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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 ...
The code "inside" the loop (the body of the loop, shown below as xxx) is obeyed a specified number of times, or once for each of a collection of items, or until some condition is met, or indefinitely. When one of those items is itself also a loop, it is called a "nested loop". [4] [5] [6]
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 ...
(Nested loops occur when one loop is inside of another loop.) One classical usage is to reduce memory access latency or the cache bandwidth necessary due to cache reuse for some common linear algebra algorithms. The technique used to produce this optimization is called loop tiling, [1] also known as loop blocking [2] or strip mine and interchange.
A causal loop diagram is a simple map of a system with all its constituent components and their interactions. By capturing interactions and consequently the feedback loops (see figure below), a causal loop diagram reveals the structure of a system. By understanding the structure of a system, it becomes possible to ascertain a system's behavior ...
Loop carried dependence graphs (LDG) gives a visual representation of all true dependencies, anti dependencies, and output dependencies that exist between different iterations in a loop. [1] Each iteration is represented with a node. It is easier to show the difference between the two graphs with a nested for loop.
Nested functions can be used for unstructured control flow, by using the return statement for general unstructured control flow.This can be used for finer-grained control than is possible with other built-in features of the language – for example, it can allow early termination of a for loop if break is not available, or early termination of a nested for loop if a multi-level break or ...
Example of a flow diagram of a nuclear submarine propulsion system. Flow diagram is a diagram representing a flow or set of dynamic relationships in a system. The term flow diagram is also used as a synonym for flowchart, [1] and sometimes as a counterpart of the flowchart. [2]