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Library targeting Intel Architecture for specialized dense and sparse matrix operations, and deep learning primitives.
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LIBXSMM is a library for specialized dense and sparse matrix operations as well as for deep learning primitives such as small convolutions targeting Intel Architecture. Small matrix multiplication kernels (SMMs) are generated for Intel SSE, Intel AVX, Intel AVX2, and Intel AVX‑512 as found in the Intel Xeon Phi processor family (KNL, KNM) and Intel Xeon processors (SKX). Highly optimized code for small convolutions is targeting Intel AVX2 and Intel AVX‑512, whereas other targets can automatically leverage specialized SMMs to perform convolutions.

The library supports statically generated code at configuration time (SMMs), uses optimized code paths based on compiler-generated code as well as Intrinsic functions, but mainly utilizes Just‑In‑Time (JIT) code specialization for compiler-independent performance (matrix multiplications, matrix transpose/copy, sparse functionality, and small convolutions). LIBXSMM is suitable for "build once and deploy everywhere" i.e., no special target flags are needed to exploit the available performance.

For a list questions and answers, please also have a look at

Where to go for documentation?

What is a small matrix multiplication? When characterizing the problem-size using the M, N, and K parameters, a problem-size suitable for LIBXSMM falls approximately within (M N K)1/3 <= 64 (which illustrates that non-square matrices or even "tall and skinny" shapes are covered as well). The library is typically used to generate code up to the specified threshold. Raising the threshold may not only generate excessive amounts of code (due to unrolling in M or K dimension), but also miss to implement a tiling scheme to effectively utilize the cache hierarchy. For auto-dispatched problem-sizes above the configurable threshold (explicitly JIT'ted code is not subject to the threshold), LIBXSMM is falling back to BLAS. In terms of GEMM, the supported kernels are limited to Alpha := 1, Beta := { 1, 0 }, and TransA := 'N'.

What is a small convolution? In the last years, new workloads such as deep learning and more specifically convolutional neural networks (CNN) emerged and are pushing the limits of today's hardware. One of the expensive kernels is a small convolution with certain kernel sizes such that calculations in the frequency space is not the most efficient method when compared with direct convolutions. LIBXSMM's current support for convolutions aims for an easy to use invocation of small (direct) convolutions, which are intended for CNN training and classification.

Getting Started: The following code is focused on a specific functionality but may be considered as "Hello LIBXSMM". Build the example with cd /path/to/libxsmm; make STATIC=0 (shared library), save the code under hello.cpp (below) and compile using g++ -I/path/to/libxsmm/include hello.cpp -L/path/to/libxsmm/lib -lxsmm -lblas -o hello (GNU CCC), and finally execute with LD_LIBRARY_PATH=/path/to/libxsmm/lib LIBXSMM_VERBOSE=2 ./hello.

#include <libxsmm.h>
#include <vector>
int main(int argc, char* argv[])
  typedef double value_type;
  int batchsize = 1000, m = 13, n = 5, k = 7;
  std::vector<value_type> a(batchsize*m*k), b(batchsize*k*n), c(m*n, 0);
  /* C/C++ and Fortran interfaces are available */
  typedef libxsmm_mmfunction<value_type> kernel_type;
  /* generates and dispatches a matrix multiplication kernel (C++ functor) */
  kernel_type kernel(LIBXSMM_GEMM_FLAG_NONE, m,n,k, 1.0/*alpha*/, 1.0/*beta*/);
  for (int i = 0; i < batchsize; ++i) { /* initialize input */
    a[i*m*k] = static_cast<value_type>(1) / (i % 25);
    b[i*k*n] = static_cast<value_type>(7) / (i % 75);
  for (int i = 0; i < batchsize; ++i) { /* C = Ai * Bi */
    kernel(&a[i*m*k], &b[i*k*n], &c[0]);

Interfaces and Domains


Please have a look at for all published functions. Get started with the following list of available domains and documented functionality:

To initialize library internal resources, an explicit initialization routine helps to avoid lazy initialization overhead when calling LIBXSMM for the first time. The library deallocates internal resources at program exit, but also provides a companion of the afore mentioned initialization (finalize).

