Our paper Anatomy of High-Performance Many-Threaded Matrix Multiplication, presented at IPDPS'14, identified five loops around the microkernel as opportunities for parallelization within level-3 operations such as gemm. Within BLIS, we have enabled parallelism for four of those loops, with the fifth planned for future work. This software architecture extends naturally to all level-3 operations except for trsm, where its application is necessarily limited to three of the five loops due to inter-iteration dependencies.
IMPORTANT: Multithreading in BLIS is disabled by default. Furthermore, even when multithreading is enabled, BLIS will default to single-threaded execution at runtime. In order to both allow and invoke parallelism from within BLIS operations, you must both enable multithreading at configure-time and specify multithreading at runtime.
To summarize: In order to observe multithreaded parallelism within a BLIS operation, you must do both of the following:
- Enable multithreading at configure-time. This is discussed in the next section.
- Specify multithreading at runtime. This is also discussed later on.
BLIS disables multithreading by default. In order to allow multithreaded parallelism from BLIS, you must first enable multithreading explicitly at configure-time.
As of this writing, BLIS optionally supports multithreading via either OpenMP or POSIX threads.
To enable multithreading via OpenMP, you must provide the --enable-threading option to the configure script:
$ ./configure --enable-threading=openmp auto
In this example, we target the auto configuration, which is like asking configure to choose the most appropriate configuration based on some detection heuristic (e.g. cpuid on x86_64). Similarly, to enable multithreading via POSIX threads (pthreads), specify the threading model as pthreads instead of openmp:
$ ./configure --enable-threading=pthreads auto
You can also use the shorthand option for --enable-threading, which is -t:
$ ./configure -t pthreads auto
For more complete and up-to-date information on the --enable-threading option, simply run configure with the --help (or -h) option:
$ ./configure --help
While we provide the ability to implement multithreading in BLIS in terms of either OpenMP or pthreads, we typically encourage users to opt for OpenMP:
$ ./configure -t openmp auto
The reason mostly comes down to the fact that most OpenMP implementations (most notably GNU) allow the user to conveniently bind threads to cores via an environment variable(s) set prior to running the application. This is important because when the operating system causes a thread to migrate from one core to another, the thread will typically leave behind the data it was using in the L1 and L2 caches. That data may not be present in the caches of the destination core. Once the thread resumes execution from the new core, it will experience a period of frequent cache misses as the data it was previously using is transmitted once again through the cache hierarchy. If migration happens frequently enough, it can pose a significant (and unnecessary) drag on performance.
Note that binding threads to cores is possible in pthreads, but it requires a runtime call to the operating system, such as sched_setaffinity(), to convey the thread binding information, and BLIS does not yet implement this behavior for pthreads.
The solution to thread migration is setting processor affinity. In this context, affinity refers to the tendency for a thread to remain bound to a particular compute core. There are at least two ways to set affinity in OpenMP. The first way offers more control, but requires you to understand a bit about the processor topology and how core IDs are mapped to physical cores, while the second way is simpler but less powerful.
Let's start with an example. Suppose I have a two-socket system with a total of eight cores, four cores per socket. By setting GOMP_CPU_AFFINITY as follows
$ export GOMP_CPU_AFFINITY="0 1 2 3 4 5 6 7"
I am communicating to OpenMP that the first thread to be created should be spawned on core 0, from which it should not migrate. The second thread to be created should be spawned on core 1, from which it should not migrate, and so forth. If socket 0 has cores 0-3 and socket 1 has 4-7, this would result in the first four threads on socket 0 and the second four threads on socket 1. (And if more than eight threads are spawned, the mapping wraps back around, staring from the beginning.) So with GOMP_CPU_AFFINITY, you are doing more than just preventing threads from migrating once they are spawned--you are specifying the cores on which they will be spawned in the first place.
