vectorized computation in C++ such as those in Matlab (Matlab toC++)?

[Luna Moon]

Dear all,

Can C++/STL/Boost do the vectorized calculation as those in Matlab?

For example, in the following code, what I really want to do is to
send in a vector of u's.

All other parameters such as t, l1, l2, l3, etc. are scalars...

But u is a vector.

Thus, t6 becomes a vector.

t9 is an element-wise multiplication. ..

The following code was actually converted from Matlab.

If vectorized computation is not facilitated, then I have to call this
function millions of times.

But if vectorized computation is okay, then I can send in just a u
vector with batch elements a time.

I have many such code in Matlab need to be converted into C++ with
vectorization.

Any thoughts?

Thank you!

double t5, t6, t7, t9, t11, t13, t16, t20, t23, t27, t32, t34, t36,
t37, t38, t42,
t44, t47, t48, t51, t52, t54, t59, t60, t61, t66, t67, t69, t74,
t75, t76, t81,
t82, t84, t87, t105, t106, t110, t112;

t5 = exp(-t * l1 - t * l2 - t * l3);
t6 = t * u;
t7 = mu1 * mu1;
t9 = u * u;
t11 = kappa * kappa;
t13 = 0.1e1 / (t9 * t7 + t11);

[dj3vande]

In article <6d************ *************** *******@x41g200 0hsb.googlegrou ps.com>,
Rune Allnor <al****@tele.nt nu.nowrote:

>On 6 Aug, 14:54, Giovanni Gherdovich
<gherdov...@st udents.math.uni fi.itwrote:

>I'm aware of Matlab "vectorizat ion" techniques; I use them to
avoid for-loops.

That's a *matlab* problem. 'Vectorization' is a concept
exclusive to matlab, which historically was caused by
what I consider to be bugs in the matlab interpreter.

To describe this property of matlab as "buggy" is inordinately harsh.

It's an inherent property of interpreters: If you're interpreting a
loop, you have to look at the loop condition code, and the loop
bookkeeping code, and the code inside the loop, every time through.
Unless you go out of your way to make this fast, you end up having to
do a lookup-decode-process for each of those steps.
Compiling to native code lets you do the lookup-decode at compile time,
and for typical loops only generates a few machine-code instructions
for the loop bookkeeping and condition checking, which substantially
reduces the total amount of work the processor is doing. But making an
interpreter clever enough to do interpreted loops that fast is a Much
Harder Problem.

(So, the answer to the OP's question is (as already noted): Don't worry
about vectorizing, write loops and ask the compiler to optimize it, and
you'll probably come close enough to Matlab's performance that you
won't be able to tell the difference.)

Since Matlab is targeting numerical work with large arrays anyways,
there's not much benefit to speeding up this part of the interpreter;
if the program is spending most of its time inside the large-matrix
code (which is compiled to native code, aggressively optimized by the
compiler, and probably hand-tuned for speed), then speeding up the
interpreter's handling of the loop won't gain you any noticeable
speedup anyways. If you're writing loopy code to do things Matlab has
primitives for, you're probably better off vectorizing it anyways,
since that will make it both clearer and faster.
So (unlike with general-purpose interpreted languages that don't have
primitives that replace common loop idioms) there's no real benefit to
speeding up the Matlab interpreter's loop handling, and there are
obvious costs (development time, increased complexity, more potential
for bugs), so there are good reasons not to bother.

If you do have code that doesn't fit Matlab's vectorization model, you
can always write it in C or Fortran and wrap it up in a Matlab FFI
wrapper; Matlab's FFI is not hard to use on the compiled-to-native-code
side, and looks exactly like a Matlab function on the Matlab code side,
so it's almost always the Right Tool For The Job in that case.
(At my day job, I've been asked to do this for the Matlab programmers a
few times, and for hard-to-vectorize loopy code getting a speedup of
two or three orders of magnitude just by doing a reasonably direct
translation into C and compiling to native code with an optimizing
compiler is pretty much expected.)

dave

--
Dave Vandervies dj3vande at eskimo dot com
Erm... wouldn't clock(), used with Bill Godfrey's follow-up, ignoring my
follow-up to him (as suggested in your follow-up to me), do the trick
quite nicely? --Joona I Palaste in comp.lang.c

[Giovanni Gherdovich]

Hello,

thank you for your answers.

Rune Allnor:

Depending on exactly what you do, matlab *can* get very
close to best-possible performance since it uses highly
tuned low-level libraries. If your operation is covered by
such a function, you might find it difficult to beat matlab.
If not, don't be surprised if C++ code beats matlab by
a factor 5-10 or more.

dave:

(So, the answer to the OP's question is (as already noted): Don't worry
about vectorizing, write loops and ask the compiler to optimize it, and
you'll probably come close enough to Matlab's performance that you
won't be able to tell the difference.)

Uwe:

I mean: taking the inverse of a matrix is linear algebra,
but multiplying two vectors component-wise is just... multiplying.

yes. but you can do some enrollment or other
access patterns for optimizing cache access.
this is a broad field, look at:
http://en.wikipedia.org/wiki/Loop_transformation

Rune Allnor:

You would be surprised: There are for-loops at the core of all
those libraries, even the BLAS libraries matlab is based on.
There are smart compilation techniques involved, but to *optimize*
the for-loops, not to *eliminate* them.