/** Initialize the library; pay for setup cost at a specific point. */
void libxsmm_init(void);
/** De-initialize the library and free internal memory (optional). */
void libxsmm_finalize(void);

Matrix Multiplication

This domain (MM) supports Small Matrix Multiplications (SMM), batches of multiple multiplications as well as the industry-standard interface for GEneral Matrix Matrix multiplication (GEMM).

The Matrix Multiplication domain (MM) contains routines for:

Deep Learning

This domain (DL) is detailed by a separate document. It may be inspiring to have a look at the light-weight GxM framework, which uses LIBXSMM for end-to-end Deep Learning.

Service Functions

For convenient operation of the library and to ease integration, some service routines are available. These routines may not belong to the core functionality of LIBXSMM (SMM or DNN domain), but users are encouraged to use this domain (AUX). There are two categories: (1) routines which are available for C and FORTRAN, and (2) routines that are only available per C interface.

The service function domain (AUX) contains routines for:


More information about the JIT-backend and the code generator can be found in a separate document, which also includes information about LIBXSMM's stand-alone generator-driver programs.

Build Instructions


The main interface file is generated, and it is therefore not stored in the code repository. Instead, one may have a look at the code generation template files for C/C++ and FORTRAN. There are two ways prepared to build and use LIBXSMM:

NOTE: LIBXSMM is available as prebuilt package for Fedora/RedHat/CentOS, Ubuntu, and FreeBSD. Further, LIBXSMM can be installed using the Spack Package Manager or per EasyBuild+EasyConfig.

Classic Library (ABI)

The build system relies on GNU Make (typically associated with the make command, but e.g. FreeBSD is calling it gmake). The build can be customized by using key‑value pairs. Key‑value pairs can be supplied in two ways: (1) after the "make" command, or (2) prior to the "make" command (env) which is effectively the same as exporting the key‑value pair as an environment variable (export, or setenv). Both methods can be mixed (the second method may require make's -e flag).

NOTE: By default, C/C++ and FORTRAN compilers are needed (some sample code is written in C++). Beside of specifying the compilers (make CXX=g++ CC=gcc FC=gfortran and maybe AR=ar), the need for a FORTRAN compiler can be relaxed (make FC= or make FORTRAN=0). The latter affects the availability of the MODule file and the corresponding 'libxsmmf' library (the interface 'libxsmm.f' is still generated).

The build system considers a set of given key-value pairs as a single unique build and triggers a rebuild for a distinct set of flags. For more advanced builds or additional background, please consult the section about Customization. To generate the interface of the library inside of the 'include' directory and to build the static library (by default, STATIC=1 is activated). Run any (or both) of the following command(s):

make STATIC=0

On CRAY systems, the CRAY Compiling Environment (CCE) should be used regardless of using the CRAY compiler, the Intel Compiler, or the GNU Compiler Collection (GCC). The CCE is eventually suppressing to build shared libraries (STATIC=0). In any case, (1) switch to the desired compiler (module load/switch), and (2) rely on:

make CXX=CC CC=cc FC=ftn

A variety of build environments is out-of-the-box compatible, see If the build process is not successful, it may help to avoid advanced GCC flags. This is useful with a tool chain, which pretends to be GCC-compatible (and is treated as such) but fails to consume the afore mentioned flags:


In case of outdated Binutils, compilation can fail to assemble code when building the library (this has nothing to do with JIT-generated code and it does not affect how JIT-code is targeting the system). In contrast to the default (INTRINSICS=2), INTRINSICS=1 enables to statically depend on the desired target e.g., AVX=3 MIC=0, or AVX=2 (if the target is omitted, the default target is used). Try to work around failing compilation with:


To test and validate a build, please consult To run some basic sanity checks, remember that each set of given key-value pairs represents a different build (and test):

make STATIC=0 tests

To remove intermediate files, or to remove all generated files and folders (including the interface and the library archives), run one of the make-targets below. An additional distclean-target recursively cleans the entire tree (after version 1.9).

make clean
make realclean

FORTRAN code can make use of LIBXSMM:

  • By using the module and linking with 'libxsmmf', 'libxsmm', and (optionally) 'libxsmmext',
  • By including 'libxsmm.f' and linking with 'libxsmm', and (optionally) 'libxsmmext', or
  • By (implicitly) calling a SUBROUTINE and linking with 'libxsmm', and (optionally) 'libxsmmext'.

