pychop: Emulating Low-Precision Arithmetic in Numerical Methods and Neural Networks

Motivated by the growing demand for reduced-precision arithmetic in computational science, we exploit lower-precision emulation in Python---widely regarded as the dominant programming language for numerical analysis and machine learning. Low-precision paradigms have revolutionized deep learning by enabling more efficient computation and reduced memory footprint while maintaining model fidelity. To better enable numerical experimentation with and exploration of reduced-precision computation, we developed the \texttt{pychop}, which supports customizable floating-point formats and a comprehensive set of rounding modes in Python, allowing users to benefit from fast, reduced-precision emulation in numerous applications. \texttt{pychop} also introduces interfaces for {array and tensor backends}, enabling efficient reduced-precision emulation on GPUs for neural network training and inference with unparalleled flexibility. In this paper, we offer a comprehensive exposition of the design and applications of \texttt{pychop}, establishing it as a foundational tool for advancing mixed-precision algorithms. Furthermore, we present empirical results on reduced-precision emulation for image classification and object detection using published datasets, illustrating the sensitivity of the use of low precision and offering valuable insights into its quantization-aware training and post-quantization impacts. \texttt{pychop} enables in-depth investigations into the effects of numerical precision, facilitates the development of novel hardware accelerators, and integrates seamlessly into existing deep learning workflows.