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Microsoft Foundation Class Library. Microsoft Foundation Class Library (MFC) is a C++ object-oriented library for developing desktop applications for Windows. MFC was introduced by Microsoft in 1992 and quickly gained widespread use. While Microsoft has introduced alternative application frameworks since then, MFC remains widely used.
Montgomery modular multiplication relies on a special representation of numbers called Montgomery form. The algorithm uses the Montgomery forms of a and b to efficiently compute the Montgomery form of ab mod N. The efficiency comes from avoiding expensive division operations. Classical modular multiplication reduces the double-width product ab ...
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 ...
The definition of matrix multiplication is that if C = AB for an n × m matrix A and an m × p matrix B, then C is an n × p matrix with entries. From this, a simple algorithm can be constructed which loops over the indices i from 1 through n and j from 1 through p, computing the above using a nested loop: Input: matrices A and B.
Directly applying the mathematical definition of matrix multiplication gives an algorithm that requires n3 field operations to multiply two n × n matrices over that field (Θ (n3) in big O notation). Surprisingly, algorithms exist that provide better running times than this straightforward "schoolbook algorithm".
Exponentiation by squaring. In mathematics and computer programming, exponentiating by squaring is a general method for fast computation of large positive integer powers of a number, or more generally of an element of a semigroup, like a polynomial or a square matrix. Some variants are commonly referred to as square-and-multiply algorithms or ...
CLMUL instruction set. Carry-less Multiplication (CLMUL) is an extension to the x86 instruction set used by microprocessors from Intel and AMD which was proposed by Intel in March 2008 [1] and made available in the Intel Westmere processors announced in early 2010. Mathematically, the instruction implements multiplication of polynomials over ...
The Object Windows Library (OWL) is a C++ object-oriented application framework designed to simplify desktop application development for Windows and (some releases) OS/2.. OWL was introduced by Borland in 1991 and eventually deprecated in 1997 in favor of their Visual Component Library (VCL).