You say starting from a more consistent place, but how consistent are =
and <= among Numbers without transitivity?
How are numbers consistent to begin with, when for all integers you have
x + 1 ~= x
but for floats, there are a multitude of values such that
x + 1.0 = x
holds? Addition is hardly the only operation that exhibits this kind of
behavior. Or how about
x = x
being true for the vast majority of cases across all sorts of numbers,
except when x is NaN? Integers and fractions don't even have a notion
of -0.0. All of these are already pretty inconsistent without
considering obvious issues such as
17 / 20 = 0.85
which in at least some Smalltalks evaluates to true even though it is
mathematically impossible.
The point is that classes like Float, Integer and Fraction may very well
have a common superclass. Nonetheless, floating point numbers and
effectively rationals obey very different rules. Both have their strong
points, those strengths are maximized with consistency.
Andres.
If we can maintain the invariant with a pair of double dispatching
methods and coordinated hash, why shouldn't we?
Why lispers did it? (Scheme too)
For me it's like saying: "since float are inexact, we have a license to
waste ulp".
We have not. IEEE 754 model insists on operations to be exactly rounded.
These are painful contortions too, but most useful!
Extending the contortion to exact comparison sounds a natural extension
to me, the main difference is that we do not round true or false to the
nearest float, so it's even nicer!
On 7/11/14 17:19 , Nicolas Cellier wrote:
2014-07-12 1:29 GMT+02:00 Andres Valloud
<avalloud@smalltalk.__comcastbiz.net
<mailto:avall...@smalltalk.comcastbiz.net>
<mailto:avalloud@smalltalk.__comcastbiz.net
<mailto:avall...@smalltalk.comcastbiz.net>>>:
I don't think it makes sense to compare floating point
numbers to
other types of numbers with #=... there's a world of
approximations
and other factors hiding behind #=, and the
occasional true
answer
confuses more than it helps. On top of that, then
you get
x = y =>
x hash = y hash, and so the hash of floating point
values
"has" to
be synchronized with integers, fractions, scaled
decimals,
etc...
_what a mess_...
Yes, that's true, hash gets more complex.
But then, this has been discussed before:
{1/2 < 0.5. 1/2 = 0.5. 1/2 > 0.5} - > #(false false false).
IOW, they are unordered.
Are we ready to lose ordering of numbers?
Practically, this would have big impacts on code base.
IME, that's because loose code appears to work. What
enables that
loose code to work is the loose mixed mode arithmetic. I could
understand integers and fractions. Adding floating point
to the mix
stops making as much sense to me.
Equality between floating point numbers does make sense.
Equality
between floating point numbers and scaled decimals or
fractions...
in general, I don't see how they could make sense. I'd
rather see
the scaled decimals and fractions explicitly converted to
floating
point numbers, following a well defined procedure, and then
compared...
Andres.
Why do such mixed arithmetic comparisons make sense?
Maybe we used floating points in some low level Graphics for
optimization reasons.
After these optimized operations we get a Float result by
contagion, but
our intention is still to handle Numbers.
It would be possible to riddle the code with explicit
asFloat/asFraction
conversions, but that does not feel like a superior solution...
OK, we can as well convert to inexact first before comparing for
this
purpose.
That's what C does, because C is too low level to ever care of
transitivity and equivalence relationship.
It's not even safe in C because the compiler can decide to
promote to a
larger precision behind your back...
But let's ignore this "feature" and see what lispers recommend
instead:
http://www.lispworks.com/__documentation/lcl50/aug/aug-__170.html
<http://www.lispworks.com/documentation/lcl50/aug/aug-170.html>
It says:
In general, when an operation involves both a rational and a
floating-point argument, the rational number is first converted to
floating-point format, and then the operation is performed. This
conversion process is called /floating-point contagion/
<http://www.lispworks.com/__reference/lcl50/aug/aug-193.__html#MARKER-9-47
<http://www.lispworks.com/reference/lcl50/aug/aug-193.html#MARKER-9-47>>.
However, for numerical equality comparisons, the arguments are
compared
using rational arithmetic to ensure transitivity of the equality (or
inequality) relation.
So my POV is not very new, it's an old thing.
It's also a well defined procedure, and somehow better to my taste
because it preserve more mathematical properties.
If Smalltalk wants to be a better Lisp, maybe it should not
constantly
ignore Lisp wisdom ;)
We can of course argue about the utility of transitivity...
As a general library we provide tools like Dictionary that rely on
transitivity.
You can't tell how those Dictionary will be used in real
applications,
so my rule of thumb is the principle of least astonishment.
I've got bitten once by such transitivity while memoizing... I
switched
to a better strategy with double indirection as workaround: class ->
value -> result, but it was surprising.
I'm pretty sure a Squeak/Pharo image wouldn't survive
that long
to such
a change
(well I tried it, the Pharo3.0 image survives, but
Graphics are
badly
broken as I expected).
That's allways what made me favour casual equality to
universal
inequality.
Also should 0.1 = 0.1 ? In case those two floats have been
produced by
different path, different approximations they might not
be equal...
(| a b | a := 0.1. b := 1.0e-20. a+b=a.)
I also prefer casual equality there too.
Those two mathematical expressions a+b and a are
different but both
floating point expressions share same floating point
approximation,
that's all what really counts because in the end, we cannot
distinguish
an exact from an inexact Float, nor two inexact Float.
We lost the history...
Also, the inexact flag is not attached to a Float, it's
only the
result
of an operation.
Statistically, it would waste one bit for nothing, most
floats
are the
result of an inexact operation.
But who knows, both might be the result of exact
operations too ;)
On 7/11/14 10:46 , stepharo wrote:
I suggest you to read the Small number chapter
of the
Deep into
Pharo.
Stef
On 11/7/14 15:53, Natalia Tymchuk wrote:
Hello.
I found interesting thing:
Why it is like this?
Best regards,
Natalia
