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From: lamaster@pioneer.arpa (Hugh LaMaster)
Newsgroups: comp.arch
Subject: Re: Transcendental functions and microcoded instructions
Message-ID: <2935@ames.arpa>
Date: Wed, 30-Sep-87 13:39:34 EDT
Article-I.D.: ames.2935
Posted: Wed Sep 30 13:39:34 1987
Date-Received: Sun, 4-Oct-87 21:38:48 EDT
References: <581@l.cc.purdue.edu> <8646@utzoo.UUCP> <705@gumby.UUCP> <8@radix>
Sender: usenet@ames.arpa
Reply-To: lamaster@ames.UUCP (Hugh LaMaster)
Organization: NASA Ames Research Center, Moffett Field, Calif.
Lines: 51
Keywords: floating-point, paranoia

In article <8@radix> jimv@radix.UUCP (Jim Valerio) writes:

>I am probably one of the few people who reads this newsgroup that has
>microcoded transcendental floating-point instructions.  I wrote significant
>portions of the transcendental microcode for the 80387.  I also have written
>significant portions of math libraries that implement transcendental
>functions.
:

>
>The MIPS implementation is laudable, but there are many more issues than
>speed involved here.  One is accuracy.  Often more important than accuracy
>is monotonicity.  (If the mathematical function is monotonic over a region,
>is the approximated function monotonic over the same region?)  Polynomial
>approximation techniques often have monotonicity problems.  Other issues
>include working on making simple transcendental identities hold in
>floating-point computations (e.g. sin(-x) = -sin(x), exp(-x) = 1/exp(x)).
>
>Now, I suspect that MIPS used the 4.3bsd libm.  This is a very good math
>library, with man-years of work put into it by floating-point experts to
>give it many of the important attributes of a good library.  It boasts of
>high accuracy and no observed monotonicity errors.
:

>
>I said that the 4.3bsd libm has no observed monotonicity errors.  That means
>that test programs running a few million points haven't found one.  That
>doesn't mean that the error doesn't exist.  A few million points is a very
:
>
>Jim Valerio	{verdix,intelca!mipos3,intel-iwarp.arpa}!omepd!radix!jimv

Are people familiar with the Kahan et. al. "paranoia" program, (available from
netlib), and, if so, what do people think of:

1) The validity of the error test results that it provides (in other words,
does it complain about things that are not valid complaints), and,

2) The completeness of the tests (how good it is at testing things which
should be tested, such as monotonicity of certain functions)?





  Hugh LaMaster, m/s 233-9,  UUCP {topaz,lll-crg,ucbvax}!
  NASA Ames Research Center                ames!pioneer!lamaster
  Moffett Field, CA 94035    ARPA lamaster@ames-pioneer.arpa
  Phone:  (415)694-6117      ARPA lamaster@pioneer.arc.nasa.gov

(Disclaimer: "All opinions solely the author's responsibility")