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
