My experience thus far has shown me that even with multi-core processors, parallelizing an algorithm won't always speed it up noticably. In fact, sometimes it can slow things down. What are some good hints that an algorithm can be sped up significantly by being parallelized?
(Of course given the caveats with premature optimization and their correlation to evil)
To gain the most benefit from parallelisation, a task should be able to be broken into similiar-sized course-grain chunks that are independent (or mostly so), and require little communication of data or synchronisation between the chunks.
Fine-grain parallelisation, almost always suffers from increased overheads, and will have a finite speed-up regardless of the number of physical cores available.
[The caveat to this, is those architectures that have a very large no. of 'cores' (such as the connection machines 64,000 cores). These are well suited to calculations that can be broken into relatively simple actions assigned to a particular topology (like a rectangular mesh).]
If you can divide the work into independent parts then it may be parallelized well.
Remember also Amdahl's Law which is a sobering reminder of how little we can expect in terms of performances gains by adding more cores to most programs.
First, check out this paper by the late Jim Gray:
Distributed Computing Economics
Actually, this will clear up some misunderstanding based on what you wrote in the question. Obviously, if the less amenable your problem set is to being discretized, the more difficult it will be.
Any time you have computations that depend on previous computations, it is not a parallel problem. Things like linear image processing, brute force methods, and genetic algorithms are all easily parallelized.
A good analogy is what could you work on that you could get a bunch of friends to do different parts at once? For example, putting ikea furniture together might parallelize well if different people can work on different sections, but rolling wallpaper might not because you need to do walls in sequence.
If you're doing large matrix computations, like simulations involving finite element models, these can often be broken down into smaller pieces in straight-forward ways. Matrix-vector multiplies can benefit well from parallelization, assuming you are dealing with very large matrices. Unless there is a real performance bottleneck that is causing code to run slowly, it's probably not necessary to hassle with parallel processing.
Well, if you need lots of locks for it to work, then its probably one of those difficult algorithms that doesn't parallelise well. Is there any part of the algorithm that can be broken up into separate parts that don't need to touch each other?
Related
I have written a new algorithm for something. Now I need to compare it with existing methods, some of which are old about 10 years.
The idea I had is to look at benchmarks of different processors over the years in order to establish how much faster my processor (i7-920) is than average processor from 2003. Then I would simply divide old methods' execution time by the speedup factor and use those numbers to compare with my own algorithm.
Has something like this been done? So I don't redo the existing work.
Can such a comparison be done some other way?
Are there some scientific papers written about such comparisons which I can reference?
I don't know which of these are possible for you, but here's a list of options I can think of:
Run their implementation side-by-side on your machine against yours.
This is the best option.
Rewrite their implementations and do (1).
You preferably need to compare it against their test to ensure you get vaguely similar results.
Find a library that implements their algorithm (or multiple libraries) and do (1).
I suggest multiple libraries, if possible, since a single one may not have implemented the algorithm efficiently. You may also want to compare these against their test.
Compare the algorithms mathematically.
This may be difficult, but it's not impossible.
Do what you presented.
(a) I would not recommend this as there are other determining factors in your computer other than the processor speed that affect the speed of an algorithm. Getting an equation that perfectly balances these will likely be very difficult.
(b) There is a massive difference between top and bottom of the line computers, so using the average is not a particularly good idea. If the author didn't provide details regarding this, I'm afraid your benchmark is not likely to be too accurate.
Go out and buy a machine of similar specs to the one used by the desired test to benchmark on.
A 10-year-old machine should be pretty cheap, if you can find one. Also, see (5.b).
Contact the author to allow for any of the other options.
Papers often provide contact details of the authors, or you should be able to find them elsewhere if they have any sort of online presence and you're half-decent at using Google.
If I were reviewing your results, I would be annoyed if you attempted to demonstrate less than an order of magnitude speedup this way. There are a lot of variables determining algorithm performance, and I would be skeptical that a generic benchmark could capture the right ones. My gold standard is old and new algorithms implemented by the same programmer, with similar effort made to optimize, running on the same hardware. Using the previous authors' implementation instead of making a new one is commonplace in the experimental algorithms literature, but using different hardware isn't.
Algorithmic performance is usually measured in big-O terms, for which it is better to count basic operations, like comparisons, and do it for a range of input sizes.
If you must measure overall time, at least eliminate other sources of difference.
As #larsmans said, do it on the same processor.
Also, if there is existing work, there's no harm in repeating it.
Generally, in science, that's a good thing.
