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The two examples below, written in Python, present a while loop with an inner for loop and a while loop without an inner loop. Although both have the same terminating condition for their while loops, the first example will finish faster because of the inner for loop. The variable innermax is a fraction of the maxticketno variable in the first ...
Loop interchange on this example can improve the cache performance of accessing b(j,i), but it will ruin the reuse of a(i) and c(i) in the inner loop, as it introduces two extra loads (for a(i) and for c(i)) and one extra store (for a(i)) during each iteration. As a result, the overall performance may be degraded after loop interchange.
For example, a single statement within an outer loop ' for i := 0 to n ' and an inner loop ' for j := 0 to i+2 ' is executed once for each (i, j) pair such that 0 <= i <= n and 0 <= j <= i+2. Once again, a transformation is legal if it preserves the temporal sequence of all dependencies. Estimating the benefits of a transformation, or finding ...
The inner loop, on the other hand, is governed by the value of j, which iterates from 1 to i. On the first pass through the outer loop, j iterates from 1 to 1: The inner loop makes one pass, so running the inner loop body (step 6) consumes T 6 time, and the inner loop test (step 5) consumes 2T 5 time.
Loop tiling partitions a loop's iteration space into smaller chunks or blocks, so as to help ensure data used in a loop stays in the cache until it is reused. The partitioning of loop iteration space leads to partitioning of a large array into smaller blocks, thus fitting accessed array elements into cache size, enhancing cache reuse and eliminating cache size requirements.
Loop unrolling, also known as loop unwinding, is a loop transformation technique that attempts to optimize a program's execution speed at the expense of its binary size, which is an approach known as space–time tradeoff. The transformation can be undertaken manually by the programmer or by an optimizing compiler.
The polyhedral method treats each loop iteration within nested loops as lattice points inside mathematical objects called polyhedra, performs affine transformations or more general non-affine transformations such as tiling on the polytopes, and then converts the transformed polytopes into equivalent, but optimized (depending on targeted ...
Loop skewing: By "skewing" the logical shape of an array, this loop optimization can (when combined with loop interchange) eliminate loop-carried dependencies, allowing an inner loop to be parallelized. [citation needed] Loop unswitching moves loop invariants out of a loop, reducing the number of conditional branches in each loop. [1]