[jlgustafson]

Actually, posits handle NaNs already, by interrupting the calculation and doing whatever you have set up to handle the exception. What they do NOT do is represent Not-a-Number with a number. If a programmer is about to compute, say, x/y and in running the code it sometimes hits the case y = 0, then any competent programmer can write a conditional test to guard against that happening. It is not reasonable to ask computer hardware to magically continue to work somehow when it hits a bug in a program.

Think of it this way: posits have a signaling NaN but do not have a quiet NaN.