You should attempt to reduce the amount of differing factors between the two runs. I think just run-timing the two algorithms side by side on the same machine and/or comparing their Big O times are both equally valid and important. You should also attempt to use updated libraries and other external functions; using outdated ones my also be the cause of timing results.
I am confused how to take inputs from file. In many of hacking challenge sites input will be in the format
-no of test cases
case1
case2
..so on
My question is what is the best way to read the inputs. Whether i should read all the cases in one loop, store it in an array and then perform operations on the inputs in separate loop OR just use one loop for both- to read and perform operations on input. Is there any performance issue between these two methods?
I'd say not significantly. Either way, the same number of operations will be performed, the question is about clumping together "the same kind" of operations. Like AndreyT said, organizing it based in stages that act on the same general area of memory might increase performance. It really depends on the kind of input and output your doing, as well as some operating system and programming language specific variables. The question basically comes down to the question of if "input output input output" is slower than "input input output output", and I think that depends highly on the programming language and the data-structures you're using. Look up how to set a timer or stopwatch on some code, and you can test it out for yourself. My hunch is that it will make very little to no difference, but you could be using different data-structures than I have in mind, so you'll just have to test it out.
So it could help, but in my experience unless you're doing some serious number crunching or need a highly optimized code, there's a certain point where gaining a fraction of a second faster operation isn't necessary. Modern computers run so blindingly fast that you usually have a lot of computational power to spare. Of course, in a case where you're doing something really computationally intensive, every little bit helps. It's all about trade-off between programming time and running time.
There's no definite answer to your question. Basically, "it depends".
A general performance-affecting principle that should be observed in many cases on modern hardware platforms is as follows: when you attempt to do many unrealted (or loosely related) things at once, involving access to several unrelated regions of memory, the memory locality of your code worsens and the cache behavior of your program worsens as well. Bad memory locality and the consequent poor cache behavior can have notable negative impact on the performance of your code. For this reason, it is usually good idea to organize your code in consequent stages, each stage working within a more-or-less well defined localized memory region.
This is a very general principle that is not directly related to input/output. It just that input/output might prove to be one of those things that could make your code to do "too many things at once". Whether it will have an impact on the performance of your code really depends on the specifics of your code.
If your code is dominated by slow input/output operations, then its cache performance will not be a significant factor at all. If, on the other hand, your code spends most of its time doing memory-intensive computations, then it might be a good idea to experiment with such things as elimination of I/O operations from the main computation cycles.
Depends on some variants:
Type of operation ? Input or Output
Parallel ? Sync call or Async call
Parallelism Degree ? is there dependency between iterations
I am planning to write a bunch of programs on computationally intensive algorithms. The programs would serve as an indicator of different compiler/hardware performance.
I would want to pick up some common set of algorithms which are used in different fields, like Bioinformatics, Gaming, Image Processing, et al. The reason I want to do this would be to learn the algorithms and have a personal mini benchmark suit that would be small | useful | easy to maintain.
Any advice on algorithm selection would be tremendously helpful.
Benchmarks are not worthy of your attention!
The very best guide is to processor performance is: http://www.agner.org/optimize/
And then someone will chuck it in a box with 3GB of RAM defeating dual-channel hopes and your beautifully tuned benchmark will give widely different results again.
If you have a piece of performance critical code and you are sure you've picked the winning algorithm you can't then go use a generic benchmark to determine the best compiler. You have to actually compile your specific piece of code with each compiler and benchmark them with that. And the results you gain, whilst useful for you, will not extrapolate to others.
Case in point: people who make compression software - like zip and 7zip and the high-end stuff like PPMs and context-mixing and things - are very careful about performance and benchmark their programs. They hang out on www.encode.ru
And the situation is this: for engineers developing the same basic algorithm - say LZ or entropy coding like arithmetic-coding and huffman - the engineers all find very different compilers are better.
That is to say, two engineers solving the same problem with the same high-level algorithm will each benchmark their implementation and have results recommending different compilers...
(I have seen the same thing repeat itself repeatedly in competition programming e.g. Al Zimmermann's Programming Contests which is an equally performance-attentive community.)
(The newer GCC 4.x series is very good all round, but that's just my data-point, others still favour ICC)
(Platform benchmarks for IO-related tasks is altogether another thing; people don't appreciate how differently Linux, Windows and FreeBSD (and the rest) perform when under stress. And benchmarks there - on the same workload, same machine, different machines or different core counts - would be very generally informative. There aren't enough benchmarks like that about sadly.)
There was some work done at Berkeley about this a few years ago. The identified 13 common application paterns for parallel programming, the "13 Dwarves". The include things like linear algebra, n-body models, FFTs etc
http://www.eecs.berkeley.edu/Pubs/TechRpts/2006/EECS-2006-183.html
See page 10 onwards.
