I'm implementing a compression algorithm. Thing is, it is taking a second for a 20 Kib files, so that's not acceptable. I think it's slow because of the calculations.
I need suggestions on how to make it faster. I have some tips already, like shifting bits instead of multiplying, but I really want to be sure of which changes actually help because of the complexity of the program. I also accept suggestions concerning compiler options, I've heard there is a way to make the program do faster mathematical calculations.
Common operations are:
pow(...) function of math library
large number % 2
large number multiplying
Edit: the program has no floating point numbers
The question of how to make things faster should not be asked here to other people, but rather in your environment to a profiler. Use the profiler to determine where most of the time is spent, and that will hint you into which operations need to be improved, then if you don't know how to do it, ask about specific operations. It is almost impossible to say what you need to change without knowing what your original code is, and the question does not provide enough information: pow(...) function: what are the arguments to the function, is the exponent fixed? how much precision do you need? can you change the function for something that will yield a similar result? large number: how large is large in large number? what is number in this context? integers? floating point?
Your question is very broad, without enough informaiton to give you concrete advise, we have to do with a general roadmap.
What platform, what compiler? What is "large number"? What have you done already, what do you know about optimization?
Test a release build with optimization (/Ox /LTCG in Visual C++, -O3 IIRC for gcc)
Measure where time is spent - disk access, or your actual compression routine?
Is there a better algorithm, and code flow? The fastest operation is the one not executed.
for 20K files, memory working set should not be an issue (unless your copmpression requries large data structures), so so code optimization are the next step indeed
a modern compiler implements a lot of optimizations already, e.g replacing a division by a power-of-two constant with a bit shift.
pow is very slow for native integers
if your code is well written, you may try to post it, maybe someone's up to the challenge.
Hints :-
1) modulo 2 works only on the last bit.
2) power functions can be implemented in logn time, where n is the power. (Math library should be fast enough though). Also for fast power you may check this out
If nothing works, just check if there exists some fast algorithm.
Related
I'm writing a program that depends a lot on complex additions and multiplications. I wanted to know whether I should use gsl_complex or std::complex.
I don't seem to find a comparison online of how much better GSL complex arithmetic is as compared to std::complex. A rudimentary google search didn't help me find a benchmarks page for GSL complex either.
I wrote a 20-line program that generates two random arrays of complex numbers (1e7 of them) and then checked how long addition and multiplication took using clock() from <ctime>. Using this method (without compiler optimisation) I got to know that gsl_complex_add and gsl_complex_mul are almost twice as fast as std::complex<double>'s + and * respectively. But I've never done this sort of thing before, so is this even the way you check which is faster?
Any links or suggestions would be helpful. Thanks!
EDIT:
Okay, so I tried again with a -O3 flag, and now the results are extremely different! std::complex<float>::operator+ is more than twice as fast as gsl_complex_add, while gsl_complex_mul is about 1.25 times as fast as std::complex<float>::operator*. If I use double, gsl_complex_add is about 30% faster than std::complex<double>::operator+ while std::complex<double>::operator* is about 10% faster than gsl_complex_mul. I only need float-level precision, but I've heard that double is faster (and memory is not an issue for me)! So now I'm really confused!
Turn on optimisations.
Any library or set of functions that you link with will be compiled WITH optimisation (unless the names of the developer are Kermit, Swedish Chef, Miss Peggy (project manager) and Cookie Monster (tester) - in other words, the development team is a bunch of Muppets).
Since std::complex uses templates, it is compiled by the compiler settings you give, so the code will be unoptimized. So your question is really "Why is function X faster than function Y that does the same thing, when function X is compiled with optimisation and Y is compiled without optimisation?" - which should really be obvious to answer: "Optimisation works nearly all of the time!" (If optimisation wasn't working most of the time, compiler developers would have a MUCH easier time)
Edit: So my above point has just been proven. Note that since templates can inline the code, it is often more efficient than an external library (because the compiler can just insert the instructions straight into the flow, rather than calling out to another function).
As to float vs. double, the only time that float is slower than double is if there is ONLY double hardware available, with two functions added to "shorten" and "lengthen" between float and double. I'm not aware of any such hardware. double has more bits, so it SHOULD take longer.
Edit2:
When it comes to choosing "one solution over another", there are so many factors. Performance is one (and in some cases, the most important, in other cases not). Other aspects are "ease of use", "availability", "fit for the project", etc.
If you look at ONLY performance, you can sometimes run simple benchmarks to determine that one solution is better or worse than another, but for complex libraries [not "real&imaginary" type complex numbers, but rather "complicated"], there are sometimes optimisations to deal with large amounts of data, where if you use a less sophisticated solution, the "large data" will not achieve the same performance, because less effort has been spent on solving the "big data" type problems. So, if you have a "simple" benchmark that does some basic calculations on a small set of data, and you are, in reality, going to run some much bigger datasets, the small benchmark MAY not reflect reality.
