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The following tables list the computational complexity of various algorithms for common mathematical operations . Here, complexity refers to the time complexity of performing computations on a multitape Turing machine. [ 1] See big O notation for an explanation of the notation used. Note: Due to the variety of multiplication algorithms, below ...
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 ...
Order of operations. In mathematicsand computer programming, the order of operationsis a collection of rules that reflect conventions about which operations to perform first in order to evaluate a given mathematical expression. These rules are formalized with a ranking of the operations. The rank of an operation is called its precedence, and an ...
Memory ordering. Memory ordering is the order of accesses to computer memory by a CPU. Memory ordering depends on both the order of the instructions generated by the compiler at compile time and the execution order of the CPU at runtime. [ 1][ 2] However, memory order is of little concern outside of multithreading and memory-mapped I/O, because ...
Fast multipole method. The fast multipole method ( FMM) is a numerical technique that was developed to speed up the calculation of long-ranged forces in the n -body problem. It does this by expanding the system Green's function using a multipole expansion, which allows one to group sources that lie close together and treat them as if they are a ...
Multiple inheritance is a frequent occurrence in Eiffel development; most of the effective classes in the widely used EiffelBase library of data structures and algorithms, for example, have two or more parents. [7] Goprevents the diamond problem at compile time.
The FMA instruction set is an extension to the 128 and 256-bit Streaming SIMD Extensions instructions in the x86 microprocessor instruction set to perform fused multiply–add (FMA) operations. [ 1] There are two variants: FMA4 is supported in AMD processors starting with the Bulldozer architecture. FMA4 was performed in hardware before FMA3 was.
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 ...