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Library for specialized dense and sparse matrix operations, and deep learning primitives.

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# LIBXSMM

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LIBXSMM is high performance library for small dense and sparse linear algebra opertions incl. GEMM and elementwise primities often seen in deep learning applications. It also serves as reference implementation of Tensor Processing Primitives ([TPP](https://arxiv.org/pdf/2104.05755)), a programming abstraction for efficient and portable deep learning and HPC workloads. With version&#160;2.0, LIBXSMM focuses on providing a complete and architecture-portable set of TPPs (small dense and sparse matrix operations as well as element-wise, GEMM, and BRGEMM primitives) from which higher-level operators such as convolutions, fully-connected layers, normalization, and pooling are composed. LIBXSMM targets Intel&#160;Architecture with Intel&#160;SSE, Intel&#160;AVX, Intel&#160;AVX2, Intel&#160;AVX&#8209;512 (with VNNI and Bfloat16), and Intel&#160;AMX (Advanced Matrix Extensions), AArch64 (NEON, SVE, and SME), RISC&#8209;V (RVV), and PowerPC&#160;64&#8209;bit&#160;little&#8209;endian (POWER10 with VSX and MMA). Code generation is mainly based on Just&#8209;In&#8209;Time (JIT) code specialization for compiler-independent performance (matrix multiplications, matrix transpose/copy, sparse functionality, and tensor primitives). LIBXSMM is suitable for "build once and deploy everywhere", i.e., no special target flags are needed to exploit the available performance. Supported GEMM datatypes are: `FP64`, `FP32`, `FP16`, `bfloat16`, `BF8`, `HF8`, `MXBF8`, `MXHF8`, `int16`, `int8`, `MXBF6`, `MXHF6`, `MXFP4`, `int4`, `int2` and `int1`. Additionally, various non-standard low precision combinations are supported.

**LIBXSMM 2.0**: This major release repositions LIBXSMM as the reference implementation of Tensor Processing Primitives. To keep the core library focused, several application-specific pieces that previously shipped here have moved to dedicated companion repositories: the deep-learning operators and convolution drivers ([LIBXSMM-DNN](https://github.com/libxsmm/libxsmm-dnn)), the PyTorch integration ([TPP PyTorch Extension](https://github.com/libxsmm/tpp-pytorch-extension)), and the spectral-element reproducers (e.g. NekBox). The core library, the JIT backend, and the TPP frontend remain here.

For a list questions and answers, please also have a look at [https://github.com/libxsmm/libxsmm/wiki/Q&A](https://github.com/libxsmm/libxsmm/wiki/Q&A).

