First steps with Julia, performance tips

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Wes McKinney

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May 1, 2012, 3:36:56 PM5/1/12
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hey guys,

I plan to have a tinker with Julia now and then, being mainly a
Python/Cython hacker. Compiled Julia from git master today in advance
of Stefan's talk tonight.

I was curious if Julia does any optimization of array expressions, so
I set up a very simple benchmark: (Note, I am _not_ trolling even if
it seems like it and just looking to understand Julia's JIT and what's
going on)

function test1()
n = 1000000
a = randn(n)
b = randn(n)
c = randn(n)
for i=1:500
result = sum(a + b + c)
end
end

@time test1()

On my machine this takes about 14-15ms per iteration. OK. Time to fire
up IPython and see how NumPy (not actually super optimized, I've had
to reimplement loads of things in NumPy by hand in Cython) does:

In [6]: timeit (a + b + c).sum()
100 loops, best of 3: 11 ms per loop

OK, not bad. Time for NumExpr:

In [13]: import numexpr as ne

In [12]: timeit ne.evaluate('sum(a + b + c)')
100 loops, best of 3: 6.9 ms per loop

So, how much performance is actually left on the table? C function:

double add_things(double *a, double *b, double *c, int n) {
register double result = 0;
register int i;

for (i = 0; i < n; ++i)
{
result += *a++ + *b++ + *c++;
}
return result;
}

Wrapped in Cython and compiled:

cdef extern from "foo.h":
double add_things(double *a, double *b, double *c, int n)


def cython_test(ndarray a, ndarray b, ndarray c):
return add_things(<double*> a.data,
<double*> b.data,
<double*> c.data, len(a))

In [6]: timeit cython_test(a, b, c)
100 loops, best of 3: 2.26 ms per loop

Turns out doing C isn't even really necessary, straight Cython will do:

def cython_test2(ndarray[float64_t] a, ndarray[float64_t] b,
ndarray[float64_t] c):
cdef:
Py_ssize_t i, n = len(a)
float64_t result = 0

for i in range(n):
result += a[i] + b[i] + c[i]

return result

In [5]: timeit cython_test2(a, b, c)
100 loops, best of 3: 2.25 ms per loop

So here's the question: am I doing it wrong? Even in NumExpr above you
can get much better performance in array operations with no true JIT
(it has a VM that tries to eliminate temporaries). But NumExpr is
extremely limited. At minimum I was very surprised that vanilla
Python, temporaries and all, wins out over Julia in this simple
benchmark. Note that the %timeit function disables Python's GC which
may be having an effect in the timings.

cheers and looking forward to tonight's talk,

Wes

Wes McKinney

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May 1, 2012, 3:48:48 PM5/1/12
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Also, do you guys have any solutions in place for systematic
performance monitoring? I wouldn't mind a little help building out
vbench (http://pydata.github.com/vbench/) into a more broadly
applicable tool. Making it work with Julia shouldn't be very difficult

- Wes

Harlan Harris

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May 1, 2012, 4:03:02 PM5/1/12
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Looks to me like for Julia, you've got the randn() calls inside the function you're timing, but not for the other languages?

 -Harlan

Bill Hart

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May 1, 2012, 4:03:35 PM5/1/12
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Your first example clearly depends on the particular random integers
a, b, c that are generated.

Is the second example actually comparable? You are adding up an array
of doubles, but I don't see where you implement the Julia equivalent
for comparison.

Bill.

Bill Hart

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May 1, 2012, 4:07:51 PM5/1/12
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Does the @time macro actually run the code more than once? If not,
then it's more like the time taken depends on the particular values a,
b, c because a, b, c are generated once for all outside the loop.

Bill.

