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Re: casts and contraction of floating expressions

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Vincent Lefevre <vincent-news@vinc17.net> writes:

> The C standard says in 6.5:
>
>   A floating expression may be contracted, that is, evaluated as
>   though it were a single operation, thereby omitting rounding errors
>   implied by the source code and the expression evaluation method.
>
> with the following note:
>
>   The intermediate operations in the contracted expression are
>   evaluated as if to infinite range and precision, while the final
>   operation is rounded to the format determined by the expression
>   evaluation method.  [...]
>
> But it says nothing about casts, which are explicit conversion
> operations that normally remove any intermediate extended precision,
> as if they were assimilated to a real rounding operation (rather
> than something that would just give an additional rounding error),
> just like the rint() function.
>
> So my question is:
>
> In the following code
>
>   volatile double a = 0x1.00000001p+0;
>   volatile double b = -1.0;
>
>   printf ("%a\n", (double) (a * a) + b);
>   printf ("%a\n", (float) (a * a) + b);
>
> may the (double) (a * a) + b and (float) (a * a) + b FP expressions
> be contracted with the use of a FMA, i.e. as if fma(a,a,b) were used?
>
> Based on my above remark, I would say "no".
>
> But GCC (at least until a 14.0.0 20231017 snapshot), Clang (at least
> until version 17) and Intel's oneAPI compiler 2021.3.0.20210619 all
> contract (double) (a * a) + b with the use of a FMA;  thus they output
> 0x1.000000008p-31 instead of 0x1p-31.
>
> However, these compilers do not contract (float) (a * a) + b:
> they output 0x1p-31.  It is rather surprising that they treat it
> differently.

I can see how an argument might be made that contraction is
allowed for the (double) cast line, and not allowed for the
line with the (float) cast.  A good test to do would be the
same exression but with a (long double) cast in place of the
(double) or (float) cast.  I think an argument could be made
either way that contraction is allowed in that situation.

I think I'm mostly on your side, the cast not preventing the
contraction is unexpected and at least at first blush at
odds with what else the standard says.  I completely agree
that the point needs clarifying.

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Thread

casts and contraction of floating expressions Vincent Lefevre <vincent-news@vinc17.net> - 2023-11-22 16:35 +0000
  Re: casts and contraction of floating expressions Tim Rentsch <tr.17687@z991.linuxsc.com> - 2023-11-27 11:11 -0800

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