Date: Sat, 21 Mar 2020 23:30:12 +0300 (MSK) From: Alexander Monakov <amonakov@...ras.ru> To: musl@...ts.openwall.com Subject: Re: [PATCH] math: move i386 sqrt to C On Sat, 21 Mar 2020, Rich Felker wrote: > 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. Indeed, I was considering only the default (to-nearest) rounding mode and did not notice the problem for upwards rounding mode. I think your change solves this nicely. Thanks Alexander
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