<a name="getting-started"></a><a name="hello-libxsmm"></a>**Getting Started**: The following C code may be considered as [Hello LIBXSMM](https://github.com/libxsmm/libxsmm/tree/main/samples/hello). It walks through the Tensor Processing Primitives: dispatch a GEMM kernel and three element-wise (unary, binary, ternary) kernels, then invoke them. Build the example with `cd /path/to/libxsmm; make STATIC=0` (shared library), save the code under `hello.c` (below) and compile with `gcc -I/path/to/libxsmm/include hello.c -L/path/to/libxsmm/lib -lxsmm -lm -o hello`, and finally execute with `LD_LIBRARY_PATH=/path/to/libxsmm/lib LIBXSMM_VERBOSE=2 ./hello`.

```c
#include <libxsmm.h>
#include <string.h>

int main(int argc, char* argv[]) {
  const libxsmm_blasint m = 13, n = 5, k = 7;
  float a[13*7], b[7*5], c[13*5], bias[13*5], tmp[13*5], out[13*5];
  libxsmm_blasint i;

/* GEMM TPP: C = A * B (column-major, all FP32) */
  const libxsmm_gemm_shape gshape = libxsmm_create_gemm_shape(m, n, k, m, k, m,
    LIBXSMM_DATATYPE_F32, LIBXSMM_DATATYPE_F32, LIBXSMM_DATATYPE_F32, LIBXSMM_DATATYPE_F32);
  libxsmm_gemmfunction gemm = libxsmm_dispatch_gemm(gshape,
    LIBXSMM_GEMM_FLAG_NONE, LIBXSMM_GEMM_PREFETCH_NONE);
  /* unary TPP: ReLU; binary TPP: bias add; ternary TPP: fused multiply-add */
  const libxsmm_meltw_unary_shape ushape = libxsmm_create_meltw_unary_shape(m, n, m, m,
    LIBXSMM_DATATYPE_F32, LIBXSMM_DATATYPE_F32, LIBXSMM_DATATYPE_F32);
  libxsmm_meltwfunction_unary relu = libxsmm_dispatch_meltw_unary(
    LIBXSMM_MELTW_TYPE_UNARY_RELU, ushape, LIBXSMM_MELTW_FLAG_UNARY_NONE);
  const libxsmm_meltw_binary_shape bshape = libxsmm_create_meltw_binary_shape(m, n, m, m, m,
    LIBXSMM_DATATYPE_F32, LIBXSMM_DATATYPE_F32, LIBXSMM_DATATYPE_F32, LIBXSMM_DATATYPE_F32);
  libxsmm_meltwfunction_binary add = libxsmm_dispatch_meltw_binary(
    LIBXSMM_MELTW_TYPE_BINARY_ADD, bshape, LIBXSMM_MELTW_FLAG_BINARY_NONE);
  const libxsmm_meltw_ternary_shape tshape = libxsmm_create_meltw_ternary_shape(m, n, m, m, m, m,
    LIBXSMM_DATATYPE_F32, LIBXSMM_DATATYPE_F32, LIBXSMM_DATATYPE_F32, LIBXSMM_DATATYPE_F32, LIBXSMM_DATATYPE_F32);
  libxsmm_meltwfunction_ternary fma = libxsmm_dispatch_meltw_ternary(
    LIBXSMM_MELTW_TYPE_TERNARY_MULADD, tshape, LIBXSMM_MELTW_FLAG_TERNARY_NONE);

libxsmm_gemm_param gp; libxsmm_meltw_unary_param up;
 libxsmm_meltw_binary_param bp; libxsmm_meltw_ternary_param tp;
 for (i = 0; i < m*k; ++i) a[i] = 1.f / (i + 1);
 for (i = 0; i < k*n; ++i) b[i] = 2.f / (i + 1);
 for (i = 0; i < m*n; ++i) bias[i] = 0.5f;

memset(&gp, 0, sizeof(gp)); gp.a.primary = a; gp.b.primary = b; gp.c.primary = c; gemm(&gp);
  memset(&up, 0, sizeof(up)); up.in.primary = c; up.out.primary = c; relu(&up);
  memset(&bp, 0, sizeof(bp)); bp.in0.primary = c; bp.in1.primary = bias; bp.out.primary = tmp; add(&bp);
  memset(&tp, 0, sizeof(tp)); tp.in0.primary = tmp; tp.in1.primary = c; tp.in2.primary = bias; tp.out.primary = out; fma(&tp);
  return 0;
}
```

Plain [C code](https://github.com/libxsmm/libxsmm/blob/main/samples/hello/hello.c) as well as [Fortran code](https://github.com/libxsmm/libxsmm/blob/main/samples/hello/hello.f) resemble the same [example](https://github.com/libxsmm/libxsmm/tree/main/samples/hello). More complete drivers are available under [samples/xgemm](https://github.com/libxsmm/libxsmm/tree/main/samples/xgemm) and [samples/eltwise](https://github.com/libxsmm/libxsmm/tree/main/samples/eltwise).

<a name="what-is-a-small-matrix-multiplication"></a>**What is a small matrix multiplication?** When characterizing the problem-size by using the M, N, and K parameters, a problem-size suitable for LIBXSMM falls approximately within (M&#160;N&#160;K)1/3&#160;&lt;=&#160;64 (which illustrates that non-square matrices or even "tall and skinny" shapes are covered as well). The library does not employ multiplevel K,M,N blocking. Using LIBXSMM for much larger sizes may generate excessive amounts of code (due to unrolling in M or K dimension), but also misses to implement a tiling scheme to effectively utilize the cache hierarchy. In terms of GEMM, the supported kernels are limited to *Alpha := 1*, *Beta := \{ 1, 0 \}*, and *TransA := 'N'*.

