💥 Fast matrix-multiplication as a self-contained Python library – no system dependencies!

blas, blas-libraries, blis, cython, linear-algebra, matrix-multiplication, neural-network, neural-networks, numpy, openblas
conda install -c anaconda cython-blis


Cython BLIS: Fast BLAS-like operations from Python and Cython, without the tears

This repository provides the Blis linear algebra routines as a self-contained Python C-extension.

Currently, we only supports single-threaded execution, as this is actually best for our workloads (ML inference).

Travis Appveyor pypi Version conda Python wheels


You can install the package via pip:

pip install blis

Wheels should be available, so installation should be fast. If you want to install from source and you're on Windows, you'll need to install LLVM.

Building BLIS for alternative architectures

The provided wheels should work on x86_86 architectures. Unfortunately we do not currently know a way to provide different wheels for alternative architectures, and we cannot provide a single binary that works everywhere. So if the wheel doesn't work for your CPU, you'll need to specify source distribution, and tell Blis your CPU architecture using the BLIS_ARCH environment variable.

a) Installing with generic arch support

BLIS_ARCH="generic" pip install spacy --no-binary blis

b) Building specific support

In order to compile Blis, cython-blis bundles makefile scripts for specific architectures, that are compiled by running the Blis build system and logging the commands. We do not yet have logs for every architecture, as there are some architectures we have not had access to.

See here for list of architectures. For example, here's how to build support for the ARM architecture cortexa57:

git clone && cd cython-blis
git pull && git submodule init && git submodule update && git submodule status
python3 -m venv env3.6
source env3.6/bin/activate
pip install -r requirements.txt
./bin/generate-make-jsonl linux cortexa57
BLIS_ARCH="cortexa57" python build_ext --inplace
BLIS_ARCH="cortexa57" python bdist_wheel

Fingers crossed, this will build you a wheel that supports your platform. You could then submit a PR with the blis/_src/make/linux-cortexa57.jsonl and blis/_src/include/linux-cortexa57/blis.h files so that you can run:

BLIS_ARCH=cortexa57 pip install spacy --no-binary=blis

Running the benchmark

After installation, run a small matrix multiplication benchmark:

$ export OMP_NUM_THREADS=1 # Tell Numpy to only use one thread.
$ python -m blis.benchmark
Setting up data nO=384 nI=384 batch_size=2000. Running 1000 iterations
Total: 11032014.6484
7.35 seconds
Numpy (Openblas)...
Total: 11032016.6016
16.81 seconds
Blis einsum ab,cb->ca
8.10 seconds
Numpy einsum ab,cb->ca
Total: 5510596.19141
83.18 seconds

The low numpy.einsum performance is expected, but the low performance is surprising. Linking numpy against MKL gives better performance:

Numpy (mkl_rt) gemm...
Total: 11032011.71875
5.21 seconds

These figures refer to performance on a Dell XPS 13 i7-7500U. Running the same benchmark on a 2015 MacBook Air gives:

Total: 11032014.6484
8.89 seconds
Numpy (Accelerate)...
Total: 11032012.6953
6.68 seconds

Clearly the Dell's numpy+OpenBLAS performance is the outlier, so it's likely something has gone wrong in the compilation and architecture detection.


Two APIs are provided: a high-level Python API, and direct Cython access. The best part of the Python API is the einsum function, which works like numpy's, but with some restrictions that allow a direct mapping to Blis routines. Example usage:

from import einsum
from numpy import ndarray, zeros

dim_a = 500
dim_b = 128
dim_c = 300
arr1 = ndarray((dim_a, dim_b))
arr2 = ndarray((dim_b, dim_c))
out = zeros((dim_a, dim_c))

einsum('ab,bc->ac', arr1, arr2, out=out)
# Change dimension order of output
out = einsum('ab,bc->ca', arr1, arr2)
assert out.shape == (dim_a, dim_c)
# Matrix vector product, with transposed output
arr2 = ndarray((dim_b,))
out = einsum('ab,b->ba', arr1, arr2)
assert out.shape == (dim_b, dim_a)

The Einstein summation format is really awesome, so it's always been disappointing that it's so much slower than equivalent calls to tensordot in numpy. The blis.einsum function gives up the numpy version's generality, so that calls can be easily mapped to Blis:

  • Only two input tensors
  • Maximum two dimensions
  • Dimensions must be labelled a, b and c
  • The first argument's dimensions must be 'a' (for 1d inputs) or 'ab' (for 2d inputs).

