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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