## Interfaces and Domains<a name="interfaces"></a>

### Overview<a name="general-interface"></a>

Please have a look at [https://github.com/libxsmm/libxsmm/tree/main/include](https://github.com/libxsmm/libxsmm/tree/main/include) for all published functions. Get started with the following list of available domains and documented functionality:

* TPP: [Tensor Processing Primitives](https://github.com/libxsmm/libxsmm/blob/main/documentation/libxsmm_tpp.md)
* MM: [Matrix Multiplication](#matrix-multiplication)
* DL: [Deep Learning](#interface-for-dl)
* AUX: [Service Functions](#service-functions)
* PERF: [Performance](#performance)
* BE: [Backend](#jit-backend)

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).

```C
/** 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<a name="interface-for-matrix-multiplication"></a>

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)](documentation/libxsmm_mm.md) contains routines for:

* [Small, tiled, and parallelized matrix multiplications](documentation/libxsmm_mm.md#overview)
* [Manual code dispatch (customized matrix batches)](documentation/libxsmm_mm.md#manual-code-dispatch)

### Deep Learning<a name="interface-for-dl"></a>

Common operators in deep learning applications (GEMM with activation function fusion, Convolutions with activation function fusion, various norming operators, and pooling operators, etc.) can be implemented using the Tensor Processing Primitives provided by LIBXSMM. With LIBXSMM&#160;2.0 the deep-learning operators and their performance drivers live in the companion repository [LIBXSMM-DNN](https://github.com/libxsmm/libxsmm-dnn/tree/main/tests), which demonstrates how these primitives compose into full operators without any platform-specific code.

### 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)&#160;routines which are available for C and FORTRAN, and (2)&#160;routines that are only available per C interface.

The [service function domain (AUX)](documentation/libxsmm_aux.md) contains routines for:

* [Getting and setting the target architecture](documentation/libxsmm_aux.md#getting-and-setting-the-target-architecture)
* [Getting and setting the verbosity](documentation/libxsmm_aux.md#getting-and-setting-the-verbosity)
* [Measuring time durations (timer)](documentation/libxsmm_aux.md#timer-facility)
* [Dispatching user-data and multiple kernels](documentation/libxsmm_aux.md#user-data-dispatch)
* [Allocating memory](documentation/libxsmm_aux.md#memory-allocation)

### Backend<a name="jit-backend"></a>

More information about the JIT-backend and the code generator can be found in a separate [document](documentation/libxsmm_be.md). The [encoder sample collection](https://github.com/libxsmm/libxsmm/tree/main/samples/encoder) can help to get started writing a kernel using LIBXSMM. Please note, LIBXSMM's stand-alone <a name="generator-driver"></a>[generator-driver](documentation/libxsmm_be.md#generator-driver) is considered legacy (deprecated).

## Build Instructions

### Overview

The main interface file is *generated*, and it is therefore **not** stored in the code repository. To inspect the interface for [C/C++](https://github.com/libxsmm/libxsmm/blob/main/src/template/libxsmm.h) and [FORTRAN](https://github.com/libxsmm/libxsmm/blob/main/src/template/libxsmm.f), one can take a look at the template files used to generate the actual interface. There are two general ways to build and use LIBXSMM:

* [Classic Library (ABI)](#classic-library-abi) and [Link Instructions](#link-instructions) (C/C++ and FORTRAN)
* [Header-Only](#header-only) (C and C++)

**Note**: LIBXSMM is available as prebuilt package for Fedora/RedHat/CentOS, Debian/Ubuntu, FreeBSD, and others. Further, LIBXSMM can be installed with the [Spack Package Manager](https://computing.llnl.gov/projects/spack-hpc-package-manager) or per [EasyBuild+EasyConfig](https://github.com/easybuilders).

### Classic Library (ABI)

LIBXSMM provides native GNU Make and CMake build systems for the classic library ABI. GNU Make remains the reference build path and exposes the full set of build-time customization options and legacy sample targets. CMake supports the core library, optional Fortran module interface, generator executables, installation, and CMake package integration. Projects using another build system can also write their own [rules for building LIBXSMM](#rules-for-building-libxsmm).

The Makefile based build system relies on GNU&#160;Make (typically associated with the `make` command, but e.g. FreeBSD is calling it `gmake`). The build can be customized by using key&#8209;value pairs. Key&#8209;value pairs can be supplied in two ways: (1)&#160;after the "make" command, or (2)&#160;prior to the "make" command (`env`) which is effectively the same as exporting the key&#8209;value pair as an environment variable (`export`, or `setenv`). Both methods can be mixed (the second method may require make's `-e` flag).

<a name="zero-config-abi"></a>In contrast to [header-only](#zero-config) which does not require configuration by default, 3rd-party build systems can compile and link LIBXSMM's sources but still avoid configuring the library (per `libxsmm_config.py`). The prerequisite to omit configuration is to opt-in by defining LIBXSMM_DEFAULT_CONFIG (`-D`). The zero-config feature is not available for LIBXSMM's Fortran interface.

**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 `libxsmm.f` 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](documentation/libxsmm_tune.md). 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):

