POSITS A NEW FLOATING POINT NUMBER FORMAT PROPOSED BY JOHN GUSTAFSON AND ISAAC YONEMOTO Kevin Colville NICIS Centre for High Performance Computing Presented at PyConZA 2020 9 October 2020
6 Plays off extended range with reduced precision Increased precision for “ordinary” scale numbers Physics calculations in MKS units Saturate instead of overflow Unsigned and Numerical error analysis has to be rebuilt factors inexact Multiplicative cancellation Non-constant relative error
Constructing a pseudo-sigmoid by manipulating bits of posit8 Speeding up ML Figure 6. §2.2. John L. Gustafson, Isaac Yonemoto. Beating Floating Point at its Own Game: Posit Arithmetic 7
Further Reading John L. Gustafson, Isaac Yonemoto. Beating Floating Point at its Own Game: Posit Arithmetic http://www.johngustafson.net/pdfs/BeatingFloatingPoint.pdf Florent de Dinechin, Luc Forget, Jean-Michel Muller, Yohann Uguen. Posits: the good, the bad and the ugly. CoNGA 2019 - Conference on Next-Generation Arithmetic, Mar 2019, Singapore, Singapore. pp.1-10, 10.1145/3316279.3316285. hal-01959581v4 https://hal.inria.fr/hal-01959581v4 9