in memory. The lower four bits
of each byte contain the representation of the number, whereas the upper four
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

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    "description": "# ml_dtypes\n\n[![Unittests](https://github.com/jax-ml/ml_dtypes/actions/workflows/test.yml/badge.svg)](https://github.com/jax-ml/ml_dtypes/actions/workflows/test.yml)\n[![Wheel Build](https://github.com/jax-ml/ml_dtypes/actions/workflows/wheels.yml/badge.svg)](https://github.com/jax-ml/ml_dtypes/actions/workflows/wheels.yml)\n[![PyPI version](https://badge.fury.io/py/ml_dtypes.svg)](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_e4m3b11fnuz`\n  * `float8_e4m3fn`\n  * `float8_e4m3fnuz`\n  * `float8_e5m2`\n  * `float8_e5m2fnuz`\n- `int4` 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### `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## `int4` and `uint4`\n\n4-bit integer types, where each element is represented unpacked (i.e., padded up\nto 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 in\nbytes. Relaxing this restriction would be a considerable engineering project.\nThe `int4` and `uint4` types therefore use an unpacked representation, where\neach element of the array is padded up to a byte in memory. The lower four bits\nof each byte contain the representation of the number, whereas the upper four\nbits 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. For the purposes of this definition, \"control\" means (i) the power, direct or indirect, to cause the direction or management of such entity, whether by contract or otherwise, or (ii) ownership of fifty percent (50%) or more of the outstanding shares, or (iii) beneficial ownership of such entity.  \"You\" (or \"Your\") shall mean an individual or Legal Entity exercising permissions granted by this License.  \"Source\" form shall mean the preferred form for making modifications, including but not limited to software source code, documentation source, and configuration files.  \"Object\" form shall mean any form resulting from mechanical transformation or translation of a Source form, including but not limited to compiled object code, generated documentation, and conversions to other media types.  \"Work\" shall mean the work of authorship, whether in Source or Object form, made available under the License, as indicated by a copyright notice that is included in or attached to the work (an example is provided in the Appendix below).  \"Derivative Works\" shall mean any work, whether in Source or Object form, that is based on (or derived from) the Work and for which the editorial revisions, annotations, elaborations, or other modifications represent, as a whole, an original work of authorship. For the purposes of this License, Derivative Works shall not include works that remain separable from, or merely link (or bind by name) to the interfaces of, the Work and Derivative Works thereof.  \"Contribution\" shall mean any work of authorship, including the original version of the Work and any modifications or additions to that Work or Derivative Works thereof, that is intentionally submitted to Licensor for inclusion in the Work by the copyright owner or by an individual or Legal Entity authorized to submit on behalf of the copyright owner. For the purposes of this definition, \"submitted\" means any form of electronic, verbal, or written communication sent to the Licensor or its representatives, including but not limited to communication on electronic mailing lists, source code control systems, and issue tracking systems that are managed by, or on behalf of, the Licensor for the purpose of discussing and improving the Work, but excluding communication that is conspicuously marked or otherwise designated in writing by the copyright owner as \"Not a Contribution.\"  \"Contributor\" shall mean Licensor and any individual or Legal Entity on behalf of whom a Contribution has been received by Licensor and subsequently incorporated within the Work.  2. Grant of Copyright License. Subject to the terms and conditions of this License, each Contributor hereby grants to You a perpetual, worldwide, non-exclusive, no-charge, royalty-free, irrevocable copyright license to reproduce, prepare Derivative Works of, publicly display, publicly perform, sublicense, and distribute the Work and such Derivative Works in Source or Object form.  3. Grant of Patent License. Subject to the terms and conditions of this License, each Contributor hereby grants to You a perpetual, worldwide, non-exclusive, no-charge, royalty-free, irrevocable (except as stated in this section) patent license to make, have made, use, offer to sell, sell, import, and otherwise transfer the Work, where such license applies only to those patent claims licensable by such Contributor that are necessarily infringed by their Contribution(s) alone or by combination of their Contribution(s) with the Work to which such Contribution(s) was submitted. If You institute patent litigation against any entity (including a cross-claim or counterclaim in a lawsuit) alleging that the Work or a Contribution incorporated within the Work constitutes direct or contributory patent infringement, then any patent licenses granted to You under this License for that Work shall terminate as of the date such litigation is filed.  4. Redistribution. You may reproduce and distribute copies of the Work or Derivative Works thereof in any medium, with or without modifications, and in Source or Object form, provided that You meet the following conditions:  (a) You must give any other recipients of the Work or Derivative Works a copy of this License; and  (b) You must cause any modified files to carry prominent notices stating that You changed the files; and  (c) You must retain, in the Source form of any Derivative Works that You distribute, all copyright, patent, trademark, and attribution notices from the Source form of the Work, excluding those notices that do not pertain to any part of the Derivative Works; and  (d) If the Work includes a \"NOTICE\" text file as part of its distribution, then any Derivative Works that You distribute must include a readable copy of the attribution notices contained within such NOTICE file, excluding those notices that do not pertain to any part of the Derivative Works, in at least one of the following places: within a NOTICE text file distributed as part of the Derivative Works; within the Source form or documentation, if provided along with the Derivative Works; or, within a display generated by the Derivative Works, if and wherever such third-party notices normally appear. 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