```bash
make STATIC=0
make
```

On CRAY systems, the CRAY Compiling Environment (CCE) should be used regardless of utilizing the CRAY compiler, the Intel Compiler, or the GNU&#160;Compiler Collection (GCC). The CCE is eventually suppressing to build shared libraries (STATIC=0). In any case, (1)&#160;switch to the desired compiler (module load/switch), and (2)&#160;rely on:

```bash
make CXX=CC CC=cc FC=ftn
```

A variety of build environments is out-of-the-box compatible, see [https://github.com/libxsmm/libxsmm/wiki/Compatibility](https://github.com/libxsmm/libxsmm/wiki/Compatibility). 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:

```bash
make COMPATIBLE=1
```

<a name="outdated-binutils"></a>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). LIBXSMM implements some functionality using compiler-intrinsics and multiple code-paths which are scheduled according to CPUID. In contrast to `INTRINSICS=2` (default), `INTRINSICS=1` enables a fully static code path according to the desired target. If no target is given (e.g., `AVX=3`, or `AVX=2`), instruction set extensions cannot be leveraged for such code-paths. Try to fix failing compilation by building the latest GNU Binutils (and `export PATH=/path/to/binutils/bin:${PATH}`). Binutils are versioned independently of GNU&#160;GCC and other compilers. If one cannot update Binutils, work around with a CPUID-value as tabulated in [libxsmm_cpuid.h](https://github.com/libxsmm/libxsmm/blob/main/include/libxsmm_cpuid.h): start at the upper end (less than 1999) and decrement until compilation passes (make INTRINSICS=_CPUID_, e.g., `make INTRINSICS=1021`). As a last resort, rely on a fully static code path:

```bash
make INTRINSICS=1
```

To test and validate a build, please consult [https://github.com/libxsmm/libxsmm/wiki/Validation](https://github.com/libxsmm/libxsmm/wiki/Validation). To run some basic sanity checks, remember that each set of given key-value pairs represents a different build (and test):

```bash
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&#160;1.9).

```bash
make clean
make realclean
```

<a name="fortran"></a>FORTRAN code can make use of LIBXSMM:

* By using the module and linking with `libxsmmf`, `libxsmm`, and `libxsmmext`,
* <a name="header-only-fortran"></a>By including `libxsmm.f` and linking with `libxsmm`, and `libxsmmext`, or
* By (implicitly) calling a SUBROUTINE and linking with `libxsmm`, and `libxsmmext`.

**Note**: `libxsmmf` requires `libxsmmext` (starting with LIBXSMM&#160;2.0), and thereby requires to link with the OpenMP runtime as well.

Using the Fortran module (or including the interface), requires at least a Fortran&#160;2003 compiler (F2K3). FORTRAN&#160;77 compatibility is only implicitly available (no interface), and the available subset of routines is documented in `libxsmm.f` and marked with [comments](https://github.com/libxsmm/libxsmm/search?q=implementation+provided+for+Fortran+77+compatibility) (part of the implementation).

#### CMake

CMake 3.13 or newer can build the classic library ABI, the optional Fortran module interface, and the generator executables. GNU Make remains the reference build path, especially when the full set of build-time customization options or legacy sample targets is needed.

Configure, build, and install LIBXSMM with:

```bash
cmake -S . -B build -DCMAKE_INSTALL_PREFIX=/path/to/libxsmm-install
cmake --build build --target install -j
```

The default CMake build produces static libraries. Add `-DBUILD_SHARED_LIBS=ON` to build shared libraries. When a Fortran compiler is detected, the Fortran module interface and `libxsmmf` are built automatically.

The installed package should be consumed through its exported targets:

```cmake
find_package(libxsmm CONFIG REQUIRED)
target_link_libraries(my_target PRIVATE libxsmm::libxsmm)
```

For the Fortran module interface:

```cmake
find_package(libxsmm CONFIG REQUIRED COMPONENTS Fortran)
target_link_libraries(my_target PRIVATE libxsmm::libxsmmf)
```

For an in-tree dependency, `add_subdirectory()` can be used. An installed package and `find_package(libxsmm CONFIG REQUIRED)` are preferred for regular downstream integration.

### Header-Only

Version&#160;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](https://github.com/libxsmm/libxsmm/tree/main/src) directory (with the implications as noted earlier).