There are some sample .NET implementations here:
http://paralleldwarfs.codeplex.com/
The typical one is Fast Fourier Transform, perhaps you can also do something like the Lucas–Lehmer primality test.
I remember a guy who tested computational performance of machines, compiler versions by inverting Hilbert matrices.
For image processing, median filtering (used for removing noise, bad pixels) is always too slow. It might make a good test, given a large enough image say 1000x1000.
Its common to hear about "highly optimized code" or some developer needing to optimize theirs and whatnot. However, as a self-taught, new programmer I've never really understood what exactly do people mean when talking about such things.
Care to explain the general idea of it? Also, recommend some reading materials and really whatever you feel like saying on the matter. Feel free to rant and preach.
Optimize is a term we use lazily to mean "make something better in a certain way". We rarely "optimize" something - more, we just improve it until it meets our expectations.
Optimizations are changes we make in the hopes to optimize some part of the program. A fully optimized program usually means that the developer threw readability out the window and has recoded the algorithm in non-obvious ways to minimize "wall time". (It's not a requirement that "optimized code" be hard to read, it's just a trend.)
One can optimize for:
Memory consumption - Make a program or algorithm's runtime size smaller.
CPU consumption - Make the algorithm computationally less intensive.
Wall time - Do whatever it takes to make something faster
Readability - Instead of making your app better for the computer, you can make it easier for humans to read it.
Some common (and overly generalized) techniques to optimize code include:
Change the algorithm to improve performance characteristics. If you have an algorithm that takes O(n^2) time or space, try to replace that algorithm with one that takes O(n * log n).
To relieve memory consumption, go through the code and look for wasted memory. For example, if you have a string intensive app you can switch to using Substring References (where a reference contains a pointer to the string, plus indices to define its bounds) instead of allocating and copying memory from the original string.
To relieve CPU consumption, cache as many intermediate results if you can. For example, if you need to calculate the standard deviation of a set of data, save that single numerical result instead looping through the set each time you need to know the std dev.
I'll mostly rant with no practical advice.
Measure First. Optimization should be done to places where it matters. Highly optimized code is often difficult to maintain and a source of problems. In places where the code does not slow down execution anyway, I alwasy prefer maintainability to optimizations. Familiarize yourself with Profiling, both intrusive (instrumented) and non-intrusive (low overhead statistical). Learn to read a profiled stack, understand where the time inclusive/time exclusive is spent, why certain patterns show up and how to identify the trouble spots.
You can't fix what you cannot measure. Have your program report through some performance infrastructure the thing it does and the times it takes. I come from a Win32 background so I'm used to the Performance Counters and I'm extremely generous at sprinkling them all over my code. I even automatized the code to generate them.
And finally some words about optimizations. Most discussion about optimization I see focus on stuff any compiler will optimize for you for free. In my experience the greatest source of gains for 'highly optimized code' lies completely elsewhere: memory access. On modern architectures the CPU is idling most of the times, waiting for memory to be served into its pipelines. Between L1 and L2 cache misses, TLB misses, NUMA cross-node access and even GPF that must fetch the page from disk, the memory access pattern of a modern application is the single most important optimization one can make. I'm exaggerating slightly, of course there will be counter example work-loads that will not benefit memory access locality this techniques. But most application will. To be specific, what these techniques mean is simple: cluster your data in memory so that a single CPU can work an a tight memory range containing all it needs, no expensive referencing of memory outside your cache lines or your current page. In practice this can mean something as simple as accessing an array by rows rather than by columns.
I would recommend you read up the Alpha-Sort paper presented at the VLDB conference in 1995. This paper presented how cache sensitive algorithms designed specifically for modern CPU architectures can blow out of the water the old previous benchmarks:
We argue that modern architectures
require algorithm designers to
re-examine their use of the memory
hierarchy. AlphaSort uses clustered
data structures to get good cache
locality...
The general idea is that when you create your source tree in the compilation phase, before generating the code by parsing it, you do an additional step (optimization) where, based on certain heuristics, you collapse branches together, delete branches that aren't used or add extra nodes for temporary variables that are used multiple times.
Think of stuff like this piece of code:
a=(b+c)*3-(b+c)
which gets translated into
-
* +
+ 3 b c
b c
To a parser it would be obvious that the + node with its 2 descendants are identical, so they would be merged into a temp variable, t, and the tree would be rewritten:
-
* t
t 3
Now an even better parser would see that since t is an integer, the tree could be further simplified to:
*
t 2
and the intermediary code that you'd run your code generation step on would finally be
int t=b+c;
a=t*2;
with t marked as a register variable, which is exactly what would be written for assembly.
