How to increase speed of large for loops

JohanSolo

If I may, std::pow for integer exponents can be trivially replaced by this small template:

template< int exponent, typename T >
T power( T base )
{
    if ( exponent == 0 )
    {
        return T( 1 );
    }
    else if ( exponent < 0 )
    {
        return T( 1 ) / power< -exponent >( base );
    }
    else if ( exponent % 2 == 0 )
    {
        return power< exponent / 2 >( base * base );
    }
    else
    {
        return power< exponent / 2 >( base * base ) * base;
    }
}

jsulm

This post is deleted!

JonB

@JohanSolo
I wondered about this too. Or in the OP's case he is always using pow() to square, he could replace with in-line single multiply. However, I don't know whether the code for pow() already takes a simple case like this into account and is already efficient?

JohanSolo

@JonB said in How to increase speed of large for loops:

@JohanSolo
However, I don't know whether the code for pow() already takes a simple case like this into account and is already efficient?

I attended this lecture long time ago, on page 5 it looks like at least at the time the std::pow was not as efficient as it could be. I cannot tell for the current implementation of std::pow though.

JonB

@JohanSolo
Yep, you may well be right. I believe for many years C compilers have turned multiplication by 2 (or power of 2) into left-shift (or for all I know modern chips' multiplication instructions do this automatically so compiler doesn't have to any more), but that's not the same as a call to function pow(). In any case, the OP should try one of these code optimisations for his squaring and see if it makes much difference.

He might also trying narrowing down just which instructions are causing time. For example, I don't know whether the cloudB->points[v[p2]] is instantaneous indexed access or what. Unless relying on the compiler to do it for you (which it may do, I don't know), there are a lot of places which could be factored into temporary variable assignments for re-use to guarantee no re-calculation, e.g. cloudB->points, cloudB->points[v[p0]], etc.

Also, in the loop conditions is ros::ok() instantaneous or costly?

But it may just be that there are an awful lot of sqrt() to perform, which I imagine is the costliest operation (how does that code calculate square roots? IIRC, at school using Newton's approximation with pen & paper was pretty time-consuming! How does it get done nowadays?). I see @J-Hilk has posted a link which should be examined in this light.

Finally, the multi-threading. Do you have evidence whether the multiple threads are using separate cores on your machine to do the work, and without waiting on each other or something else? In any case, a spare couple of cores are only going to reduce the time by a factor of 2, which may be of little help for what the OP wants. Verify that the separate threads are not actually slowing the whole calculation down!

BTW, how often does the result follow the if(p0p1>10) route, causing the inner loop? Is that where it's "slow"? If so, one small possible optimisation: if you are then only interested in the if(p0p2>10 && p1p2>10) route, after you have calculated p0p2 if it is not >10 you don't need to calculate p1p2, don't know how many calculations that would eliminate overall. "Every little helps", as a certain supermarket here says :)

J.Hilk

@JonB said in How to increase speed of large for loops:

Also, in the loop conditions is ros::ok() instantaneous or costly?

that's actually a good point,

v.size() and ros::ok() are called each cycle. at least size() is something the op can rationalize away

for(size_t p1=0;p1<v.size() && ros::ok();++p1) {

to

for(size_t p1 (0), end(v.size()); p1<end && ros::ok();++p1) {

aha_1980

@kane9x

If your code does not work as fast as expected, you should do two things first:

Ask yourself if you use the best algorithm for the given problem
Profile your alogrithm to find out the slowest part. Store the result for later comparism.

You cannot start optimizing before these two steps are finished. Next, set up good unit tests that make sure the behavior does not change when refactoring. Then, replace the slowest part with a better implementation.

Regards

kane9x

@aha_1980 Thank you, I think what I should do now is to find some algorithm to help me optimize it

JonB

@kane9x

nearly about 8e+12 iterations

I don't know quite what you're trying to do why, but if you mean you have approx a trillion iterations/square roots etc. to calculate that's a very large number to be executing if speed is critical....

kshegunov

@JonB said in How to increase speed of large for loops:

I don't know quite what you're trying to do why, but if you mean you have approx a trillion iterations/square roots etc. to calculate that's a very large number to be executing if speed is critical....

