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From: hrubin@pop.stat.purdue.edu (Herman Rubin)
Newsgroups: comp.arch
Subject: Re: Frequency of elementary functions (and other things)
Message-ID: <12505@mentor.cc.purdue.edu>
Date: 19 May 91 12:58:30 GMT
Article-I.D.: mentor.12505
References: <9105171235.AA20139@ucbvax.Berkeley.EDU> <104811@sgi.sgi.com> <1991May19.080051.29716@lth.se>
Sender: news@mentor.cc.purdue.edu
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In article <1991May19.080051.29716@lth.se>, bengtl@maths.lth.se (Bengt Larsson) writes:
> In article <12488@mentor.cc.purdue.edu> hrubin@pop.stat.purdue.edu (Herman Rubin) writes:
> >
> >The original thread, even cited, was the communication between integer and
> >floating units.  Even such simple things as multiplication by variable
> >integers are very likely as common as exponentiation.  
> 
> Give some qualified reason for it being likely common. 

Other than having personally used it quite a bit, I cannot give you examples
immediately.  And again we have the "chicken and the egg" phenomenon; those
who understand the weaknesses of the hardware will try to avoid running into
the problems.  The use of the index of a do loop for floating point operations
internally is not unusual.

Also, how would you know if it is being used?  On some machines, converting
an integer to floating is done by a normalized addition of 0.  On the CRAYs,
there is a very odd instruction used for the purpose, but the instruction 
may be used once for converting many integers to floating.  It COULD be
detected, but not that easily.

> >Another situation
> >is Boolean operations on both fixed-point and floating numbers; fixed point
> >is not restricted to integers.  
> 
> In what algorithms?

Many function programs use table lookup.  This requires extracting the
relevant bits from the floating point number, and frequently obtaining
the difference.  Consider the sheer number of operations required on
hardware without the communications capabilities.  Pipelining can reduce
the effect of operation time, but not of number of sequential instructions
required to do a simple task.

Fixed point arithmetic is little used now because the hardware to support
it reasonably well does not exist.  It is worse than the floating problems
before hardware floating arithmetic, especially if floating is automatically
normalized.  THAT feature of "modern" architectures is, in my opinion, a sheer
horror.

In the early FP computers, much function calculation was done in fixed point,
to get increased accuracy at little cost.

> >Also, the availability of hardware operations
> >leads to their increased use; on a machine with no communication between the
> >units, a knowledgeable programmer would  avoid the need by using some other
> >algorithm, for example.
> 
> Apparently not, if the analysis of various (old) CISC machines count.
> There were many operations which were very seldom used, even though
> they existed.

How do you expect users who do not even know of the existence of the operations
to use them?  

There are many more algorithms than are in the philosophy of software, and
especially hardware, designers.
-- 
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
Phone: (317)494-6054
hrubin@l.cc.purdue.edu (Internet, bitnet)   {purdue,pur-ee}!l.cc!hrubin(UUCP)