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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.
As a result, the vector processor either gains the ability to perform loops itself, or exposes some sort of vector control (status) register to the programmer, usually known as a vector Length. The self-repeating instructions are found in early vector computers like the STAR-100, where the above action would be described in a single instruction ...
Here, c[i:i+3] represents the four array elements from c[i] to c[i+3] and the vector processor can perform four operations for a single vector instruction. Since the four vector operations complete in roughly the same time as one scalar instruction, the vector approach can run up to four times faster than the original code.
The following simple example demonstrates the advantage of using SSE. Consider an operation like vector addition, which is used very often in computer graphics applications. To add two single precision, four-component vectors together using x86 requires four floating-point addition instructions.
Vectorial addition chains are well suited to perform multi-exponentiation: [1] Input: Elements x 0,...,x k-1 of an abelian group G and a vectorial addition chain of dimension k computing [n 0,...,n k-1] Output:The element x 0 n 0...x k-1 n r-1. for i =-k+1 to 0 do y i → x i+k-1; for i = 1 to s do y i →y j ×y r; return y s
In Python NumPy arrays implement the flatten method, [note 1] while in R the desired effect can be achieved via the c() or as.vector() functions. In R , function vec() of package 'ks' allows vectorization and function vech() implemented in both packages 'ks' and 'sn' allows half-vectorization.
In computer graphics, swizzles are a class of operations that transform vectors by rearranging components. [1] Swizzles can also project from a vector of one dimensionality to a vector of another dimensionality, such as taking a three-dimensional vector and creating a two-dimensional or five-dimensional vector using components from the original vector. [2]
Typical examples of binary operations are the addition (+) and multiplication of numbers and matrices as well as composition of functions on a single set. For instance, For instance, On the set of real numbers R {\displaystyle \mathbb {R} } , f ( a , b ) = a + b {\displaystyle f(a,b)=a+b} is a binary operation since the sum of two real numbers ...