And there is no way that I, or anyone else, can tell you which solution will give you the best performance on YOUR system with YOUR datasets, unless we have access to your datasets, know exactly which calculations you are performance (that is, pretty much have your code), and have experience with running that with both "packages".
And going on to the rest of the criteria ("ease of use", etc), those are much more "personal opinion" based, so wouldn't be a good fit for an SO question in the first place.
This answer depends not only on the optimization flags, but also on the compiler used to compile GSL library and your particular code. Example: if you compile gsl with gcc and your program with icc, then you may see a (significant) difference (I have done this test with std::pow vs gsl_pow). Also, the standard makefile generated by ./configure does not compile GSL with aggressive float point optimizations (example: it does not include fast-math flag in gcc) because some GSL routines (differential equation solver for example) fail their stringent accuracy tests when these optimizations are present.
One of the great points about GSL is the modularity of the library. If you don't need double accuracy, then you can compile gsl_complex.h, gsl_complex_math.h and math.c separately with aggressive float number optimizations (however you need to delete the line #include <config.h> in math.c). Another strategy is to compile a separate version of the whole library with aggressive float number optimizations and test if accuracy is not an issue for your particular problem (that is my favorite approach).
EDIT: I forgot to mention that gsl_complex.h also has a float version of gsl_complex
typedef struct
{
float dat[2];
}
gsl_complex_float;
I have a very large program which I have been compiling under visual studio (v6 then migrated to 2008). I need the executable to run as fast as possible. The program spends most of its time processing integers of various sizes and does very little IO.
Obviously I will select maximum optimization, but it seems that there are a variety of things that can be done which don't come under the heading of optimization which do still affect the speed of the executable. For example selecting the __fastcall calling convention or setting structure member alignment to a large number.
So my question is: Are there other compiler/linker options I should be using to make the program faster which are not controlled from the "optimization" page of the "properties" dialog.
EDIT: I already make extensive use of profilers.
Another optimization option to consider is optimizing for size. Sometimes size-optimized code can run faster than speed-optimized code due to better cache locality.
Also, beyond optimization operations, run the code under a profiler and see where the bottlenecks are. Time spent with a good profiler can reap major dividends in performance (especially it if gives feedback on the cache-friendliness of your code).
And ultimately, you'll probably never know what "as fast as possible" is. You'll eventually need to settle for "this is fast enough for our purposes".
Profile-guided optimization can result in a large speedup. My application runs about 30% faster with a PGO build than a normal optimized build. Basically, you run your application once and let Visual Studio profile it, and then it is built again with optimization based on the data collected.
1) Reduce aliasing by using __restrict.
2) Help the compiler in common subexpression elimination / dead code elimination by using __pure.
3) An introduction to SSE/SIMD can be found here and here. The internet isn't exactly overflowing with articles about the topic, but there's enough. For a reference list of intrinsics, you can search MSDN for 'compiler intrinsics'.
4) For 'macro parallelization', you can try OpenMP. It's a compiler standard for easy task parallelization -- essentially, you tell the compiler using a handful of #pragmas that certain sections of the code are reentrant, and the compiler creates the threads for you automagically.
5) I second interjay's point that PGO can be pretty helpful. And unlike #3 and #4, it's almost effortless to add in.
You're asking which compiler options can help you speed up your program, but here's some general optimisation tips:
1) Ensure your algorithms are appropriate for the job. No amount of fiddling with compiler options will help you if you write an O(shit squared) algorithm.
2) There's no hard and fast rules for compiler options. Sometimes optimise for speed, sometimes optimise for size, and make sure you time the differences!
3) Understand the platform you are working on. Understand how the caches for that CPU operate, and write code that specifically takes advantage of the hardware. Make sure you're not following pointers everywhere to get access to data which will thrash the cache. Understand the SIMD operations available to you and use the intrinsics rather than writing assembly. Only write assembly if the compiler is definitely not generating the right code (i.e. writing to uncached memory in bad ways). Make sure you use __restrict on pointers that will not alias. Some platforms prefer you to pass vector variables by value rather than by reference as they can sit in registers - I could go on with this but this should be enough to point you in the right direction!
Hope this helps,
-Tom
Forget micro-optimization such as what you are describing. Run your application through a profiler (there is one included in Visual Studio, at least in some editions). The profiler will tell you where your application is spending its time.
Micro-optimization will rarely give you more than a few percentage points increase in performance. To get a really big boost, you need to identify areas in your code where inefficient algorithms and/or data structures are being used. Focus on those, for example by changing algorithms. The profiler will help identify these problem areas.