Note: Using the Fortran module or including the interface, requires at least a Fortran 2003 compiler (F2K3). FORTRAN 77 compatibility is only implicitly available (no interface), and the available subset of routines is documented in 'libxsmm.f' and marked with comments (part of the implementation).


Version 1.4.4 introduced support for "header-only" usage in C and C++. By only including 'libxsmm_source.h' allows to get around building the library. However, this gives up on a clearly defined application binary interface (ABI). An ABI may allow for hot-fixes after deploying an application (when relying on the shared library form), and it may also ensure to only rely on the public interface of LIBXSMM. In contrast, the header-only form not only exposes the internal implementation of LIBXSMM but can also increase the turnaround time during development of an application (due to longer compilation times). The header file is intentionally named "libxsmm_source.h" since this header file relies on the src directory (with the implications as noted earlier).

To use the header-only form, 'libxsmm_source.h' needs to be generated. The build target shown below ('header-only') has been introduced in LIBXSMM 1.6.2 but make cheader can be used alternatively (or must be used instead in case of earlier versions). Generating the C interface is necessary since the library must be configured (see configuration template).

make header-only

NOTE: building an application applies the same build settings to LIBXSMM! For instance, to omit debug code inside of LIBXSMM NDEBUG must be defined (-DNDEBUG).

Link Instructions

Using the classic ABI (including Fortran code), requires linking LIBXSMM against the application. The library is agnostic with respect to the threading-runtime, and therefore an application is free to use any threading runtime (e.g., OpenMP). The library is also thread-safe, and multiple application threads can call LIBXSMM's routines concurrently. Enabling OpenMP for LIBXSMM's main library is supported as well (OMP=1), and mostly affects the synchronization primitives used inside of the library. All of the "omp" functionality (function postfix) is served by the 'libxsmmext' library, which is automatically built with OpenMP enabled. When using this "omp" functionality, 'libxsmmext' needs to be present at the link line.

Library Purpose
libxsmm Thread-safe core functions (same routine can be called concurrently). Contains routines that can take a thread-ID and the number of library-external threads.
libxsmmf Necessary when using the Fortran MODule but not when including libxsmm.f or relying on implicit interfaces (Fortran 77).
libxsmmext Provides library-internal OpenMP-threaded functions carrying the omp postfix when compared to function name names of the core library.
libxsmmnoblas Supplies faked symbols for dgemm (and others) and thereby removes the need to link against a LAPACK/BLAS library.

To ease linking with LIBXSMM, pkg-config can be used. For example:

export PKG_CONFIG_PATH=/path/to/libxsmm/lib
pkg-config libxsmm --libs

Similarly, an application is free to choose any BLAS or LAPACK library (if the link model available on the OS supports this), and therefore linking GEMM routines when linking LIBXSMM itself (by supplying BLAS=1|2) may prevent a user from making this decision at the time of linking the actual application. To use LIBXSMM without GEMM-related functionality, any BLAS-dependency can be removed in two ways: (1) building a special library with make BLAS=0, or (2) linking the application against the 'libxsmmnoblas' library. If an application however uses BLAS already, the Call Wrapper can be used to intercept existing BLAS calls (and to rely on LIBXSMM instead).

NOTE: LIBXSMM does not support to dynamically link 'libxsmm' or 'libxsmmext' ("so"), when BLAS is linked statically ("a"). If BLAS is linked statically, the static version of LIBXSMM must be used!


Installing LIBXSMM makes possibly the most sense when combining the JIT backend (enabled by default) with a collection of statically generated SSE kernels (by specifying M, N, K, or MNK). If the JIT backend is not disabled, statically generated kernels are only registered for dispatch if the CPUID flags at runtime are not supporting a more specific instruction set extension (code path). Since the JIT backend does not support or generate SSE code by itself, the library is compiled by selecting SSE code generation if not specified otherwise (AVX=1|2|3, or with SSE=0 falling back to an "arch-native" approach). Limiting the static code path to SSE4.2 allows to practically target any deployed system, however using SSE=0 and AVX=0 together is falling back to generic code, and any static kernels are not specialized using the assembly code generator.

