Path: utzoo!utgpu!jarvis.csri.toronto.edu!rutgers!cs.utexas.edu!uunet!mcvax!ukc!dcl-cs!aber-cs!pcg
From: pcg@aber-cs.UUCP (Piercarlo Grandi)
Newsgroups: comp.arch
Subject: Re: Double Width Integer Multiplication and Division
Message-ID: <1046@aber-cs.UUCP>
Date: 1 Jul 89 12:49:40 GMT
Reply-To: pcg@cs.aber.ac.uk (Piercarlo Grandi)
Organization: Dept of CS, UCW Aberystwyth
	(Disclaimer: my statements are purely personal)
Lines: 68

In article <1370@l.cc.purdue.edu> cik@l.cc.purdue.edu (Herman Rubin) writes:

    In article <1035@aber-cs.UUCP>, pcg@aber-cs.UUCP (Piercarlo Grandi) writes:
    > In article <1989Jun26.195044.4197@cs.rochester.edu> crowl@cs.rochester.edu
    > (Lawrence Crowl) writes:
    > 
    > 	[1] You are not supposed to write assembler programs on a RISC
    > 	    machine. The compilers have sophisticated algorithms to generate
    > 	    "optimal" multiplication/division out of simpler instructions.
    
    I find this attitude arrogant.  Neither you nor anyone else knows what 
    complicated operations I want to do.

Ehi! Two notes: First, I wrote point [1]. Lawrence Crowl has no fault :->.

Second, The attitude of RISC designers is not "arrogant"; one of the well
publicized tenets of their philosophy is to make the instruction set
simpler, and compensate at the compiler level. This is in most cases
remarkably successful.

    Why should you try to make it difficult for me to use the power of the
    computer?

Well, RISC advocates don't try to make life harder for you; they try to make
the machine faster by having simpler hardware at the price of more complex
code generation. They don't see more complex code generation as a goal in
itself (well, occasionally I have my doubts :->).
    
    > 	[2] Fixed point and the "muldiv()" idea to me look very much in the
    > 	    RISC philosphy of minimalism. Fixed point, and multiple precision
    > 	    integer arithmetic, are in many many cases preferable to floating
    > 	    point and its complexities. Too bad that mathematicians are lulled
    > 	    in a false sense of familiarity by floating point's "scientific
    > 	    notation" and apparent support for real numbers.
    
    Do any mathematicians take this attitude?

A lot, a lot. Most mathematicians doing programming are not numerical
analysts (and even numerical analysts often are not as diffident of floating
point as they should be).

    Maybe if their only knowledge of computers comes from HLLs and they
    swallow the hype.

Fortran is very popular, isn't it?  Well, I would also argue that Fortran is
so popular with mathematicians precisely because it was *designed* as a
FORmula TRANslator, i.e. to give the illusion of dealing in familiar
mathematical formulas, to the point of using the same temrinology.
    
    Mathematicians who know that floating point numbers are, in reality, only
    approximations to real numbers will not be so confused.

But in my experience many mathematicians (or physicists) are not numerical
analysts at all, and expect the computer to do their calculations as they
intend them to be. Such people are not aware of the fact that floating point
is *not* (emphatically!) an approximation of R^n; floating point is
*radically* different from R^n (even fundamental properties of arithmetic are
not the same!).

As a palliative, a lot of effort in the design of the IEEE floating point
standard has been devoted to make floating point calculations *safer*, i.e.
a bit less surprising to those that think in terms of R^n. A laudable goal,
in some respects, but one that has costs in architectural terms, and in
perpetuating comfortable delusions.
-- 
Piercarlo "Peter" Grandi           | ARPA: pcg%cs.aber.ac.uk@nsfnet-relay.ac.uk
Dept of CS, UCW Aberystwyth        | UUCP: ...!mcvax!ukc!aber-cs!pcg
Penglais, Aberystwyth SY23 3BZ, UK | INET: pcg@cs.aber.ac.uk