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arXiv · 2402.02301

MATLAB Simulator of Level-Index Arithmetic

Mantas Mikaitis
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Abstract

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.

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Mantas Mikaitis. 2024-04-26. MATLAB Simulator of Level-Index Arithmetic. https://arxiv.org/abs/2402.02301

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