body of the loop multiple times, in order to decrease the number of times the loop condition is tested and the number of jumps, which may degrade performance by impairing the instruction pipeline. Completely unrolling a loop eliminates all overhead (except multiple instruction fetches and increased program load time), but requires that the number of iterations be known at compile time (except in the case of Just-in-time compilation). Care must also be taken to ensure that multiple re-calculation of indexed variables is not a greater overhead than advancing pointers within the original loop. Unswitching – moves a conditional from inside a loop to outside of it by duplicating the loop's body, and placing a version of it inside each of the if and else clauses of the conditional. Sectioning or strip-mining – introduced for vector processors, loop-sectioning is a loop-transformation technique for enabling SIMD (single instruction, multiple data)-encodings of loops and improving memory performance. This involves each vector operation being done for a size less-than or equal-to the maximum vector length on a given vector machine. The unimodular transformation framework The unimodular transformation approach uses a single unimodular matrix to describe the combined result of a sequence of many of the above transformations. Central to this approach is the view of the set of all executions of a statement within n loops as a set of integer points in an n-dimensional space, with the points being executed in lexicographical order. For example, the executions of a statement nested inside an outer loop with index i and an inner loop with index j can be associated with the pairs of integers . The application of a unimodular transformation corresponds to the multiplication of the points within this space by the matrix. For example, the interchange of two loops corresponds to the matrix . A unimodular transformation is legal if it preserves the temporal sequence of all dependencies; measuring the performance impact of a unimodular transformation is more difficult. Imperfectly nested loops and some transformations (such as tiling) do not fit easily into this framework. The polyhedral or constraint-based framework The polyhedral model handles a wider class of programs and transformations than the unimodular framework. The set of executions of a set of statements within a possibly imperfectly nested set of loops is seen as the union of a set of polytopes representing the executions of the statements. Affine transformations are applied