Non-linear memory layout transformations and data prefetching ...

2.9 Data Reuse 21Dependence Vector of a nested loop iteration is the dierence between two vectors: the vector⃗j = (j 1 , . . . , j n ), that represents the iteration in issue, and the vector ⃗j ′ = (j 1 ′ , . . . , j n ′ ), thatrepresents the dependent iteration (the results of iteration ⃗j ′ are directly used in processing ofiteration ⃗j).Every dependence vector is represented by an n-dimensional vector: ⃗ d i = (d i1 , . . . , d in ).2.9 Data ReuseSince transformations change iteration order, identifying reuse, guides transformations to exploitlocality. In some cases we need to evaluate dierent kinds of reuse, in order to nd the bestcombination of transformations [WL91].There are four dierent types of reuse.In order to better explain the dierent types of reuse, we will use the following nestedloop, as an example:for (i = 0; i