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Date: Sun, 19 Mar 2017 10:53:40 -0400
From: Rich Felker <dalias@...c.org>
To: musl@...ts.openwall.com
Subject: Re: [PATCH] fix underflow exception in fma and fmal

On Sun, Mar 19, 2017 at 03:39:53PM +0100, Szabolcs Nagy wrote:
> * Rich Felker <dalias@...c.org> [2017-03-19 10:12:49 -0400]:
> > On Sun, Mar 19, 2017 at 04:36:14AM +0100, Szabolcs Nagy wrote:
> > > another corner case in the freebsd fma code where signaling underflow
> > > may be missed for an inexact subnormal result.
> > > (fmaf and x86 fma are not affected)
> > > ---
> > >  src/math/fma.c  | 7 +++++++
> > >  src/math/fmal.c | 8 ++++++++
> > >  2 files changed, 15 insertions(+)
> > > 
> > > diff --git a/src/math/fma.c b/src/math/fma.c
> > > index 741ccd75..c69918d1 100644
> > > --- a/src/math/fma.c
> > > +++ b/src/math/fma.c
> > > @@ -279,6 +279,13 @@ static inline double add_and_denormalize(double a, double b, int scale)
> > >  			uhi.i += 1 - (((uhi.i ^ ulo.i) >> 62) & 2);
> > >  			sum.hi = uhi.f;
> > >  		}
> > > +#ifdef FE_UNDERFLOW
> > > +		/*
> > > +		 * Raise underflow manually because scalbn won't do it if all
> > > +		 * lost bits are 0: fma(-0x1p-1000, 0x1.000001p-74, 0x1p-1022)
> > > +		 */
> > > +		feraiseexcept(FE_UNDERFLOW);
> > > +#endif
> > 
> > Can you explain why it should happen if all lost bits are zero
> > (usually that's an exact case). I imagine it's something specific to
> > fma or its implementation but it's not obvious to me.
> > 
> 
> this case is for nearest rounding mode when the
> result is in the subnormal range, at this point the
> result is represented as hi,lo,scale but the final
> returned value is computed as scalbn(hi,scale)
> (the last bits of hi are adjusted if required for
> correct rounding), however scalbn fails to raise
> underflow if lo!=0 and all lost bits of hi are 0.
> 
> the example is such a case: 0x1p-1022 - 0x1.000001p-1074
> then hi=1-eps,lo=-0x1p-76,scale=-1022 or maybe with
> shifted scale and exponents, but in the end only one
> bit is lost from hi which is zero, alternatively i
> could do scalbn(lo,scale) too to raise underflow.

That makes sense. I tend to prefer the scalbn(lo,scale) approach if
there aren't good reasons (performance?) against it, simply because
it's more self-documenting and less special-cased. But whichever you
like is fine. BTW we should probably check that scalbn raises inexact
in all cases it should; I'm not sure what it (especially asm versions)
does in cases where the scale is smaller than the min exponent.

Rich

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