Level-index arithmetic appeared in the 1980s. One of its principal purposes is to abolish the issues caused by underflows and overflows in floating point. However, level-index arithmetic does not expand the set of numbers but spaces out the numbers of large magnitude even more than floating-point representations to move the infinities further away from zero: gaps between numbers on both ends of the range become very large. We revisit level index by presenting a custom precision simulator in MATLAB. This toolbox is useful for exploring performance of level-index arithmetic in research projects, such as using 8-bit and 16-bit representations in machine learning algorithms where narrow bit-width is desired but overflow/underflow of floating-point representations causes difficulties.

翻译：层级索引算术诞生于20世纪80年代，其主要目的之一是消除浮点数中下溢和上溢引发的问题。然而，层级索引算术并未扩展数值集合，而是通过比浮点表示更稀疏的方式排布大数值，将无穷远点进一步推离零点：数值范围两端点之间的间距变得极大。本文通过MATLAB自定义精度仿真器重新审视层级索引技术。该工具包有助于在科研项目中探索层级索引算术的性能，例如在需要窄位宽但浮点表示的上溢/下溢会造成困难的机器学习算法中，可采用8位和16位表示。