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From: mouse@mcgill-vision.UUCP (der Mouse)
Newsgroups: net.arch
Subject: Re: Right shift vs. divide (change divide!)
Message-ID: <345@mcgill-vision.UUCP>
Date: Mon, 13-Jan-86 03:29:58 EST
Article-I.D.: mcgill-v.345
Posted: Mon Jan 13 03:29:58 1986
Date-Received: Wed, 15-Jan-86 08:13:55 EST
References: <124000005@ima.UUCP> <4772@alice.UUCP> <1016@turtlevax.UUCP>, <32@calgary.UUCP>
Organization: McGill University, Montreal
Lines: 57

Radford Neal (radford@calgary), U of Calgary, writes (in <32@calgary.UUCP>):
> Rather than get rid of the arithmetic right shift, one could instead
> change the divide instruction so it does what mathematicians have
> always thought division meant.
> [ ie, truncate towards negative infinity rather than zero ]
> [ example: -3/2 versus 3/2 ]
> With this definition, a right shift divides by two and masking off
> the lower bit gives you the remainder.
> Does anyone know any reason, other than inertia, why divides shouldn't
> be changed to work this way.

Gee....and I always thought mathematicians thought -3/2 was -1.5 (;-).

[
 Note: By x%y I mean x mod y (remainder when x is divided by y)
          x>>y       x right-shifted y bits
          x^y        x raised to the power y
 No flames please, some people out there probably don't know
  C (I can hear it now:  "Doesn't >> mean `much greater than'?").
]

     Only reason I can see for a  mathematician -- for anyone -- to want
it  to   work  this  way  is   that  then  x-(y*(x/y))  is  always  >=0.
Unfortunately, doing  this  breaks other nice  properties, in particular
that  x/y  equals -((-x)/y).   It  therefore  means that  hardware can't
handle  negative  numbers  by  simply  negating  before  and  after  the
operation.    I  don't  see  why you aren't satisfied with  -3/2=-1  and
-3%2=-1.   You still  have  that x=(x%y)+(y*(x/y)), which is  really all
mathematicians demand, as far as I know (flame retardant:  my  knowledge
of number theory is limited to undergrad level).

     What do you want done with -3/-2 or 3/-2?

     There are some  algorithms which are easier to implement with  your
sort of division, but I would be surprised if it were not the case  that
in most of them, the divisor *is* a power of two and  hence right shifts
are appropriate.  You seem to want x%(2^y)=(x>>y).

     Inertia is a powerful reason.   There  has been  much discussion on
groups like net.lang.c and net.unix  about portability; the general idea
is  that  a  programmer  should  assume   as   little  as   possible.   
Unfortunately, programmers tend to assume that  things like the  laws of
arithmetic will not change and hence  assumptions about  them can safely
be wired into the code.  I feel certain there is a lot of code out there
which would break on any such machine.  I know I would  consider such  a
machine broken  (out of incompatibility with the  rest of the  world and
with existing code -- yes, I know that's what you mean by inertia).
-- 
					der Mouse

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