Formal comment #141 (enhancement)

It is not clear what negating 0.0 produces
Reported by: 	Felix Klock
Version:	5.92


summary: It is not clear what negating -0.0 produces (if it is even
specified)

description:

(FYI this whole comment is modulo the assumption that we're talking
about an implementation of R6RS that uses IEEE binary floating point
numbers.)

The specification of - says on page 40 that when - is applied to a
single argument, it returns the additive inverse of its
argument. Likewise, the specification of fl- says on page 101 that
when fl- is applied to a single argument, it returns the additive
flonum inverse of its argument.

I am not sure that these descriptions uniquely specify the value of (-
0.0) or (fl- 0.0). In particular, aren't 0.0 and -0.0 both additive
inverses of 0.0? That is, for any number x, (= x (+ x 0.0 -0.0) (+ x
0.0 0.0)), right?

I do not believe there is an obviously correct choice between 0.0 and
-0.0. In support of this statement, here is an informal tally of
Scheme system behaviors (a * means that particular scheme
implementation does not yield negative infinity from (/ 1.0 (* -1.0
0.0)), and therefore there may be no way to actually observe a -0.0):

(- 0.0) is -0.0
MzScheme
Chicken*
Gambit
Chez
Kawa

(- 0.0) is 0.0
Larceny
Scheme48*
Bigloo
SCM*
MIT Scheme*

(Corrections to the above tally are welcome.)

If R6RS does specify whether (- 0.0) produces -0.0 or 0.0, there is
some support for choosing -0.0 given in Goldberg [1], where he says
that the identity "-x = 0 - x fails for x = +0.".

Perhaps the choice between the two possible results is meant to be
left unspecified. But even then I think it should be explicitly stated
as being unspecified, in the same manner that (fllog -0.0) is given as
an example producing an unspecified

Proposals for how to fix the issue:

Either:

   1. Specify that (fl- 0.0) produces -0.0 and (fl- -0.0) produces
      0.0, and likewise for -.

   2. Specify that (fl- 0.0) produces -0.0 and (fl- -0.0) produces
      0.0. For (- 0.0) and (- -0.0), explicitly state that the result
      is either -0.0 or 0.0, but the choice is otherwise unspecified.

   3. For both fl- and -, explicitly state that the result is either
      -0.0 or 0.0, but the choice is otherwise unspecified.

-Felix

[1] "What Every Computer Scientist Should Know About Floating-Point Arithmetic"

    http://docs.sun.com/source/806-3568/ncg_goldberg.html


RESPONSE:

Since the draft R6RS does not insist upon IEEE arithmetic, and
implementations are free to use IEEE arithmetic to implement
non-IEEE arithmetic, the draft R6RS can only recommend how these
operations should operate on inexact zeroes.

As of this writing, the IEEE-754 and IEEE-854 standards have
expired and their (combined) replacement has not yet received
formal approval.

Following IEEE-754R Draft 1.2.5, the R6RS should recommend

    (fl- 0.0)       => -0.0
    (fl- -0.0)      => 0.0
    (fl+ 0.0 -0.0)  => 0.0
    (fl+ -0.0 0.0)  => 0.0
    (fl+ 0.0 0.0)   => 0.0
    (fl+ -0.0 -0.0) => -0.0
    (fl- 0.0 -0.0)  => 0.0
    (fl- -0.0 0.0)  => -0.0
    (fl- 0.0 0.0)   => 0.0
    (fl- -0.0 -0.0) => 0.0
    (flsqrt -0.0)   => -0.0

and should refer readers to the anticipated IEEE standard for
more details.