All entries for September 2018

September 19, 2018

Scheduling and processor affinity

We're taking a brief break from data structures to talk about something a bit different : scheduling and processor affinity. This is dealing with a problem that a user or developer doesn't usually think about, but is crucial to the performance of modern computers. Describing the problem is quite simple : if you have a computer that is doing multiple tasks what order should they happen in and what processor (if you have more than one) should take on each task? Working this out is the preserve of the very core part of the operating system (OS), generalled called the kernel (after the part of the nut). While the term is most familiar from the Linux/Unix world (technically Linux is the name for just the kernel and not the rest of the OS), macOS has the Mach microkernel at it's core and ntoskrnl.exe (the Windows New Technology Kernel! It was new in the mid 90s at least) is at the core of modern versions of Windows.

The simplest solution is for the kernel to just create a queue of programs that have to be done and then run them one after the other, with each new program being handed to the next free processor and programs running until they are finished. This is typically called First In, First Out scheduling (FIFO, which is a very common acronym in computing. Do not confuse this with GIGO (garbage in, garbage out) which is also a very common acronym in computing). FIFO scheduling works very well for computers that are working on lists of tasks having equal priority. So batch processing of data for example works very well with FIFO scheduling. But you can immediately see that it won't work well for all computers that humans actually work with interactively. If all of your processors are working on long, slow processes then your computer would stop working completely and you wouldn't even be able to stop the processes because the computer wouldn't be processing your keyboard or mouse input.

Normal computers tend to work using a system of preemptive scheduling. This works by taking a program and letting it run for a while on a processor and then saving its state, stopping it and then giving the processor another program to run on that processor for a while until stopping it etc. etc. Eventually you get back to a process that has been running before and you restore it's state and start it running again. Because the state of the program is stored completely it is entirely unaware that this has happened to it, so it just runs on regardless. (as a historical note, this is called preemptive scheduling because the OS kernel preempts the programs running on it. It basically says "you're done, get out of the way" and lets other programs run. Older systems used cooperative scheduling where a program would have code in it where it said to the kernel "I'm ready to be switched away from". This worked fine until a badly behaved program didn't reach this point whereupon every other program on the computer stopped working.)

There are disadvantages to preemptive scheduling. The saving and restoring of the state of programs is generally called "context switching" and it does take time for this to happen. (FIFO schedulers don't have this problem because programs run until they complete, but even now you can't really use FIFO schedulers because there tend to be dozens of programs running on a computer at once and some of the effectively nevercomplete until the computer shuts down). If you only have one processor then context switching is the inevitable price of allowing multiple programs to run at once, but if you have two processors and two programs then they can happily run alongside each other so long as they are each running on their own processor.

But what if you have four programs and two processors? As you'd guess, in general you'll put two programs on each processor. But what happens if the processors aren't running through their jobs at quite the same rate? This can happen because real schedulers are rather more complex than I suggested here. In that case, you can come to a situation where the program that was running on processor 1 reaches the point where it should run again but processor 1 is still busy. Should it then be run on processor 2? The answer, is "maybe". Sometimes programs benefit a lot from data being held in the fast CPU cache memory and if it now runs on a different processor then that benefit is lost. Under that circumstance it would be better to keep that program running on the same processor even if it has to wait a bit longer until it runs again.

All common operating systems let you do this and it is called "processor" affinity. You tell the kernel which processor (or processors) you want a given program to run on and it guarantees that it will respect that rather than giving that program to the next available processor.

I've glossed over a lot of things about scheduling here (in particular Intel's Hyperthreading technology is a nightmare for scheduling because it creates "virtual" processors to try and take advantage of the fact that most programs don't use all of the parts of a processor at once. The problem is that these virtual processors don't behave the same way as real processors so the scheduler has to be much more careful about what programs it should run on them.), but this is a decent overview of how scheduling and process affinity works on modern computers and generally it works quite well. General purpose programs don't set CPU affinity and just run as quickly as possible when a processor is free, and programs that do heavy numerical computation set CPU affinity to try and maximise cache performance. But there are interesting cases where it can fail.

