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From: bartho@obs.unige.ch (PAUL BARTHOLDI)
Newsgroups: comp.arch,misc.wanted,comp.sources.wanted
Subject: Re: Double Width Integer Multiplication and Division
Message-ID: <255@obs.unige.ch>
Date: 30 Jun 89 09:17:14 GMT
References: <57125@linus.UUCP> <1989Jun24.230056.27774@utzoo.uucp> <22218@winchester.mips.COM> <1989Jun26.195044.4197@cs.rochester.edu>
Organization: University of Geneva, Switzerland
Lines: 40

In article <1989Jun26.195044.4197@cs.rochester.edu>, crowl@cs.rochester.edu (Lawrence Crowl) writes:
>>When we were [designing integer division support on the MIPS processors], we
>>couldn't think of any languages whose natural implementation on a 32-bit
>>machine would expect generation of a 64 by 32 bit divide as the expected
>>operation.  Does anybody know of any such, or is this strictly something one
>>would use in handcoded routines?
>  
> Languages which support fixed-point arithmetic, e.g. PL/I and Ada, could use
> such a feature to substantially improve fixed-point performance ...

FORTH is the only language to my knowledge that use explicitely integer double
precision intermediate for multiplication/division/modulo.  The original and
standard forth have 16 bits integers, so double are 32 bits.  The point is
that, as soon you do integer arithmetic, you need to (re)scale your operands,
specialy during multiplication/division.  So, most of time, a multiplication
is immediately followed by a division, or a division preceded by a 
multiplication, and a double precision intermediate results means you do not
loose precision.  For example, suppose you want to multiply a number by 'pi'.
You would then multiply this number by 31415 and divide the result by 10000
(16 bits) or by 314159265 and 100000000 ...  Notice that the high level
operator has now three operands and should be called 'ternary'.  This is
exactely what forth does.  forth use reverse polish notation, which is very
nice for ternary operators :    a b c */  ('*/" is the operator) means
take the product of a and b in double precision, and divide it immediately by
c, getting a single precision integer as result.  you can have *mod that would
leave a*b mod c or even */mod that will leave both quotient and modulo of
a*b by c.  all these operators have been extremely usefull in process control,
data acquisition etc, in particular with small computer or micro without FPA.

for more information about forth, see :
  MG Kelly and N Spies : FORTH: a text and reference , Prentice-Hall 1986
  L Brodie             : Starting FORTH,               Prentice-HAll 1982
  L Brodie             : Thinking FORTH,               Prentice-Hall 1984

regards,               Paul Bartholdi

  Dr Paul Bartholdi                 bartho@cgeuge54.bitnet
  Observatoire de Geneve            bartho@obs.unige.ch
  CH-1290 Sauverny                  02284682161350::bartho (psi)
  Switzerland                       20579::ugobs::bartho