There are two main mechanisms to install LIBXSMM (both mechanisms can be combined): (1) building the library in an out‑of‑tree fashion, and (2) installing into a certain location. Building in an out‑of‑tree fashion looks like:

cd libxsmm-install
make -f /path/to/libxsmm/Makefile

Installation into a specific location looks like (PREFIX or DESTDIR):

make MNK="1 2 3 4 5" PREFIX=/path/to/libxsmm-install install

Both PREFIX and DESTDIR are equivalent and can be relative or absolute paths. An installation can be repeated for different locations without triggering a rebuild. The prefix directory inside of each of the package configuration files is set to where LIBXSMM is built (staging folder) unless PREFIX or DESTDIR is specified. The effect of PREFIX (or DESTDIR) with respect to the pkg-config files is independent of whether the install-target is invoked or not (make).

Further, performing make install-minimal omits the documentation (default: 'PREFIX/share/libxsmm'). Moreover, PINCDIR, POUTDIR, PBINDIR, and PDOCDIR allow to customize the locations underneath of the PREFIX location. To build a general package for an unpredictable audience (Linux distribution, or similar), it is advised to not over-specify or customize the build step i.e., JIT, SSE, AVX, OMP, BLAS, etc. should not be used. The following is building and installing a complete set of libraries where the generated interface matches both the static and the shared libraries:

make PREFIX=/path/to/libxsmm-install STATIC=0 install
make PREFIX=/path/to/libxsmm-install install

Runtime Control

Verbose Mode

The verbose mode (level of verbosity) allows for an insight into the code dispatch mechanism by receiving a small tabulated statistic as soon as the library terminates. The design point for this functionality is to not impact the performance of any critical code path i.e., verbose mode is always enabled and does not require symbols (SYM=1) or debug code (DBG=1). The statistics appears (stderr) when the environment variable LIBXSMM_VERBOSE is set to a non-zero value. For example:

LIBXSMM_VERBOSE=1 ./myapplication
[... application output]

HSW/SP      TRY    JIT    STA    COL
   0..13      0      0      0      0
  14..23      0      0      0      0
 24..128      3      3      0      0

The tables are distinct between single-precision and double-precision, but either table is pruned if all counters are zero. If both tables are pruned, the library shows the code path which would have been used for JIT'ting the code: LIBXSMM_TARGET=hsw (otherwise the code path is shown in the table's header). The actual counters are collected for three buckets: small kernels (MNK1/3 <= 13), medium-sized kernels (13 < MNK1/3 <= 23), and larger kernels (23 < MNK1/3 <= 64; the actual upper bound depends on LIBXSMM_MAX_MNK as selected at compile-time). Keep in mind, that "larger" is supposedly still small in terms of arithmetic intensity (which grows linearly with the kernel size). Unfortunately, the arithmetic intensity depends on the way a kernel is used (which operands are loaded/stored into main memory) and it is not performance-neutral to collect this information.

The TRY counter represents all attempts to register statically generated kernels, and all attempts to dynamically generate and register kernels. The TRY counter includes rejected JIT requests due to unsupported GEMM arguments. The JIT and STA counters distinct the successful cases of the afore mentioned event (TRY) into dynamically (JIT) and statically (STA) generated code. In case the capacity (O(n) = 105) of the code registry is exhausted, no more kernels can be registered although further attempts are not prevented. Registering many kernels (O(n) = 103) may ramp the number of hash key collisions (COL), which can degrade performance. The latter is prevented if the small thread-local cache is utilized effectively.

Since explicitly JIT-generated code (libxsmm_?mmdispatch) does not fall under the THRESHOLD criterion, the above table is extended by one line if large kernels have been requested. This indicates a missing threshold-criterion (customized dispatch), or asks for cache-blocking the matrix multiplication. The latter is already implemented by LIBXSMM's "medium-sized" GEMM routines (libxsmm_?gemm_omp), which perform a tiled multiplication. Setting a verbosity level of at least two summarizes the number of registered JIT-generated kernels, which includes the total size and counters for GEMM, MCOPY (matrix copy), and TCOPY (matrix transpose) kernels.