Another example: Suppose the hardware numbers the cores alternatingly between sockets, such that socket 0 gets even-numbered cores and socket 1 gets odd-numbered cores. In such a scenario, you might want to use GOMP_CPU_AFFINITY as follows
$ export GOMP_CPU_AFFINITY="0 2 4 6 1 3 5 7"
Because the first four entries are 0 2 4 6, threads 0-3 would be spawned on the first socket, since that is where cores 0, 2, 4, and 6 are located. Similarly, the subsequent 1 3 5 7 would cause threads 4-7 to be spawned on the second socket, since that is where cores 1, 3, 5, and 7 reside. Of course, setting GOMP_CPU_AFFINITY in this way implies that BLIS benefits from this kind of grouping of threads--which, generally, it does. As a general rule, you should try to fill up a socket with one thread per core before moving to the next socket.
A second method of specifying affinity is via OMP_PROC_BIND, which is much simpler to set:
$ export OMP_PROC_BIND=close
This binds the threads close to the master thread, in contiguous "place" partitions. (There are other valid values aside from close.) Places are specified by another variable, OMP_PLACES:
$ export OMP_PLACES=cores
The cores value is most appropriate for BLIS since we usually want to ignore hardware threads (symmetric multithreading, or "hyperthreading" on Intel systems) and instead map threads to physical cores.
Setting these two variables is often enough. However, it obviously does not offer the level of control that GOMP_CPU_AFFINITY does. Sometimes, it takes some experimentation to determine whether a particular mapping is performing as expected. If multithreaded performance on eight cores is only twice what it is observed of single-threaded performance, the affinity mapping may be to blame. But if performance is six or seven times higher than sequential execution, then the mapping you chose is probably working fine.
Unfortunately, the topic of thread-to-core affinity is well beyond the scope of this document. (A web search will uncover many great resources discussing the use of GOMP_CPU_AFFINITY and OMP_PROC_BIND.) It's up to the user to determine an appropriate affinity mapping, and then choose your preferred method of expressing that mapping to the OpenMP implementation.
There are three broad methods of specifying multithreading in BLIS:
- Globally via environment variables
- Globally at runtime
- Locally at runtime (that is, on a per-call, thread-safe basis)
Within these three broad methods there are two specific ways of expressing a request for parallelism. First, the user may express a single number--the total number of threads, or ways of parallelism, to use within a single operation such as gemm. We call this the "automatic" way. Alternatively, the user may express the number of ways of parallelism to obtain within each loop of the level-3 operation. We call this the "manual" way. The latter way is actually what BLIS eventually needs before it can perform its multithreading; the former is viable only because we have a heuristic of determining a reasonable instance of the latter when given the former.
This pattern--automatic or manual--holds regardless of which of the three methods is used.
Regardless of which method is employed, and which specific way within each method, after setting the number of threads, the application may call the desired level-3 operation (via either the typed API or the object API) and the operation will execute in a multithreaded manner. (When calling BLIS via the BLAS API, only the first two (global) methods are available.)
Note: Please be aware of what happens if you try to specify both the automatic and manual ways, as it could otherwise confuse new users. Here are the important points:
- Regardless of which broad method is used, if multithreading is specified via both the automatic and manual ways, the values set via the manual way will always take precedence.
- Specifying parallelism for even one loop counts as specifying the manual way (in which case the ways of parallelism for the remaining loops will be assumed to be 1). And in the case of the environment variable method, setting the ways of parallelism for a loop to 1 counts as specifying parallelism! If you want to switch from using the manual way to automatic way, you must not only set (
export) theBLIS_NUM_THREADSvariable, but you must alsounsetall of theBLIS_*_NTvariables. - If you have specified multithreading via both the automatic and manual ways, BLIS will not complain if the values are inconsistent with one another. (For example, you may request 8 total threads be used while also specifying 4 ways of parallelism within each of two matrix multiplication loops, for a total of 16 ways.) Furthermore, you will be able to query these inconsistent values via the runtime API both before and after multithreading executes.
- If multithreading is disabled, you may still specify multithreading values via either the manual or automatic ways. However, BLIS will silently ignore all of these values. A BLIS library that is built with multithreading disabled at configure-time will always run sequentially (from the perspective of a single application thread).