One final note: you can optimize for more than just run time speed. You can also optimize for memory consumption, which is the opposite. Where unrolling loops and creating temporary copies would help speed up your code, they would also use more memory, so it's a trade off on what your goal is.
Here is an example of some optimization (fixing a poorly made decision) that I did recently. Its very basic, but I hope it illustrates that good gains can be made even from simple changes, and that 'optimization' isn't magic, its just about making the best decisions to accomplish the task at hand.
In an application I was working on there were several LinkedList data structures that were being used to hold various instances of foo.
When the application was in use it was very frequently checking to see if the LinkedListed contained object X. As the ammount of X's started to grow, I noticed that the application was performing more slowly than it should have been.
I ran an profiler, and realized that each 'myList.Contains(x)' call had O(N) because the list has to iterate through each item it contains until it reaches the end or finds a match. This was definitely not efficent.
So what did I do to optimize this code? I switched most of the LinkedList datastructures to HashSets, which can do a '.Contains(X)' call in O(1)- much better.
This is a good question.
Usually the best practice is 1) just write the code to do what you need it to do, 2) then deal with performance, but only if it's an issue. If the program is "fast enough" it's not an issue.
If the program is not fast enough (like it makes you wait) then try some performance tuning. Performance tuning is not like programming. In programming, you think first and then do something. In performance tuning, thinking first is a mistake, because that is guessing.
Don't guess what to fix; diagnose what the program is doing.
Everybody knows that, but mostly they do it anyway.
It is natural to say "Could be the problem is X, Y, or Z" but only the novice acts on guesses. The pro says "but I'm probably wrong".
There are different ways to diagnose performance problems.
The simplest is just to single-step through the program at the assembly-language level, and don't take any shortcuts. That way, if the program is doing unnecessary things, then you are doing the same things, and it will become painfully obvious.
Another is to get a profiling tool, and as others say, measure, measure, measure.
Personally I don't care for measuring. I think it's a fuzzy microscope for the purpose of pinpointing performance problems. I prefer this method, and this is an example of its use.
Good luck.
ADDED: I think you will find, if you go through this exercise a few times, you will learn what coding practices tend to result in performance problems, and you will instinctively avoid them. (This is subtly different from "premature optimization", which is assuming at the beginning that you must be concerned about performance. In fact, you will probably learn, if you don't already know, that premature concern about performance can well cause the very problem it seeks to avoid.)
Optimizing a program means: make it run faster
The only way of making the program faster is making it do less:
find an algorithm that uses fewer operations (e.g. N log N instead of N^2)
avoid slow components of your machine (keep objects in cache instead of in main memory, or in main memory instead of on disk); reducing memory consumption nearly always helps!
Further rules:
In looking for optimization opportunities, adhere to the 80-20-rule: 20% of typical program code accounts for 80% of execution time.
Measure the time before and after every attempted optimization; often enough, optimizations don't.
Only optimize after the program runs correctly!
Also, there are ways to make a program appear to be faster:
separate GUI event processing from back-end tasks; priorize user-visible changes against back-end calculation to keep the front-end "snappy"
give the user something to read while performing long operations (every noticed the slideshows displayed by installers?)
However, as a self-taught, new programmer I've never really understood what exactly do people mean when talking about such things.
Let me share a secret with you: nobody does. There are certain areas where we know mathematically what is and isn't slow. But for the most part, performance is too complicated to be able to understand. If you speed up one part of your code, there's a good possibility you're slowing down another.
Therefore, anyone who tells you that one method is faster than another, there's a good possibility they're just guessing unless one of three things are true:
They have data
They're choosing an algorithm that they know is faster mathematically.
They're choosing a data structure that they know is faster mathematically.
Optimization means trying to improve computer programs for such things as speed. The question is very broad, because optimization can involve compilers improving programs for speed, or human beings doing the same.
I suggest you read a bit of theory first (from books, or Google for lecture slides):
Data structures and algorithms - what the O() notation is, how to calculate it,
what datastructures and algorithms can be used to lower the O-complexity
Book: Introduction to Algorithms by Thomas H. Cormen, Charles E. Leiserson, and Ronald L. Rivest
Compilers and assembly - how code is translated to machine instructions
Computer architecture - how the CPU, RAM, Cache, Branch predictions, out of order execution ... work
Operating systems - kernel mode, user mode, scheduling processes/threads, mutexes, semaphores, message queues
After reading a bit of each, you should have a basic grasp of all the different aspects of optimization.