Registry: 20 MB (gemm=0 mcopy=14 tcopy=0)

If the call-wrapper is used, an additional runtime statistic becomes available (see Call Wrapper).

NOTE: Setting LIBXSMM_VERBOSE to a negative value will binary-dump each generated JIT kernel to a file with each file being named like the function name shown in Intel VTune. Disassembly of the raw binary files can be accomplished by:

objdump -D -b binary -m i386 -M x86-64 [JIT-dump-file]

Call Trace

During the initial steps of employing the LIBXSMM API, one may rely on a debug version of the library (make DBG=1). The latter also implies console output (stderr) in case of an error/warning condition inside of the library. It is also possible to print the execution flow (call trace) inside of LIBXSMM (can be combined with DBG=1 or OPT=0):

make TRACE=1

Building an application which traces calls (inside of the library) requires the shared library of LIBXSMM, alternatively the application is required to link the static library of LIBXSMM in a dynamic fashion (GNU tool chain: -rdynamic). Tracing calls (without debugger) can be then accomplished by an environment variable called LIBXSMM_TRACE.

LIBXSMM_TRACE=1 ./myapplication

Syntactically up to three arguments separated by commas (which allows to omit arguments) are taken (tid,i,n): tid signifies the ID of the thread to be traced with 1...NTHREADS being valid and where LIBXSMM_TRACE=1 is filtering for the "main thread" (in fact the first thread running into the trace facility); grabbing all threads (no filter) can be achieved by supplying a negative id (which is also the default when omitted). The second argument is pruning higher levels of the call-tree with i=1 being the default (level zero is the highest at the same level as the main function). The last argument is taking the number of inclusive call levels with n=-1 being the default (signifying no filter).

Although the ltrace (Linux utility) provides similar insight, the trace facility might be useful due to the afore mentioned filtering expressions. Please note that the trace facility is severely impacting the performance (even with LIBXSMM_TRACE=0), and this is not just because of console output but rather since inlining (internal) functions might be prevented along with additional call overhead on each function entry and exit. Therefore, debug symbols can be also enabled separately (make SYM=1; implied by TRACE=1 or DBG=1) which might be useful when profiling an application.


Profiling an application, which uses LIBXSMM's JIT-code is well-supported. The library supports Intel VTune Amplifier and Linux perf. Details are given on how to include profiler support, and how to run the application.

At build time, a variety of options exist to customize LIBXSMM. The library is setup for a broad range of use cases, which include sophisticated defaults for typical use.

To find performance results of applications or performance reproducers, the repository provides an orphaned branch called "results" which collects collateral material such as measured performance results along with explanatory figures. The results can be found at, or the results can be cloned as shown below.

git clone --branch results \ \

Please note that comparing performance results depends on whether the operands of the matrix multiplication are streamed or not. For example, multiplying with all matrices covered by the L1 cache may have an emphasis towards an implementation which perhaps performs worse for the real workload (if this real workload needs to stream some or all matrices from the main memory). Most of the code samples are aimed to reproduce performance results, and it is encouraged to model the exact case or to look at real applications.


High Performance Computing (HPC)

[1] Open Source Molecular Dynamics using the DBCSR library to process batches of small matrix multiplications. The batches originate from a distributed block-sparse with problem-specific small matrix shapes. Starting with CP2K 3.0, LIBXSMM can substitute CP2K's 'libsmm' library.

[2] SeisSol is one of the leading codes for earthquake scenarios, for simulating dynamic rupture processes. LIBXSMM provides highly optimized assembly kernels which form the computational back-bone of SeisSol (see

[3] NekBox is a highly scalable and portable spectral element code, which is inspired by the Nek5000 code. NekBox is specialized for box geometries and intended to prototype new methods as well as to leverage FORTRAN beyond the FORTRAN 77 standard. LIBXSMM can be used to substitute the MXM_STD code. Please also note LIBXSMM's NekBox reproducer.

