How would you solve the following problem?

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Design a CUDA program to perform matrix multiplication C$=$A xx B$.$ The size of each

matrix is $1$K xx$1$K$.$ Each element is $1$ byte. The matrices are initially stored in the global

memory of GPU. The GPU has one streaming multiprocessor $($SM$)$ with $1$K CUDA cores.

Each CUDA core runs at $1$ GHz and can perform one floating point operation in each clock

cycle. The peak bandwidth between the GPU and the global memory is $100$GB$//$s and the

cache of GPU has been disabled.

Assuming the GPU has an on$-$chip buffer $($shared memory$)$ which can store $3$xx$32$ xx$32$

elements and has a peak access bandwidth of $1$TB$//$s$.$

Write the pseudo code for an optimized CUDA program using block matrix mul$-$

tiplication approach including both kernel function and host function.

Derive a lower bound on the computation time, the local data access time in SM$,$

and the global data access time of your optimized kernel function. Explain.