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Re: [RFC] Fix PR28684

On Tue, 14 Nov 2006, Roger Sayle wrote:

> On Tue, 14 Nov 2006, Revital1 Eres wrote:
> > > Perhaps pragmatically, reciprocal-math-optimizations can be those
> > > that strength reduce divisions into (an equal number of)
> > > multiplications.
> >
> > but  x / y   into  x * (1/y) seems to not fit it which might hurt
> > targets which support reciprocal but not division operations (i.e.
> > Altivec).
> >
> > I still prefer the former definition... but that just me :-)
> I'm trying to constructively work towards some kind of resolution.
> To me the fundamental issue is why not use "-ffast-math"?

One popular reason of not using -ffast-math is that on i?86 it enables
some "interesting" intrinsics (fsin, etc.) which are broken in multiple
ways.  Another popular reason is that at least "strength reducing"
divisions can have very bad impact on the stability of simulation codes.

So from that perspective I would argue to split -freciprocal-math and
-mfancy-math-387 (or what it is called - maybe just add a new
-mbroken-math-387 flag) from -ffast-math making -ffast-math more usable?

At least one of the problems with -ffast-math (or 
-funsafe-math-optimizations) is, that it is poorly documented.  Separating
different issues to different flags seems like an improvement to me.

Especially -freciprocal-math and -fassociative-math seem to be good
choices here (I'd include contraction to -fassociative-math, as well
as violating signedness-of-zero issues).  Of course I'd love to be
just able to disable the broken i387 intrinsics (not _all_ of the
fancy-math stuff is broken after all...).

So if we fix the special brokeness of i?86 (80bit excess precision
comes to my mind here, too) and split -freciprocal-math from
-funsafe-math-optimizations we can make that option more sound by
renaming it to -faccurate-math (like you suggested below).


> Some of the arguments have focused on "because I don't understand which
> transformations that enables".  The ignorance of users is not normally
> a great motivation for change.  If someone can't come up with a concrete
> example of a problematic transformation, then there's probably no reason
> not to trust GCC's optimizers.
> Clint Whaley's bug report, PR middle-end/28684, survived not being
> immediately closed a "not-a-bug/wont-fix" because if provided an
> interesting use case.  When benchmarking hardware on numerical kernels,
> it's useful to establish an Mflop number, which is the number of
> floating point operations.  This allows several forms of associativity,
> but not the full range of -ffast-math.  This is a well-defined problem,
> useful to a small group of specialists, and it seems reasonable to
> support it.
> Your interest from the point of view of vectorization is unrelated,
> and not clearly defined.  For better or worse, historically GCC's
> attitude to floating point optimizations is to only transformations
> that produce bit-identical results by default.  A constraint much
> stronger than other compilers.  Anything less than this has gone under
> the name of "unsafe" math optimizations.  Any numerical expert will
> tell you only have to ignore sign depenendent rounding, or re-associate
> an expression to produce a last bit error, which after only a few
> additional steps can make the results uncomparable.  The numeric
> errors you get from ignoring the sign of zeros, are no different in
> magnitude than converting divisions into multiplications, or implementing
> pow by multiplications, or using extra precision on x87, or use of
> fmadd instructions.
> On this scale, there are very few vectorization transformations that
> GCC would consider "safe" and produce bit identical results.  A sad
> fact is the vectorizaton is what GCC calls "unsafe".  The semantics
> and wording you prefer in your patch allows for an unbounded error in
> the result, so the distinction can't be a "quality" argument.
> So we now need to consider what semantics it is that you are trying
> to address.  You wish to allow "X/Y" as "(1/Y)*X", but ultimately
> how is that any different from plain -ffast-math, which should be
> used routinely by GCC users.  Perhaps rather than say we'd like a
> mysterious new option to include transformation FOO or BAR, perhaps
> we need to look at it the other way and ask which transformations
> do you want to disallow.  If there are none, then the current
> defintion should work well for you.
> I think there's still some merit in Clint's request for an Mflop
> preserving subset of -ffast-math, which is PR28684, but I see any
> thing else as solving a different (and perhaps irrelevant) problem.
> I agree the wording (and naming) of -funsafe-math-optimizations
> needs to be improved.  In my mind, -funsafe-math-optimizations is
> restricted to all of the mathematically valid transformations that
> are permissable assuming unbounded precision arithmetic.  Things
> like x+0 -> x.  Unfortunately we live in a world where the
> limitations of our (IEEE) hardware mean that arithmetic performed
> in a computer doesn't match or perfectly model a Newtonian universe.
> For example, Richard Gunether has recently proposed a patch to
> transform pow(x,1.5) into x*sqrt(x), but didn't appreciate why
> the transformation was guarded by -funsafe-math-optimizations.
> The answer is that although the two expressions are equivalent
> mathematically, and the later is not only faster but may often be
> more accurate on most inputs, they are not guaranteed to be identical.
> Hence codes that assume "y = 1.5; if (pow(x,1.5) == pow(x,y))" may
> start to fail.  Even though the numerical accuracy has improved,
> we disallow this transformation.  Indeed both Robert Scott Ladd,
> my own OpenEye experience, an other gcc postings have confirmed that
> numerical accuracy is usually improved, but at the expense of
> numerical precision.
> Perhaps we should rename this option -faccurate-math and describe
> the default as -fprecise-math. :-)
> I'm a bit disappointed that neither the ATLAS folks nor yourself have
> yet articulated a strong functionality request.  I appreciate that you're
> somehow unhappy with -ffast-math, but apart from the Mflops argument
> you've failed to put your finger on precisely (or exactly :-) what
> about it you believe needs fixing.  Even in the Mflops argument is
> seems ambiguous whether operations of constant arguments may be evaluated
> at compile-time, "2.0 + 3.0 -> 5.0"?
> Anyway, I'm pleased that we're discussing the issues.
> Roger
> --

Richard Guenther <>
Novell / SUSE Labs

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