Problem$7.(21$ points$)$ Roofline Model

Consider the below figure showing the roofline model of a hypothetical GPU as a solid line along with data points from two applications $($Application $x$ and $Y)$ run on the GPU.

baseline GPU

A$.(12$ points$)$ For each of the changes to the GPU architecture below, what would be the resulting roofline? Provide your choices between $($a$)$ through $($d$).$

i$.$ Clock frequency of the SMs is increased.

ii$.$ The original GPU had DDR$4$ memory, but it was replaced with HBM$.$

iii. DRAM capacity is increased by improving per$-$bank cell array density.

iv$.$ The applications mostly consist of matrix multiply and tensor cores were added to improve performance.

B$.(3$ points$)$ Classify applications $x$ and $Y$ as either memory$-$intensive or compute$-$intensive.

C$.(3$ points$)$ If Application $x$ is modified for better coalescing, resulting in fewer DRAM accesses, how would the corresponding dot on the plot move? Provide the direction of movement $($e$.$g$.,$ up$,$ up$-$right, right, down$-$right, stay the same, etc$).$

D$.(3$ points$)$ If Application $Y$ is modified to improve load$-$balancing, resulting in better SM utilization, how would the corresponding dot on the plot move? Provide the direction of movement $($e$.$g$.,$ up$,$ up$-$right, right, down$-$right, stay the same, etc$).$