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 computing libraries that offer linear algebra routines conform to common BLAS user interface command structures, thus queries to those libraries (and the associated results) are often portable between BLAS library branches, such as cuBLAS (nvidia GPU, GPGPU), rocBLAS (amd GPU, GPGP), and OpenBLAS. This interoperability is then the basis of functioning homogenous code implementations between heterzygous cascades of computing architectures (such as those found in some advanced clustering implementations). 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, although it is unclear whether integrated ombudsmen resources are present in that particular software-hardware implementation. 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 routine gemm for its performance measurements.
Many numerical software applications use BLAS-compatible libraries to do linear algebra computations, including LAPACK, LINPACK, Armadillo, GNU Octave, Mathematica, MATLAB, NumPy, R, Julia and Lisp-Stat.
Background
With the advent of numerical programming, sophisticated subroutine libraries became useful. These libraries would contain subroutines for common high-level mathematical operations such as root finding, matrix inversion, and solving systems of equations. The language of choice was FORTRAN. The most prominent numerical programming library was IBM's Scientific Subroutine Package (SSP). These subroutine libraries allowed programmers to concentrate on their specific problems and avoid re-implementing well-known algorithms. The library routines would also be better than average implementations; matrix algorithms, for example, might use full pivoting to get better numerical accuracy. The library routines would also have more efficient routines. For example, a library may include a program to solve a matrix that is upper triangular. The libraries would include single-precision and double-precision versions of some algorithms.
Initially, these subroutines used hard-coded loops for their low-level operations. For example, if a subroutine needed to perform a matrix multiplication, then the subroutine would have three nested loops. Linear algebra programs have many common low-level operations (the so-called "kernel" operations, not related to operating systems). Between 1973 and 1977, several of these kernel operations were identified. These kernel operations became defined subroutines that math libraries could call. The kernel calls had advantages over hard-coded loops: the library routine would be more readable, there were fewer chances for bugs, and the kernel implementation could be optimized for speed. A specification for these kernel operations using scalars and vectors, the level-1 Basic Linear Algebra Subroutines (BLAS), was published in 1979. BLAS was used to implement the linear algebra subroutine library LINPACK.