With these restrictions, there are ony 15 valid combinations – which correspond to all the things you would otherwise do with the gemm, gemv, ger and axpy functions. You can therefore forget about all the other functions and just use the einsum. Here are the valid einsum strings, the calls they correspond to, and the numpy equivalents:

Equation Maps to Numpy
'a,a->a' axpy(A, B) A+B
'a,b->ab' ger(A, B) outer(A, B)
'a,b->ba' ger(B, A) outer(B, A)
'ab,a->ab' batch_axpy(A, B) A*B
'ab,a->ba' batch_axpy(A, B, trans1=True) (A*B).T
'ab,b->a' gemv(A, B) A*B
'ab,a->b' gemv(A, B, trans1=True) A.T*B
'ab,ac->cb' gemm(B, A, trans1=True, trans2=True) dot(B.T, A)
'ab,ac->bc' gemm(A, B, trans1=True, trans2=False) dot(A.T, B)
'ab,bc->ac' gemm(A, B, trans1=False, trans2=False) dot(A, B)
'ab,bc->ca' gemm(B, A, trans1=False, trans2=True) dot(B.T, A.T)
'ab,ca->bc' gemm(A, B, trans1=True, trans2=True) dot(B, A.T)
'ab,ca->cb' gemm(B, A, trans1=False, trans2=False) dot(B, A)
'ab,cb->ac' gemm(A, B, trans1=False, trans2=True) dot(A.T, B.T)
'ab,cb->ca' gemm(B, A, trans1=False, trans2=True) dot(B, A.T)

We also provide fused-type, nogil Cython bindings to the underlying Blis linear algebra library. Fused types are a simple template mechanism, allowing just a touch of compile-time generic programming:

A = <float*>calloc(nN * nI, sizeof(float))
B = <float*>calloc(nO * nI, sizeof(float))
C = <float*>calloc(nr_b0 * nr_b1, sizeof(float)),,
             nO, nI, nN,
             1.0, A, nI, 1, B, nO, 1,
             1.0, C, nO, 1)

Bindings have been added as we've needed them. Please submit pull requests if the library is missing some functions you require.


To build the source package, you should run the following command:


This populates the blis/_src folder for the various architectures, using the flame-blis submodule.

Updating the build files

In order to compile the Blis sources, we use jsonl files that provide the explicit compiler flags. We build these jsonl files by running Blis's build system, and then converting the log. This avoids us having to replicate the build system within Python: we just use the jsonl to make a bunch of subprocess calls. To support a new OS/architecture combination, we have to provide the jsonl file and the header.


The Linux build files need to be produced from within the manylinux1 docker container, so that they will be compatible with the wheel building process.

First, install docker. Then do the following to start the container:

sudo docker run -it

Once within the container, the following commands should check out the repo and build the jsonl files for the generic arch:

mkdir /usr/local/repos
cd /usr/local/repos
git clone && cd cython-blis
git pull && git submodule init && git submodule update && git submodule
/opt/python/cp36-cp36m/bin/python -m venv env3.6
source env3.6/bin/activate
pip install -r requirements.txt
./bin/generate-make-jsonl linux generic --export
BLIS_ARCH=generic python build_ext --inplace
# N.B.: don't copy to /tmp, docker cp doesn't work from there.
cp blis/_src/include/linux-generic/blis.h /linux-generic-blis.h
cp blis/_src/make/linux-generic.jsonl /

Then from a new terminal, retrieve the two files we need out of the container:

sudo docker ps -l # Get the container ID
# When I'm in Vagrant, I need to go via cat -- but then I end up with dummy
# lines at the top and bottom. Sigh. If you don't have that problem and
# sudo docker cp just works, just copy the file.
sudo docker cp aa9d42588791:/linux-generic-blis.h - | cat > linux-generic-blis.h
sudo docker cp aa9d42588791:/linux-generic.jsonl - | cat > linux-generic.jsonl