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Groups > comp.std.c > #6589

casts and contraction of floating expressions

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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.

Notes:
  * With GCC, at least the -O2 optimization level is needed for
    contraction of FP expressions, and options like -std=c17 must not
    be used, because GCC disables the contraction of FP expressions
    if such an option is present, due to the fact that GCC doesn't
    support the STDC FP_CONTRACT pragma.
  * A compiler option like -march=native may be needed in case the
    default architecture is assumed not to have a hardware FMA.
  * Intel's oneAPI compiler 2021.3.0.20210619 is actually buggy as
    it contracts FP expressions even with -ffp-contract=off and the
    STDC FP_CONTRACT pragma set to OFF.

-- 
Vincent Lefèvre <vincent@vinc17.net> - Web: <https://www.vinc17.net/>
100% accessible validated (X)HTML - Blog: <https://www.vinc17.net/blog/>
Work: CR INRIA - computer arithmetic / AriC project (LIP, ENS-Lyon)

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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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