On Thu, Oct 13, 2022 at 7:57 PM Jakub Jelinek <jakub@redhat.com> wrote:
>
> On Thu, Oct 13, 2022 at 02:36:49PM +0200, Aldy Hernandez wrote:
> > +// Like real_arithmetic, but round the result to INF if the operation
> > +// produced inexact results.
> > +//
> > +// ?? There is still one problematic case, i387.  With
> > +// -fexcess-precision=standard we perform most SF/DFmode arithmetic in
> > +// XFmode (long_double_type_node), so that case is OK.  But without
> > +// -mfpmath=sse, all the SF/DFmode computations are in XFmode
> > +// precision (64-bit mantissa) and only occassionally rounded to
> > +// SF/DFmode (when storing into memory from the 387 stack).  Maybe
> > +// this is ok as well though it is just occassionally more precise. ??
> > +
> > +static void
> > +frange_arithmetic (enum tree_code code, tree type,
> > +                REAL_VALUE_TYPE &result,
> > +                const REAL_VALUE_TYPE &op1,
> > +                const REAL_VALUE_TYPE &op2,
> > +                const REAL_VALUE_TYPE &inf)
> > +{
> > +  REAL_VALUE_TYPE value;
> > +  enum machine_mode mode = TYPE_MODE (type);
> > +  bool mode_composite = MODE_COMPOSITE_P (mode);
> > +
> > +  bool inexact = real_arithmetic (&value, code, &op1, &op2);
> > +  real_convert (&result, mode, &value);
> > +
> > +  // If real_convert above has rounded an inexact value to towards
> > +  // inf, we can keep the result as is, otherwise we'll adjust by 1 ulp
> > +  // later (real_nextafter).
> > +  bool rounding = (flag_rounding_math
> > +                && (real_isneg (&inf)
> > +                    ? real_less (&result, &value)
> > +                    : !real_less (&value, &result)));
>
> I thought the agreement during Cauldron was that we'd do this always,
> regardless of flag_rounding_math.
> Because excess precision (the fast one like on ia32 or -mfpmath=387 on
> x86_64), or -frounding-math, or FMA contraction can all increase precision
> and worst case it all behaves like -frounding-math for the ranges.
>
> So, perhaps use:
>   if ((mode_composite || (real_isneg (&inf) ? real_less (&result, &value)
>                                             : !real_less (&value, &result))
>       && (inexact || !real_identical (&result, &value))))

Done.

> ?
> No need to do the real_isneg/real_less stuff for mode_composite, then
> we do it always for inexacts, but otherwise we check if the rounding
> performed by real.cc has been in the conservative direction (for upper
> bound to +inf, for lower bound to -inf), if yes, we don't need to do
> anything, if yes, we frange_nextafter.
>
> As discussed, for mode_composite, I think we want to do the extra
> stuff for inexact denormals and otherwise do the nextafter unconditionally,
> because our internal mode_composite representation isn't precise enough.
>
> > +  // Be extra careful if there may be discrepancies between the
> > +  // compile and runtime results.
> > +  if ((rounding || mode_composite)
> > +      && (inexact || !real_identical (&result, &value)))
> > +    {
> > +      if (mode_composite)
> > +     {
> > +       bool denormal = (result.sig[SIGSZ-1] & SIG_MSB) == 0;
>
> Use real_isdenormal here?

Done.

> Though, real_iszero needs the same thing.

So... real_isdenormal() || real_iszero() as in the attached patch?

>
> > +       if (denormal)
> > +         {
> > +           REAL_VALUE_TYPE tmp;
>
> And explain here why is this, that IBM extended denormals have just
> DFmode precision.

Done.

> Though, now that I think about it, while this is correct for denormals,
>
> > +           real_convert (&tmp, DFmode, &value);
> > +           frange_nextafter (DFmode, tmp, inf);
> > +           real_convert (&result, mode, &tmp);
> > +         }
>
> there are also the cases where the higher double exponent is in the
> [__DBL_MIN_EXP__, __LDBL_MIN_EXP__] aka [-1021, -968] or so.
> https://en.wikipedia.org/wiki/Double-precision_floating-point_format
> If the upper double is denormal in the DFmode sense, so smaller absolute
> value than __DBL_MIN__, then doing nextafter in DFmode is the right thing to
> do, the lower double must be always +/- zero.
> Now, if the result is __DBL_MIN__, the upper double is already normalized
> but we can add __DBL_DENORM_MIN__ to it, which will make the number have
> 54-bit precision.
> If the result is __DBL_MIN__ * 2, we can again add __DBL_DENORM_MIN__
> and make it 55-bit precision.  Etc. until we reach __DBL_MIN__ * 2e53
> where it acts like fully normalized 106-bit precision number.
> I must say I'm not really sure what real_nextafter is doing in those cases,
> I'm afraid it doesn't handle it correctly but the only other use
> of real_nextafter is guarded with:
>   /* Don't handle composite modes, nor decimal, nor modes without
>      inf or denorm at least for now.  */
>   if (format->pnan < format->p
>       || format->b == 10
>       || !format->has_inf
>       || !format->has_denorm)
>     return false;

Dunno.  Is there a conservative thing we can do for mode_composites
that aren't denormal or zero?

How does this look?
Aldy