Note: I wiki-ed this so people can add book recommendations.
I am going with the idea that optimizing a code is to get the same results in less time. And fully optimized only means they ran out of ideas to make it faster. I throw large buckets of scorn on claims of "fully optimized" code! There's no such thing.
So you want to make your application/program/module run faster? First thing to do (as mentioned earlier) is measure also known as profiling. Do not guess where to optimize. You are not that smart and you will be wrong. My guesses are wrong all the time and large portions of my year are spent profiling and optimizing. So get the computer to do it for you. For PC VTune is a great profiler. I think VS2008 has a built in profiler, but I haven't looked into it. Otherwise measure functions and large pieces of code with performance counters. You'll find sample code for using performance counters on MSDN.
So where are your cycles going? You are probably waiting for data coming from main memory. Go read up on L1 & L2 caches. Understanding how the cache works is half the battle. Hint: Use tight, compact structures that will fit more into a cache-line.
Optimization is lots of fun. And it's never ending too :)
A great book on optimization is Write Great Code: Understanding the Machine by Randall Hyde.
Make sure your application produces correct results before you start optimizing it.
Let's just assume for now that you have narrowed down where the typical bottlenecks in your app are. For all you know, it might be the batch process you run to reindex your tables; it could be the SQL queries that runs over your effective-dated trees; it could be the XML marshalling of a few hundred composite objects. In other words, you might have something like this:
public Result takeAnAnnoyingLongTime(Input in) {
// impl of above
}
Unfortunately, even after you've identified your bottleneck, all you can do is chip away at it. No simple solution is available.
How do you measure the performance of your bottleneck so that you know your fixes are headed in the right direction?
Two points:
Beware of the infamous "optimizing the idle loop" problem. (E.g. see the optimization story under the heading "Porsche-in-the-parking-lot".) That is, just because a routine is taking a significant amount of time (as shown by your profiling), don't assume that it's responsible for slow performance as perceived by the user.
The biggest performance gains often come not from that clever tweak or optimization to the implementation of the algorithm, but from realising that there's a better algorithm altogether. Some improvements are relatively obvious, while others require more detailed analysis of the algorithms, and possibly a major change to the data structures involved. This may include trading off processor time for I/O time, in which case you need to make sure that you're not optimizing only one of those measures.
Bringing it back to the question asked, make sure that whatever you're measuring represents what the user actually experiences, otherwise your efforts could be a complete waste of time.
Profile it
Find the top line in the profiler, attempt to make it faster.
Profile it
If it worked, go to 1. If it didn't work, go to 2.
I'd measure them using the same tools / methods that allowed me to find them in the first place.
Namely, sticking timing and logging calls all over the place. If the numbers start going down, then you just might be doing the right thing.
As mentioned in this msdn column, performance tuning is compared to the job of painting Golden Gate Bridge: once you finish painting the entire thing, it's time to go back to the beginning and start again.
This is not a hard problem. The first thing you need to understand is that measuring performance is not how you find performance problems. Knowing how slow something is doesn't help you find out why. You need a diagnostic tool, and a good one. I've had a lot of experience doing this, and this is the best method. It is not automatic, but it runs rings around most profilers.
It's an interesting question. I don't think anyone knows the answer. I believe that significant part of the problem is that for more complicated programs, no one can predict their complexity. Therefore, even if you have profiler results, it's very complicated to interpret it in terms of changes that should be made to the program, because you have no theoretical basis for what the optimal solution is.
I think this is a reason why we have so bloated software. We optimize only so that quite simple cases would work on our fast machines. But once you put such pieces together into a large system, or you use order of magnitude larger input, wrong algorithms used (which were until then invisible both theoretically and practically) will start showing their true complexity.
Example: You create a string class, which handles Unicode. You use it somewhere like computer-generated XML processing where it really doesn't matter. But Unicode processing is in there, taking part of the resources. By itself, the string class can be very fast, but call it million times, and the program will be slow.
I believe that most of the current software bloat is of this nature. There is a way to reduce it, but it contradicts OOP. There is an interesting book There is an interesting book about various techniques, it's memory oriented but most of them could be reverted to get more speed.
I'd identify two things:
1) what complexity is it? The easiest way is to graph time-taken verses size of input.
2) how is it bound? Is it memory, or disk, or IPC with other processes or machines, or..
Now point (2) is the easier to tackle and explain: Lots of things go faster if you have more RAM or a faster machine or faster disks or move over to gig ethernet or such. If you identify your pain, you can put some money into hardware to make it tolerable.