Date: Mon, 24 Apr 2017 00:35:33 +0200 From: Szabolcs Nagy <nsz@...t70.net> To: musl@...ts.openwall.com Subject: Re: [PATCH] math: rewrite fma with mostly int arithmetics * Szabolcs Nagy <nsz@...t70.net> [2017-04-24 00:34:48 +0200]: > * Rich Felker <dalias@...c.org> [2017-04-23 11:15:39 -0400]: > > On Sun, Apr 23, 2017 at 01:00:52PM +0200, Szabolcs Nagy wrote: > > > * Rich Felker <dalias@...c.org> [2017-04-22 18:24:25 -0400]: > > > > Is it difficult to determine when the multiplication part of an fma is > > > > exact? If you can determine this quickly, you can just return x*y+z in > > > > this special case and avoid all the costly operations. For normal > > > > range, I think it's roughly just using ctz to count mantissa bits of x > > > > and y, and checking whether the sum is <= 53. Some additional handling > > > > for denormals is needed of course. > > > > > > it is a bit more difficult than that: > > > > > > bits(a) + bits(b) < 54 || (bits(a) + bits(b) == 54 && a*b < 2) > > > > > > this is probably possible to handle when i do the int mul. > > > > > > however the rounding mode special cases don't get simpler > > > and inexact flag still may be raised incorrectly when tail > > > bits of x*y beyond 53 bits are eliminated when z is added > > > (the result is exact but the dekker algorithm raises inexact). > > > > One thing to note: even if it's not a replacement for the whole > > algorithm, this seems like a very useful optimization for a case > > that's easy to test. "return x*y+z;" is going to be a lot faster than > > anything else you can do. But maybe it's rare to hit cases where the > > optimization works; it certainly "should" be rare if people are using > > fma for the semantics rather than as a misguided optimization. > > i didn't see a simple way to check for exact x*y result > (if it were easy then that could capture the exact 0 result > case which means one less special case later, but this is > not easy if x*y is in the subnormal range or overflows) > > > > > If the only constraint here is that top 10 bits and last bit are 0, I > > > > don't see why clz is even needed. You can meet this constraint for > > > > denormals by always multiplying by 2 and using a fixed exponent value. > > > > > > yeah that should work, but i also use clz later > > > > Ah, I missed that. Still it might be a worthwhile optimization here; I > > think it shaves off a few ops in normalize(). > > attached a new version with updated normalize. > now really > on my laptop latency and code size: > > old x86_64: 67 ns/call 893 bytes > new x86_64: 20 ns/call 960 bytes > old i386: 80 ns/call 942 bytes > new i386: 75 ns/call 1871 bytes > old arm: - 960 bytes > new arm: - 1200 bytes View attachment "fma.c" of type "text/x-csrc" (3625 bytes)
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