Maybe I can help with your confusion. The OP is trying to calculate the euclidean distance for a set of three points and do so by using a permutation of those three points from the whole set. Something they should've precalculated and stored and something they should've used the SIMD instructions for.

kshegunov

PS.
Just to be clear, the indirection cloudB->points[v[p0]] is a cache line invalidation every time.

JonB

@kshegunov said in How to increase speed of large for loops:

Maybe I can help with your confusion. The OP is trying to calculate the euclidean distance for a set of three points

Yes, I realised it was this sort of thing. However, AFAIK Euclid did not have the aid of a PC and presumably would have struggled to calculate a trillion distances by hand... :)

kshegunov

@JonB said in How to increase speed of large for loops:

AFAIK Euclid did not have the aid of a PC and presumably would have struggled to calculate a trillion distances by hand...

Probably not. But I imagine, him being a smart guy, he'd've tabulated whatever he had already calculated so he didn't need to do it again ... at least seems logical to me.

JonB

@kshegunov
Trouble is, writing down the answers to a trillion square roots takes a lot of space. And with that many even look-up time is going to get considerable....

kshegunov

@JonB said in How to increase speed of large for loops:

Trouble is, writing down the answers to a trillion square roots takes a lot of space. And with that many even look-up time is going to get considerable....

Mayhaps. I do like the "we create hardware out of software" approach, I admit, unfortunately this rarely works in practice. Leaving the metaphors to rest for a moment, I implore you to really try to imagine how this is supposed to work and do the following:

Notice the inner loop is only interesting if the distance between two points is more than some magic number (not having semi-divine in-code numbers is a matter for another discussion).
Notice the inner if is checking if two distances (between two pairs of points) are larger than some arbitrary numbers.
Notice that the distance between two points is the same no matter which is first and which is second.
Notice that distances are recalculated for every conceivable case of point pairing.
Finally (and least importantly), notice that the indirection through some permutation vector brakes data locality and thus invalidates the cache.

Now after a quick think, I hallucinate that 1), 2), 3) and 4) can be fixed rather easily in a single step, without throwing recursive template instantiations at pow, mind you. My "genius" idea is as follows:

Go through the pairs of points and save in a container only these pairs (and the distance between them) that satisfy the threshold.
1.1) When doing that it's useful to not repeat, thus the distance from A to B is going to be the same as the distance from B to A, unless living in an alternate world. This should help shave off some unnecessary duplication.
1.2) Before doing that it's also useful to throw away the permutation vector if possible, so 5) to be solved by construction.
For the resulting container from 1) (probably a vector) one can see that the innermost if is directly satisfied for any pair of elements ...
Step 1) can be parallelized very easily for additional yield.
Step 1) can make use of SSE/AVX.

JonB

@kshegunov Indeedy, these are all good points, FAO the OP, @kane9x, not me!

kshegunov

And I was just thinkin' we are having a nice easygoing conversation ... 'cause when I see this:

template< int exponent, typename T >
T power( T base )
{
    // ...
}

I cringe so badly my face is contorted for a week.

JonB

@kshegunov
No idea what's foul about it, or the bit you've quoted, so you'd better explain? Unless you mean the whole idea of using templates, which of course I never used: C didn't need them, C++ added them as an obfuscation layer, so I'm quite happy without ;-)

Mind you, I looked at @JohanSolo's code above. His definition is a recursive one (return power< exponent / 2 >( base * base ) * base;). I'm surprised. This would be all very well in my old Prolog, but I don't think the C++ compiler is going to recognise & remove tail recursion in the definition. So I don't know what he means by "trivially replaced", why would one want to use such a definition?

JohanSolo

I never though my little post could produce so much noise... First the snippet is not mine, as I already stated, I took it from a lecture I followed at CERN in 2009. The lecturer was Dr Walter Brown, who was presented as: "Dr. Brown has worked for Fermilab since 1996. He is now part of the Computing Division's Future Programs and Experiments Quadrant, specializing in C++ consulting and programming. He participates in the international C++ standardization process and is responsible for several aspects of the forthcoming updated C++ Standard. In addition, he is the Project Editor for the forthcoming C++ Standard on Mathematical Special Functions."

