Floating point wasn't on the Alto, but I think that the motivation 
was much more about how easy it was to create all the different 
number systems including rationals in objects.

Also, I seem to recall (but not vividly) that since we could define 
our fonts as we wished back then, we at some point used the other 
division sign  -- shown as a horizonal dash with a dot above and 
below (it's very annoying that in 2003 I can't be sure that typing 
this on my Mac will actually render correctly on everyone elses email 
system) -- to mean "give me a float back regardless".

Cheers,

Alan

------

At 4:16 AM +0200 6/12/03, Andreas Raab wrote:
>Hi Dan,
>
>Thanks for this interesting response. One more question on "historical"
>grounds: I was wondering if there actually had been any (reasonably good)
>floating point point operations on the hardware you were dealing with. These
>days, floats are a zillion times faster to compute than fractions but this
>hasn't always been the case - so I wonder if "back then" fractional
>arithmetic was at essentially the same speed as floating point arithmetic
>(which, from my POV, would be a clear reason to use fractions instead of
>floats as you don't buy anything with floats in this case).
>
>Cheers,
>   - Andreas
>
>PS. Of course what "most people" think is always hard to estimate - but
>that's exactly why I'm soliciting responses and both Johns and your reply
>give valuable insights ;-) I'm hoping for more.
>
>>  -----Original Message-----
>>  From: squeak-dev-bounces at lists.squeakfoundation.org
>>  [mailto:squeak-dev-bounces at lists.squeakfoundation.org] On
>>  Behalf Of Dan Ingalls
>>  Sent: Thursday, June 12, 2003 3:39 AM
>>  To: The general-purpose Squeak developers list
>>  Subject: Re: [Curious] Integer division => fraction
>>
>>
>>  "Andreas Raab" <andreas.raab at gmx.de> wrote...
>>
>>  >Just had an interesting discussion with Dean (over on
>>  e-Lang) about integer
>>  >division semantics. He pointed out (and I agree) that most
>>  people tend to
>>  >find it it confusing that "3/4" results in a fraction rather
>>  than coercing
>>  >to Float by default.
>>  >
>>  >My questions: What do you think about this issue? Are you personally
>>  >surprised if you get a fraction back? Has it bitten you in unexpected
>>  >places? Have you actually ever had the need for coercing to fractions
>>  >instead of floats? Can you think of "typical" applications
>>  that would be
>>  >harmed by coercing to floats?
>>
>>  There is of course no assurance that a simple and consistent
>>  design will be what "most people expect".  I mean, most
>>  people expect C or Java or Basic.  That said, I think there
>>  are interesting underlying issues here.
>>
>>  I think I agree that "most people" think about arithmetic as
>>  operator-based, and not as object-oriented (ie dependent on
>>  who is receiving the message).  This was NOT how we thought
>>  about it when we first asked ourselves "Hmm, here we have a
>>  world of objects; how should they behave" back in the early
>>  70's.  In those days (for a while) 3 + 0.14 gave you a
>>  different result from 0.14 + 3.  This caused a LOT of
>>  confusion, and so we introduced coercion.  The current
>>  coercion scheme fits pretty well with what "most people
>>  expect" in spite of giving full receiver control over semantics.
>>
>>  On the eve of the Smalltalk-80 release, we had a lot of
>>  serious discussion about the various arithmetic operations --
>>  integer division, real division, how modulo works with
>>  negative numbers, etc., etc.  While I participated, it was
>>  others (Peter, Glenn, Ted, Adele, and anyone with traditional
>>  math sensitivity) who made the final decisions on these.  The
>>  question here is one of definition.  What does "/" mean?  In
>>  St-80 it is supposed to mean "exact" division, not "give me
>>  the best you can" (except for Floats who can't do anything else ;-).
>>
>>  However, I think that "most people" have come to accept "give
>>  me the best you can" for "/" because "most systems" don't
>  > offer fractions and so, in their own desire to approximate
>>  what "most people expect" they deliver floating point results.
>>
>>  Now, unfortunately IMO, for "most people" acceptance becomes
>>  expectation (a human tendency), while the definition of "/"
>>  in Smalltalk has not changed, and 355/113 is not pi, even
>>  though in a lot of systems you might think so.  That's the
>>  purist perspective, which John Sarkela articulated in a lot
>>  less words.  I know the tension you feel, and yet I don't
>>  think we have to feel ashamed of our position.
>>
>>  Besides simply remembering and advertising that "/" means
>>  exact division, there are a couple of other possibilities, of
>>  course.  One is to have a preference to print fractions as
>>  floats.  Another is to change "/" to mean produce a float. 
>>  If anyone opts for this, then I would certainly  agitate for
>>  SOME other operator that means exact division.
>>
>>  I would be interested to hear what the MathMorphs folks would
>>  have to say about this, or anyone familiar with, eg, MathLab
>>  or the good Lisp math libraries.
>>
>>	- Dan
>>


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