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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.
For example, the feasible set defined by the constraint set {x ≥ 0, y ≥ 0} is unbounded because in some directions there is no limit on how far one can go and still be in the feasible region. In contrast, the feasible set formed by the constraint set { x ≥ 0, y ≥ 0, x + 2 y ≤ 4} is bounded because the extent of movement in any ...
Some engineering applications of SOCP include filter design, antenna array weight design, truss design, and grasping force optimization in robotics. [4] Applications in quantitative finance include portfolio optimization ; some market impact constraints, because they are not linear, cannot be solved by quadratic programming but can be ...
A diagram depicting an optimizing compiler removing a potentially useless call to assembly instruction "b" by sinking it to its point of use. Code Sinking, also known as lazy code motion, is a term for a technique that reduces wasted instructions by moving instructions to branches in which they are used: [1] If an operation is executed before a branch, and only one of the branch paths use the ...
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.
Superoptimization is the process where a compiler automatically finds the optimal sequence for a loop-free sequence of instructions. Real-world compilers generally cannot produce genuinely optimal code, and while most standard compiler optimizations only improve code partly, a superoptimizer's goal is to find the optimal sequence, the canonical form.
The boundaries of the polytopes, the data dependencies, and the transformations are often described using systems of constraints, and this approach is often referred to as a constraint-based approach to loop optimization. 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 ...
In compiler construction, strength reduction is a compiler optimization where expensive operations are replaced with equivalent but less expensive operations. [1] The classic example of strength reduction converts strong multiplications inside a loop into weaker additions – something that frequently occurs in array addressing.