April 4 @ 9am PT - Community Meeting: Thanh Son Nguyen on Rigorous Error Analysis for Logarithmic Number Systems

[Zachary Tatlock]

Howdy folks!

This Thursday, April 4 at 9:00-10:00 AM pacific time, will be the next FPBench Community Meeting.

Here's the Zoom link for the meeting:

https://washington.zoom.us/j/92831331326

We are very excited to welcome Thanh Son Nguyen from the University of Utah to present on Rigorous Error Analysis for Logarithmic Number Systems.

Logarithmic Number Systems (LNS) hold considerable promise in helping reduce the number of bits needed to represent a high dynamic range of real-numbers with finite precision, and also efficiently support multiplication and division. However, under LNS, addition and subtraction turn into non-linear functions that must be approximated—typically using precomputed table-based functions. Additionally, multiple layers of error correction are typically needed to improve result accuracy. Unfortunately, previous efforts have not characterized the resulting error bound. We provide the first rigorous analysis of LNS, covering detailed techniques such as co-transformation that are crucial to implementing subtraction with reasonable accuracy. We provide theorems capturing the error due to table interpolations, the finite precision of pre-computed values in the tables, and the error introduced by fix-point multiplications involved in LNS implementations. We empirically validate our analysis using a Python implementation, showing that our analytical bounds are tight, and that our testing campaign generates inputs diverse-enough to almost match (but not exceed) the analytical bounds. We close with discussions on how to adapt our analysis to LNS systems with different bases and also discuss many pragmatic ramifications of our work in the broader arena of scientific computing and machine learning.

Looking forward to seeing y'all and getting into new number system analysis techniques!

Z

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Zachary Tatlock

https://ztatlock.net

Associate Professor

Paul G. Allen School of Computer Science & Engineering

University of Washington