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From: eachus@spectre.mitre.org (Robert I. Eachus)
Subject: Re: Can compilers do this?
Date: 1996/02/26
Message-ID: <EACHUS.96Feb26114315@spectre.mitre.org>#1/1
X-Deja-AN: 141239388
references: <4gjd6g$mfq@newsbf02.news.aol.com>
organization: The Mitre Corp., Bedford, MA.
newsgroups: comp.lang.ada
Date: 1996-02-26T00:00:00+00:00
List-Id: <comp.lang.ada>

In article <4gjd6g$mfq@newsbf02.news.aol.com> bwburnsed@aol.com (BWBurnsed) writes:

  > I came across some very strange looking code that someone else wrote,
  > long, long ago, and (apparently) in a universe far, far away. But before I

  > make too many critical comments, I want to be sure I'm not missing
  > something.

  > Repeatedly in this code (in many files), there are places where a floating
  > point variable is tested to see if it is negative. However, the way it is
  > done is:

  >	if  X * abs(X)  <  0.0  then  ...

  > Is there (or was there ever) some pathological anomaly about
  > floating point implementations that would make a conversion (abs)
  > and floating point multiply preferable to testing a sign bit? Can,
  > and will, optimizing compilers recognize the real test desired in
  > such constructs, i.e. reduce it to a sign bit test?

   A lot of answers have shown up here which focused on hardware which
supports negative zeros.  But anyone with a through understanding of
floating-point should recognize that there are many legitimate
negative numbers for which this expression is false.  In fact it
becomes much more understandable if written:

   if X < 0.0 and then X * X > Float'Model_Small then  ...

  (Replace Model_Small with Safe_Small in Ada 83, and Float with the
appropriate type name if it isn't Float.)

   But of course this is just a (portable) approximation to the
behavior on your hardware.  In any case it looks as if the author of
the code is trying to avoid treating small deviations from zero,
probably due to floating point arithmetic errors, as negative.

   Of course if this is the intended effect, the "best" portable
source would be:

   Fuzz: constant Float := Sqrt(Float'Model_Small);  -- or whatever
   ...
   if X + Fuzz < 0.0 then ...

--

					Robert I. Eachus

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