Low-precision matrix multiplication
C++ Python Other
Latest commit bc3491e Jan 10, 2017 @bjacob bjacob committed on GitHub Merge pull request #66 from bjacob/generalize-usage-of-correct-roundi…

Generalize usage of correct rounding shifts in output stages.


gemmlowp: a small self-contained low-precision GEMM library

This is not a full linear algebra library, only a GEMM library: it only does general matrix multiplication ("GEMM").

The meaning of "low precision" is detailed in this document: doc/low-precision.md

Some of the general design is explained in doc/design.md.


This is not an official Google product (experimental or otherwise), it is just code that happens to be owned by Google.

Mailing list

gemmlowp-related discussion, about either development or usage, is welcome on this Google Group (mailing list / forum):


Portability, target platforms/architectures

Should be portable to any platform with some C++11 and POSIX support, while we have optional optimized code paths for specific architectures.


  • C++11 (a small conservative subset of it)

Required for some features:

  • Some POSIX interfaces:
    • pthreads (for multi-threaded operation and for profiling).
    • sysconf (for multi-threaded operation to detect number of cores; may be bypassed).


  • Architecture-specific code paths use intrinsics or inline assembly. See "Architecture-specific optimized code paths" below.

Architecture-specific optimized code paths

We have some optimized code paths for specific instruction sets. Some are written in inline assembly, some are written in C++ using intrinsics. Both GCC and Clang are supported.

Current optimized code paths:

  • ARM with NEON (both 32bit and 64bit).
  • Intel x86 with SSE 4.1 (both 32bit and 64bit).

If you are building for x86, it's important that you pass in the -msse4.1 compiler flag when building, or you'll end up using slow reference code. If you're building with Bazel, you can do this by running bazel build gemmlowp:all --copt=-msse4.1. If you're building for a machine with no SIMD support in gemmlowp then by default you'll see an error. If you want to run with the reference implementations anyway, you can override the error by specifying GEMMLOWP_ALLOW_SLOW_SCALAR_FALLBACK as a build define.

Details of what it takes to make an efficient port of gemmlowp, namely writing a suitable GEMM kernel and accompanying packing code, are explained in this file: doc/kernel.md.

Public interfaces

The gemmlowp public interface

gemmlowp's main public interface is in the public/ subdirectory.

This is a headers-only library, so there is nothing to link to.

Usage documentation, and comments on the deprecation status of each public entry point, may be found in doc/public.md .

A full, self-contained usage example, showing how to quantize float matrices and perform a quantized matrix multiplication approximating a float matrix multiplication, is given in doc/quantization_example.cc.

Old EightBitIntGemm legacy deprecated interface

The eight_bit_int_gemm/ subdirectory contains an alternate interface that should be considered purely legacy, deprecated, and going to be removed at some point in the future.


Building by manually invoking your compiler

Because gemmlowp is so simple, working with it involves only single-command-line compiler invocations. Therefore we expect that most people working with gemmlowp will either manually invoke their compiler, or write their own rules for their own preferred build system.

Keep in mind (previous section) that gemmlowp itself is a pure-headers-only library so there is nothing to build.

For a Android gemmlowp development workflow, the scripts/ directory contains a script to build and run a program on an Android device:


Building using Bazel

That being said, we also maintain a Bazel BUILD system as part of gemmlowp. Its usage is not mandatory at all and is only one possible way that gemmlowp libraries and tests may be built. If you are interested, Bazel's home page is http://bazel.build/ And you can get started with using Bazel to build gemmlowp targets by first creating an empty WORKSPACE file in a parent directory, for instance:

$ cd gemmlowp/..  # change to parent directory containing gemmlowp/
$ touch WORKSPACE # declare that to be our workspace root
$ bazel build gemmlowp:all


Testing by manually building and running tests

The test/ directory contains unit tests. The primary unit test is


Since it covers also the EightBitIntGemm interface, it needs to be linked against


It also uses realistic data captured from a neural network run in


Thus you'll want to pass the following list of source files to your compiler/linker:


The scripts/ directory contains a script to build and run a program on an Android device:


It expects the CXX environment variable to point to an Android toolchain's C++ compiler, and expects source files (and optionally, cflags) as command-line parameters. To build and run the above-mentioned main unit test, first set CXX e.g.:

$ export CXX=/some/toolchains/arm-linux-androideabi-4.8/bin/arm-linux-androideabi-g++

Then run:

$ ./scripts/test-android.sh \
test/test.cc \
eight_bit_int_gemm/eight_bit_int_gemm.cc \

Testing using Bazel

Alternatively, you can use Bazel to build and run tests. See the Bazel instruction in the above section on building. Once your Bazel workspace is set up, you can for instance do:

$ bazel test gemmlowp:all

Troubleshooting Compilation

If you're having trouble finding the compiler, follow these instructions to build a standalone toolchain: https://developer.android.com/ndk/guides/standalone_toolchain.html

Here's an example of setting up Clang 3.5:

$ export INSTALL_DIR=~/toolchains/clang-21-stl-gnu
$ $NDK/build/tools/make-standalone-toolchain.sh \
--toolchain=arm-linux-androideabi-clang3.5 --platform=android-21 \
$ export CXX="$INSTALL_DIR/bin/arm-linux-androideabi-g++ \

Some compilers (e.g. the default clang++ in the same bin directory) don't support NEON assembly. The benchmark build process will issue a warning if support isn't detected, and you should make sure you're using a compiler like arm-linux-androideabi-g++ that does include NEON.


The main benchmark is


It doesn't need to be linked to any other source file. We recommend building with assertions disabled (-DNDEBUG).

For example, the benchmark can be built and run on an Android device by doing:

$ ./scripts/test-android.sh test/benchmark.cc -DNDEBUG

If GEMMLOWP_TEST_PROFILE is defined then the benchmark will be built with profiling instrumentation (which makes it slower) and will dump profiles. See next section on profiling.


The profiling/ subdirectory offers a very simple, naive, inaccurate, non-interrupting sampling profiler that only requires pthreads (no signals).

It relies on source code being instrumented with pseudo-stack labels. See profiling/instrumentation.h. A full example of using this profiler is given in the top comment of profiling/profiler.h.


Contribution-related discussion is always welcome on the gemmlowp mailing list (see above).

We try to keep a current list of TODO items in the todo/ directory. Prospective contributors are welcome to pick one to work on, and communicate about it on the gemmlowp mailing list.

Details of the contributing process, including legalese, are in CONTRIBUTING.

Performance goals

Our performance goals differ from typical GEMM performance goals in the following ways:

  1. We care not only about speed, but also about minimizing power usage. We specifically care about charge usage in mobile/embedded devices. This implies that we care doubly about minimizing memory bandwidth usage: we care about it, like any GEMM, because of the impact on speed, and we also care about it because it is a key factor of power usage.

  2. Most GEMMs are optimized primarily for large dense matrix sizes (>= 1000). We do care about large sizes, but we also care specifically about the typically smaller matrix sizes encountered in various mobile applications. This means that we have to optimize for all sizes, not just for large enough sizes.