Greetings, and thanks to all for the very helpful feedback!
I'd also like to note in passing that the excellent SBCL out of the box
triggers an error, which we separately refer to as an 'exception trap',
when NaN is passed to the comparison functions, e.g. '=. And low and
behold, gcl does the same when 'trapping' is turned on, but gcl turns
trapping off 'out of the box'. NaN does not trigger an exception nor
I hope you will consider changing the default to trap on invalid operations so that instead of returning NaN, an error is signaled. I certainly hate this behaviour, because after you do a long set of numerical computations, all the results are NaN. I've just wasted a whole bunch of time. This is super-annying in _javascript_ where you don't have an option of disabling traps. Now you get to go through all the code and either put prints or checks for NaN to see what caused it. What a colossal waste of time when the computer could have told me.
error when passed to '+,'*,'cos etc. but returns NaN. This is the
current state of play. What follows is a discussion of what it means
and the best way to fit NaN into the common-lisp type lattice so it does
not get in the way of the compiler.
In summary, NaN seems indistinguishable to me from an ignorable error
indicator at the hardware level. It is not conceptually a 'valid input'
to any of these functions, but is a clever design to propagate the error
properly when ignored. Conceptually, it seems no different from
'ignore-errors in common-lisp. So really the spec is not all that far
away from IEEE.
I suppose that that is true, but I don't think any Lisp programmer would wrap their entire programs in a ignore-errors form. That's usually one done on a very limited scope. Having traps off to get NaN, is basically the same idea.
As for common-lisp types, the obvious path is what GCL and others
currently implement, double precision NaN is of type 'long-float and
hence 'number. This actually means that lisp will *stray* from IEEE and
I think one thing that confuses me, is that for gcl, single-float = double-float = double precision. short-float is single precision. I think long-float is double-precision. I think all other lisps have single-float = single precision, double-float = double precision. Short-float is usually the same as single-float. Long-float is usually double-float, if they don't have a separate long-float (like clisp).
So whenever you say long-float, I sometimes think of actual long-floats like clisp, but you're actually talking about double-precision floats.