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Automatic vectorization, in parallel computing, is a special case of automatic parallelization, where a computer program is converted from a scalar implementation, which processes a single pair of operands at a time, to a vector implementation, which processes one operation on multiple pairs of operands at once.
The following are important identities in vector algebra.Identities that only involve the magnitude of a vector ‖ ‖ and the dot product (scalar product) of two vectors A·B, apply to vectors in any dimension, while identities that use the cross product (vector product) A×B only apply in three dimensions, since the cross product is only defined there.
A two-vector or bivector [1] is a tensor of type () and it is the dual of a two-form, meaning that it is a linear functional which maps two-forms to the real numbers (or more generally, to scalars). The tensor product of a pair of vectors is a two-vector. Then, any two-form can be expressed as a linear combination of tensor products of pairs of ...
With AVX-512F, these instructions can operate on 512-bit vectors, and AVX-512VL further adds support for 128- and 256-bit vectors. A later AVX-VNNI extension adds VEX encodings of these instructions which can only operate on 128- or 256-bit vectors. AVX-VNNI is not part of the AVX-512 suite, it does not require AVX-512F and can be implemented ...
A graph exemplifying merge sort. Two red arrows starting from the same node indicate a split, while two green arrows ending at the same node correspond to an execution of the merge algorithm. The merge algorithm plays a critical role in the merge sort algorithm, a comparison-based sorting algorithm. Conceptually, the merge sort algorithm ...
The three-way merge looks for sections which are the same in only two of the three files. In this case, there are two versions of the section, and the version which is in the common ancestor "C" is discarded, while the version that differs is preserved in the output.
Consider a library representing vectors and operations on them. One common mathematical operation is to add two vectors u and v, element-wise, to produce a new vector.The obvious C++ implementation of this operation would be an overloaded operator+ that returns a new vector object:
In general, two dyadics can be added to get another dyadic, and multiplied by numbers to scale the dyadic. However, the product is not commutative; changing the order of the vectors results in a different dyadic. The formalism of dyadic algebra is an extension of vector algebra to include the dyadic product of vectors. The dyadic product is ...