Taking your naive/brute force trial-by-division prime number program from pnc0, implement some algorithmic optimizations and analysis its improvements to performance over similar workloads.

Implement program in Vircon32 C, that:

• performs the “trial-by-division” process on a range of values, 2-N
  • in addition to the naive/brute force implementation from pnc0, you should implement optimizations for:
    • break on composite
    • odds-only
    • sqrt trick
    • and all the combinations of these optimizations thereof. With brute, there should be 8 total variations you are testing.
  • the values for N are some sufficient quantity still small enough to fit within an integer
  • the values for N will have some relationship (powers of 2, powers of 10/magnitudes) that ideally can be computed via some loop/equation (ie 1024, 2048, 4098, 8192, 16384, etc.)
    • the upper bound should be fairly easy to change, even if it requires an edit and recompile.
  • the values for N have some sufficient quantity large enough where its upper set values will take some amount of time to compute (fast enough to have some relatable value, not to exceed 16 seconds)
  • for each value of N:
    • display that N/upper bound
    • tally: display the number of primes identified (2-N)
    • display the amount of time taken to do the total computation for that value of N, out to at least 4 decimal places
    • display each N value and result in an arrangement on the screen that can be clearly identified and read by the viewer
• timing should go out, as reasonable, to a few decimal places, and should be consistent across all attempts.
  • timing is on the computational process only, not the display of results.
• create a graph (using some external tool) that plots the performance of the C implementation working on various workloads of this brute force algorithm according to the various N's and the time it took. Share your graph of your results on the class discord and on the project documentation page.
  • a line graph is the suggested best candidate
• this will not be an interactive program: it starts up, does its thing, outputs it results, then halts.
• the brute force implementation is meant as our baseline. As such, it should not contain any optimizations or attempted improvements. Here in pnc1, this base implementation should be the least efficient. This is important, to allow us to realize the impact of various improvements we will be making in those upcoming projects.

The following are reference screenshots of what your implementations should approximate.

You will want to go here to edit and fill in the various sections of the document:

• https://lab46.g7n.org/notes/fall2024/projects/pnc1

To be successful in this project, the following criteria (or their equivalent) must be met:

• Project must be submit on time, by the deadline.
  • Late submissions will lose 33% credit per day, with the submission window closing on the 3rd day following the deadline.
• Executed programs must display in a manner similar to provided output
  • output formatted, where applicable, must match that of project requirements
• Processing must be correct based on input given and output requested
• Output, if applicable, must be correct based on values input
• Code must be nicely and consistently indented
• Code must be consistently written, to strive for readability from having a consistent style throughout
• Code must be commented
  • Any “to be implemented” comments MUST be removed
    • these “to be implemented” comments, if still present at evaluation time, will result in points being deducted.
    • Sufficient comments explaining the point of provided logic MUST be present
• No global variables (without instructor approval), no goto statements, no calling of main()!
• Track/version the source code in your lab46 semester repository
• Submit a copy of your source code to me using the submit tool by the deadline.

Let's say you have completed work on the project, and are ready to submit, you would do the following:

lab46:~/src/SEMESTER/DESIG/PROJECT$ submit DESIG PROJECT file1 file2 file3 ... fileN

You should get some sort of confirmation indicating successful submission if all went according to plan. If not, check for typos and or locational mismatches.

I'll be evaluating the project based on the following criteria:

208:pnc1:final tally of results (208/208)
*:pnc1:code, XML, build script, and cartridge submitted [26/26]
*:pnc1:processing and output is correct, and to specifications [26/26]
*:pnc1:break on composite optimization present and functional [26/26]
*:pnc1:odds only processing optimization present and functional [26/26]
*:pnc1:sqrt trick processing optimization present and functional [26/26]
*:pnc1:graph produced from timing data produced of all 8 variants [26/26]
*:pnc1:graph posted to discord and documentation page [26/26]
*:pnc1:timing data is the taken out to at least 4 decimal places [26/26]

• each class member is to participate in the contribution of relevant information and formatting of the documentation
  • minimal member contributions consist of:
    • near the class average edits (a value of at least four productive edits)
    • near the average class content change average (a value of at least 1024 bytes (absolute value of data content change))
    • no zero-sum commits (adding in one commit then later removing in its entirety for the sake of satisfying edit requirements)
  • adding and formatting data in an organized fashion, aiming to create an informative and readable document that anyone in the class can reference
  • content contributions will be factored into a documentation coefficient, a value multiplied against your actual project submission to influence the end result:
    • no contributions, co-efficient is 0.50
    • less than minimum contributions is 0.75
    • met minimum contribution threshold is 1.00

• Solutions not abiding by spirit of project will be subject to a 50% overall deduction
• Solutions not utilizing descriptive why and how comments will be subject to a 25% overall deduction
• Solutions not utilizing indentation to promote scope and clarity or otherwise maintaining consistency in code style and presentation will be subject to a 25% overall deduction
• Solutions not organized and easy to read (assume a terminal at least 90 characters wide, 40 characters tall) are subject to a 25% overall deduction