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BLAS (Basic Linear Algebra Subprograms) 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 and Fortran. 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. Most libraries that offer linear algebra routines conform to the BLAS interface, allowing library users to develop programs that are agnostic of the BLAS library being used. Examples of such libraries include: AMD Core Math Library (ACML), ATLAS, Intel Math Kernel Library (MKL), and OpenBLAS. ACML is no longer supported. MKL 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. ATLAS is a portable library that automatically optimizes itself for an arbitrary architecture. The LINPACK benchmarks rely heavily on the BLAS routine gemm for its performance measurements.Much numerical software uses BLAS-compatible libraries to do linear algebra computations, including Armadillo, LAPACK, LINPACK, GNU Octave, Mathematica, MATLAB, NumPy, and R. ==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 need 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).〔Even the SSP (which appeared around 1966) had some basic routines such as RADD (add rows), CADD (add columns), SRMA (scale row and add to another row), and RINT (row interchange). These routines apparently were not used as kernel operations to implement other routines such as matrix inversion. See .〕 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 subrouting library LINPACK. The BLAS abstraction allows customization for high performance. For example, LINPACK is a general purpose library that can be used on many different machines without modification. LINPACK could use a generic version of BLAS. To gain performance, different machines might use tailored versions of BLAS. As computer architectures became more sophisticated, vector machines appeared. BLAS for a vector machine could use the machine's fast vector operations. (While vector processors eventually fell out of favor, vector instructions in modern CPUs are essential for optimal performance in BLAS routines.) Other machine features became available and could also be exploited. Consequently, BLAS was augmented from 1984 to 1986 with level-2 kernel operations that concerned vector-matrix operations. Memory hierarchy was also recognized as something to exploit. Many computers have cache memory that is much faster than main memory; keeping matrix manipulations localized allows better usage of the cache. In 1987 and 1988, the level 3 BLAS were identified to do matrix-matrix operations. The level 3 BLAS encouraged block-partitioned algorithms. The LAPACK library uses level 3 BLAS. The original BLAS concerned only densely stored vectors and matrices. Further extensions to BLAS, such as for sparse matrices, have been addressed. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Basic Linear Algebra Subprograms」の詳細全文を読む スポンサード リンク
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