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Date: Sat, 21 Mar 2020 13:57:43 -0400
From: Rich Felker <dalias@...c.org>
To: musl@...ts.openwall.com
Subject: Re: [PATCH] math: move i386 sqrt to C

On Sat, Mar 21, 2020 at 01:53:51PM -0400, Rich Felker wrote:
> On Tue, Jan 07, 2020 at 04:06:05PM +0300, Alexander Monakov wrote:
> > ---
> > Since union ldshape does not have a dedicated field for 32 least significant
> > bits of the x87 long double mantissa, keeping the original approach with
> > 
> >     ux.i.m -= (fpsr & 0x200) - 0x100;
> > 
> > would lead to a 64-bit subtraction that is not trivial for the compiler to
> > optimize to 32-bit subtraction as done in the original assembly. Therefore
> > I have elected to change the approach and use
> > 
> >     ux.i.m ^= (fpsr & 0x200) + 0x200;
> > 
> > which is easier to optimize to a 32-bit rather than 64-bit xor.
> > 
> > Thoughts?
> 
> I'm getting test failures with sqrt and this seems to be the culprit
> -- I don't think it's equivalent. The original version could offset
> the value by +0x100 or -0x100 before rounding, and offsets in the
> opposite direction of the rounding that already occurred. Your version
> can only offset it by +0x200 or -0x400.
> 
> The (well, one) particular failing case is:
> 
> src/math/ucb/sqrt.h:49: RU sqrt(0x1.fffffffffffffp+1023) want 0x1p+512
> got 0x1.fffffffffffffp+511 ulperr -0.250 = -0x1p-1 + 0x1p-2
> 
> Here the mantissa is
> 
> fffffffffffffc00
> 
> and offset by -0x400 yields:
> 
> fffffffffffff800
> 
> which has exactly 53 bits and therefore does not round up like it
> should.
> 
> I still like your approach better if there's a way to salvage it. Do
> you see one?

And, I think I do. Changing it to:

    ux.i.m ^= (fpsr & 0x200) + 0x300;

yields an offset of +0x300 (^0x300) or -0x300 (^0x500). This looks
like it should work theoretically, and indeed it passes libc-test.

Rich

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