Example of cache friendly code - c++

template<size_t size>
class Objects{
std::array<int,size> a;
std::array<int,size> b;
std::array<int,size> c;
void update(){
for (size_t i = 0; i < size; ++i){
c[i] = a[i] + b[i];
}
}
};
I am gathering information of how to write cache friendly code since a week and I read though several articles but I still haven't understood the basics.
Code like I have written above is used in most of the examples, but for me this is not cache friendly at all.
For me the memory layout should look like this
aaaabbbbcccc
and in the first loop it will access
[a]aaa[b]bbb[c]ccc
If I understood it correctly, the cpu prefetches elements that are near in memory. I am not sure how intelligent this method is but I assume it's primitive and it just fetches the nth nearest elements.
The problem is that [a]aaa[b]bbb[c]ccc will not access the elements in order at all. So it might fetch the next '3' elements a[aaa]bbbbcccc which is nice for the next a because it will be a cache hit but not for the b.
Is the example above cache friendly code?

I suggest you use an array of structures:
struct Cache_Item
{
int a;
int b;
int c;
};
Cache_Item cache_line[size];
for (unsigned int i = 0; i < size; ++i)
{
cache_line[i].c = cache_line[i].a + cache_line[i].b;
}
The structure arrangement allows for all the variables in use to be next to each other in the cache line or very close.
In your array method, element b[0] ideally is at location a[size], so they are size items apart. This could mean that they are on different cache lines. The result location, c[0], is at a[size + size], which means it could be 2 cache lines away.

Your code is not particularly unfriendly. It requires three active cache lines at a time instead of one, but that isn't too much to ask. Your code would be a lot more cache-unfriendly if instead of
std::array<int,size> a;
you had
std::array<struct { int x; char description[5000]; }, size> a;
because then the CPU would have to pick out the lone x among the thousands of bytes of description (which your loop never uses).
Your example would also be more cache-unfriendly if you had not just a, b, and c, but also d-z and aa-az and maybe a few more. (How far you have to go depends on the sophistication of your cache - how many way-associative it is, etc.)
Have you profiled yours vs Thomas Matthews' code?

You should trust the compiler optimization work (and of course enable optimizations); it probably deals quite well with the CPU cache (perhaps by issuing appropriate prefetch instructions).
Sometimes you can hint the compiler thru builtins or pragmas. For example with GCC on x86-64 you might -with care- use the __builtin_prefetch. Usually it is not worth the effort (and if you misuse it performance will suffer). See this answer to a related question.

Related

How can I make this parallel sum function use vector instructions?

