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/nh59nt$1097$1...@digitalmars.com
"The compiler" means: implementation defined. That is the same as
not being well-defined. :-)
It is indeed random, or arbitrary (which is the same thing):
No, they're not the same thing: rules can be arbitrarily set
yet consistent over time, whereas random usually means both
arbitrary and inconsistent over time.
In this case it is the same thing then. I have no guarantee that
my unit tests and production code will behave the same.
I believe that means any calculation used to compute y at
compile-time will be done in 80-bit or larger reals, then
rounded to a const float for run-time, so your code comments
would be wrong.
No. The "const float y" will not be coerced to 32 bit, but the
"float y" will be coerced to 32 bit. So you get two different y
values. (On a specific compiler, i.e. DMD.)
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!
:-)
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".
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.
Fast floating point code depends on the specifics of the
hardware. A system level language should not introduce a
different kind of bias that isn't present in the hardware!
He's doing this to take advantage of the hardware, not the
opposite!
I don't understand what you mean. He is not taking advantage of
the hardware?
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?
What I said is that D is doing it wrong because the
"improvements" is forcing me to write code that is 10-100x slower
to get the same level of reliability and required accuracy as I
would get without the "improvements".
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.
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.
You can still test with approxEqual, so I don't understand why
you think that's not testing.
It is not testing anything if the compiler can change the
semantics when you use a different context.
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.
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.
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. ;-)
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.
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.
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).
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.
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.
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.
