The MIPS system includes a CPU that handles integer instructions and two coprocessors: CP$0$ the system coprocessor that records information needed to handle exceptions and interrupts, and CP$1$ to handle floating point instructions. The control unit determines what operation an instruction performs by examining the instruction opcode. Indicate for each of the following instructions whether it is executed by the CPU, by CP$0$ or by CP$1$:

div

mult

cvt$.$w$.$s

mtc$1$

lwc$1$

mfc$1$

swc$1$

A processor has a clock rate of $2$ GHz and executes $150$ million instructions from a program with an average CPI of $4.$ Three techniques that can be used to improve the performance of the program are:

$$ Option $1$: optimize the program so that it only executes $100$ million instructions.

$$ Option $2$: double the clock rate of the processor.

$$ Option $3$: carefully select the instructions in the program so that the average CPI is reduced from $4$ to $2\mathrm{.}5.$

For each of these options used alone, compute the resulting speedup for the program. Speedup is defined as the ratio of the execution time before the change to the execution time after the change.

$(3)$ Speedup provided by option $1=\_\_\_\_\_\_\_$

$(3)$ Speedup provided by option $2=\_\_\_\_\_\_\_$

$(3)$ Speedup provided by option $3=\_\_\_\_\_\_\_$

The native MIPS rating for a machine code program on processor $1$ is $800.$ The program on processor $1$ has an average CPI of $2\mathrm{.}5.$ Compiling the same program for processor $2$ produces a machine code program that executes the same number of machine instructions but with an average CPI of $4.$ Both processors run at a $2$ GHz clock rate. What is the relative MIPS rating for the program running on processor $2$ compared to the program running on processor $1?$