Re: [PATCH] fix underflow exception in fma and fmal

[Szabolcs Nagy <nsz@port70.net>]

* Rich Felker <dalias@libc.org> [2017-03-19 10:53:40 -0400]:
> On Sun, Mar 19, 2017 at 03:39:53PM +0100, Szabolcs Nagy wrote:
> > 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.

ok i can do it with scalbn.

generic scalbn is correct and i386 should be correct too:
it does a mul at the end which should raise the flags
(i added tests for this now).

i think we should fix the fma underflow before- vs
after-rounding issue, the current code is only correct
for after-rounding archs (x86, mips, sh) even with the
fix, but doing it correctly is tricky.