[4] Nek5000 is the open-source, highly-scalable, always-portable spectral element code from The development branch of the Nek5000 code incorporates LIBXSMM.

[5] PyFR is an open-source Python based framework for solving advection-diffusion type problems on streaming architectures using the flux reconstruction approach. PyFR 1.6.0 optionally incorporates LIBXSMM as a matrix multiplication provider for the OpenMP backend. Please also note LIBXSMM's PyFR-related code sample.

[6] The Extreme-scale Discontinuous Galerkin Environment (EDGE) is a solver for hyperbolic partial differential equations with emphasis on seismic simulations. The EDGE source code optionally relies on LIBXSMM, but for high performance LIBXSMM's kernels are highly recommended.

[7] SpECTRE is an open-source code for multi-scale, multi-physics problems in astrophysics and gravitational physics which runs at petascale and is designed for exascale computers. In the future, SpECTRE may be applied to problems across discipline boundaries in fluid dynamics, geoscience, plasma physics, nuclear physics, and engineering.

[8] The Center for Efficient Exascale Discretizations (CEED) is building on the efforts of the Nek5000, MFEM, MAGMA, OCCA and PETSc projects to develop application program interfaces (APIs), both at high-level and at low-level to enable applications to take advantage of high-order methods. The CEED low-level API, libCEED uses LIBXSMM as a backend for high performance on CPUs.

Machine Learning (ML)

[9] The primary purpose of DeepBench is to benchmark operations that are important to deep learning on different hardware platforms. LIBXSMM's DNN primitives have been incorporated into DeepBench to demonstrate an increased performance of deep learning on Intel hardware. In addition, LIBXSMM's DNN sample folder contains scripts to run convolutions extracted from popular benchmarks in a stand-alone fashion.

[10] TensorFlow™ is an open source software library for numerical computation using data flow graphs. TensorFlow was originally developed by researchers and engineers working on the Google Brain Team for the purposes of conducting machine learning and deep neural networks research. LIBXSMM can be used to increase the performance of TensorFlow on Intel hardware.

[11] SkimCaffe from Intel Labs is a Caffe branch for training of sparse CNNs, which provide 80-95% sparsity in convolutions and fully-connected layers. LIBXSMM's SPMDM domain (SParseMatrix-DenseMatrix multiplication) evolved from SkimCaffe, and since then LIBXSMM implements the sparse operations in SkimCaffe.

Automated Driving (AD)

[12] Accelerating The Eigen Math Library for Automated Driving Workloads: The Need for Speed in Kalman Filtering. An article in Issue 31 of The Parallel Universe magazine.


[1] Anatomy of High-Performance Deep Learning Convolutions on SIMD Architectures (arXiv:1808.05567v2 paper). SC'18: The International Conference for High Performance Computing, Networking, Storage, and Analysis, Dallas (Texas).

[2] Understanding the Performance of Small Convolution Operations for CNN on Intel Architecture (poster and abstract), SC’17: The International Conference for High Performance Computing, Networking, Storage, and Analysis, Denver (Colorado).

[3] LIBXSMM: Accelerating Small Matrix Multiplications by Runtime Code Generation (paper). SC'16: The International Conference for High Performance Computing, Networking, Storage and Analysis, Salt Lake City (Utah).

[4] LIBXSMM: A High Performance Library for Small Matrix Multiplications (poster and abstract). SC'15: The International Conference for High Performance Computing, Networking, Storage and Analysis, Austin (Texas).


[1] LIBXSMM: An Open Source-Based Inspiration for Hardware and Software Development at Intel. An article written by Hans Pabst, Greg Henry, and Alexander Heinecke, 2018.

[2] LIBXSMM Brings Deep-learning "Lessons Learned" to Many HPC Applications. An article written by Rob Farber, 2018.

[3] Largest Supercomputer Simulation of Sumatra-Andaman Earthquake. An article written by Linda Barney, 2018.

[4] Intel Xeon Phi Delivers Competitive Performance For Deep Learning - And Getting Better Fast. Article mentioning LIBXSMM's performance of convolution kernels with DeepBench. Intel Corporation, 2016.

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