Vector Processors are a class of processors that are designed to give good performance when operating on vector $($arrays$)$ of data. Assume that we are considering enhancing a machine by adding a vector mode to it$.$ When a computation is performed in vector mode, it is $20$ times faster than the normal mode of execution. We call the percentage of time that could be spent using vector mode as the percentage of vectorization.

a$)$ What percentage of vectorization is needed to achieve a speedup of $2?$

b$)$ What percentage of vectorization is needed to achieve one$-$half of the maximum speedup attainable by using vector mode?

c$)$ Suppose you have measured the percentage of vectorization for programs to be $70\%.$ The hardware design group says they can double the speed $(2$x$20)$ of the vector rate with the significant additional engineering investment. On the other hand, the compiler design group could increase the use of vector mode as another approach to increasing performance. How much of the increase in the percentage of vectorization $($relative to the current usage$)$ would the compiler team need to obtain the same performance gain as obtained by the hardware design group?Vector Processors are a class of processors that are designed to give good performance when operating on vector $($arrays$)$ of data. Assume that we are considering enhancing a machine by adding a vector mode to it$.$ When a computation is performed in vector mode, it is $20$ times faster than the normal mode of execution. We call the percentage of time that could be spent using vector mode as the percentage of vectorization.

a$)$ What percentage of vectorization is needed to achieve a speedup of $2?$

b$)$ What percentage of vectorization is needed to achieve one$-$half of the maximum speedup attainable by using vector mode?

c$)$ Suppose you have measured the percentage of vectorization for programs to be $70\%.$ The hardware design group says they can double the speed $(2$x$20)$ of the vector rate with the significant additional engineering investment. On the other hand, the compiler design group could increase the use of vector mode as another approach to increasing performance. How much of the increase in the percentage of vectorization $($relative to the current usage$)$ would the compiler team need to obtain the same performance gain as obtained by the hardware design group?