<a name="zero-config"></a>The header-only form depends on `libxsmm_source.h` which is *generated* according to the content of the source folder (`src`). LIBXSMM&#160;1.16 (and later) provides header-only support without invoking a make-target (zero configuration) for any given checkout of LIBXSMM. To use configured header-only (non-default), LIBXSMM_CONFIGURED must be defined (`-D`). Previously, it was necessary to invoke `make header-only` (v1.6.2 or later), `make cheader` (prior to v1.6.2), or any target building the library (`make`). The zero-config feature allows 3rd-party build systems an easier integration of LIBXSMM, which also holds true if the system builds LIBXSMM from source (see [classic ABI](#zero-config-abi)). Fortran code may [include](#header-only-fortran) `libxsmm.f` but still requires that interface to be generated.

**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`).

## Rules for building LIBXSMM

Projects using CMake should use the native CMake build described above rather than maintaining a duplicate list of LIBXSMM source files. Other build systems can compile and link LIBXSMM directly. Such builds may generate the configured interfaces first, or opt into zero-config mode by defining `LIBXSMM_DEFAULT_CONFIG` (`-D`). Zero-config mode is not available for LIBXSMM's Fortran interface.

## Link Instructions

Using the [classic ABI](#classic-library-abi) (including [Fortran](#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 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.

<a name="table-of-libraries"></a>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](https://github.com/libxsmm/libxsmm/search?q=implementation+provided+for+Fortran+77+compatibility)).

<a name="pkg-config"></a>To ease linking with LIBXSMM, `pkg-config` can be used. For example:

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

### Installation

There are two main mechanisms to install LIBXSMM (both mechanisms can be combined): (1)&#160;building the library in an out&#8209;of&#8209;tree fashion, and (2)&#160;installing into a certain location. <a name="install-build"></a>Building in an out&#8209;of&#8209;tree fashion looks like:

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

<a name="install-prefix"></a>Installation into a specific location looks like (`PREFIX` or `DESTDIR`):

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

<a name="install-destdir"></a>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](#pkg-config) 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:

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

## Runtime Control<a name="running"></a>

### Handling Errors

The library handles errors with mechanisms available to the C programming language (no exceptions). The backend uses result codes passed by an argument rather than an actual return value. Such an argument is often a descriptor (struct) guiding and covering the state of the code generation. The frontend however may not hand-out any error state, which can be a big relief on the call-side. Instead, the frontend implements a [verbose mode](#verbose-mode) to inform about unexpected input or an error captured from the backend. Guiding principles of LIBXSMM are muted operation by default (non-verbose) and no unexpected exit from execution.

### Verbose Mode

The [verbose mode](documentation/libxsmm_aux.md#getting-and-setting-the-verbosity) (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:

```bash
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&#160;&lt;=&#160;13), medium-sized kernels (13&#160;&lt;&#160;MNK1/3&#160;&lt;=&#160;23), and larger kernels (23&#160;&lt;&#160;MNK1/3&#160;&lt;=&#160;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*)&#160;=&#160;105) of the code registry is exhausted, no more kernels can be registered although further attempts are not prevented. Registering many kernels (O(*n*)&#160;=&#160;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.

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

If the call-wrapper is used, an additional runtime statistic becomes available (see [Call Wrapper](documentation/libxsmm_mm.md#call-wrapper)).

<a name="objdump"></a>**Note**: Setting LIBXSMM_VERBOSE to a negative value dumps each generated JIT kernel to a file (binary) with each file being named like the function name shown in [Intel VTune](documentation/libxsmm_prof.md#intelvtuneamplifier). Disassembly of the raw binary files can be accomplished by:

```bash
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):

```bash
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.

```bash
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.

### Verification

This section refers to testing correctness of an application using LIBXSMM utilities, i.e., using `libxsmm_matdiff` or `libxsmm_matdiff_epsilon` in particular. The former function (`libxsmm_matdiff`) compares two matrices (which can degenerate to vector shape), and yields a structure with information about the difference of both matrices (gold vs. test). The latter function (`libxsmm_matdiff_epsilon`) combines absolute and relative norms (given by afore mentioned structure) and calculates a scalar "epsilon" which can be used to check against a margin.

Using `libxsmm_matdiff_epsilon` in an application exposes an environment variable `LIBXSMM_MATDIFF` which can specify a file or directory path (`LIBXSMM_MATDIFF=1` simply uses some filename as default). In any case, the application appends one line to the respective file for each call of `libxsmm_matdiff_epsilon`. A data record consists of the epsilon and the command line used to launch the application. A generated file can be further evaluated, e.g., `sort -gk1 libxsmm_matdiff.log | tail -n 10` which yields the largest ten epsilon values discovered along with the application's command line.