Recently we had an interesting discovery using the OpenMPI parallel programming library. This is a distributed programming library intended to write programs to run on large "cluster" computers that consist of lots of single compute nodes connected by a network. But it does also work to run programs on a single computer. We were testing a computer with 16 cores and found that running a single 16 processor job was about 16 times faster than the same problem on a single core. When we tried the same problem with 4 simultaneous 4 processor jobs things were very different. The 4 processor jobs were all slower than they were when running on a single core. After a couple of hours we found out why: OpenMPI sets processor affinity for all of the programs that it runs, but it always sets them for the lowest numbered processors. So running a 16 core job ran them on cores 0 to 15, but running 4 sets of 4 core jobs ran them allon processors 0 to 3, so they all basically got a quarter of 4 cores. Add in some overhead from context switching and you get that it's slower than running on a single core. One quick parameter to the library to tell it not to use processor affinity and we were back to where we expected to be, but the lesson to take away is that you can get far to used to things like schedulers just working. If you're finding that things are running slower than you expected, check whether or not there's something odd going on with how your processors are being used.

September 05, 2018

Data structures 2 – Arrays Part 2

Part 2 of arrays is about dynamic (run time) sized arrays. That is arrays where you don't know how large they're going to be until the code is running. First, I'll go through it in Fortran because it is really easy in Fortran, and powerful array operations are one of the major advantages of Fortran.

Dynamic arrays in Fortran are generally called ALLOCATABLE arrays (there are also POINTER arrays, but they are generally harder to use for only fairly specific benefits), and you declare them pretty much the same way that you declare any array in Fortran


You then allocate it using


First, note that the DIMENSION(:) syntax in the variable declaration is the same as when you're passing an array to a function where you don't know how big the array is. This is the general way of telling Fortran "I don't know what size this is until runtime" (there are a few features where it's * instead for things like the length of strings, but in general it's :). Also note that I have explicitly allocated the array bounds, with the array running from 0 to 100 inclusive. If I'd just used


then the array would have run from 1 to 100 inclusive. In Fortran you can have any upper and lower bounds for arrays that you want which is sometimes useful. You do have to be careful though because unless you are careful when you pass arrays into functions these bound markers are ignored inside the function and the array just runs from 1:n.

Moving to multidimensional arrays in Fortran is easy.

ALLOCATE(myarray(0:100, -1:101))
myarray(10,10) = 1

will create a 2D column major array with the array bounds that I specified in my allocate statement. Job done. Fortran ALLOCATABLE arrays also have the nice property that they are automatically deallocated when they go out of scope so it's much harder to have memory leaks with Fortran ALLOCATABLE arrays (you don't have this guarantee with POINTER arrays because this doesn't make use of reference counting and garbage collection. It relies on the fact that there can only be a single reference to a Fortran allocatable.). If you want more control over when memory is returned to you then you can also manually DEALLOCATE the array


Before I start on the C section, I should note one thing: C99 and later standards do define variable length arrays (usually referred to by the acronym VLA). They aren't really very common in scientific code and they have all sorts of oddities about how you use pointers to them and where you can and can't use them (you can't have them in structs for example). Given their general rarity and strangeness (and the fact that they aren't valid in C++ before C++14) I'm not going to talk any more about them, but they do exist and you might want to look them up if you're writing a new code in C. 1D run time arrays in C are traditionally created using the "malloc" memory allocation function. You tell malloc how many bytes of memory you want and it creates a chunk of memory that long and hands you a pointer to it. The syntax is easy enough

#include <stdlib.h>
int main(int argc, char **argv){
int * myarray;
myarray = malloc(sizeof(int) * 100);
myarray[0] = 10;

