Part $1$: Coding Task $$ you need to write two subroutines

The project is about finding the mean $($i$.$e$.,$ E$[$cos$($x$)])$ and mean square $($i$.$e$.,$ E$[$cos$2($x$)])$ of the

cosine function.

You are asked to write two subroutines called array$\_$average and array$\_$square$\_$Qm whose

contracts are given in the file $$project$.$asm$$ posted to Carmen. Download this file and add your

code to it as indicated. This asm file comes with the test code and three subroutines that you will

use when computing the average and do the squaring. You are not allowed to modify any of the

code that is already provided in the file project.asm.

The subroutine array$\_$average takes a pointer to an array of $16-$bit signed numbers and the

number of elements in the array of length and returns the average of the values in the array.

This subroutine will call the two subroutines x$\_$div$\_2$powerP and log$\_$x$\_$base$2$ that are

provided in the asm file on Carmen.

The subroutine array$\_$square$\_$Qm takes two pointers to word$-$arrays of the same length n$.$

One of the pointers points to an input array with elements $($x $1,$ x$2,...,$ xn $),$ and the other one points

to an output array with elements $($y $1,$ y$2,...,$ yn $).$ Each of the elements $($x$1,$ x$2,...,$ xn $)$ in the input

array is assumed to be a signed $16-$bit number with Q$-$value m$.$ The subroutine

array$\_$square$\_$Qm will compute the square of each of these elements, correct for the Q$-$value,

and write the result to the output array. In particular,

$!=1$

$2"(!)$#

Recall that if both factors of a multiplication have Q$-$value m$,$ the product will have Q$-$value $2$m$.$ If

we want to have the product have Q$-$value m$,$ we must adjust the product value and divide by $2$m $.$