As sort of a side project, I'm working on a multithreaded sum algorihm, which would outperform std::accumulate when working on a large enough array. First I'm going to describe my thought process leading up to this, but if you want to skip straight to the problem, feel free to scroll down to that part.
I found many parallel sum algorihms online, most of which take the following approach:
template <typename T, typename IT>
T parallel_sum(IT _begin, IT _end, T _init) {
const auto size = distance(_begin, _end);
static const auto n = thread::hardware_concurrency();
if (size < 10000 || n == 1) return accumulate(_begin, _end, _init);
vector<future<T>> partials;
partials.reserve(n);
auto chunkSize = size / n;
for (unsigned i{ 0 }; i < n; i++) {
partials.push_back(async(launch::async, [](IT _b, IT _e){
return accumulate(_b, _e, T{0});
}, next(_begin, i*chunkSize), (i==n-1)?_end:next(_begin, (i+1)*chunkSize)));
}
for (auto& f : partials) _init += f.get();
return _init;
}
Assuming there are 2 threads available (as reported by thread::hardware_concurrency()), this function would access the elements in memory the following way:
As a simple example, we are looking at 8 elements here. The two threads are indicated by red and blue. The arrows show the location from with the threads wish to load data. Once the cells turn either red or blue, they have been loaded by the corresponding thread.
This approach (at least in my opinion) is not the best, since the threads load data from different parts of memory simultaneously. If you have many processing threads, say 16 on an 8-core hyper-threaded CPU, or even more than that, the CPU's prefetcher would have a very hard time keeping up with all these reads from completely different parts of memory (assuming the array is far too big to fit in cache). This is why I think the second example should be faster:
template <typename T, typename IT>
T parallel_sum2(IT _begin, IT _end, T _init) {
const auto size = distance(_begin, _end);
static const auto n = thread::hardware_concurrency();
if (size < 10000 || n == 1) return accumulate(_begin, _end, _init);
vector<future<T>> partials;
partials.reserve(n);
for (unsigned i{ 0 }; i < n; i++) {
partials.push_back(async(launch::async, [](IT _b, IT _e, unsigned _s){
T _ret{ 0 };
for (; _b < _e; advance(_b, _s)) _ret += *_b;
return _ret;
}, next(_begin, i), _end, n));
}
for (auto& f : partials) _init += f.get();
return _init;
}
This function accesses memory in a sort-of-sequential way, like so:
This way the prefetcher is always able to stay ahead, since all the threads access the same-ish part of memory, so there should be less cache misses, and faster load times over all, at least I think so.
The problem is that while this is all fine and dandy in theory, actual compiled versions of these show a different result. The second one is way slower. I dug a little deeper into the problem, and found out that the assembly code that is produced for the actual addition is very different. These are the "hot loops" in each one that perform the addition (remember that the first one uses std::accumulate internally, so you're basically looking at that):
Please ignore the percentages and the colors, my profiler sometimes gets things wrong.
I noticed that std::accumulate when compiled, uses an AVX2 vector instruction, vpaddq. This can add four 64-bit integers at once. I think the reason why the second version cannot be vectorized, is that each thread only accesses one element at a time, then skips over some. The vector addition would load several contiguous elements then add them together. Clearly this cannot be done, since the threads don't load elements contiguously. I tried manually unrolling the for loop in the second version, and that vector instruction did appear in the assembly, but the whole thing became painfully slow for some reason.
The above results and assembly code comes from a gcc-compiled version, but the same kind of behavior can be observed with Visual Studio 2015 as well, although I haven't looked at the assembly it produces.
So is there a way to take advante of vector instructions while retaining this sequential memory access model? Or is this memory access method something that would help at all when compared to the first version of the function?
I wrote a little benchmark program, which is ready to compile and run, just in case you want to see the performance yourself.
PS.: My primary target hardware is modern x86_64 (like haswell and such).
Each core has its own cache and prefetching.
You should look at each thread as independently executing program. In this case shortcomings of second approach will be clear: you do not access sequental data in single thread. There are holes which should not be processed, so thread cannot use vector instructions.
Another problem: CPU prefetches data in chunks. Due to how different cache levels work, changing some data within chunk marks that cache stale, and if other core tries to do some operation on same chunk of data it will be required to wait until first core will write changes and retrieve that chunk again. Basicly in your second example cache is always stale and you see raw memory access perfomance.
The best way to handle concurrent processing is to process data in large sequental chunks.