About the recursive template: the compiler expands it at compile time, therefore leading to power< 4 >( x ) being replaced by x*x * x*x, which is apparently (or at least was) way faster than calling std::pow. Therefore, I expect power< 2 >( something ) to be faster than std::pow( something, 2 ).

kshegunov

@JonB said in How to increase speed of large for loops:

No idea what's foul about it, or the bit you've quoted, so you'd better explain? Unless you mean the whole idea of using templates, which of course I never used: C didn't need them, C++ added them as an obfuscation layer, so I'm quite happy without ;-)

Recurrently instantiating a function for no apparent reason, basically invoking the sophisticated copy-paste machinery that is the compiler's template engine to produce: x * x, especially when the latter would suffice.

Mind you, I looked at @JohanSolo's code above. His definition is a recursive one (return power< exponent / 2 >( base * base ) * base;). I'm surprised. This would be all very well in my old Prolog, but I don't think the C++ compiler is going to recognise & remove tail recursion in the definition. So I don't know what he means by "trivially replaced", why would one want to use such a definition?

Code inlining is kind of a religion. Surely it has its values in the proper places, and most certainly templates make some things easier, then again ... it's very much like chocolate, when you don't eat it, you want it, when you eat it, you want more of it, but in the ultimate scheme of things it makes you fat ...

The most ugly thing about templates, however, is that everything has to be defined for instantiation to take place, which is of course expected. So you can't have abstractions manifested without spilling the guts of the implementations. And of course there exists no such thing as binary compatibility, as everything is recompiled every time ... such a wonderful idea.

@JohanSolo said in How to increase speed of large for loops:

I never though my little post could produce so much noise...

Well yeah, I'm from eastern europe - all simmering under the hood.

First the snippet is not mine, as I already stated, I took it from a lecture I followed at CERN in 2009.

Yes, I glanced at the slides. FYI even boost's math module doesn't do that kind of nonsense because fast exponentiation algorithms for integral powers was (and is known) for 50+ years. And if the compiler actually inlines all the (unnecessary) instantiations, depending on the optimizations it applies, you could end up in the same x * x * x * ... * x case. The point is computers are rather stupid, they do what we tell them to do, and ultimately everything you write is going to be compiled to binary, not to a cool concept from a book (or lecture, or w/e).

The lecturer was Dr Walter Brown, who was presented as: "Dr. Brown has worked for Fermilab since 1996. He is now part of the Computing Division's Future Programs and Experiments Quadrant, specializing in C++ consulting and programming. He participates in the international C++ standardization process and is responsible for several aspects of the forthcoming updated C++ Standard. In addition, he is the Project Editor for the forthcoming C++ Standard on Mathematical Special Functions."

Good for him. I don't know him, nor do I hold people in esteem for their titles. He might be a contemporary Einstein for all I know, but I place merit whenever I judge there to be reason for. In this case, I have not. The lecture, and all the proof of it boiling down to a synthetic test, is not nearly enough for me.
Just as a disclaimer, I've seen quite a lot of "scientific code" to be cynical to the point of not believing academia can (or should) write programs.

About the recursive template: the compiler expands it at compile time, therefore leading to power< 4 >( x ) being replaced by x*x * x*x

No it leads to power<4>(x) being replaced by power<2>(x) * power<2>(x) where power<2> is a distinct function. This may lead to x * x * x * x in assembly, which of course would have the same performance as multiplying the argument manually, or it may lead to be evaluated as (x * x), which is then multiplied by itself, where you may gain a multiplication. The point is your template can't tell the compiler how to produce the efficient binary code.

Therefore, I expect power< 2 >( something ) to be faster than std::pow( something, 2 ).

I expect them to be exactly the same up to a couple of push/pops and a single call.

I did find it rather surprising that pow and sqrt were implicated here. I'd like to top off this missive with a quotation that I love from a fictional character:

You wake up in the morning, your paint's peeling, your curtains are gone, and the water is boiling. Which problem do you deal with first?
...
None of them! The building's on fire!