pychop 0.2.8

Python code for simulating low precision floating-point arithmetic

pychop

A Python package for simulating low precision arithmetic

With the increasing availability and support of lower-precision floating-point arithmetics beyond the IEEE Standard 64-bit double and 32-bit single precisions in both hardware and software simulation, low-precision arithmetic operations as well as the number formats, e.g., 16-bit half precision, have been widely studied and exploited in numerous applications in the modern scientific computing and machine learning algorithms. Low-precision floating point arithmetic offers greater throughput, reduced data communication, and less energy usage. pychop is a Python library for efficient quantization, it enable to convert single or double precision numbers into low-bitwidth representation. The purpose of pychop, following the same function of chop in Matlab provided by Nick higham, is to simulate the low precision formats as well as fixed-point/integer quantization based on single and double precisions, which is pravalent on modern machine architecture. pychop also provides Torch and JAX backend, which enables to simulate training Neural Network in low precision.

This package provides consistent APIs to the chop software by Nick higham as much as possible. For the first four rounding mode, with the same user-specific parameters, pychop generates exactly same result as that of the chop software. For stochastic rounding (rmode as 5 and 6), both output same results if random numbers is given the same.

Install

The proper running environment of pychop should by Python 3, which relies on the following dependencies:

• python > 3.8
• numpy >=1.7.3
• pandas >=2.0
• torch
• jax

To install the current current release via PIP use:

pip install pychop

The supported floating point formats

The supported floating point arithmetic formats include:

format	description
'q43', 'fp8-e4m3'	NVIDIA quarter precision (4 exponent bits, 3 significand (mantissa) bits)
'q52', 'fp8-e5m2'	NVIDIA quarter precision (5 exponent bits, 2 significand bits)
'b', 'bfloat16'	bfloat16
'h', 'half', 'fp16'	IEEE half precision (the default)
's', 'single', 'fp32'	IEEE single precision
'd', 'double', 'fp64'	IEEE double precision
'c', 'custom'	custom format

The code example can be found on the quick start page.

Contributing

We welcome contributions in any form! Assistance with documentation is always welcome. To contribute, feel free to open an issue or please fork the project make your changes and submit a pull request. We will do our best to work through any issues and requests.

Acknowledgement

This project is supported by the European Union (ERC, InEXASCALE, 101075632). Views and opinions expressed are those of the authors only and do not necessarily reflect those of the European Union or the European Research Council. Neither the European Union nor the granting authority can be held responsible for them.

To do

• Generate data using Nick's chop
• Expand unittests for pychop
• Write quant_dot
• Write FMA
• BLAS

References

[1] Nicholas J. Higham and Srikara Pranesh, Simulating Low Precision Floating-Point Arithmetic, SIAM J. Sci. Comput., 2019.

[2] IEEE Standard for Floating-Point Arithmetic, IEEE Std 754-2019 (revision of IEEE Std 754-2008), IEEE, 2019.

[3] Intel Corporation, BFLOAT16---hardware numerics definition, 2018

[4] Muller, Jean-Michel et al., Handbook of Floating-Point Arithmetic, Springer, 2018