On Wednesday, 18 May 2016 at 09:21:30 UTC, Ola Fosheim Grøstad
wrote:
On Wednesday, 18 May 2016 at 07:21:30 UTC, Joakim wrote:
On Wednesday, 18 May 2016 at 05:49:16 UTC, Ola Fosheim Grøstad
wrote:
On Wednesday, 18 May 2016 at 03:01:14 UTC, Joakim wrote:
There is nothing "random" about increasing precision till
the end, it follows a well-defined rule.
Can you please quote that well-defined rule?
It appears to be "the compiler carries everything internally
to 80 bit precision, even if they are typed as some other
precision."
http://forum.dlang.org/post/[email protected]
"The compiler" means: implementation defined. That is the same
as not being well-defined. :-)
Welcome to the wonderful world of C++! :D
More seriously, it is well-defined for that implementation, you
did not raise the issue of the spec till now. In fact, you
seemed not to care what the specs say.
I don't understand why you're using const for one block and
not the other, seems like a contrived example. If the
precision of such constants matters so much, I'd be careful to
use the same const float everywhere.
Now, that is a contrived defense for brittle language
semantics! :-)
No, it has nothing to do with language semantics and everything
to do with bad numerical programming.
If matching such small deltas matters so much, I wouldn't be
using floating-point in the first place.
Why not? The hardware gives the same delta. It only goes wrong
if the compiler decides to "improve".
Because floating-point is itself fuzzy, in so many different
ways. You are depending on exactly repeatable results with a
numerical type that wasn't meant for it.
It depends on the unit tests running with the exact same
precision as the production code.
What makes you think they don't?
Because the language says that I cannot rely on it and the
compiler implementation proves that to be correct.
You keep saying this: where did anyone mention unit tests not
running with the same precision till you just brought it up out
of nowhere? The only prior mention was that compile-time
calculation of constants that are then checked for bit-exact
equality in the tests might have problems, but that's certainly
not all tests and I've repeatedly pointed out you should never be
checking for bit-exact equality.
D is doing it wrong because it makes it is thereby forcing
programmers to use algorithms that are 10-100x slower to get
reliable results.
That is _wrong_.
If programmers want to run their code 10-100x slower to get
reliably inaccurate results, that is their problem.
Huh?
The point is that what you consider reliable will be less
accurate, sometimes much less.
If you're so convinced it's exact for a few cases, then check
exact equality there. For most calculation, you should be
using approxEqual.
I am sorry, but this is not a normative rule at all. The rule
is that you check for the bounds required. If it is exact, it
just means the bounds are the same value (e.g. tight).
It does not help to say that people should use "approxEqual",
because it does not improve on correctness. Saying such things
just means that non-expert programmers assume that guessing the
bounds will be sufficient. Well, it isn't sufficient.
The point is that there are _always_ bounds, so you can never
check for the same value. Almost any guessed bounds will be
better than incorrectly checking for the bit-exact value.
Since the real error bound is always larger than that, almost
any error bound you pick will tend to be closer to the real
error bound, or at least usually bigger and therefore more
realistic, than checking for exact equality.
I disagree. It is much better to get extremely wrong results
frequently and therefore detect the error in testing.
What you are saying is that is better to get extremely wrong
results infrequently which usually leads to error passing
testing and enter production.
In order to test well you also need to understand for input
makes the algorithm unstable/fragile.
Nobody is talking about the general principle of how often you
get wrong results or unit testing. We were talking about a very
specific situation: how should compile-time constants be checked
and variables compared to constants, compile-time or not, to
avoid exceptional situations. My point is that both should
always be thought about. In the latter case, ie your f(x)
example, it has nothing to do with error bounds, but that your
f(x) is not only invalid at 2, but in a range around 2.
Now, both will lead to less "wrong results," but those are wrong
results you _should_ be trying to avoid as early as possible.
