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The effectiveness of loop interchange depends on and must be considered in light of the cache model used by the underlying hardware and the array model used by the compiler. In C programming language , array elements in the same row are stored consecutively in memory (a[1,1], a[1,2], a[1,3]) ‒ in row-major order .
Because the entire inner loop is performed for each iteration of the outer loop, optimizations of the inner loop will have much greater effect than optimizations of the outer loop. In many languages there are at least two types of loops – for loops and while loops – and they can be nested within each other. [1]
algorithm nested_loop_join is for each tuple r in R do for each tuple s in S do if r and s satisfy the join condition then yield tuple <r,s> This algorithm will involve n r *b s + b r block transfers and n r +b r seeks, where b r and b s are number of blocks in relations R and S respectively, and n r is the number of tuples in relation R.
The definition of matrix multiplication is that if C = AB for an n × m matrix A and an m × p matrix B, then C is an n × p matrix with entries = =. From this, a simple algorithm can be constructed which loops over the indices i from 1 through n and j from 1 through p, computing the above using a nested loop:
A block-nested loop (BNL) is an algorithm used to join two relations in a relational database. [ 1 ] This algorithm [ 2 ] is a variation of the simple nested loop join and joins two relations R {\displaystyle R} and S {\displaystyle S} (the "outer" and "inner" join operands, respectively).
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 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.
In the C programming language, Duff's device is a way of manually implementing loop unrolling by interleaving two syntactic constructs of C: the do-while loop and a switch statement. Its discovery is credited to Tom Duff in November 1983, when Duff was working for Lucasfilm and used it to speed up a real-time animation program.