NaN in Lua 5.3 Reference Manual

["John Hind" <john.hind@...>]

I notice that Lua 5.3 Reference Manual has been extensively edited over 
the last few point releases, but one aspect that is still not very well 
described is NaN. There are three references to it, all tangential. Two 
state that it is not a valid table key while the third describes its 
treatment by comparison operators. The thing itself is never properly 
introduced.

First we have to face up to a logical incongruity: Not-a-Number (NaN) 
*is* a number (type(0/0) == "number")! We probably just have to blame 
the IEEE for that bit of stupidity (these standards committees!) and 
face up to it instead of glossing over it.

The first reference to NaN occurs in 'Basic Concepts' (2.1) in the 
description of the 'table' type: it is stated that, along with nil, NaN 
is not a valid table key. Then in parenthesis "Not a Number is a special 
value used to represent undefined or unrepresentable numerical results, 
such as 0/0." Leaving aside this further logical incongruity (can one 
represent the unrepresentable?), it would be clearer to give this 
definition earlier, in the paragraph introducing the 'number' type.

Indeed the introduction of two number subtypes 'integer' and 'float' 
opens up an opportunity for conceptual clarification. 'NaN' could be 
presented as a third subtype. This would not necessarily imply an 
implementation change, just a change in the way the concept is presented 
in documentation and conceptualised by Lua users. Actually I think it 
does in fact pretty accurately describe the current implementation.

Of course, for the next major release, changing the implementation of 
math.type to return a third distinguished string key for NaN should be 
considered. But this could be independent of changing the conceptual 
representation in the Manual which could be done in a point release.