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From: phil@osiris.UUCP (Philip Kos)
Newsgroups: comp.arch
Subject: Re: Multiply as Shift-Add(Subtract)
Message-ID: <1096@osiris.UUCP>
Date: Wed, 13-May-87 16:36:43 EDT
Article-I.D.: osiris.1096
Posted: Wed May 13 16:36:43 1987
Date-Received: Sat, 16-May-87 06:45:38 EDT
References: <1270@aw.sei.cmu.edu> <8012@utzoo.UUCP> <16640@amdcad.AMD.COM> <6651@mimsy.UUCP>
Organization: Johns Hopkins Hospital
Lines: 19
Summary: guard bits

In article <6651@mimsy.UUCP>, chris@mimsy.UUCP (Chris Torek) writes:
> In article <27685@rochester.ARPA> crowl@rochester.ARPA (Lawrence Crowl) writes:
> >... how do implementations using subtracts in the shift-add approach
> >to multiplication detect overflow for an entire multiplication?
> 
> I suspect, however, that the usual answer is `they do not bother'.

Would you believe internal guard bits?  Maybe not everyone does this,
but it does give you the nice property that: given enough internal
guard bits (you really only need a couple), any iterative operation
like a multiple or divide (integer or floating point, it doesn't really
matter) whose result is exactly representible in size of the target
will be represented.  Oh yeah, for the preceding property, it also helps
a lot for the algorithm to be correct.  :-)


...!decvax!decuac!\                                               Phil Kos
  ...!seismo!mimsy!aplcen!osiris!phil           The Johns Hopkins Hospital
...!allegra!/                                                Baltimore, MD