How Vector Processors Work: An Example Best to understand a vector processor by looking at a vector loop for RV$64$V$.$ Let$$s take a typical vector problem, which we use throughout this section:

Y $=$ a X $+$ Y

X and Y are vectors, initially resident in memory, and a is a scalar. This problem is the SAXPY or DAXPY loop that forms the inner loop of the Linpack benchmark $($Dongarra et al$.,2003).($SAXPY stands for single$-$precision aX plus Y$,$ and DAXPY for double precision aX plus Y$.)$ Linpack is a collection of linear algebra routines, and the Linpack benchmark consists of routines for performing Gaussian elimination.

For now, let us assume that the number of elements, or length, of a vector register $(32)$ matches the length of the vector operation we are interested in$.($This restriction will be lifted shortly.$)$

Suppose we have $8$ memory banks with a bank busy time of $6$ clocks and a total memory latency of $12$ cycles. How long will it take to complete a $64-$element vector load with a stride of $1?$ With a stride of $32?$