Article 1503 of alt.sys.pdp10: Path: nntp1.ba.best.com!news1.best.com!feeder.via.net!newshub2.rdc1.sfba.home.com!news.home.com!news2.rdc2.tx.home.com.POSTED!not-for-mail Message-ID: <39E4AB75.F734DE93@home.net> From: cks X-Mailer: Mozilla 4.7 [en] (X11; U; Linux 2.2.5-16 alpha) X-Accept-Language: en MIME-Version: 1.0 Newsgroups: alt.sys.pdp10 Subject: Re: Floating-point test cases ? References: <8rvgb6$26rn$1@nntp1.ba.best.com> <8s1ld2$lqa$4@bob.news.rcn.net> Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Lines: 36 Date: Wed, 11 Oct 2000 18:03:33 GMT NNTP-Posting-Host: 24.11.22.12 X-Complaints-To: abuse@home.net X-Trace: news2.rdc2.tx.home.com 971287413 24.11.22.12 (Wed, 11 Oct 2000 11:03:33 PDT) NNTP-Posting-Date: Wed, 11 Oct 2000 11:03:33 PDT Organization: @Home Network Xref: nntp1.ba.best.com alt.sys.pdp10:1503 jmfbahciv@aol.com wrote: > What did happen to Mary's work? Did Digital shitcan that, too? No indeed, Alpha's math library is just about the best around. I haven't studied it in detail but it might be *the* best. (IBM is awfully good at it too.) There was a series of articles in Transactions on Mathematical Software that showed clear signs of somebody disassembling the Vax codes and figuring out the cool tricks. I think his funding ran out before he got to the good part though. (That being pow().) On the original topic, I had some tests for gfloat but they're lost. But there's nothing surprising about PDP10 floating point semantics. Rounds away from zero, and if either operand is negative take the absolute value and later attach the result sign. (It need not be computed that way but that gives the right answer.) Round before checking for overflow/underflow, of course. You can figure out unnormalized operands from knowing what adding 233000000000 did (Fortran AINT or ANINT, for FAD and FADR respectively). Unnormalized operands to mul and div were possibly never used, and the various processors might have been different for all anybody would know. I speculate -- very hazy -- the result was the same as normalizing the operands first. An unnormalized denominator in div was allowed to or required to fault. gfloat didn't have UFA et al -- getting those right without a real 10 would indeed be tough. And 400000000000 is not a useful f.p. number, but I forget what the hardware did with it. Article 1538 of alt.sys.pdp10: Path: nntp1.ba.best.com!news1.best.com!nntp.primenet.com!nntp.gblx.net!newsfeed.direct.ca!look.ca!newshub2.rdc1.sfba.home.com!news.home.com!news2.rdc2.tx.home.com.POSTED!not-for-mail Message-ID: <39E88FE9.34C29B86@home.net> From: cks X-Mailer: Mozilla 4.7 [en] (X11; U; Linux 2.2.5-16 alpha) X-Accept-Language: en MIME-Version: 1.0 Newsgroups: alt.sys.pdp10 Subject: Re: Floating-point test cases ? References: <8rvgb6$26rn$1@nntp1.ba.best.com> <8s1ld2$lqa$4@bob.news.rcn.net> <39E4AB75.F734DE93@home.net> <8s9pad$n08$11@bob.news.rcn.net> Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Lines: 37 Date: Sat, 14 Oct 2000 16:55:06 GMT NNTP-Posting-Host: 24.11.22.12 X-Complaints-To: abuse@home.net X-Trace: news2.rdc2.tx.home.com 971542506 24.11.22.12 (Sat, 14 Oct 2000 09:55:06 PDT) NNTP-Posting-Date: Sat, 14 Oct 2000 09:55:06 PDT Organization: @Home Network Xref: nntp1.ba.best.com alt.sys.pdp10:1538 jmfbahciv@aol.com wrote: > Mary did an awful lot of work to make sure we knew how to > add :-). That she did. The basic trick is to end with A+(B+C) where A is exact and B+C is much smaller. Usually A and C come from a table and B is the computed approximation. B+C should be added with FAD, and A should be added in with FADR. I think Mary may be why IEEE, and Alpha, can do this -- she was irritated that Vax could not. The Vax math lib is the real Mary Payne one. The -10 one was written by IMSL, under the guidance of their consultant W. Cody. The book Cody & Waite was the result of the 10 math lib rewrite. Well, a corollary, I don't know which was primary, but they got a book out of it. Cody's work was not always up to Mary's standard -- not many people's was -- and there were some ideas of hers that they wouldn't adopt. My favorite is the Vax lib's pi table -- it stores 1/pi to a monstrous number of bits, so if you want the sine of 1.234q+1234 it can subtract off exactly some enormous multiple of pi and tell you. > What's a pow? power function, y**x. Very hard to get both correct and fast. > Are you my Chris Smith? Yep -- hi Barb -- normally I post as Myself but not to alt groups, my normal news setup doesn't. Hence this foolish what-you-see-is-not-what-you-think newsreader etc.