Note the use of the "sizeof" operator to find out how many bytes are needed to store an integer. If you want to write code that works on multiple machines you'll have to use this because integers are not always the same size. In most senses you can consider a pointer and a 1D array to be very similar in C. When you use the square bracket operator you get the same element of your array in both cases, and in fact the layout of the memory behind the scenes is conceptually similar (although if you want to be precise a static array will generally be allocated on the stack, while malloc gives you memory from the heap). Also, note that I have used the function "free" to delete the memory when I am finished. If I don't do this then there will be a memory leak. C explicitly does not keep track of memory at all. Sadly it gets rather harder in multiple dimensions.

malloc always gives you a 1D strip of memory, and there is no equivalent function to give you a multidimensional array in standard C. My preferred solution is just to allocate a 1D array and then use an indexing function to access the element that you want. For example

#include <stdlib.h>
int main(int argc, char **argv){
int * myarray;
int nx, ny; /*Size of array to be filled somehow*/
int ix, iy; /*index of element to access to be filled somehow*/
myarray = malloc(sizeof(int) * nx * ny);
myarray[ix*ny + iy] = 10;

This will work perfectly and will give pretty good performance. Usually you'd write some kind of helper function or macro rather than having ix*ny+iy all over your code, but this shows the general technique. You do have to be careful writing your index function though because [ix*ny + iy] gives you a row major array and [iy*nx + ix] gives you column major. This can be useful but you need to be sure what you're doing. The other problem with this is that you can't just access your array as if it was a compile time multidimensional array. If you try to access this using myarray[ix][iy] you will get a compile error. This is because behind the scenes the [] operator dereferences your pointer with an offset (you can replace myarray[ix] with *(myarray+ix) if you like pointer arithmetic). Because of this when the first square bracket has happened you are just left with an integer, so the second square bracket operator is an invalid operation. So can you keep the multidimensional access? Yes, but there are always downsides.

#include <stdlib.h>

int main(int argc, char **argv){
int **myarray;
int nx, ny; /*Size of array to be filled somehow*/
int ix, iy; /*index of element to access to be filled somehow*/
int ind; /*Loop index*/
myarray = malloc(sizeof(int*) * nx);
for (ind = 0; ind<nx;++ind) myarray[ind] = malloc(sizeof(int) * ny);
myarray[ix][iy] = 10;
for (ind = 0; ind<nx;++ind) free(myarray[ind]);

This works by making myarray a pointer to a pointer to an int (int **myarray). You then allocate the outer pointer to be an array of nx pointers to int (note that my first sizeof is now sizeof(int*), not sizeof(int)!). You then go through all of these pointers to integers and allocate those pointers to themselves be ny element long arrays of integers (note that the second sizeof is sizeof(int)). This will work as expected, and you can now index your array with square bracket operators as normal, so what's the problem. The problem is that malloc doesn't give any guarantees about where the memory that you get back from it is located. In this simple test case the memory that you get will probably be layed out in a contiguous block, but in general this won't be true. By splitting your memory allocation up like this you are potentially creating a memory prefetch problem much like the one that you get by accessing an array in the wrong order, with similar effects on performance. There is a fringe benefit for this type of array : because the rows are allocated separately they don't have to be the same length as each other. It's tricky to make use of this property (because you have to keep track of how long each row is yourself) it can be very powerful for certain types of problem. On a related note you will often find that multidimensional arrays in C++ are created using std::vector<std::vector<int>> types. This in general has the same type of problem with memory not being contiguous, as you can clearly see from the fact that you can push back into each vector individually.

The final solution is to create a 1 dimensional chunk of memory and then rather than using an indexer function use a separate list of pointers to the start of the row. There are lots of ways of doing this, and this example isn't a terribly clever one but it does work

#include <stdlib.h>

int main(int argc, char **argv){

int nx = 10, ny=10;
int ind;
int **myarray;
int *buffer;
myarray = malloc(sizeof(int*) * nx);
buffer = malloc(sizeof(int) * nx * ny);
for (ind = 0; ind< nx; ++ind) myarray[ind] = &buffer[ind * ny];

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