The computer doesn't know that, so it will just plug that x in
and keep cranking, till you get nonsense data out the end, if
you don't tell it to check that x isn't too close to 2 and not
just 2.
Huh? I am not getting nonsense data. I am getting what I am
asking for, I only want to avoid dividing by zero because it
will make the given hardware 100x slower than the test.
Zero is not the only number that screws up that calculation.
You have a wrong mental model that the math formulas are the
"real world," and that the computer is mucking it up.
Nothing wrong with my mental model. My mental model is the
hardware specification + the specifics of the programming
platform. That is the _only_ model that matters.
What D prevents me from getting is the specifics of the
programming platform by making the specifics hidden.
Your mental model determines what you think is valid input to
f(x) and what isn't, that has nothing to do with D. You want D
to provide you a way to only check for 0.0, whereas my point is
that there are many numbers in the neighborhood of 0.0 which will
screw up your calculation, so really you should be using
approxEqual.
The truth is that the computer, with its finite maximums and
bounded precision, better models _the measurements we make to
estimate the real world_ than any math ever written.
I am not estimating anything. I am synthesising artificial
worlds. My code is the model, the world is my code running at
specific hardware.
It is self contained. I don't want the compiler to change my
model because that will generate the wrong world. ;-)
It isn't changing your model, you can always use a very small
threshold in approxEqual. Yes, a few more values would be
disallowed as input and output than if you were to compare
exactly to 0.0, but your model is almost certainly undefined
there too.
If your point is that you're modeling artificial worlds that have
nothing to do with reality, you can always change your threshold
around 0.0 to be much smaller, and who cares if it can't go all
the way to zero, it's all artificial, right? :) If you're
modeling the real world, any function that blows up and gives you
bad data, blows up over a range, never a single point, because
that's how measurement works.
Oh, it's real world alright, you should be avoiding more
than just 2 in your example above.
Which number would that be?
I told you, any numbers too close to 2.
All numbers close to 2 in the same precision will work out ok.
They will give you large numbers that can be represented in the
computer, but do not work out to describe the real world, because
such formulas are really invalid in a neighborhood of 2, not just
at 2.
On the contrary, it is done because 80-bit is faster and more
precise, whereas your notion of reliable depends on an
incorrect notion that repeated bit-exact results are better.
80 bit is much slower. 80 bit mul takes 3 micro ops, 64 bit
takes 1. Without SIMD 64 bit is at least twice as fast. With
SIMD multiply-add is maybe 10x faster in 64bit.
I have not measured this speed myself so I can't say.
And it is neither more precise or more accurate when you don't
get consistent precision.
In the real world you can get very good performance for the
desired accuracy by using unstable algorithms by adding a stage
that compensate for the instability. That does not mean that it
is acceptable to have differences in the bias as that can lead
to accumulating an offset that brings the result away from zero
(thus a loss of precision).
A lot of hand-waving about how more precision is worse, with no
real example, which is what Walter keeps asking for.
You noted that you don't care that the C++ spec says similar
things, so I don't see why you care so much about the D spec
now.
As for that scenario, nobody has suggested it.
I care about what the C++ spec. I care about how the platform
interprets the spec. I never rely on _ONLY_ the C++ spec for
production code.
Then you must be perfectly comfortable with a D spec that says
similar things. ;)
You have said previously that you know the ARM platform. On
Apple CPUs you have 3 different floating point units: 32 bit
NEON, 64 bit NEON and 64 bit IEEE.
It supports 1x64bit IEEE, 2x64bit NEON and 4x32 bit NEON.
You have to know the language, the compiler and the hardware to
make this work out.
Sure, but nobody has suggested interchanging the three randomly.
And so is "float" behaving differently than "const float".
I don't believe it does.
I have proven that it does, and posted it in this thread.
I don't think that example has much to do with what we're talking
about. It appears to be some sort of constant folding in the
assert that produces the different results, as Joe says, which
goes away if you use approxEqual. If you look at the actual
const float initially, it is very much a float, contrary to your
assertions.