efficiency when handling consecutive blocks vs. non consecutive blocks of memory

i have a struct
struct A
{
int v[10000000];
};
if i have A a[2]; and wish to calculate the total sum of values which of these 2 methods is the fastest?
int method_1(const A &a[],int length)
{
int total = 0;
for(int i=0;i<length;i++)
for(int j=0;j<10000000;j++)
total+=a[i][j];
return total;
}
int method_2(const A &a[],int length)
{
int total = 0;
for(int j=0;j<10000000;j++)
for(int i=0;i<length;i++)
total+=a[i][j];
return total;
}
a[2] is declared as two consective blocks of struct A as so:
----a[0]---- /--- a[1]----
[][][][][][][][]/[][][][][][][][]
so, i might be tempted to say that method_1 is faster, based on intuition that the blocks are consecutive and the iteration through each block's v is also consecutive.
What i am really interested in is how the memory is really accessed and how is the most efficient way to access it.
EDIT
i have changed the v size from 32 to 10000000, because apparently it wasn't understood that i was referring to a general case
Each time a memory fragment is read a whole cache line will be read from main memory to the CPU cache, today you'll probably have a 32byte long cache lines. Mostly because of this reading consecutive memory blocks is fast.
Now there is more then one cache line...
In your case both cases may have similar performance as both arrays will most probably not collide into the same cache line and so both may be in the cache on different lines so I suspect performance will be similar.
One related thing you may consider in this case to change the performance is NOT using the [] operators in favor of iterating more using "iterators" like this:
int method_1(const A &a[],int length)
{
int total = 0;
for(const A* aIt=a;aIt<a+length;++aIt)
for(const v* vIt=aIt->v;vIt<aIt->v+10000000;++vIt)
total+=*vIt;
return total;
}
This way you avoid a double [] which is simply a multiplication by the sizeof of an array element (which may be optimized but may not and if not it will be costly when called millions of times). Your compiler may be smart enough to optimize the code just as I've shown to only use additions but... it very well may not be and I've seen this make a big difference when the operation performed for each of the elements is as trivial as an incrementation - you're best to measure this and see how these options work out in your environment.
Accessing elements in the order they appear in memory will improve performance in most cases since it allows the prefetcher to load data before you even use it. Besides, if you use data in a non-contiguous way, you might load and discard the same cache line many times and this has a cost.
Data size is small enough to be fit completely in a single cache line on modern CPUs. I'm not sure about vertorizing this code by compiler
I don't think method_2 is slower than method_1. The chunk of memory will be taken to CPUs main memory and then accessing a[0] and a[1] both will be take same time.
For a safer side, method_1 can always be considered better than method_2.

The simple task of iterating through an array. Which of these solutions is the most efficient?

Recently, I've been thinking about all the ways that one could iterate through an array and wondered which of these is the most (and least) efficient. I've written a hypothetical problem and five possible solutions.
Problem
Given an int array arr with len number of elements, what would be the most efficient way of assigning an arbitrary number 42 to every element?
Solution 0: The Obvious
for (unsigned i = 0; i < len; ++i)
arr[i] = 42;
Solution 1: The Obvious in Reverse
for (unsigned i = len - 1; i >= 0; --i)
arr[i] = 42;
Solution 2: Address and Iterator
for (unsigned i = 0; i < len; ++i)
{ *arr = 42;
++arr;
}
Solution 3: Address and Iterator in Reverse
for (unsigned i = len; i; --i)
{ *arr = 42;
++arr;
}
Solution 4: Address Madness
int* end = arr + len;
for (; arr < end; ++arr)
*arr = 42;
Conjecture
The obvious solutions are almost always used, but I wonder whether the subscript operator could result in a multiplication instruction, as if it had been written like *(arr + i * sizeof(int)) = 42.
The reverse solutions try to take advantage of how comparing i to 0 instead of len might mitigate a subtraction operation. Because of this, I prefer Solution 3 over Solution 2. Also, I've read that arrays are optimized to be accessed forwards because of how they're stored in the cache, which could present an issue with Solution 1.
I don't see why Solution 4 would be any less efficient than Solution 2. Solution 2 increments the address and the iterator, while Solution 4 only increments the address.
In the end, I'm not sure which of these solutions I prefer. I'm think the answer also varies with the target architecture and optimization settings of your compiler.
Which of these do you prefer, if any?
Just use std::fill.
std::fill(arr, arr + len, 42);
Out of your proposed solutions, on a good compiler, neither should be faster than the others.
The ISO standard doesn't mandate the efficiency of the different ways of doing things in code (other than certain big-O type stuff for some collection algorithms), it simply mandates how it functions.
Unless your arrays are billions of elements in size, or you're wanting to set them millions of times per minute, it generally won't make the slightest difference which method you use.
If you really want to know (and I still maintain it's almost certainly unnecessary), you should benchmark the various methods in the target environment. Measure, don't guess!
As to which I prefer, my first inclination is to optimise for readability. Only if there's a specific performance problem do I then consider other possibilities. That would be simply something like:
for (size_t idx = 0; idx < len; idx++)
arr[idx] = 42;
I don't think that performance is an issue here - those are, if at all (I could imagine the compiler producing the identical assembly for most of them), micro optimizations hardly ever necessary.
Go with the solution that is most readable; the standard library provides you with std::fill, or for more complex assignments
for(unsigned k = 0; k < len; ++k)
{
// whatever
}
so it is obvious to other people looking at your code what you are doing. With C++11 you could also
for(auto & elem : arr)
{
// whatever
}
just don't try to obfuscate your code without any necessity.
For nearly all meaningful cases, the compiler will optimize all of the suggested ones to the same thing, and it's very unlikely to make any difference.
There used to be a trick where you could avoid the automatic prefetching of data if you ran the loop backwards, which under some bizarre set of circumstances actually made it more efficient. I can't recall the exact circumstances, but I expect modern processors will identify backwards loops as well as forwards loops for automatic prefetching anyway.
If it's REALLY important for your application to do this over a large number of elements, then looking at blocked access and using non-temporal storage will be the most efficient. But before you do that, make sure you have identified the filling of the array as an important performance point, and then make measurements for the current code and the improved code.
I may come back with some actual benchmarks to prove that "it makes little difference" in a bit, but I've got an errand to run before it gets too late in the day...