The environment variable `LIBXSMM_MATDIFF` can carry optional space-separated arguments to amend each file entry like `export LIBXSMM_MATDIFF="libxsmm_matdiff.log hello world"`. In sophisticated cases this can be used to amend a value only known at runtime, e.g., the actual margin which is used to judge the epsilon (`putenv`).

## Performance

<a name="profiling"></a>Profiling an application, which uses LIBXSMM's JIT-code is well-supported. The library supports Intel&#160;VTune&#160;Amplifier and Linux&#160;perf. Details are given on how to include profiler support, and how to run the application.

* [Profiling using Intel VTune Amplifier](documentation/libxsmm_prof.md#intelvtuneamplifier)
* [Profiling using Linux perf](documentation/libxsmm_prof.md#linuxperf)

<a name="tuning"></a>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.

* [Customizing performance](documentation/libxsmm_tune.md#tuning)
* <a name="auto-dispatch"></a>[Tuning auto-dispatch](documentation/libxsmm_tune.md#auto-dispatch)

## Applications

### High Performance Computing (HPC)

[1]&#160;[https://cp2k.org/](https://cp2k.org/): Open Source Molecular Dynamics and the [DBCSR library](https://github.com/cp2k/dbcsr), which processes batches of small matrix multiplications. The batches originate from a distributed block-sparse matrix with problem-specific small matrices. Starting with [CP2K&#160;3.0](https://www.cp2k.org/version_history), LIBXSMM can substitute CP2K's `libsmm` library.

[2]&#160;[https://github.com/SeisSol/SeisSol/](https://github.com/SeisSol/SeisSol/): 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 [https://github.com/TUM-I5/seissol_kernels/](https://github.com/TUM-I5/seissol_kernels/).

[3]&#160;[https://github.com/NekBox/NekBox](https://github.com/NekBox/NekBox): NekBox is a highly scalable and portable spectral element code, which is inspired by the [Nek5000](https://nek5000.mcs.anl.gov/) code. NekBox is specialized for box geometries and intended to prototype new methods as well as to leverage FORTRAN beyond the FORTRAN&#160;77 standard. LIBXSMM can be used to substitute the [MXM_STD](https://github.com/Nek5000/NekBox/blob/box/mxm_std.F90) code.

[4]&#160;[https://github.com/Nek5000/Nek5000](https://github.com/Nek5000/Nek5000): Nek5000 is the open-source, highly-scalable, always-portable spectral element code from [https://nek5000.mcs.anl.gov/](https://nek5000.mcs.anl.gov/). The development branch of the Nek5000 code [incorporates](https://github.com/Nek5000/Nek5000/blob/master/core/mxm_wrapper.f) LIBXSMM.

[5]&#160;[https://www.pyfr.org/](https://www.pyfr.org/): PyFR is an open-source Python based framework for solving advection-diffusion type problems on streaming architectures by using the flux reconstruction approach. PyFR incorporates LIBXSMM as a matrix multiplication provider for the OpenMP backend.

[6]&#160;[http://dial3343.org/about/](http://dial3343.org/about/): The Extreme-scale Discontinuous Galerkin Environment (EDGE) is a solver for hyperbolic partial differential equations with emphasis on seismic simulations. The EDGE [source code](https://github.com/3343/edge) optionally relies on LIBXSMM, but for high performance LIBXSMM's kernels are highly recommended.

[7]&#160;[https://sxs-collaboration.github.io/spectre/](https://sxs-collaboration.github.io/spectre/): 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]&#160;[https://ceed.exascaleproject.org/ceed-code/](https://ceed.exascaleproject.org/ceed-code/): The Center for Efficient Exascale Discretizations (CEED) is building on the efforts of the Nek5000, MFEM, MAGMA, OCCA and PETSc [10] 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](https://ceed.exascaleproject.org/libceed/) uses LIBXSMM as a [backend](https://github.com/CEED/libCEED#backends) for high performance on CPUs.

[9]&#160;[https://github.com/romeric/Fastor](https://github.com/romeric/Fastor): Fastor is a lightweight high performance tensor algebra framework for modern C++ and can optionally use LIBXSMM as [JIT-backend](https://github.com/romeric/Fastor/wiki/9.-Using-the-LIBXSMM-MKL-JIT-backend).

[10]&#160;[https://petsc.org/](https://petsc.org/): The Portable, Extensible Toolkit for Scientific Computation (PETSc) can use LIBXSMM for sparse block matrix times dense matrix product kernels to deliver high intra-process performance, while PETSc handles MPI communications across processes.