Check which /precision mode you are using. Each one generates quite different code and you need to choose based on what accuracy is required in your app. Our code needs precision (geometry, graphics code) but we still use /fp:fast (C/C++ -> Code generation options).
Also make sure you have /arch:SSE2, assuming your deployment covers processors that all support SSE2. This will result is quite a big difference in performance, as compile will use very few cycles. Details are nicely covered in the blog SomeAssemblyRequired
Since you are already profiling, I would suggest loop unrolling if it is not happening. I have seen VS2008 not doing it more frequently (templates, references etc..)
Use __forceinline in hotspots if applicable.
Change hotspots of your code to use SSE2 etc as your app seems to be compute intense.
You should always address your algorithm and optimise that before relying on compiler optimisations to get you significant improvements in most cases.
Also you can throw hardware at the problem. Your PC may already have the necessary hardware lying around mostly unused: the GPU! One way of improving performance of some types of computationally expensive processing is to execute it on the GPU. This is hardware specific but NVIDIA provide an API for exactly that: CUDA. Using the GPU is likely to get you far greater improvement than using the CPU.
I agree with what everyone has said about profiling. However you mention "integers of various sizes". If you are doing much arithmetic with mismatched integers a lot of time can be wasted in changing sizes, shorts to ints for example, when the expressions are evaluated.
I'll throw in one more thing too. Probably the most significant optimisation is in choosing and implementing the best algorithm.
You have three ways to speed up your application:
Better algorithm - you've not specified the algorithm or the data types (is there an upper limit to integer size?) or what output you want.
Macro parallelisation - split the task into chunks and give each chunk to a separate CPU, so, on a two core cpu divide the integer set into two sets and give half to each cpu. This depends on the algorithm you're using - not all algorithms can be processed like this.
Micro parallelisation - this is like the above but uses SIMD. You can combine this with point 2 as well.
You say the program is very large. That tells me it probably has many classes in a hierarchy.
My experience with that kind of program is that, while you are probably assuming that the basic structure is just about right, and to get better speed you need to worry about low-level optimization, chances are very good that there are large opportunities for optimization that are not of the low-level kind.
Unless the program has already been tuned aggressively, there may be room for massive speedup in the form of mid-stack operations that can be done differently. These are usually very innocent-looking and would never grab your attention. They are not cases of "improve the algorithm". They are usually cases of "good design" that just happen to be on the critical path.
Unfortunately, you cannot rely on profilers to find these things, because they are not designed to look for them.
This is an example of what I'm talking about.
I am writing an application where in a certain block I need to exponentiate reals around 3*500*500 times. When I use the exp(y*log(x)) algorithm, the program noticeably lags. It is significantly faster if I use another algorithm based on playing with data types, but that algorithm isn't very precise, although provides decent results for the simulation, and it's still not perfect in terms of speed.
Is there any precise exponentiation algorithm for real powers faster than exp(y*log(x))?
Thank you in advance.
If you need good accuracy, and you don't know anything about the distribution of bases (x values) a priori, then pow(x, y) is the best portable answer (on many -- not all -- platforms, this will be faster than exp(y*log(x)), and is also better behaved numerically). If you do know something about what ranges x and y can lie in, and with what distribution, that would be a big help for people trying to offer advice.
The usual way to do it faster while keeping good accuracy is to use a library routine designed to do many of these computations simultaneously for an array of x values and an array of y values. The catch is that such library implementations tend to cost money (like Intel's MKL) or be platform-specific (vvpowf in the Accelerate.framework on OS X, for example). I don't know much about MinGW, so someone else will need to tell you what's available there. The GSL may have something along these lines.
Depending on your algorithm (in particular if you have few to no additions), sometimes you can get away with working (at least partially) in log-space. You've probably already considered this, but if your intermediate representation is log_x and log_y then log(x^y) = exp(log_y) * log_x, which will be faster. If you can even be selective about it, then obviously computing log(x^y) as y * log_x is even cheaper. If you can avoid even just a few exponentiations, you may win a lot of performance. If there's any way to rewrite whatever loops you have to get the exponentiation operations outside of the innermost loop, that's a fairly certain performance win.
Lets say we have a negative integer say
int a;
is there a faster implementation of
-a?
Do I have to do some bitwise operation on this?
There's almost certainly nothing faster than the machine code NEG instruction that your compiler will most likely turn this into.
If there was, I'm sure the compiler would use it.
For a twos-complement number, you could NOT it and add 1 but that's almost certainly going to be slower. But I'm not entirely certain that the C/C++ standards mandate the use of twos-complement (they may, I haven't checked).
I think this question belongs with those that attempt to rewrite strcpy() et al to get more speed. Those people naively assume that the C library strcpy() isn't already heavily optimized by using special machine code instructions (rather than a simplistic loop that would be most people's first attempt).