C++ heap memory performance improvement

I'm writing a function where I need a significant amount of heap memory. Is it possible to tell the compiler that those data will be accessed frequently within a specific for loop, so as to improve performance (through compile options or similar)?
The reason I cannot use the stack is that the number of elements I need to store is big, and I get segmentation fault if I try to do it.
Right now the code is working but I think it could be faster.
UPDATE:
I'm doing something like this
vector< set<uint> > vec(node_vec.size());
for(uint i = 0; i < node_vec.size(); i++)
for(uint j = i+1; j < node_vec.size(); j++)
// some computation, basic math, store the result in variable x
if( x > threshold ) {
vec[i].insert(j);
vec[j].insert(i);
}
some details:
- I used hash_set, little improvement, beside the fact that hash_set is not available in all machines I have for simulation purposes
- I tried to allocate vec on the stack using arrays but, as I said, I might get segmentation fault if the number of elements is too big
If node_vec.size() is, say, equal to k, where k is of the order of a few thousands, I expect vec to be 4 or 5 times bigger than node_vec. With this order of magnitude the code appears to be slow, considering the fact that I have to run it many times. Of course, I am using multithreading to parallelize these calls, but I can't get the function per se to run much faster than what I'm seeing right now.
Would it be possible, for example, to have vec allocated in the cache memory for fast data retrieval, or something similar?
I'm writing a function where I need a significant amount of heap memory ... will be accessed frequently within a specific for loop
This isn't something you can really optimize at a compiler level. I think your concern is that you have a lot of memory that may be "stale" (paged out) but at a particular point in time you will need to iterate over all of it, maybe several times and you don't want the memory pages to be paged out to disk.
You will need to investigate strategies that are platform specific to improve performance. Keeping the pages in memory can be achieved with mlockall or VirtualLock but you really shouldn't need to do this. Make sure you know what the implications of locking your application's memory pages into RAM is, however. You're hogging memory from other processes.
You might also want to investigate a low fragmentation heap (however it may not be relevant at all to this problem) and this page which describes cache lines with respect to for loops.
The latter page is about the nitty-gritty of how CPUs work (a detail you normally shouldn't have to be concerned with) with respect to memory access.
Example 1: Memory accesses and performance
How much faster do you expect Loop 2 to run, compared Loop 1?
int[] arr = new int[64 * 1024 * 1024];
// Loop 1
for (int i = 0; i < arr.Length; i++) arr[i] *= 3;
// Loop 2
for (int i = 0; i < arr.Length; i += 16) arr[i] *= 3;
The first loop multiplies every value in the array by 3, and the second loop multiplies only every 16-th. The second loop only does about 6% of the work of the first loop, but on modern machines, the two for-loops take about the same time: 80 and 78 ms respectively on my machine.
UPDATE
vector< set<uint> > vec(node_vec.size());
for(uint i = 0; i < node_vec.size(); i++)
for(uint j = i+1; j < node_vec.size(); j++)
// some computation, basic math, store the result in variable x
if( x > threshold ) {
vec[i].insert(j);
vec[j].insert(i);
}
That still doesn't show much, because we cannot know how often the condition x > threshold will be true. If x > threshold is very frequently true, then the std::set might be the bottleneck, because it has to do a dynamic memory allocation for every uint you insert.
Also we don't know what "some computation" actually means/does/is. If it does much, or does it in the wrong way that could be the bottleneck.