Wes McKinney

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May 1, 2012, 4:13:01 PM5/1/12
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Sorry Harlan, sloppy of me:


def f():
n = 1000000
a = np.random.randn(1000000)
b = np.random.randn(1000000)
c = np.random.randn(1000000)
for i in range(100):
result = (a + b + c).sum()

import numexpr as ne

def g():
n = 1000000
a = np.random.randn(1000000)
b = np.random.randn(1000000)
c = np.random.randn(1000000)
for i in range(100):
result = ne.evaluate('sum(a + b + c)')

from pandas._sandbox import cython_test

def h():
n = 1000000
a = np.random.randn(1000000)
b = np.random.randn(1000000)
c = np.random.randn(1000000)
for i in range(100):
result = cython_test(a, b, c)

In [8]: %time f()
CPU times: user 0.68 s, sys: 0.52 s, total: 1.20 s
Wall time: 1.20 s

In [9]: %time g()
CPU times: user 0.85 s, sys: 0.00 s, total: 0.85 s
Wall time: 0.85 s

In [5]: %time h()
CPU times: user 0.39 s, sys: 0.01 s, total: 0.40 s
Wall time: 0.40 s

According to line_profiler almost 50% of the runtime in the final case
is spent in generating the random numbers

In [6]: lprun -f h h()
Timer unit: 1e-06 s

File: <ipython-input-4-de3fa5fa2eae>
Function: h at line 1
Total time: 0.396024 s

Could not find file <ipython-input-4-de3fa5fa2eae>
Are you sure you are running this program from the same directory
that you ran the profiler from?
Continuing without the function's contents.

Line # Hits Time Per Hit % Time Line Contents
==============================================================
1
2 1 2 2.0 0.0
3 1 68803 68803.0 17.4
4 1 57343 57343.0 14.5
5 1 56980 56980.0 14.4
6 101 459 4.5 0.1
7 100 212437 2124.4 53.6

now bench.jl


function test1()
n = 1000000
a = randn(n)
b = randn(n)
c = randn(n)
@time for i=1:100
result :: Float64 = sum(a + b + c)
end
end

test1()
test1()
test1()
test1()
test1()

16:09 ~/code/repos/julia (master)$ ./julia bench.jl
elapsed time: 1.4287188053131104 seconds
elapsed time: 1.416337013244629 seconds
elapsed time: 1.5676219463348389 seconds
elapsed time: 1.4460339546203613 seconds
elapsed time: 1.4082918167114258 seconds

- Wes

Andrei Jirnyi

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May 1, 2012, 4:14:02 PM5/1/12
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On May 1, 2:36 pm, Wes McKinney <w...@lambdafoundry.com> wrote:
> On my machine this takes about 14-15ms per iteration. OK. Time to fire

Same here.

> up IPython and see how NumPy (not actually super optimized, I've had
> 100 loops, best of 3: 11 ms per loop
[..]
> In [12]: timeit ne.evaluate('sum(a + b + c)')
> 100 loops, best of 3: 6.9 ms per loop

FWIW, in Matlab (R2011b) I get about 4 ms/loop.

--aj

Jeff Bezanson

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May 1, 2012, 4:15:21 PM5/1/12
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Ok, fair enough. No, I wouldn't say you're doing it wrong.

The reason for the performance difference is probably that our sum()
and + are written entirely in julia, while numpy is running loops
written in C. We could have a library of C kernels like these to call,
but we'd rather put the effort into improving our compiler.

We do things this way because when we're slower on some microbenchmark
(compared to C, numpy, etc.) it's generally by a factor of 2x or 4x,
but when we're faster (compared to python, matlab, R, etc.) it's
generally by a factor of 10x or even 50x. In other words, we feel the
most real-world performance is to be gained not from maxing out simple
kernels like sum() but by generating better code over the whole
application. Obviously this isn't true for every application; if
sum(a+b+c) is your bottleneck then julia today doesn't help you, but
hopefully it will in the near future.

Second part of the answer: I tried this with the inner loop written out by hand:

function test2()
n = 1000000
a = randn(n)
b = randn(n)
c = randn(n)
for i=1:500
s = 0.0
for j=1:length(a)
s += a[j]+b[j]+c[j]
end
end
end

Your test1() takes about 16ms for me. But, test2() takes 1.3ms. So if
you need to tweak performance you can "unvectorize" by hand with less
effort than cython, and usually without giving up polymorphism. This
is where julia really does well, but of course the big gap between
test1 and test2 is still something for us to work on.