Have you run performance tests which seem to indicate that your negations are taking an overly long time?
<subtle-humor-or-what-my-wife-calls-unfunny>
A NEG on a 486 (state of the art the last time I had to worry
about clock cycles) takes 3 clock cycles (memory version,
register only takes 1) - I'm assuming the later chips will be
similar. On a 3Ghz CPU, that means you can do 1 billion of
these every second. Is that not fast enough?
</subtle-humor-or-what-my-wife-calls-unfunny>
Have you ever heard the phrase "premature optimization"? If you've optimized all of your code, and this is the only thing left, fine. If not, you're wasting your time.
To clarify Pax's statement,
C++ compilers are not mandated to use two's complement, except in 1 case. When you convert a signed type to an unsigned type, if the number is negative, the result of the conversion must be the 2's complement representation of the integer.
In short, there is not a faster way than -a; even if there were, it would not be portable.
Keep in mind as well that premature optimization is evil. Profile your code first and then work on the bottlenecks.
See The C++ Programming Language, 3rd Ed., section C.6.2.1.
Negating a number is a very simple operation in terms of CPU hardware. I'm not aware of a processor that takes any longer to do negation than to do any bitwise operation - and that includes some 30 year old processors.
Just curious, what led you to ask this question? It certainly wasn't because you detected a bottleneck.
Perhaps you should think about optimizing your algorithms more-so than little things like this. If this is the last thing to optimize, your code is as fast as it's going to get.
All good answers.
If (-a) makes a difference, you've already done some really aggressive performance tuning.
Performance tuning a program is like getting water out of a wet sponge. As a program is first written, it is pretty wet. With a little effort, you can wring some time out of it. With more effort you can dry it out some more.
If you're really persistent you can get it down to where you have to put it in the hot sun to get the last few molecules of time out of it.
That's the level at which (-a) might make a difference.
Are you seeing a performance issue with negating numbers? I have a hard time thinking that most compilers would do a bitwise op against integers to negate them.
I'm trying to find out some matrix multiplication/inversion benchmarks online. My C++ implementation can currently invert a 100 x 100 matrix in 38 seconds, but compared to this benchmark I found, my implementation's performances really suck. I don't know if it's a super-optimized something or if really you can easily invert a 200 x 200 matrix in about 0.11 seconds, so I'm looking for more benchmarks to compare the results. Have you god some good link?
UPDATE
I spotted a bug in my multiplication code, that didn't affect the result but was causing useless cycle waste. Now my inversion executes in 20 seconds. It's still a lot of time, and any idea is welcome.
Thank you folks
This sort of operation is extremely cache sensitive. You want to be doing most of your work on variables that are in your L1 & L2 cache. Check out section 6 of this doc:
http://people.redhat.com/drepper/cpumemory.pdf
He walks you through optimizing a matrix multiply in a cache-optimized way and gets some big perf improvements.
Check if you are passing huge matrix objects by value (As this could be costly if copying the whole matrix).
If possable pass by reference.
The thing about matricies and C++ is that you want to avoid copying as much as possable.
So your main object should probably not conatain the "matrix data" but rather contain meta data about the matrix and a pointer (wrapped in by somthing smart) to the data portion. Thus when copying an object you only copy a small chunk of data not the whole thing (see string implementation for an example).
Why do you need to implement your own matrix library in the first place? As you've already discovered, there are already extremely efficient libraries available doing the same thing. And as much as people like to think of C++ as a performance language, that's only true if you're really good at the language. It is extremely easy to write terribly slow code in C++.
I don't know if it's a super-optimized
something or if really you can easily
invert a 200 x 200 matrix in about
0.11 seconds
MATLAB does that without breaking a sweat either. Are you implementing the LAPACK routines for matrix inversion (e.g. LU decomposition)?
Have you tried profiling it?
Following this paper (pdf), the calculation for a 100x100 matrix with LU decomposition will need 1348250 (floating point operations). A core 2 can do around 20 Gflops (processor metrics). So theoretically speaking you can do an inversion in 1 ms.
Without the code is pretty difficult to assert what is the cause of the large gap. From my experience trying micro-optimization like loop unrolling, caching values, SEE, threading, etc, you only will get a speed up, which at best is only a constant factor of you current (which maybe enough for you).
But if you want an order of magnitude speed increase you should take a look at your algorithm, perhaps your implementation of LU decomposition have a bug. Another place to take a look is the organization of your data, try different organization, put row/columns elements together.
The LINPACK benchmarks are based on solving linear algebra problems. They're available for different machines and languages. Maybe they can help you, too.
LINPACK C++ libraries available here, too.
I actually gained about 7 seconds using **double**s instead of **long double**s, but that's not a great deal since I lost half of my precision.