Part $1$: Coding task $-$ Average Absolute Deviation of an Array of Numbers

Task: Write a short assembly program that finds the average absolute deviation $($of a given

array. You are given an array with elements $\{x_1,x_2,x_3,$dots,$x_n\}$ and your code computes

$\frac{1}{n}{\displaystyle \underset{i=1}{\overset{n}{}}}|x_i-(\stackrel{}{x})|$

where $\stackrel{}{x}=\frac{1}{n}{\displaystyle \underset{i=1}{\overset{n}{}}}{x}_i$ is the mean value of the elements.

The average absolute deviation is a measure of the statistical dispersion of a set of given

samples. The standard deviation, defined as the square root of the variance, is another widely

used measure of statistical dispersion but requires multiplication and taking square roots to

compute. The average absolute deviation is easier to compute and more suitable for

microcontroller applications with a limited instruction set.

Note that, in most cases, the computed average absolute deviation will only be an

approximation due to limitations of available operations. Recall that there is no instruction to do

division unless we are dividing by a power of two. Even then, we will make rounding errors if the

outcome of the division is not an integer value.

For this assignment, you do not need to worry about approximation errors. You will work on a

set with $16$ numbers to facilitate easy division $($you know how to divide by $16)$ and you can

neglect rounding errors due to discarded fractional bits $($do not attempt to fix rounding errors$).$

$.$data ; Assemble into RAM

$.$retain ; Override ELF conditional linking

$.$retainrefs ; And retain any sections that have

samples: $.$word $45,76,11,23,49,91,43,17,71,27,63,41,34,83,67,59$

LENGTH: $.$set $2*16$

buff: $.$word $0$x$8000$

mean: $.$word $0$ ; Your code will return the mean here

aad: $.$word $0$ ; Your code will return the avg. absolute deviation here

foot: $.$word $0$x$7$FFF

$24$

$25$; Do NOT modify any of these definition for your submission

$26$; You can experiment while debugging, but submit your results for the given set

$27$;

Your code needs to follow all these requirements or constraints:

Your code needs to compute the mean value of the samples in mean.

Your code needs to compute the average absolute deviation of the samples in aad.

Your code is not allowed to modify the RAM or FRAM otherwise. That means

Your code is not allowed to modify the samples, buff, or foot.

Your code is not allowed to create new variables, arrays etc. in RAM or FRAM $($nor

does it need to$).$

Your code needs to use indexed mode with the label samples when accessing the

elements in the given array and use the constant LENGTH instead of hardcoded values.

$($This is a good restriction since using indexed mode will actually make your life easier.$)$

Your code is allowed to use core registers as needed.

Your code must not be wasteful with resources.

Your code must not use more core registers than necessary.

Your code must not use unnecessary jumps $($aka no spaghetti$).$

Your code must not have unnecessary instructions and the like.

You code should have comments and use descriptive labels.