On Tue, May 1, 2012 at 3:36 PM, Wes McKinney <w...@lambdafoundry.com> wrote:

Wes McKinney

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May 1, 2012, 4:19:47 PM5/1/12
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Got it, thanks.

Jeff Bezanson

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May 1, 2012, 4:20:51 PM5/1/12
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Sorry, the 16ms and 1.3ms numbers were the times divided by 500, which
is a silly thing to measure given that the randn()s are in there. But
that makes the overall times 8 seconds and 0.65 seconds.

On Tue, May 1, 2012 at 4:15 PM, Jeff Bezanson <jeff.b...@gmail.com> wrote:

Elliot Saba

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May 1, 2012, 4:23:39 PM5/1/12
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I think this is important enough to mention in the manual, perhaps here: http://julialang.org/manual/performance-tips/

This extremely counter-intuitive (at least, when coming from other languages!) method of "optimization" by pulling operations _out_ of library functions, rather than the typical "try to mash everything possible _into_ the library functions" approach, is something that should really be stressed as a defining feature of this language.
-E

John Myles White

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May 1, 2012, 4:33:14 PM5/1/12
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Agreed. This is also the reason some people are so upset by the examples I give of Julia being faster than R: I always use unpacked code in both Julia and R, though R would be much faster with vectorized code.

 -- John

Bill Hart

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May 1, 2012, 4:36:31 PM5/1/12
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I was just recompiling Julia, so wasn't able to run the code Wes
posted, and didn't realise that it was generating __arrays__ of random
numbers to sum.

So my comments were totally wrong.

I actually misread the manual. Somehow I misread:

randi(n) — Generate a random integer from 1 to n inclusive

as

randn(n) — Generate a random integer from 1 to n inclusive

and simply assumed sum(n) summed the numbers from 1 to n inclusive.

Sorry about this.

Bill.

Bill Hart

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May 1, 2012, 4:54:22 PM5/1/12
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It looks like the C and Cython examples effectively do much more like
what Jeff posted.

So the only odd data point here is the NumExpr timing. But is it
possible that NumExpr effectively just does this?

julia> function test3()
n = 1000000
a = randn(n)
b = randn(n)
c = randn(n)
d = a + b + c
for i=1:500
result = sum(d)
end
end

That's about 4.7 times faster on my machine than the original.

From this perspective, it look to me as if there could possibly be a
Julia compiler optimisation opportunity that is missed here. (I hope I
am not still misinterpreting the intent of the original code or I will
go an even brighter shade of red).

Bill.

david tweed

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May 1, 2012, 5:13:13 PM5/1/12
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On May 1, 9:23 pm, Elliot Saba <staticfl...@gmail.com> wrote:
> I think this is important enough to mention in the manual, perhaps here:http://julialang.org/manual/performance-tips/
>
> This extremely counter-intuitive (at least, when coming from other
> languages!) method of "optimization" by pulling operations _out_ of library
> functions, rather than the typical "try to mash everything possible _into_
> the library functions" approach, is something that should really be
> stressed as a defining feature of this language.

My understanding is that this is not really a defining feature of the
language as much as "the way things are for today's Julia compiler".
While it may remain the case that manual optimization will beat the
compiler, hopefully in future it will become the case that the
compiler generally beats things for the amount of optimization you are
prepared (or allowed in the case of shared code) to do.

(If I understand the Julia documents, the design principle is the
ability to use loops when they're the clearest way of presenting an
algorithm, rather than needing to do that if the algorithm is
naturally presented in a "vectorised" way.)

Bill Hart

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May 1, 2012, 5:13:53 PM5/1/12
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No, once again I am being silly. Of course NumExpr cannot be rewriting
things the way I suggested. I guess it must ultimately be rearranging
things much as in the C and Cython examples.

Bill.

Andrei Jirnyi

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May 1, 2012, 7:51:46 PM5/1/12
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On May 1, 3:15 pm, Jeff Bezanson <jeff.bezan...@gmail.com> wrote:
> Your test1() takes about 16ms for me. But, test2() takes 1.3ms. So if
> you need to tweak performance you can "unvectorize" by hand with less
> effort than cython, and usually without giving up polymorphism. This
> is where julia really does well, but of course the big gap between
> test1 and test2 is still something for us to work on.

