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external representations

This page is part of the web mail archives of SRFI 70 from before July 7th, 2015. The new archives for SRFI 70 contain all messages, not just those from before July 7th, 2015.

I have four things to say.

1.  Defining a distinct external syntax for every NaN,
or providing some other means for programs to create
specific NaNs, would interfere with a representation
that is likely to be of great importance on 64-bit

2.  The proposed 1/0 and -1/0 syntax for infinities
has two related problems: it looks like these things
are exact, and allowing this syntax will require a
more complicated rule for deciding whether a numeric
literal is exact or inexact.

3.  The +inf.0 and -inf.0 syntax is already used by
several implementations, which agreed to standardize
upon it several years ago, before the SRFI process
began.  Th +inf.0 and -inf.0 syntaxes (and +nan.0)
also appear within The Revised R6RS Status Report of
October 2004, which is online at www.schemers.org.

4.  So far as I can tell, the R5RS does not require
every number to have an external representation.

With regard to the first point, one of the most
attractive 64-bit representations is to represent
all non-NaN inexact reals in IEEE double precision
format, and to represent all other Scheme values as
NaNs.  This works because there are about 2^53 NaNs,
which is about 2^53 more NaNs than are needed to
represent the results of floating point computation.

Using these excess NaNs to encode all of Scheme's
non-flonum values is practical, and results in very
efficient floating point calculation.  I would oppose
any proposed external syntax for NaNs that might
interfere with the representation of Scheme values
as NaNs.

With regard to 2 and 3, I think SRFIs and other
standardization processes should attempt to build on
past standardization; otherwise we'll just be going
around in circles.  The proposed 1/0 and -1/0 syntax
is contrary to the R5RS rule for determining whether
an external representation names an exact or inexact
number.  It is also contrary to the informal standard
that several major implementations have already agreed
upon and have used for several years.  Finally, it is
contrary to the syntax being considered by the R6RS
editors.  Their progress report of October 2004 listed
+inf.0 and -inf.0 among the things that are "probably
not terribly controversial".