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Re: Conflicts between C standard and 754-2008



As everyone else has noted, Hossam Fahmy is asking about associativity (which 
is not allowed), not commutativity (which is allowed), so there's not conflict 
there.

Michel is correct that FP addition (or multiplication) may be non-commutative 
in the presence of NaNs -- specifically, if you have two NaNs with differing 
payloads, the result of a*b or a+b my differ from that of b*a or b+a.  This 
does not cause a conflict with 754 either, however.

The clause of 754 at work is 6.2.3 NaN propagation:
"If two or more inputs are NaN, then the payload of the resulting NaN should be 
identical to the payload of one of the input NaNs if representable in the 
destination format. This standard does not specify which of the input NaNs will 
provide the payload."

So (1) we're in a should clause, and (2) even if it were a shall clause, 754 
still wouldn't specify *which* NaN payload propagates, so even on an 
implementation that always propagated the payload of the first argument, (a+b) 
--> (b+a) would be allowed.

- Steve

On Jan 6, 2011, at 5:20 AM, Michel Hack wrote:

Hossam Fahmy wrote:
and without any parenthesis I assumed that the evaluation will always
proceed from left to right and I swapped the second and third term.
So we are getting:
(z-y)+x = 100
and
(z+x)-y=0

Without associativity there is no such thing as a "third term", so you
can't swap 2nd and 3rd terms, and the cited optimization rule does not
apply.

What would be allowed is replacing z-y+x with x+(z-y).

In any case, in the presence of NaNs FP addition may be non-commutative.

Michel.
---Sent: 2011-01-06 13:25:41 UTC


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