### Machine and Deep Learning (AI)

[11]&#160;[https://github.com/plaidml/plaidml](https://github.com/plaidml/plaidml): PlaidML is an open source tensor compiler aiming for performance portability across a wide range of CPUs, GPUs and other accelerators. Combined with Intel’s nGraph compiler, PlaidML is targeting popular deep learning frameworks such as PyTorch, Keras (TensorFlow), and OpenVino. [PlaidML/v1](https://github.com/plaidml/plaidml/tree/plaidml-v1) (development branch) adopted [MLIR](https://mlir.llvm.org/), an extensible compiler infrastructure gaining industry-wide adoption. PlaidML/v1 started using LIBXSMM as backend for targeting CPUs.

[12]&#160;[https://github.com/intel/intel-extension-for-pytorch](https://github.com/intel/intel-extension-for-pytorch): Intel Extension for PyTorch aims for a smooth user experience of PyTorch on CPUs by the means of good performance. The extension pack started to rely on [LIBXSMM for achieving high performance on CPUs](https://arxiv.org/abs/2005.04680).

[13]&#160;[https://github.com/libxsmm/tpp-pytorch-extension](https://github.com/libxsmm/tpp-pytorch-extension): Intel(R) Tensor Processing Primitive Extension for pytorch is an open source software library the integrates Tensor Processing Primitives ([TPP](https://arxiv.org/abs/2104.05755)) into pytorch. It is aiming for a smooth user experience of PyTorch on CPUs by the means of good performance. Intel's MLPerf Training submission codes leverage this [project](https://github.com/mlcommons/training_results.1/tree/main/Intel/benchmarks/bert/implementations/pytorch-cpu).

[14]&#160;[https://github.com/libxsmm/libxsmm-dnn](https://github.com/libxsmm/libxsmm-dnn): LIBXSMM-DNN is an open source software library that demonstrates how Tensor Processing Primitives ([TPP](https://arxiv.org/abs/2104.05755)) can be used to implement various deep learning primitives such as convolutions, linear layers or even pooling and norming. Due to the use of TPP not a single line of platform-specific code is needed.

### Automated Driving (AD)

[16]&#160;[https://software.seek.intel.com/accelerating-eigen-math-library](https://software.seek.intel.com/accelerating-eigen-math-library): Accelerating The Eigen Math Library for Automated Driving Workloads: The Need for Speed in Kalman Filtering. An article in [Issue&#160;31](https://software.intel.com/content/www/us/en/develop/download/parallel-universe-magazine-issue-31-january-2018.html) of The Parallel Universe magazine ([pdf](https://software.intel.com/content/dam/develop/public/us/en/documents/parallel-universe-issue-31.pdf)).

## References

[1]&#160;[https://sc19.supercomputing.org/proceedings/tech_poster/tech_poster_pages/rpost244.html](https://sc19.supercomputing.org/proceedings/tech_poster/tech_poster_pages/rpost244.html): High-Performance Deep Learning via a Single Building Block ([poster](https://sc19.supercomputing.org/proceedings/tech_poster/poster_files/rpost244s2-file2.pdf) and [abstract](https://sc19.supercomputing.org/proceedings/tech_poster/poster_files/rpost244s2-file3.pdf)), SC’19: The International Conference for High Performance Computing, Networking, Storage, and Analysis, Denver (Colorado).

[2]&#160;[https://dl.acm.org/doi/10.1109/SC.2018.00069](https://dl.acm.org/doi/10.1109/SC.2018.00069): Anatomy of High-Performance Deep Learning Convolutions on SIMD Architectures ([paper](https://arxiv.org/pdf/1808.05567.pdf)). SC'18: The International Conference for High Performance Computing, Networking, Storage, and Analysis, Dallas (Texas).

[3]&#160;[https://pasc17.pasc-conference.org/fileadmin/user_upload/pasc17/program/post116s2.pdf](https://pasc17.pasc-conference.org/fileadmin/user_upload/pasc17/program/post116s2.pdf): DBCSR: A Sparse Matrix Multiplication Library for Electronic Structure Codes (poster), PASC’17: The PASC17 Conference, Lugano (Switzerland).

