(j3.2006) the IEEE modules and distinguishing zero values

[Fred J. Tydeman]

On Wed, 16 Nov 2011 16:04:10 -0600 Craig Dedo wrote:
>
>            The Fortran standard (ISO/IEC 1539-1) is intentionally silent on this issue.
>It has been this way since at least the Fortran 90 standard.  The method of computing
>values on a standard-conforming Fortran processor is defined to be beyond the scope of the
>standard.  In Fortran 2008, this exemption is in section 1.1, paragraph 4, bullet point 8.
>Specifically, this passage says, "This part of ISO/IEC 1539 does not specify . . . the
>physical properties of the representation of quantities and the method of rounding,
>approximating, or computing numeric values on a particular processor, except by reference
>to the IEEE International Standard under conditions specified in Clause 14".

OK.  But, I do not understand "IEEE International Standard" (as far as I know,
IEEE is a USA group, not an international group).  I think it should be
"IEEE-754 Standard" or perhaps "ISO/IEC 60559 International Standard".

>            The requirements for IEEE arithmetic are in section 14.9.  In paragraph 1, the
>Fortran standard says, in part, "Complete conformance with IEC 60559:1989 is not required
>but
>
>         The normal numbers shall be exactly those of IEC 60559:1989 floating-point
>format,
>
>         For at least one rounding mode, the intrinsic operations of addition,
>subtraction, and multiplication  shall conform whenever the operands and result specified
>by IEC 60559:1989 are normal numbers,
>
>.. . .
>
>for that kind of real."

I see that both divide and non-normal numbers are missing from that.  I see that
later paragraphs talk about those missing items.

>            I checked my copy of IEC 60559:1989 and it is silent on the operations that
>you mention above.  

Agreed.

>Therefore, if a Fortran processor claims conformance with IEC
>60559:1989, it can compute any result that it pleases.

So, it must compute a value?  I just stumbled upon:
7.1.5.2.4#1:  
 The execution of any numeric operation whose result is not 
 defined by the arithmetic used by the processor is prohibited. 
 Raising a negative-valued primary of type real to a real power 
 is prohibited.

>            I also checked my copy of the IEC 60559:2010 FDIS.  It includes tables of
>results for the exponentiation operation on pages 42-44, in sections 9.2 and 9.2.1.  For
>the case that you give, IEC 60559:2010 specifies that the result of ?0 ** y is "+? and
>signals the divideByZero exception for finite y < 0".

I disagree.

pown(+/-0,n) is +/-inf and signals the dividByZero exception for 
odd integral n < 0
  Therefore, (-0.0) ** (-1)  is -inf

pow(+/-0,y) is +/-inf and signals the dividByZero exception for y
an odd integer < 0
  Therefore, (-0.0) ** (-1.0)  is -inf

>            Therefore, a standard-conforming Fortran compiler that claims full conformance
>to the IEC 60559:2010 FDIS should return + Infinity and signal the divide-by-zero
>exception.  Otherwise, the Fortran compiler can return any value that it feels like
>returning.

It should be -inf, not +inf.

Even if IEC 60559:2010 is conformed to, the alternative forms in 
Note 7.19 would change the signed zero computed.

---
Fred J. Tydeman        Tydeman Consulting
tydeman at tybor.com      Testing, numerics, programming
+1 (775) 358-9748      Vice-chair of PL22.11 (ANSI "C")
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