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From: jimv@omepd (Jim Valerio)
Newsgroups: comp.lang.c
Subject: Re: Optimizing Floating-Point Expression Evaluation
Message-ID: <589@omepd>
Date: Mon, 20-Apr-87 23:02:09 EST
Article-I.D.: omepd.589
Posted: Mon Apr 20 23:02:09 1987
Date-Received: Wed, 22-Apr-87 05:35:10 EST
References: <16646@sun.uucp> <4616@utcsri.UUCP>
Reply-To: jimv@omepd.UUCP (Jim Valerio)
Organization: Intel Corp., Hillsboro
Lines: 39
Summary: floating-point arithmetic is not associative

In article <4616@utcsri.UUCP> flaps@utcsri.UUCP (Alan J Rosenthal) writes:
>please explain how you can know whether or not I care about
>evaluation order in the following:
>	#define THING (a + 3.5)
>	...
>	c = (THING + 1.1) * 2.6;
>How do I say that I want the 3.5 and 1.1 to be added at compile time?

The answer is simple: the compiler can't read your mind.  In this
particular example, assume for example that all the variables are IEEE
single precision numbers, all intermediate arithmetic is done in single
precision, and `a' has the value -4.6, correctly rounded.  In this case,
	(a + (3.5 + 1.1))
is zero and
	((a + 3.5) + 1.1)
is nonzero and long ways away from underflowing.  Which answer is "right"?

Can you guarantee that `a' is never -4.6 here, so the only difference
between the two expressions is a rounding error?  When computing the
expression, in which direction do you want rounding errors to be
incurred?  How is the result going to be used?  Will errors cancel
out here, or will they accumulate?

Welcome to the world of error analysis.


But I think you are asking the wrong question.  I would ask: why
partake in the reprehensible practice of hiding the floating-point
arithmetic behind a macro name if you don't want it to be taken a an
indivisible entity?  Why declare `THING' unless you want to treat it in
the program as a single variable?  If `THING' is imitating a single
variable, then the parentheses should be honored.  If `THING' is
imitating a cheap function call, then following the parentheses exactly
mimics the desired semantics.

My point is that this is an example of intent to evaluate the expression
in the parenthesized order, or plain poor code.
--
Jim Valerio	{verdix,intelca!mipos3}!omepd!jimv, jimv@omepd.intel.com