Vectorization

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For vectorization in mathematics, see Vectorization (mathematics). For the use of the term in computer graphics, see Raster to vector.

Vectorization, in computer science, is the process of converting a computer program from a scalar implementation, which does an operation on a pair of operands at a time, to a vectorized program where a single instruction can perform multiple operations on a pair of vector (series of adjacent values) operands. Vector processing is a major feature of both conventional and modern supercomputers.

One major research topic in computer science is the search for methods of automatic vectorization; seeking methods that would allow a compiler to convert scalar programs into vectorized programs without human assistance.

[edit] Automatic vectorization

Automatic vectorization, in the context of a computer program, refers to the automatic transformation of a series of operations performed sequentially, one operation at a time, to operations performed in parallel, several at once, in a manner suitable for processing by a vector processor.

An example would be a program to multiply two vectors of numeric data. A scalar approach would be something like:

 for (i = 0; i < 1024; i++)
 {
    C[i] = A[i]*B[i];
 }

This could be transformed to vectorized code something like:

 for (i = 0; i < 1024; i+=4)
 {
    C[i:i+3] = A[i:i+3]*B[i:i+3];
 }

Here, C[i:i+3] represents the four array elements from C[i] to C[i+3] and we assume that the vector processor can perform four operations for a single vector instruction. Since four operations are performed for an execution time roughly similar to time taken for one scalar instruction, the vector code can run up to four times faster than the original code.

There are two distinct compiler approaches: one based on the conventional vectorization technique and the other based on loop unrolling. Some compilers such as GNU C Compiler and Intel compiler can generate vector instructions automatically.

Vectorization is also used to describe the process of representing (or converting raster bitmap) graphics, text, and images as scale independent affine objects.