Basic Linear Algebra Subprograms

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Basic Linear Algebra Subprograms (BLAS) is a specification that prescribes a set of low-level routines for performing common linear algebra operations such as vector addition, scalar multiplication, dot products, linear combinations, and matrix multiplication. They are the de facto standard low-level routines for linear algebra libraries; the routines have bindings for both C ("CBLAS interface") and Fortran ("BLAS interface"). Although the BLAS specification is general, BLAS implementations are often optimized for speed on a particular machine, so using them can bring substantial performance benefits. BLAS implementations will take advantage of special floating point hardware such as vector registers or SIMD instructions. It originated as a Fortran library in 1979 and its interface was standardized by the BLAS Technical (BLAST) Forum, whose latest BLAS report can be found on the netlib website. This Fortran library is known as the reference implementation (sometimes confusingly referred to as the BLAS library) and is not optimized for speed but is in the public domain. Most libraries that offer linear algebra routines conform to the BLAS interface, allowing library users to develop programs that are indifferent to the BLAS library being used. Many BLAS libraries have been developed, targeting various different hardware platforms. Examples includes cuBLAS (NVIDIA GPU, GPGPU), rocBLAS (AMD GPU), and OpenBLAS. Examples of CPU-based BLAS library branches include: OpenBLAS, BLIS (BLAS-like Library Instantiation Software), Arm Performance Libraries, ATLAS, and Intel Math Kernel Library (iMKL). AMD maintains a fork of BLIS that is optimized for the AMD platform. ATLAS is a portable library that automatically optimizes itself for an arbitrary architecture. iMKL is a freeware and proprietary vendor library optimized for x86 and x86-64 with a performance emphasis on Intel processors. OpenBLAS is an open-source library that is hand-optimized for many of the popular architectures. The LINPACK benchmarks rely heavily on the BLAS...