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From: henry@utzoo.UUCP (Henry Spencer)
Newsgroups: comp.arch
Subject: Re: What should be in hardware but isn't
Message-ID: <8668@utzoo.UUCP>
Date: Mon, 28-Sep-87 21:06:49 EDT
Article-I.D.: utzoo.8668
Posted: Mon Sep 28 21:06:49 1987
Date-Received: Mon, 28-Sep-87 21:06:49 EDT
References: <581@l.cc.purdue.edu> <8646@utzoo.UUCP>, <705@gumby.UUCP>
Organization: U of Toronto Zoology
Lines: 27

> > The transcendentals in (say) the 68881 are *better* than anything you will
> > come up with in software without large amounts of work...
> 
> The 68881 transcendentals are not implemented in hardware; they are
> implemented in microcode.  I believe the extra 0.5-1.5ulp of accuracy
> of the 68881 is due to the use of extended precision calculations, not
> to either hardware or algorithm (simple rational approximations are
> very accurate too when evaluated in extended precision)...

Nope, sorry, you have misunderstood slightly.  I wasn't saying "the 68881
is more accurate than carefully-implemented double-precision software such
as one would expect from e.g. MIPSco"; I was saying "the 68881 is more
accurate than the sloppy first-cut software that one confidently expects
XYZ Vaporboxes Inc. to ship as its `production' release".  The point is not
that the 68881 has inherent advantages over software, but that it represents
a *cheap* *prepackaged* high-quality solution.  In principle one could find
the same thing in software, but commercial realities make this unlikely
unless it comes from a university:  the 68881 can be cheaply and widely
sold at a profit because *it cannot be pirated easily*.

I agree that the right way to do transcendentals is in software, with help
(e.g. extended-precision arithmetic) in the hardware when appropriate.
But how much carefully-written software can you buy for the price of one
68881?
-- 
"There's a lot more to do in space   |  Henry Spencer @ U of Toronto Zoology
than sending people to Mars." --Bova | {allegra,ihnp4,decvax,utai}!utzoo!henry