Re: [PATCH] [PR24021] Implement PLUS_EXPR range-op entry for floats.

[Jakub Jelinek <jakub@redhat.com>]

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))))
?
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?
Though, real_iszero needs the same thing.

> +	  if (denormal)
> +	    {
> +	      REAL_VALUE_TYPE tmp;

And explain here why is this, that IBM extended denormals have just
DFmode precision.
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;
so it isn't that big deal except for ranges.

	Jakub