标题： 基于FFT的新兴机器数格式中的谱方法：OFP8、Bfloat16、Posit和Takum算术 显示英文标题

标题： Spectral Methods via FFTs in Emerging Machine Number Formats: OFP8, Bfloat16, Posit, and Takum Arithmetics

摘要： 快速傅里叶变换（FFT）是高性能计算中最广泛使用的算法之一，在信号处理和偏微分方程（PDEs）数值解的谱分析中有关键应用。 这些数据密集型工作负载主要受到内存墙的限制，这促使人们探索新兴的数字格式——如OFP8（E4M3和E5M2）、bfloat16以及渐进精度的posit和takum格式——作为传统IEEE 754浮点表示的潜在替代方案。 本文评估了从8位到64位的各种格式下基于FFT的计算的准确性和稳定性。对一组多样化的图像应用了往返FFT，并对音频信号应用了短时傅里叶变换（STFT）。 结果确认了低位精度下posit算术性能强劲，takum紧随其后。posit在较高精度下表现出稳定性问题，而OFP8格式不合适，bfloat16的表现低于float16和takum。 显示英文摘要

摘要： The Fast Fourier Transform (FFT) is one of the most widely used algorithms in high performance computing, with critical applications in spectral analysis for both signal processing and the numerical solution of partial differential equations (PDEs). These data-intensive workloads are primarily constrained by the memory wall, motivating the exploration of emerging number formats -- such as OFP8 (E4M3 and E5M2), bfloat16, and the tapered-precision posit and takum formats -- as potential alternatives to conventional IEEE 754 floating-point representations. This paper evaluates the accuracy and stability of FFT-based computations across a range of formats, from 8 to 64 bits. Round-trip FFT is applied to a diverse set of images, and short-time Fourier transform (STFT) to audio signals. The results confirm posit arithmetic's strong performance at low precision, with takum following closely behind. Posits show stability issues at higher precisions, while OFP8 formats are unsuitable and bfloat16 underperforms compared to float16 and takum.