Posits vs. logarithmic number systems

[Joe Duarte]

Hi all – Have posits/unums been formally compared to logarithmic number systems? I'm particularly interested in 1) speed, 2) accuracy/precision (actually, are accuracy and precision different in this context?).

The Wikipedia article on logarithmic number systems provides links to several of the major papers, including the European Logarithmic Microprocessor research: https://en.wikipedia.org/wiki/Logarithmic_number_system

Thanks,

JD

[John Gustafson]

Joe,

Both Peter Lindstrom (LLNL) and Jeff Johnson (Facebook) noticed that the advantages of logarithmic number systems (LNS) and posits could be combined, very easily. The regime and exponent serve the same purpose, representing the characteristic (integer part) of the log base 2 of the number, but the fraction is replaced with the mantissa. (This is one of the biggest reasons people need to stop using the word "mantissa" when talking about floating-point or posit numbers. Mantissas are the part of a logarithm to the right of the radix point). 

When you do this, the jagged accuracy of the accuracy plots goes away and the accuracy becomes a step function. Like for 16-bit posits with es = 2, the accuracy as a function of the magnitude looks like this: