On Tue, Jun 5, 2012 at 2:58 PM, Stephen Canon <[email protected]> wrote:
> On Jun 5, 2012, at 2:45 PM, John McCall <[email protected]> wrote: > > > On Jun 5, 2012, at 2:15 PM, Stephen Canon wrote: > > > >> On Jun 5, 2012, at 1:51 PM, Chandler Carruth <[email protected]> > wrote: > >> > >>> That said, FP_CONTRACT doesn't apply to C++, and it's quite unlikely > to become a serious part of the standard given these (among other) > limitations. Curiously, in C++11, it may not be needed to get the benefit > of fused multiply-add: > >> > >> Perversely, a strict reading of C++11 seems (to me) to not allow FMA > formation in C++ at all: > >> > >> • The values of the floating operands and the results of floating > expressions may be represented in greater precision and range than that > required by the type; the types are not changed thereby. > >> > >> FMA formation does not increase the precision or range of the result > (it may or may not have smaller error, but it is not more precise), so this > paragraph doesn't actually license FMA formation. I can't find anywhere > else in the standard that could (though I am *far* less familiar with C++11 > than C11, so I may not be looking in the right places). > > > > Correct me if I'm wrong, but I thought that an FMA could be formalized > as representing the result of the multiply with greater precision than the > operation's type actually provides, and then using that as the operand of > the addition. It's understand that that can change the result of the > addition in ways that aren't just "more precise". Similarly, performing > 'float' operations using x87 long doubles can change the result of the > operation, but I'm pretty sure that the committees explicitly had hardware > limitations like that in mind when they added this language. > > That's an interesting point. I'm inclined to agree with this > interpretation (there are some minor details about whether or not 0*INF + > NAN raises the invalid flag, but let's agree to ignore that). > > I'm not familiar enough with the language used in the C++ spec to know > whether this makes C++ numerics equivalent to STDC FP_CONTRACT on, or > equivalent to "allow greedy FMA formation". Anyone? > If you agree w/ John's interpretation, and don't consider the flag case you mention, AFAICT, this allows greedy FMA formation, unless the intermediate values are round-tripped through a cast construct such as I described. It definitely doesn't match STDC FP_CONTRACT ON as there is no special status granted due to the expressions being written in different source statements.
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