# 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)).

{ "_id": null, "home_page": "", "name": "ml-dtypes", "maintainer": "", "docs_url": null, "requires_python": ">=3.9", "maintainer_email": "", "keywords": "", "author": "", "author_email": "ml_dtypes authors <ml_dtypes@google.com>", "download_url": "https://files.pythonhosted.org/packages/16/6e/9a7a51ee1ca24b8e92109128260c5aec8340c8fe5572e9ceecddae559abe/ml_dtypes-0.3.1.tar.gz", "platform": null, "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```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```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```python\n>>> bfloat16(256) + bfloat16(1)\n256\n```\nAfter 256, the next representable value in bfloat16 is 258:\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```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```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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