MATLAB Simulator of Level-Index Arithmetic
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866929328374153216 |
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| author | Mikaitis, Mantas |
| author_facet | Mikaitis, Mantas |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_02301 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | MATLAB Simulator of Level-Index Arithmetic Mikaitis, Mantas Mathematical Software Hardware Architecture Numerical Analysis 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. |
| title | MATLAB Simulator of Level-Index Arithmetic |
| topic | Mathematical Software Hardware Architecture Numerical Analysis |
| url | https://arxiv.org/abs/2402.02301 |