The most common method of specifying multithreading in BLIS is globally via environment variables. With this method, the user sets one or more environment variables in the shell before launching the BLIS-linked executable.
Regardless of whether you end up using the automatic or manual way of expressing a request for multithreading, note that the environment variables are read (via getenv()) by BLIS only once, when the library is initialized. Subsequent to library initialization, the global settings for parallelization may only be changed via the global runtime API. If this constraint is not a problem, then environment variables may work fine for you. Otherwise, please consider local settings. (Local settings may used at any time, regardless of whether global settings were explicitly specified, and local settings always override global settings.)
Note: Regardless of which way (automatic or manual) environment variables are used to specify multithreading, that specification will affect operation of BLIS through both the BLAS compatibility layer as well as the native typed and object APIs that are unique to BLIS.
The automatic way of specifying parallelism entails simply setting the total number of threads you wish BLIS to employ in its parallelization. This total number of threads is captured by the BLIS_NUM_THREADS environment variable. You can set this variable prior to executing your BLIS-linked executable:
$ export GOMP_CPU_AFFINITY="..." # optional step when using GNU libgomp.
$ export BLIS_NUM_THREADS=16
$ ./my_blis_program
This causes BLIS to automatically determine a reasonable threading strategy based on what is known about the operation and problem size. If BLIS_NUM_THREADS is not set, BLIS will attempt to query the value of OMP_NUM_THREADS. If neither variable is set, the default number of threads is 1.
Note: We highly discourage use of the OMP_NUM_THREADS environment variable and may remove support for it in the future. If you wish to set parallelism globally via environment variables, please use BLIS_NUM_THREADS.
The manual way of specifying parallelism involves communicating which loops within the matrix multiplication algorithm to parallelize and the degree of parallelism to be obtained from each of those loops.
The below chart describes the five loops used in BLIS's matrix multiplication operations.
| Loop around microkernel | Environment variable | Direction | Notes |
|---|---|---|---|
| 5th loop | BLIS_JC_NT |
n |
|
| 4th loop | N/A | k |
Not enabled |
| 3rd loop | BLIS_IC_NT |
m |
|
| 2nd loop | BLIS_JR_NT |
n |
|
| 1st loop | BLIS_IR_NT |
m |
Note: Parallelization of the 4th loop is not currently enabled because each iteration of the loop updates the same part of the output matrix C. Thus, to safely parallelize it requires either a reduction or mutex locks when updating C.
Parallelization in BLIS is hierarchical. So if we parallelize multiple loops, the total number of threads will be the product of the amount of parallelism for each loop. Thus the total number of threads used is the product of all the values:
BLIS_JC_NT * BLIS_IC_NT * BLIS_JR_NT * BLIS_IR_NT.
Note that if you set at least one of these loop-specific variables, any others that are unset will default to 1.
In general, the way to choose how to set these environment variables is as follows: The amount of parallelism from the M and N dimensions should be roughly the same. Thus BLIS_IR_NT * BLIS_IC_NT should be roughly equal to BLIS_JR_NT * BLIS_JC_NT.
Next, which combinations of loops to parallelize depends on which caches are shared. Here are some of the more common scenarios:
- When compute resources have private L3 caches (example: multi-socket systems), try parallelizing the
JCloop. This means threads (or thread groups) will pack and compute with different row panels from matrix B. - For compute resources that have private L2 caches but that share an L3 cache (example: cores on a socket), try parallelizing the
ICloop. In this situation, threads will share the same packed row panel from matrix B, but pack and compute with different blocks of matrix A. - If compute resources share an L2 cache but have private L1 caches (example: pairs of cores), try parallelizing the
JRloop. Here, threads share the same packed block of matrix A but read different packed micropanels of B into their private L1 caches. In some situations, parallelizing theIRloop may also be effective.
If you still wish to set the parallelization scheme globally, but you want to do so at runtime, BLIS provides a thread-safe API for specifying multithreading. Think of these functions as a way to modify the same internal data structure into which the environment variables are read. (Recall that the environment variables are only read once, when BLIS is initialized).