It is quite a big difference -- what is the reason for it? I would
imagine the Julia code for sum() must be pretty similar to the loop
inside your test2(), so why does it not run just as fast? Is the
function call overhead the culprit here -- and if this is the case
should one avoid calling functions in loops and manually inline?

--aj

Tim Holy

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May 1, 2012, 9:29:32 PM5/1/12
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Not certain (I don't know anything about the guts of the Julia compiler), but
I'd guess that
a+b+c = (a+(b+c))
creates two temporaries, one for b+c, and one for a+(b+c), and that the memory
allocation is a big part of the time cost.

Memory allocation is evil and should be avoided whenever possible :-).

The recent "delayed execution" work represents a promising framework to
optimize this (as well as push it onto the GPU, etc.).

--Tim

Jeff Bezanson

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May 1, 2012, 9:39:12 PM5/1/12
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Darn, that is suspicious, isn't it. Actually that number is totally
bogus; I looked at it again and I think LLVM's optimizer was deleting
a lot of the code since the result value wasn't used! If I return the
value, the times for the two versions are about the same. SO sorry
about this; it didn't occur to me the optimizer would be that clever.

So there is bad news and good news:

bad news: you can't necessarily get C performance in julia by manually
unvectorizing.

good news: there isn't a huge mysterious gap between our library and
manually-inlined code, so don't worry about function calls :)

Again, apologies!

Elliot Saba

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May 1, 2012, 11:10:07 PM5/1/12
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good news: there isn't a huge mysterious gap between our library and
manually-inlined code, so don't worry about function calls :)

I was about to come on here and clarify, but it all seems to be a moot point now. :)

I guess the object lesson here is.... Julia is a young thing, and she needs a few more tricks up her sleeves before she can battle with the big boys.  :)
-E

Tom Short

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May 2, 2012, 7:30:35 AM5/2/12
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On Tue, May 1, 2012 at 9:39 PM, Jeff Bezanson <jeff.b...@gmail.com> wrote:
> Darn, that is suspicious, isn't it. Actually that number is totally
> bogus; I looked at it again and I think LLVM's optimizer was deleting
> a lot of the code since the result value wasn't used! If I return the
> value, the times for the two versions are about the same. SO sorry
> about this; it didn't occur to me the optimizer would be that clever.

I got a reduction of about a factor of three when unvectorizing. Much of
the time seems to be spent on array referencing.

function test1()
n = 1000000
a = randn(n)
b = randn(n)
c = randn(n)
for i=1:500
result = sum(a + b + c)
end
end

function test2()
n = 1000000
a = randn(n)
b = randn(n)
c = randn(n)
result = 0.0
for i=1:500
for j = 1:length(a)
result += a[j] + b[j] + c[j]
end
end
result
end

function test3() # no summing here
n = 1000000
a = randn(n)
b = randn(n)
c = randn(n)
result = 0.0
for i=1:1500 # * 3
for j = 1:length(a)
result = a[j]
end
end
result
end


@time test1() # elapsed time: 6.3725199699401855 seconds

@time test2() # elapsed time: 2.0483860969543457 seconds

@time test3() # elapsed time: 1.5573301315307617 seconds

david tweed

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May 2, 2012, 10:24:31 AM5/2/12
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On May 2, 12:30 pm, Tom Short <tshort.rli...@gmail.com> wrote:
Note that not only are you not summing but you also aren't accessing
the elements of b or c. 1 million doubles takes about 7 and a half
megabytes. Depending on your CPU (eg, I'm using a puny netbook with an
Atom for most stuff where changing memory patterns is really
noticeable) the "memory bandwidth" _may_ be one of the factors
limiting performance. (Short of running under perf counters/cachegrind
this is just a hypothesis.)

That being said, the generated code for accesses may still be the
dominant contribution.

Dag Sverre Seljebotn

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May 2, 2012, 10:55:40 AM5/2/12
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Yes, this kind of data is pretty useless for synthetic benchmarks --
either use 1 MB or 100 MB, in order to stay clearly CPU-limited or
clearly memory bus limited.

