NaNs library proposal

Library proposal

(nan? <obj>)

nan? returns #t if <obj> is a NaN.

(nan)

Returns a NaN}}} with an implementation-defined chosen payload. Implementations are free to return different {{{NaNs}}} for each `nan` invocation or not. The reader calls the `nan` function with no parameter each time it encounters a {{{NaN representation such as "+nan.0".

(nan <payload>)

Returns a NaN with the given payload as its content. Valid values for <payload> are implementation-dependent.

(nan->payload <obj>)

Returns the payload content of <obj> if it is a NaN.

Rationale

This library is about NaNs operation handling.

For IEEE Standard for Floating-Point Arithmetic (IEEE 754) implementation there is one NaN}}} concept but many different {{{NaNs}}}. From the purpose of {{{NaNs}}}, we have to be able to distinguish between {{{NaNs}}}. For that effect, {{{NaNs}}} carry a ''payload'' intended to put diagnosis information about what caused a {{{NaN to be produced.

Purposes of NaNs

• allowing computation to continue even in the presence of incorrect computation, instead of aborting with an error.

• to be able to discover what kind of error has been encountered if needed, by propagating a NaN value.

When the reader reads "+nan.0", it has to choose one particular internal representation for it. It is free to choose one representation shared for all "+nan.0" or to choose a different one each time it encounters another "nan.0". This is what the following means:

(eqv? +nan.0 +nan.0) => unspecified

However the identity of a particular NaN should not be questioned. I mean I think we should have this:

(let ((a +nan.0)) (eqv? a a)) => #t

The following is a desirable behaviour, but I would not push for it into the standard:

(let ((a (/ 0.0 0.0)) (b (sin +inf.0))) (eqv? a b)) => #f

Use cases examples

• Report invalid sensor values

Instead of returning strange values such as 99999 which could be mistaken for real ones and cause dramatic effects, sensors may use NaNs to report invalid values. A payload may be added to report an additional message.

• Mark undefined values in a vector of reals

In order to identify wrong usage of uninitialased vectors, one could fill vectors with NaNs containing indexes in their payloads.

(define (make-reals-vector N) (if (>= N 0) (let ((result (make-vector N))) (let loop ((i 0)) (if (< i N) (begin (vector-set! result i (nan i)) (loop (+ i 1))) result ))) (error "make-float-vector: negative argument")))

Comments by John Cowan

I think the payload should be constrained to be an exact non-negative integer interpreted as a sequence of bits. In IEEE formats, the sign bit is part of the payload, and should be extractable separately from the payload using nan-negative? or some such predicate. In addition, the sense of the signaling/quiet bit is implementation-dependent (it is always the highest-order bit of the mantissa, but whether 1 is signaling or quiet depends on the hardware), and so nan-signaling? should also be added.

In addition, the requirement that read invoke nan seems pointless to me. If read returns any old NaN, that should be good enough.Â