Note: Regardless of which way (automatic or manual) the global runtime API is used to specify multithreading, that specification will affect operation of BLIS through both the BLAS compatibility layer as well as the native typed and object APIs that are unique to BLIS.
If you simply want to specify an overall number of threads and let BLIS choose a thread factorization automatically, use the following function:
void bli_thread_set_num_threads( dim_t n_threads );This function takes one integer--the total number of threads for BLIS to utilize in any one operation. So, for example, if we call
bli_thread_set_num_threads( 4 );we are requesting that the global number of threads be set to 4. You may also query the global number of threads at any time via
dim_t bli_thread_get_num_threads( void );Which may be called in the usual way:
dim_t nt = bli_thread_get_num_threads();If you want to specify the number of ways of parallelism to obtain for each loop, use the following function:
void bli_thread_set_ways( dim_t jc, dim_t pc, dim_t ic, dim_t jr, dim_t ir );This function takes one integer for each loop in the level-3 operations. (Note: even though the function takes a pc argument, it will be ignored until parallelism is supported in the KC loop.)
So, for example, if we call
bli_thread_set_ways( 2, 1, 4, 1, 1 );we are requesting two ways of parallelism in the JC loop and 4 ways of parallelism in the IC loop.
Unlike environment variables, which only allow the user to set the parallelization strategy prior to running the executable, bli_thread_set_ways() may be called any time during the normal course of the BLIS-linked application's execution.
In addition to the global methods based on environment variables and runtime function calls, BLIS also offers a local, per-call method of requesting parallelism at runtime. This method has the benefit of being thread-safe and flexible; your application can spawn two threads at the application level, with each thread requesting different degrees of parallelism from their respective calls to level-3 BLIS operations.
As with environment variables and the global runtime API, there are two ways to specify parallelism: the automatic way and the manual way. Both ways involve allocating a BLIS-specific object, initializing the object and encoding the desired parallelization, and then passing a pointer to the object into one of the expert interfaces of either the typed or object APIs. We provide examples of utilizing this threading object below.
Note: Neither way (automatic nor manual) of specifying multithreading via the local runtime API can be used via the BLAS interfaces. The local runtime API may only be used via the native typed and object APIs, which are unique to BLIS. (Furthermore, the expert interfaces of each API must be used. This is demonstrated later on in this section.)
Before specifying the parallelism (automatically or manually), you must first allocate a special BLIS object called a rntm_t (runtime). The object is quite small (about 64 bytes), and so we recommend allocating it statically on the function stack:
rntm_t rntm;We strongly recommend initializing the rntm_t. This can be done in either of two ways.
If you want to initialize it as part of the declaration, you may do so via the default BLIS_RNTM_INITIALIZER macro:
rntm_t rntm = BLIS_RNTM_INITIALIZER;Alternatively, you can perform the same initialization by passing the address of the rntm_t to an initialization function:
bli_rntm_init( &rntm );As of this writing, BLIS treats a default-initialized rntm_t as a request for single-threaded execution.
Note: If you choose to not initialize the rntm_t object, you must set its parallelism via either the automatic way or the manual way, described below. Passing a completely uninitialized rntm_t to a level-3 operation will almost surely result in undefined behavior!
Once your rntm_t is initialized, you may request automatic parallelization by encoding only the total number of threads into the rntm_t via the following function:
void bli_rntm_set_num_threads( dim_t n_threads, rntm_t* rntm );As with bli_thread_set_num_threads() discussed previously, this function takes a single integer. It also takes the address of the rntm_t to modify. So, for example, if (after declaring and initializing a rntm_t as discussed above) we call
bli_rntm_set_num_threads( 6, &rntm );the rntm_t object will be encoded to use a total of 6 threads.
Once your rntm_t is initialized, you may manually encode the ways of parallelism for each loop into the rntm_t by using the following function:
void bli_rntm_set_ways( dim_t jc, dim_t pc, dim_t ic, dim_t jr, dim_t ir, rntm_t* rntm );As with bli_thread_set_ways() discussed previously, this function takes one integer for each loop in the level-3 operations. It also takes the address of the rntm_t to modify.