Dag

Wes McKinney

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May 2, 2012, 12:09:41 PM5/2/12
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On Tue, May 1, 2012 at 9:39 PM, Jeff Bezanson <jeff.b...@gmail.com> wrote:
> Darn, that is suspicious, isn't it. Actually that number is totally
> bogus; I looked at it again and I think LLVM's optimizer was deleting
> a lot of the code since the result value wasn't used! If I return the
> value, the times for the two versions are about the same. SO sorry
> about this; it didn't occur to me the optimizer would be that clever.
>
> So there is bad news and good news:
>
> bad news: you can't necessarily get C performance in julia by manually
> unvectorizing.
>
> good news: there isn't a huge mysterious gap between our library and
> manually-inlined code, so don't worry about function calls :)
>
> Again, apologies!
>

Cool, thanks for looking deeper into this. Well, you have some new
optimization targets now. I doubt I need to tell you that getting
close to C speed (or sub C speed-- you should theoretically be able to
wedge yourself in between C and Fortran) in trivial benchmarks like
these is absolutely necessary if you want to attract performance
obsessed library implementers like myself.

I reiterate that you guys should be setting up performance tracking /
monitoring just as I've done for pandas (see e.g.
http://pandas.pydata.org/pandas-docs/vbench/vb_groupby.html or
http://speed.pypy.org/) and owe up to your performance shortcomings.
Since Julia is a young language I don't think you'll be sabotaging
yourselves by being clear and up front about where you have room for
improvement. It would also be an area where users could contribute
more complex benchmarks than the simple ones you are advertising (I
have close to 100 that I track using vbench now).

At some point in the future when I have some more time, I may
implement some of the critical data algorithms that I use in pandas
and it would be good to be able to look at a vbench-like graph over
time to see how the performance improves as Julia's JIT improves.

best regards,
Wes

Jeff Bezanson

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May 2, 2012, 12:28:33 PM5/2/12
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Totally agree about performance tracking. I'd love to have more
complex benchmarks and show more numbers. It's hard to add stuff to
our current table since implementing the benchmarks in all the
languages is really tedious. It will be easier to track julia
performance vs. itself over time.
I think it's already clear that we're slower than C; basically all of
our current numbers show that.

david tweed

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May 2, 2012, 1:02:30 PM5/2/12
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On May 2, 5:09 pm, Wes McKinney <w...@lambdafoundry.com> wrote:
> Cool, thanks for looking deeper into this. Well, you have some new
> optimization targets now. I doubt I need to tell you that getting
> close to C speed (or sub C speed-- you should theoretically be able to
> wedge yourself in between C and Fortran) in trivial benchmarks like
> these is absolutely necessary if you want to attract performance
> obsessed library implementers like myself.

To remake the point that Jeff Bezanson made upthread, it would be
unfortunate if the impetus of microbenchmark tracking led to
"premature" optimization of individual kernels which makes it much
harder to do the analysis to get bigger gains by combining/optimizing
larger groups of consecutive operations, particularly since this is
the kind of thing C or Fortran can't do because they have language
semantics that make it difficult to infer independencies.

So it'd be great to track performance, but keep focused on systematic
IR/JIT improvements that will have the biggest effect on "actual
usage" code patterns.

Wes McKinney

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May 2, 2012, 1:50:28 PM5/2/12
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Agreed. I'd be very interested to monitor the performance of more
complex iterative algorithms as the language matures, say Kalman
filters / Bayesian DLMs or things of that nature.