[4]&#160;[https://sc17.supercomputing.org/SC17%20Archive/tech_poster/tech_poster_pages/post190.html](https://sc17.supercomputing.org/SC17%20Archive/tech_poster/tech_poster_pages/post190.html): Understanding the Performance of Small Convolution Operations for CNN on Intel Architecture ([poster](https://sc17.supercomputing.org/SC17%20Archive/tech_poster/poster_files/post190s2-file2.pdf) and [abstract](https://sc17.supercomputing.org/SC17%20Archive/tech_poster/poster_files/post190s2-file3.pdf)), SC’17: The International Conference for High Performance Computing, Networking, Storage, and Analysis, Denver (Colorado).

[5]&#160;[https://www.computer.org/csdl/proceedings-article/sc/2016/8815a981/12OmNCeaQ1D](https://www.computer.org/csdl/proceedings-article/sc/2016/8815a981/12OmNCeaQ1D): LIBXSMM: Accelerating Small Matrix Multiplications by Runtime Code Generation. SC'16: The International Conference for High Performance Computing, Networking, Storage and Analysis, Salt Lake City (Utah).

[6]&#160;[http://sc15.supercomputing.org/sites/all/themes/SC15images/tech_poster/tech_poster_pages/post137.html](http://sc15.supercomputing.org/sites/all/themes/SC15images/tech_poster/tech_poster_pages/post137.html): LIBXSMM: A High Performance Library for Small Matrix Multiplications ([poster](http://sc15.supercomputing.org/sites/all/themes/SC15images/tech_poster/poster_files/post137s2-file2.pdf) and [abstract](http://sc15.supercomputing.org/sites/all/themes/SC15images/tech_poster/poster_files/post137s2-file3.pdf)). SC'15: The International Conference for High Performance Computing, Networking, Storage and Analysis, Austin (Texas).

[7]&#160;[Tensor Processing Primitives: A Programming Abstraction for Efficiency and Portability in Deep Learning & HPC Workloads](https://arxiv.org/abs/2104.05755) SC'21: The International Conference for High Performance Computing, Networking, Storage and Analysis, St Louis.

## Articles

[1]&#160;[https://www.nextplatform.com/2019/10/09/cloudy-supercomputers-join-the-hpc-petascale-club/](https://www.nextplatform.com/2019/10/09/cloudy-supercomputers-join-the-hpc-petascale-club/): Cloudy Supercomputers Join the HPC Petascale Club. An article written by Rob Farber, 2019. The article covers LIBXSMM in a separate section.

[2]&#160;[https://www.nextplatform.com/2019/06/26/counting-the-cost-of-scaling-hpc-applications/](https://www.nextplatform.com/2019/06/26/counting-the-cost-of-scaling-hpc-applications/): Counting The Cost Of Scaling HPC Applications. An article written by Timothy Prickett Morgan, 2019. This article is about CP2K Open Source Molecular Dynamics and not about LIBXSMM. However, LIBXSMM was key for application performance.

[3]&#160;[https://www.nextplatform.com/2019/06/26/counting-the-cost-of-scaling-hpc-applications/](https://www.nextplatform.com/2019/06/26/counting-the-cost-of-scaling-hpc-applications/): Azure Benchmarks HC-series Across Twenty-thousand Cores for HPC. An article written by John Russell, 2019. This article is about CP2K Open Source Molecular Dynamics and not about LIBXSMM. However, LIBXSMM was key for application performance.

[4]&#160;[https://software.intel.com/sites/default/files/parallel-universe-issue-34.pdf](https://software.intel.com/content/www/us/en/develop/download/parallel-universe-magazine-issue-34-october-2018.html): LIBXSMM: An Open Source-Based Inspiration for Hardware and Software Development at Intel ([pdf](https://software.intel.com/content/dam/develop/public/us/en/documents/parallel-universe-issue-34.pdf)). An article written by Hans Pabst, Greg Henry, and Alexander Heinecke, 2018.

[5]&#160;[https://medium.com/@rmfarber/libxsmm-brings-deep-learning-lessons-learned-to-many-hpc-applications-9143c6c93125](https://medium.com/@rmfarber/libxsmm-brings-deep-learning-lessons-learned-to-many-hpc-applications-9143c6c93125): LIBXSMM Brings Deep-learning "Lessons Learned" to Many HPC Applications. An article written by Rob Farber, 2018.

[6]&#160;[https://www.rdworldonline.com/largest-supercomputer-simulation-of-sumatra-andaman-earthquake/](https://www.rdworldonline.com/largest-supercomputer-simulation-of-sumatra-andaman-earthquake/): Largest Supercomputer Simulation of Sumatra-Andaman Earthquake. An article written by Linda Barney, 2018.

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