And we don't know how you need to access the result.
Anyway, on a hunch:
vector<pair<int, int> > vec1;
vector<pair<int, int> > vec2;
for (uint i = 0; i < node_vec.size(); i++)
{
for (uint j = i+1; j < node_vec.size(); j++)
{
// some computation, basic math, store the result in variable x
if (x > threshold)
{
vec1.push_back(make_pair(i, j));
vec2.push_back(make_pair(j, i));
}
}
}
If you can use the result in that form, you're done. Otherwise you could do some post-processing. Just don't copy it into a std::set again (obviously). Try to stick to std::vector<POD>. E.g. you could build an index into the vectors like this:
// ...
vector<int> index1 = build_index(node_vec.size(), vec1);
vector<int> index2 = build_index(node_vec.size(), vec2);
// ...
}
vector<int> build_index(size_t count, vector<pair<int, int> > const& vec)
{
vector<int> index(count, -1);
size_t i = vec.size();
do
{
i--;
assert(vec[i].first >= 0);
assert(vec[i].first < count);
index[vec[i].first] = i;
}
while (i != 0);
return index;
}
ps.: I'm almost sure your loop is not memory-bound. Can't be sure though... if the "nodes" you're not showing us are really big it might still be.
Original answer:
There is no easy I_will_access_this_frequently_so_make_it_fast(void* ptr, size_t len)-kind-of solution.
You can do some things though.
Make sure the compiler can "see" the implementation of every function that's called inside critical loops. What is necessary for the compiler to be able to "see" the implementation depends on the compiler. There is one way to be sure though: define all relevant functions in the same translation unit before the loop, and declare them as inline.
This also means you should not by any means call "external" functions in those critical loops. And by "external" functions I mean things like system-calls, runtime-library stuff or stuff implemented in a DLL/SO. Also don't call virtual functions and don't use function pointers. And or course don't allocate or free memory (inside the critical loops).
Make sure you use an optimal algorithm. Linear optimization is moot if the complexity of the algorithm is higher than necessary.
Use the smallest possible types. E.g. don't use int if signed char will do the job. That's something I wouldn't normally recommend, but when processing a large chunk of memory it can increase performance quite a lot. Especially in very tight loops.
If you're just copying or filling memory, use memcpy or memset. Disable the intrinsic version of those two functions if the chunks are larger then about 50 to 100 bytes.
Make sure you access the data in a cache-friendly manner. The optimum is "streaming" - i.e. accessing the memory with ascending or descending addresses. You can "jump" ahead some bytes at a time, but don't jump too far. The worst is random access to a big block of memory. E.g. if you have to work on a 2 dimensional matrix (like a bitmap image) where p[0] to p[1] is a step "to the right" (x + 1), make sure the inner loop increments x and the outer increments y. If you do it the other way around performance will be much much worse.
If your pointers are alias-free, you can tell the compiler (how that's done depends on the compiler). If you don't know what alias-free means I recommend searching the net and your compiler's documentation, since an explanation would be beyond the scope.
Use intrinsic SIMD instructions if appropriate.
Use explicit prefetch instructions if you know which memory locations will be needed in the near future.
You can't do that with compiler options. Depending on your usage (insertion, random-access, deleting, sorting, etc.), you could maybe get a better suited container.
The compiler can already see that the data is accessed frequently within the loop.
Assuming you're only allocating the data from the heap once before doing the looping, note, as #lvella, that memory is memory and if it's accessed frequently it should be effectively cached during execution.

