RfD: D>F and S>F second draft

From	C G Montgomery <cgm@physics.utoledo.edu>
Newsgroups	comp.lang.forth
Subject	RfD: D>F and S>F second draft
Date	2015-11-29 17:19 -0500
Organization	the wetware works
Message-ID	<n3fth9$em1$1@dont-email.me> (permalink)

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Author:

Charles G. Montgomery <cgm@physics.utoledo.edu>

Changes from first draft:

A few minor rewordings, non-normative.
New Comments on integers outside range of floating-point values.

Problem:

The current Forth Standard specification for D>F states that an ambiguous 
condition
exists if the double number D cannot be precisely represented as a 
floating-point
value.
Similarly, the specification for S>F calls for an ambiguous condition if 
the single
number N can not be precisely represented as a floating-point value.

The purpose of this proposal is to eliminate these ambiguous conditions by 
instead specifying that if no floating-point value is precisely equivalent 
to the provided integer the word provides the floating-point value which 
is closest to the integer.

This is the behavior provided by some Standard Forth systems, and is often 
what is most useful for the programmer.

Preliminary Remarks:

While Forth is largely untyped, it recognizes the distinction between 
integer and floating-point values.  Section 12.3.1.2 says "The internal 
representation of a floating-point number, including the format and 
precision of the significand and the format and range of the exponent, is 
implementation defined."  This seems to presume that the representation of 
a floating-point value is of the form
    (significand) * (base)^(exponent)  
where (significand), (base), and (exponent) are integers.  Since Section 
12.3.2 refers to the "least significant bit" in defining "round to 
nearest", (base) is presumably 2.
I am not aware of any Forth which is not consistent with these 
presumptions.
So the "representable values" of floating-point numbers is a countable 
subset of the uncountable real numbers.

Integers in Forth may be signed or unsigned.  Floating point values are 
almost invariably signed, so (significand) includes a sign.  D in D>F is 
presumably signed.

Proposal:

In 2.6.1.1130 D>F  (d -- )(F: -- r) replace 
"r is the floating point equivalent of d.  An ambiguous condition exists 
if d cannot be precisely represented as a floating-point value"
with
"r is the floating-point value which is nearest to d in the sense of 
'round to nearest' as given in 12.3.2."

In 12.6.2.2175 S>F  (n -- )(F: -- r) replace 
"r is the floating-point equivalent of the single-cell value n.  An 
ambiguous condition exists if n can not be precisely represented as a 
floating-point value."
with
"r is the floating-point value which is nearest to n in the sense of 
'round to nearest' as given in 12.3.2."

Remove the documentation requirements in section 12.4.1.2 for the no 
longer existing ambiguous conditions from D>F and S>F.

Further Remarks:

D>F is in the FLOATING word set; S>F is in the FLOATING EXT word set.

The reverse operations, F>D and F>S, are unchanged.  For each, the 
Standard includes a note pointing out that rounding a floating-point value 
before using them may be desirable.

No change is needed for the possibly relevant words >FLOAT and REPRESENT.

It remains easy to determine whether the conversion between floats and 
integers is exact, by comparing an initial integer value with the result 
of D>F F>D or S>F F>S.

Implementation and Testing:

For any system which provides the FLOATING and FLOATING EXT word sets and 
does not already comply with this proposal it should not be difficult to 
implement.
Whether floating-point support is in hardware or software, if FROUND and 
similar words can be provided it should be no harder to provide the 
proposed behavior of D>F and S>F.

The intentional flexibility of the Standard in specifying floating point 
internal representations makes it difficult to provide tests which have 
universal applicability to all Standard systems.

Comments:

Discussion has called attention to the situation where an integer lies
outside the range of representable floating-point values.
This proposal clearly calls for the valid extreme floating-point value.
A Standard System could not return something like "inf" or "nan".
The Forth Standard does not address the use of things like "nan" or "+-
inf", which can be useful if they are available from a floating-point
implementation.
To comply with this proposal, a system might need to test for the 
condition and provide the required result as the default.  At the cost of 
one more word in the dictionary, another version could be retained as 
available.
A Standard Program should have no problem in testing for the condition and
taking any desired action. 

An alternative, which I like less but could accept, would be to add to 
both D>F and S>F "An ambiguous condition exists if the integer value lies
outside the range of representable floating point values."
The documentation requirement for this could be considered as included
already in 12.4.1.2 under
  "floating point result out of range (e.g.,in 12.6.1.1430 F/)"
or a separate entry could be devised.

(  end of RfD  )

Regards to all   cgm

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RfD: D>F and S>F second draft C G Montgomery <cgm@physics.utoledo.edu> - 2015-11-29 17:19 -0500
  Re: D>F and S>F second draft "HAA" <someone@microsoft.com> - 2015-12-06 13:02 +1100
    Re: D>F and S>F second draft Bernd Paysan <bernd.paysan@gmx.de> - 2015-12-06 03:28 +0100
      Re: D>F and S>F second draft "Rod Pemberton" <boo@fasdfrewar.cdm> - 2015-12-06 04:01 -0500
    Re: D>F and S>F second draft Albert van der Horst <albert@spenarnc.xs4all.nl> - 2015-12-06 02:27 +0000
      Re: D>F and S>F second draft krishna.myneni@ccreweb.org - 2015-12-06 12:55 -0800
  RfD: D>F and S>F second draft krishna.myneni@ccreweb.org - 2015-12-06 10:18 -0800
    RfD: D>F and S>F second draft krishna.myneni@ccreweb.org - 2015-12-06 10:55 -0800
      Re: RfD: D>F and S>F second draft "Elizabeth D. Rather" <erather@forth.com> - 2015-12-06 09:31 -1000
        Re: RfD: D>F and S>F second draft Paul Rubin <no.email@nospam.invalid> - 2015-12-06 11:48 -0800
          Re: RfD: D>F and S>F second draft krishna.myneni@ccreweb.org - 2015-12-06 12:15 -0800
            Re: RfD: D>F and S>F second draft "Elizabeth D. Rather" <erather@forth.com> - 2015-12-06 14:57 -1000
        Re: RfD: D>F and S>F second draft krishna.myneni@ccreweb.org - 2015-12-06 12:07 -0800
          Re: RfD: D>F and S>F second draft C G Montgomery <cgm@physics.utoledo.edu> - 2015-12-06 20:04 -0500

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