400 lines
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400 lines
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Metadata-Version: 2.1
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Name: ml-dtypes
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Version: 0.2.0
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Author-email: ml_dtypes authors <ml_dtypes@google.com>
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License:
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Apache License
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http://www.apache.org/licenses/
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Classifier: Programming Language :: Python :: 3
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# ml_dtypes
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[![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)
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[![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)
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[![PyPI version](https://badge.fury.io/py/ml_dtypes.svg)](https://badge.fury.io/py/ml_dtypes)
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`ml_dtypes` is a stand-alone implementation of several NumPy dtype extensions used in machine learning libraries, including:
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- [`bfloat16`](https://en.wikipedia.org/wiki/Bfloat16_floating-point_format):
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an alternative to the standard [`float16`](https://en.wikipedia.org/wiki/Half-precision_floating-point_format) format
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- `float8_*`: several experimental 8-bit floating point representations
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including:
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* `float8_e4m3b11fnuz`
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* `float8_e4m3fn`
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* `float8_e4m3fnuz`
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* `float8_e5m2`
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* `float8_e5m2fnuz`
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- `int4` and `uint4`: low precision integer types.
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See below for specifications of these number formats.
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## Installation
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The `ml_dtypes` package is tested with Python versions 3.8-3.11, and can be installed
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with the following command:
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```
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pip install ml_dtypes
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```
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To test your installation, you can run the following:
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```
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pip install absl-py pytest
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pytest --pyargs ml_dtypes
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```
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To build from source, clone the repository and run:
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```
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git submodule init
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git submodule update
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pip install .
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```
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## Example Usage
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```python
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>>> from ml_dtypes import bfloat16
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>>> import numpy as np
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>>> np.zeros(4, dtype=bfloat16)
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array([0, 0, 0, 0], dtype=bfloat16)
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```
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Importing `ml_dtypes` also registers the data types with numpy, so that they may
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be referred to by their string name:
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```python
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>>> np.dtype('bfloat16')
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dtype(bfloat16)
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>>> np.dtype('float8_e5m2')
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dtype(float8_e5m2)
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```
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## Specifications of implemented floating point formats
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### `bfloat16`
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A `bfloat16` number is a single-precision float truncated at 16 bits.
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Exponent: 8, Mantissa: 7, exponent bias: 127. IEEE 754, with NaN and inf.
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### `float8_e4m3b11fnuz`
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Exponent: 4, Mantissa: 3, bias: 11.
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Extended range: no inf, NaN represented by 0b1000'0000.
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### `float8_e4m3fn`
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Exponent: 4, Mantissa: 3, bias: 7.
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Extended range: no inf, NaN represented by 0bS111'1111.
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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.
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### `float8_e4m3fnuz`
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8-bit floating point with 3 bit mantissa.
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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.
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This type has the following characteristics:
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* bit encoding: S1E4M3 - `0bSEEEEMMM`
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* exponent bias: 8
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* infinities: Not supported
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* NaNs: Supported with sign bit set to 1, exponent bits and mantissa bits set to all 0s - `0b10000000`
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* denormals when exponent is 0
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### `float8_e5m2`
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Exponent: 5, Mantissa: 2, bias: 15. IEEE 754, with NaN and inf.
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### `float8_e5m2fnuz`
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8-bit floating point with 2 bit mantissa.
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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.
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This type has the following characteristics:
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* bit encoding: S1E5M2 - `0bSEEEEEMM`
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* exponent bias: 16
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* infinities: Not supported
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* NaNs: Supported with sign bit set to 1, exponent bits and mantissa bits set to all 0s - `0b10000000`
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* denormals when exponent is 0
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## `int4` and `uint4`
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4-bit integer types, where each element is represented unpacked (i.e., padded up
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to a byte in memory).
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NumPy does not support types smaller than a single byte. For example, the
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distance between adjacent elements in an array (`.strides`) is expressed in
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bytes. Relaxing this restriction would be a considerable engineering project.
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The `int4` and `uint4` types therefore use an unpacked representation, where
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each element of the array is padded up to a byte in memory. The lower four bits
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of each byte contain the representation of the number, whereas the upper four
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bits are ignored.
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## Quirks of low-precision Arithmetic
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If you're exploring the use of low-precision dtypes in your code, you should be
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careful to anticipate when the precision loss might lead to surprising results.
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One example is the behavior of aggregations like `sum`; consider this `bfloat16`
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summation in NumPy (run with version 1.24.2):
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```python
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>>> from ml_dtypes import bfloat16
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>>> import numpy as np
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>>> rng = np.random.default_rng(seed=0)
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>>> vals = rng.uniform(size=10000).astype(bfloat16)
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>>> vals.sum()
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256
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```
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The true sum should be close to 5000, but numpy returns exactly 256: this is
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because `bfloat16` does not have the precision to increment `256` by values less than
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`1`:
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```python
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>>> bfloat16(256) + bfloat16(1)
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256
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```
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After 256, the next representable value in bfloat16 is 258:
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```python
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>>> np.nextafter(bfloat16(256), bfloat16(np.inf))
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258
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```
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For better results you can specify that the accumulation should happen in a
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higher-precision type like `float32`:
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```python
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>>> vals.sum(dtype='float32').astype(bfloat16)
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4992
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```
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In contrast to NumPy, projects like [JAX](http://jax.readthedocs.io/) which support
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low-precision arithmetic more natively will often do these kinds of higher-precision
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|
accumulations automatically:
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|
```python
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|
>>> import jax.numpy as jnp
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>>> jnp.array(vals).sum()
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|
Array(4992, dtype=bfloat16)
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||
|
```
|
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## License
|
||
|
|
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|
*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)).
|