Wes McKinney

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May 2, 2012, 4:34:57 PM5/2/12
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On Wed, May 2, 2012 at 12:28 PM, Jeff Bezanson <jeff.b...@gmail.com> wrote:
> Totally agree about performance tracking. I'd love to have more
> complex benchmarks and show more numbers. It's hard to add stuff to
> our current table since implementing the benchmarks in all the
> languages is really tedious. It will be easier to track julia
> performance vs. itself over time.
> I think it's already clear that we're slower than C; basically all of
> our current numbers show that.
>

To further dangle a carrot, the work you're doing on the compiler is
probably the most critical part of Julia but also the most opaque to
end users. Having a daily updating graph of Julia performance is a
concrete way to demonstrate progress and more importantly to get lots
of kudos from the community ;)

david tweed

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May 4, 2012, 1:19:47 PM5/4/12
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Hi Wes,

I saw your blog post

http://wesmckinney.com/blog/?p=475

and tried to comment there, but unfortunately whatever ID system it
expects I don't belong to so it won't let me post, so the below
relates to that:

I think there's something that you're missing. You write "It may be in
a couple of years when the JIT-compiler improves", but I that suggests
that it's just a case of coding the JIT. However, I think one of the
things that's exciting the people who are excited about Julia is
precisely that it's at an early stage of development and there's not
yet a huge set of library codes. Consequently, if some changes are
discovered related to the user language which would make it easier to
run faster then things can be changed now (assuming that there's
consensus that it's a good trade-off, etc). In contrast the thing
about all the other languages mentioned is that as mature languages,
even things that everyone agrees were bad choices can't be changed
short of a "Python 3000" set of big changes all-at-once to minimise
porting problems. And you still here that many code/communities are
still on Python 2.x because they don't have the immediate block of
time to fix things that have changed in 3.0.

Hopefully Julia still has maybe a few months ahead where "good"
breaking changes (like the change in comprehension syntax) can happen.
And I'd pin my hopes on higher-level language changes rather than the
JIT for performance improvements.

On May 2, 9:34 pm, Wes McKinney <w...@lambdafoundry.com> wrote:
> On Wed, May 2, 2012 at 12:28 PM, Jeff Bezanson <jeff.bezan...@gmail.com> wrote:
> > Totally agree about performance tracking. I'd love to have more
> > complex benchmarks and show more numbers. It's hard to add stuff to
> > our current table since implementing the benchmarks in all the
> > languages is really tedious. It will be easier to track julia
> > performance vs. itself over time.
> > I think it's already clear that we're slower than C; basically all of
> > our current numbers show that.
>
> To further dangle a carrot, the work you're doing on the compiler is
> probably the most critical part of Julia but also the most opaque to
> end users. Having a daily updating graph of Julia performance is a
> concrete way to demonstrate progress and more importantly to get lots
> of kudos from the community ;)
>
>
>
> > On Wed, May 2, 2012 at 12:09 PM, Wes McKinney <w...@lambdafoundry.com> wrote:
> >>> On Tue, May 1, 2012 at 7:51 PM, Andrei Jirnyi <laxyf...@gmail.com> wrote:
> >>>> On May 1, 3:15 pm, Jeff Bezanson <jeff.bezan...@gmail.com> wrote:
> >>>>> Your test1() takes about 16ms for me. But, test2() takes 1.3ms. So if
> >>>>> you need to tweak performance you can "unvectorize" by hand with less
> >>>>> effort than cython, and usually without giving up polymorphism. This
> >>>>> is where julia really does well, but of course the big gap between
> >>>>> test1 and test2 is still something for us to work on.
>
> >>>> It is quite a big difference -- what is the reason for it? I would
> >>>> imagine the Julia code for sum() must be pretty similar to the loop
> >>>> inside your test2(), so why does it not run just as fast? Is the
> >>>> function call overhead the culprit here -- and if this is the case
> >>>> should one avoid calling functions in loops and manually inline?
>
> >>>> --aj- Hide quoted text -
>
> - Show quoted text -

Stefan Karpinski

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May 4, 2012, 2:35:27 PM5/4/12
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Thanks for the post, Wes. I just posted a comment on there:

Message has been deleted

Michael Smith

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Aug 15, 2014, 9:37:21 PM8/15/14
to juli...@googlegroups.com
Interesting conversation, but I can't find Stefan's comment in this link. (In fact, I cannot see any comment in Wes' blog entry.)  Would love to read what you have replied. 

And, on another note, it has been some time since this was run. Would be interesting to see what has changed in the meantime. 

Stefan Karpinski

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Aug 16, 2014, 10:42:35 AM8/16/14
to Julia Dev
It looks like Wes may have turned off the comments.
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