C++ fixed size arrays vs multiple objects of same type

I was wondering whether (apart from the obvious syntax differences) there would be any efficiency difference between having a class containing multiple instances of an object (of the same type) or a fixed size array of objects of that type.
In code:
struct A {
double x;
double y;
double z;
};
struct B {
double xvec[3];
};
In reality I would be using boost::arrays which are a better C++ alternative to C-style arrays.
I am mainly concerned with construction/destruction and reading/writing such doubles, because these classes will often be constructed just to invoke one of their member functions once.
Thank you for your help/suggestions.
Typically the representation of those two structs would be exactly the same. It is, however, possible to have poor performance if you pick the wrong one for your use case.
For example, if you need to access each element in a loop, with an array you could do:
for (int i = 0; i < 3; i++)
dosomething(xvec[i]);
However, without an array, you'd either need to duplicate code:
dosomething(x);
dosomething(y);
dosomething(z);
This means code duplication - which can go either way. On the one hand there's less loop code; on the other hand very tight loops can be quite fast on modern processors, and code duplication can blow away the I-cache.
The other option is a switch:
for (int i = 0; i < 3; i++) {
int *r;
switch(i) {
case 0: r = &x; break;
case 1: r = &y; break;
case 1: r = &z; break;
}
dosomething(*r); // assume this is some big inlined code
}
This avoids the possibly-large i-cache footprint, but has a huge negative performance impact. Don't do this.
On the other hand, it is, in principle, possible for array accesses to be slower, if your compiler isn't very smart:
xvec[0] = xvec[1] + 1;
dosomething(xvec[1]);
Since xvec[0] and xvec[1] are distinct, in principle, the compiler ought to be able to keep the value of xvec[1] in a register, so it doesn't have to reload the value at the next line. However, it's possible some compilers might not be smart enough to notice that xvec[0] and xvec[1] don't alias. In this case, using seperate fields might be a very tiny bit faster.
In short, it's not about one or the other being fast in all cases. It's about matching the representation to how you use it.
Personally, I would suggest going with whatever makes the code working on xvec most natural. It's not worth spending a lot of human time worrying about something that, at best, will probably only produce such a small performance difference that you'll only catch it in micro-benchmarks.
MVC++ 2010 generated exactly the same code for reading/writing from two POD structs like in your example. Since the offsets to read/write to are computable at compile time, this is not surprising. Same goes for construction and destruction.
As for the actual performance, the general rule applies: profile it if it matters, if it doesn't - why care?
Indexing into an array member is perhaps a bit more work for the user of your struct, but then again, he can more easily iterate over the elements.
In case you can't decide and want to keep your options open, you can use an anonymous union:
struct Foo
{
union
{
struct
{
double x;
double y;
double z;
} xyz;
double arr[3];
};
};
int main()
{
Foo a;
a.xyz.x = 42;
std::cout << a.arr[0] << std::endl;
}
Some compilers also support anonymous structs, in that case you can leave the xyz part out.
It depends. For instance, the example you gave is a classic one in favor of 'old-school' arrays: a math point/vector (or matrix)
has a fixed number of elements
the data itself is usually kept
private in an object
since (if?) it has a class as an
interface, you can properly
initialize them in the constructor
(otherwise, classic array
inialization is something I don't
really like, syntax-wise)
In such cases (going with the math vector/matrix examples), I always ended up using C-style arrays internally, as you can loop over them instead of writing copy/pasted code for each component.
But this is a special case -- for me, in C++ nowadays arrays == STL vector, it's fast and I don't have to worry about nuthin' :)
The difference can be in storing the variables in memory. In the first example compiler can add padding to align the data. But in your paticular case it doesn't matter.
raw arrays offer better cache locality than c++ arrays, as presented however, the array example's only advantage over the multiple objects is the ability to iterate over the elements.
The real answer is of course, create a test case and measure.