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(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.
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.
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.
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).
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 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.
Loop-invariant code motion – this can vastly improve efficiency by moving a computation from inside the loop to outside of it, computing a value just once before the loop begins, if the resultant quantity of the calculation will be the same for every loop iteration (i.e., a loop-invariant quantity). This is particularly important with address ...