[Numpy-discussion] Upcasting

Pitts, Todd A., Ph.D. pitts.todd at mayo.edu
Wed Feb 9 13:05:02 CST 2000

Here are my two cents worth on the subject...

	Most of what has been said in this thread (at least what I
have read) I find very valuable.  Apparently, many people have been
thinking about the subject.  I view this problem as inherent in a
language without an Lvalue (like C) that allows a very explicit and
clear definition from the programmer's point of view as to the size of
the container you are going put things in.  The language in many cases
simply returns an object to you and has made some decision as to what
you "needed" or "wanted".  Of course, this is one of the things that
makes languages such an Numerical Python, Matlab, IDL, etc. very nice
for protyping and investigating.  In many cases this decision will be
adequate or acceptable.  In some, quite simply, it will not be.  At
this point the programmer has to have a good means of managing this
decision himself.

If memory is not a constraint, I can think of very few situations
(none, actually) where I would choose to go with something other than
the Numerical Python default of double.  In general, that is what you
get when creating python arrays unless you make some effort to obtain
some other type.  However, in some important (read "cases that affect
the author") situations memory is a very critical constraint.
Typically, in Numerical Python I use 4-byte floats.  In fact, one of
the reasons I use Numerical Python is because I don't *need* doubles
and matlab for example is really only setup to work gracefully with
doubles.  I do *need* to conserve memory as I deal with very large
data sets.  It seems the question we are discussing is not really
"what *should* be done in terms of casting?" but "what provides good
enough decisions much of the time *and* a gracefull way to manage the
decisions when "good enough" no longer applies to you?"

Currently, this is not a trivial thing to manage.  Reading in a 100 MB
data set and multiplying by the python scalar 2 produces a 200 MB data
set.  I manage this by wrapping the 2 in an array.  This happens, of
course, all the time.  Having to do this once is not a big deal, but
doing everywhere in code that uses floats makes for cluttered code --
not something which I expect to have to write in an otherwise very
elegant and concise language.  Also, I often find myself trudging
through code looking for the subtlety that converted my floats to
doubles, doubled my memory usage and then caused subsequent float only
routines to error out.  To those who are constrained to use floats
this is awkward and time consuming.  To those who are not I would say
-- use doubles.  The flag that causes an array to be a "space saving
array" seems to be a temporary fix (that doesn't mean it was a bad
idea -- just that it feels messy and effectively adds complexity that
shouldn't be there).  It also, mearly postpones the problem as I
understand it -- what happens when I multiply two space saving arrays?

We simply will never get away from situations where we have to manage
the interaction ourselves and so we should be careful not to make that
management so awkward (and currently I think it is awkward) that the
floats, bytes, shorts, etc. become marginalized in their
utility.  My suggestion is to go with the rule that a simple hirearchy
(in which downcasting is the rule)

doubles  complex doubles     <--- default
floats   complex floats
for the most part makes good decisions: Principally because people who
are not constrained to conserve memory will use the larger, default
types all the time and not wince.  They don't *need* floats or bytes.
If anyone gives them a float a simple astype('d') or astype('D') to
make sure it becomes a double lets them go on their way.  Types like
integers and bytes are effectively treated as being precise.  If you
are constrained to conserve memory by staying with floats or bytes
instead of just reading things in from disk and making them doubles it
will not be so awkward to manage the types in large programs.  If I
use someones code and they have a scalar anywhere in it at some point,
even if I (or they) cast the output, memory usage swells at least for
intermediate calculations.  Effectively, python *has* 4-byte floats
but programming with them is awkward.

This means, of course, that multiplying a float array by a double
array produces a float.  Multiplying a double array by anything above
it produces a double. etc.  For my work, if I have a float anywhere in
the calculation I don't believe precision beyond that in the output so
getting a float back is reasonable. I know that some operations
produce "more precision" and so I would cast the array if I needed to
take advantage of that.

Perhaps the downcasting is *not* the way to go.  However, I definately
think the current awkwardness should be eliminated.  I hope my
comments will not be percieved as being critical of the original
language designers.  I find python to be very useful or I wouldn't
have bothered to make the comments at all.

-Todd Pitts

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