I was among the user who are "conditione d to believe that the
problem lies with for-loops as such, and not with matlab",
to use Rune's words.
Thank you all to point it out.

About the performance of numerical computation done using
std::valarray<> 's features:

Uwe:

My question:
When writing C++ code, do you thing I can have faster code
if I use std::valarray<i n "the Matlab way", instead
of using, say, std::vector<and for-loops?

I do not know how optimized valarray<is. You
should compare it using different matrix-/vector-sizes
and different optimization flags
of your compiler and post your results.

Rune Allnor:

I don't know. I haven't used std::valarray<> . I know I have
seen some comment somewhere that std::valarray<w as an early
attempt at a standardized way to handle numbercrunching in C++,
which was, well, not quite as successful as one might have
whished for.

It seems that nobody knows if it's worth to use std::valarray<>
and related "vectorized " operators (provided by the standard
library) to do numerical computing in C++.

Googling this topic, I've found this interesting thread in
a forum of a site called "www.velocityre views.com"
http://www.velocityreviews.com/forum...s-vectors.html

One of the poster, who (like me) took the chapter "Vector Arithmetic"
on Stroustrup's book as The Truth, says that with valarray<>
you can do math at the speed of light, blah blah optimization
blah blah vectorization and so on.

Another user answers with what I find a more reasonable argument:
std::valarray<w as designed to meet the characteristic of vector
machines, like the Cray. If you don't have the Cray, there is
no point in doing math with valarray<and related operators.

Anyway, as soon as I have some spare time I will check it on
my own, comparing the results with ATLAS as Uwe suggests.

Regards,
Giovanni Gherdovich

[Jerry Coffin]

In article <a47fac46-bb33-4608-bd97-
f7**********@d7 7g2000hsb.googl egroups.com>,
gh********@stud ents.math.unifi .it says...

[ ... ]

Another user answers with what I find a more reasonable argument:
std::valarray<w as designed to meet the characteristic of vector
machines, like the Cray. If you don't have the Cray, there is
no point in doing math with valarray<and related operators.

In theory that's right: the basic idea was to provide something that
could be implemented quite efficiently on vector machines. In fact, I've
never heard of anybody optimizing the code for a vector machine, so it
may be open to question whether it provides any real advantage on them.

OTOH, valarray _can_ make some code quite readable, so it's not always a
complete loss anyway.

--
Later,
Jerry.

The universe is a figment of its own imagination.

[Francis Glassborow]

Jerry Coffin wrote:

In article <a47fac46-bb33-4608-bd97-
f7**********@d7 7g2000hsb.googl egroups.com>,
gh********@stud ents.math.unifi .it says...

[ ... ]

>Another user answers with what I find a more reasonable argument:
std::valarray< was designed to meet the characteristic of vector
machines, like the Cray. If you don't have the Cray, there is
no point in doing math with valarray<and related operators.

In theory that's right: the basic idea was to provide something that
could be implemented quite efficiently on vector machines. In fact, I've
never heard of anybody optimizing the code for a vector machine, so it
may be open to question whether it provides any real advantage on them.

During the mid-90s both C and C++ were involved in adding features that
would support numerically intense programming. Unfortunately a couple of
years later the companies whose numerical experts doing the grunt work
withdrew support. By hindsight it might have been better to have shelved
the work but both WG14 and WG21 opted to continue hoping that they would
still produce something useful.

It is not obvious to those outside the numerical fields that actually
developing things like complex number support, support for array
arithmetic etc. is fraught with subtle traps.

>
OTOH, valarray _can_ make some code quite readable, so it's not always a
complete loss anyway.

--
Note that robinton.demon. co.uk addresses are no longer valid.

[Giovanni Gherdovich]

Hello,

During the mid-90s both C and C++ were involved in adding features that
would support numerically intense programming. Unfortunately a couple of
years later the companies whose numerical experts doing the grunt work
withdrew support.

Just for the sake of historical investigation, I found a thread on
this newsgroup from the far 1991, where Walter Bright (who might
be the same Walter Bright who designed the D programming language,
http://www.walterbright.com/
http://en.wikipedia.org/wiki/Walter_Bright , but I'm not sure)
lists some shortcomings for the C++ numerical programmer,
and item #6 is

"Optimizati on of array operations is inhibited by the 'aliasing'
problems."
http://en.wikipedia.org/wiki/Aliasing_(computing)

(retrieved from
http://groups.google.com/group/comp....b0ec8ea7b24189

Then he mentions some solutions to this (two libraries, which
might be completely out of date nowaday).
Just to say that the Original Poster isn't the first to
address this issue...

By hindsight it might have been better to have shelved
the work but both WG14 and WG21 opted to continue hoping that they would
still produce something useful.

Mmmh... I skimmed over the pages of Working Groups 14 and 21
http://www.open-std.org/jtc1/sc22/wg14
http://www.open-std.org/jtc1/sc22/wg21
and they don't seem to have vector arithmetic among their priorities.
Anyway, from what I've learned from this thread, the overall
theme can very well make no sense, because of CPUs characteristics .

Regards,
Giovanni Gh.