(Note: even though the function takes a pc argument, it will be ignored until parallelism is supported in the KC loop.)
So, for example, if we call
bli_rntm_set_ways( 1, 1, 2, 3, 1, &rntm );we are requesting two ways of parallelism in the IC loop and three ways of parallelism in the JR loop.
Regardless of whether you specified parallelism into your rntm_t object via the automatic or manual method, eventually you must use the data structure when calling a BLIS operation.
Let's assume you wish to call gemm. To so do, simply use the expert interface, which takes two additional arguments: a cntx_t (context) and a rntm_t. For the context, you may simply pass in NULL and BLIS will select a default context (which is exactly what happens when you call the basic/non-expert interfaces). Here is an example of such a call:
bli_gemm_ex( &alpha, &a, &b, &beta, &c, NULL, &rntm );This will cause gemm to execute and parallelize in the manner encoded by rntm.
To summarize, using a rntm_t involves three steps:
// Declare and initialize a rntm_t object.
rntm_t rntm = BLIS_RNTM_INITIALIZER;
// Call ONE (not both) of the following to encode your parallelization into
// the rntm_t. (These are examples only--use numbers that make sense for your
// application!)
bli_rntm_set_num_threads( 6, &rntm );
bli_rntm_set_ways( 1, 1, 2, 3, 1, &rntm );
// Finally, call BLIS via an expert interface and pass in your rntm_t.
bli_gemm_ex( &alpha, &a, &b, &beta, &c, NULL, &rntm );Note that rntm_t objects may be reused over and over again once they are initialized; there is no need to reinitialize them and re-encode their threading values!
Also, you may pass in NULL for the rntm_t* parameter of an expert interface. This causes the current global settings to be used.
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Internal transposition and manual parallelism. BLIS supports both row- and column-stored matrices (and tensor-like general storage). However, typically the
gemmmicrokernel prefers to read and write microtiles of matrix C by rows, or by columns. If the storage of the user-provided matrix C does not match that of the microkernel preference, BLIS logically transpose the entire operation so that by the time the microkernel sees matrix C, it will appear to be stored according to its storage preference. If the caller is employing the automatic style of parallelism, whereby only the total number of threads is specified, this transposition happens before the the total number of threads is factored into the various loop-specific ways of parallelism and everything works as expected. However, if the caller employs the manual style of parallelism, the transposition must (by definition) happen after the thread factorization is done since, in this situation, the caller has taken responsibility for providing that factorization explicitly.This situation could lead to unexpectedly low multithreaded performance. Suppose the user calls
gemmon a problem with a large m dimension and small k and n dimensions, and explicitly requests parallelism only in the IC loop, but also suppose that the storage of C does not match that of the microkernel's preference. After BLIS transposes the operation internally, the effective m dimension will no longer be large; instead, it will be small (because the original m and n dimension will have been swapped). The multithreaded implementation will then proceed to parallelize this small m dimension.There are currently no good and easy solutions to this problem. Eventually, though, we plan to add support for two microkernels per datatype per configuration--one for use with matrices C that are row-stored, and one for those that are column-stored. This will obviate the logic within BLIS that sometimes induces the operation transposition, and the problem will go away.
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Thread affinity when BLIS and MKL are used together. Some users have reported that when running a program that links both BLIS (configured with OpenMP) and MKL, and when OpenMP thread affinity has been specified (e.g. via
OMP_PROC_BINDandOMP_PLACES), that very poor performance is observed. This may be due to incorrect thread masking in this case, causing all threads to run on one physical core. The exact circumstances leading to this behavior have not been identified, but unsetting the OpenMP thread affinity variables appears to be a solution.
Please send us feedback if you have any concerns or questions, or open an issue if you observe any reproducible behavior that you think is erroneous. (You are welcome to use the issue feature to start any non-trivial dialogue; we don't restrict them only to bug reports!)
Thanks for your interest in BLIS.