From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.org/gmane.linux.lib.musl.general/11275 Path: news.gmane.org!.POSTED!not-for-mail From: Szabolcs Nagy Newsgroups: gmane.linux.lib.musl.general Subject: Re: [PATCH] math: rewrite fma with mostly int arithmetics Date: Mon, 24 Apr 2017 00:34:48 +0200 Message-ID: <20170423223448.GR2082@port70.net> References: <20170418224140.GN2082@port70.net> <20170422222425.GI17319@brightrain.aerifal.cx> <20170423110052.GQ2082@port70.net> <20170423151539.GO17319@brightrain.aerifal.cx> Reply-To: musl@lists.openwall.com NNTP-Posting-Host: blaine.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii X-Trace: blaine.gmane.org 1492986906 21780 195.159.176.226 (23 Apr 2017 22:35:06 GMT) X-Complaints-To: usenet@blaine.gmane.org NNTP-Posting-Date: Sun, 23 Apr 2017 22:35:06 +0000 (UTC) User-Agent: Mutt/1.6.0 (2016-04-01) To: musl@lists.openwall.com Original-X-From: musl-return-11290-gllmg-musl=m.gmane.org@lists.openwall.com Mon Apr 24 00:34:57 2017 Return-path: Envelope-to: gllmg-musl@m.gmane.org Original-Received: from mother.openwall.net ([195.42.179.200]) by blaine.gmane.org with smtp (Exim 4.84_2) (envelope-from ) id 1d2Q5p-0005U7-EH for gllmg-musl@m.gmane.org; Mon, 24 Apr 2017 00:34:57 +0200 Original-Received: (qmail 15588 invoked by uid 550); 23 Apr 2017 22:35:01 -0000 Mailing-List: contact musl-help@lists.openwall.com; run by ezmlm Precedence: bulk List-Post: List-Help: List-Unsubscribe: List-Subscribe: List-ID: Original-Received: (qmail 15567 invoked from network); 23 Apr 2017 22:35:00 -0000 Mail-Followup-To: musl@lists.openwall.com Content-Disposition: inline In-Reply-To: <20170423151539.GO17319@brightrain.aerifal.cx> Xref: news.gmane.org gmane.linux.lib.musl.general:11275 Archived-At: * Rich Felker [2017-04-23 11:15:39 -0400]: > On Sun, Apr 23, 2017 at 01:00:52PM +0200, Szabolcs Nagy wrote: > > * Rich Felker [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. 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