Date: Wed, 09 Jun 1999 12:08:29 -0500
From: Eric Rudd <rudd AT cyberoptics DOT com>
Subject: Re: libm sources from cyberoptics
To: Hans-Bernhard Broeker <broeker AT physik DOT rwth-aachen DOT de>
Cc: DJGPP-WORKERS <djgpp-workers AT delorie DOT com>
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Hans-Bernhard Broeker wrote:

> Therefore, this limit cannot possibly exist, and 0^0 cannot
> be given any single, well-defined value.

I agree entirely, and that's why I have pow(0., 0.) returning NaN with EDOM.

> But on looking a bit deeper into the draft standard for C9x (not
> 'the law' yet, but it's going to be), I find in Annex F.9.4.4:
>
>        F.9.4.4  The pow functions
>
>        [#1]
>
>          -- pow(x, ±0) returns 1 for any x, even a NaN.
>
> Unlike some other Annexes, this one is 'normative', not just 'informative'
> stuff. This implies that pow(0,0)==1, by word of the (coming) standard.

(Sigh.) I (and several others) expressed reservations to Annex F in formal public
comments on the committee draft.  Some suggestions were accepted, but Annex F still
specifies return values that (in my opinion) are mathematically indefensible.  For
instance, atan2(INF,INF) is specified to return +/- PI/4 or +/- 3*PI/4, depending on
the signs of the infinities.  This behavior is tantamount to agreeing that INF/INF =
+/- 1.  Also, pow(-2., INF) returns INF, based on the reasoning that infinity is an
even integer.

In my library, I followed the dictates of classical mathematics and C90.  If the
present Annex F survives in the C9x standard, I don't know what I'll do.

-Eric Rudd