πŸ’₯ Fast matrix-multiplication as a self-contained Python library – no system dependencies!
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README.rst

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).

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Overview

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.

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
Blis...
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 numpy.dot 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:

Blis...
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.

Usage

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 blis.py 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->bc' gemm(A, B, trans1=True, trans2=False) dot(A.T, B)
'ab,ac->cb' gemm(B, A, trans1=True, trans2=True) dot(B.T, A)
'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:

cimport blis.cy
A = <float*>calloc(nN * nI, sizeof(float))
B = <float*>calloc(nO * nI, sizeof(float))
C = <float*>calloc(nr_b0 * nr_b1, sizeof(float))
blis.cy.gemm(blis.cy.NO_TRANSPOSE, blis.cy.NO_TRANSPOSE,
             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.

Development

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

./bin/copy-source-files.sh

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