<WRAP centeralign round box>
<WRAP><color red><fs 200%>Corning Community College</fs></color></WRAP>
<WRAP><fs 150%>CSCS1320 C/C++ Programming</fs></WRAP>
</WRAP>

~~TOC~~

======Project: OPTIMIZING ALGORITHMS WITH SPACE - PRIME NUMBER CALCULATION (pnc2)======

=====Objective=====
To apply your skills in algorithmic optimization through the implementation of improved prime number calculating programs.

=====Algorithmic Complexity=====
A concept in Computer Science curriculum is the notion of computational/algorithmic complexity.

Basically, a solution to a problem exists on a spectrum of efficiency (typically constrained by time vs. space). Once you've hashed out an implementation:

  * if optimizing for (or trying to take up less) time, the code size tends to grow or become more complex.
  * if optimizing for (or trying to take up less) space, the program runtime can grow.

Let it be clear: using modern computers bound by fourth dimensional constraints, we **cannot** write solutions without some foothold in both space and time (any program has statements in it that accomplish the task at hand (space occupied), and that same program takes time to run (even if it happens rather quickly)). What we can do is influence where on the space-time spectrum our implementation falls, and if done strategically for the particular constraint at hand, can aid us in achieving desired improvements in program efficiency.

In the previous projects, we focused on algorithms that were more constrained by time- taking progressively more time the larger the data set to be processed. These time-constrained algorithms also happen to be the type of algorithm you're most familiar with (or at least, were indoctrinated into thinking with...) your third grade self, on the other hand,  potentially would have found more familiarity with the space-constrained methods this project will explore.

So in contrast to time-constrained approaches we have space-constrained approaches, which will utilize more space (ie allocating memory) in the solving of the program to the benefit of requiring less time.

We can never be entirely time- or space-free... some element of the other will always be present. But by embracing the advantages of an approach, we can really make an impact in the desired area.

What we will be looking at in this project is a type of prime number calculating algorithm known as a sieve. It will make strategic use of space to aid us in the solving of the problem instead of exclusively relying on time.

Of note, the "mainstream" prime number computing efforts typically make use of sieves.

=====Optimizing the prime number calculation=====
Following will be the optimized algorithms I'd like you to implement for comparison with all the others.

For this project, please assume the following:

  * unless otherwise specified, you are doing all values (odds AND evens).
  * if you exceed 64 million and get "--error!---" from primerun that's okay. I have memory limits in place (just like I have time limits in place).
  * as the space-based approach to solving our prime number computation problem is fundamentally different from those we took in previous projects, you will want to look to start from scratch. Trying to reuse old code and shoehorn it into what effectively amounts to an entirely different paradigm will create a lot of problems.

But, the conceptual level we'll be pursuing will be the space-based equivalent of **primebrute**/**primebrk**, that is, no fancy optimizations for odd numbers, nor the **sqrt()** trick, just straight up processing of the values that need to be processed.

=====Sieve of Eratosthenes (primesoe)=====
Your next program, and first sieve, will be the Sieve of Eratosthenes. Perhaps among the best  and likely longest-known sieves, its origins date from antiquity.

This sieve, instead of calculating to determine the eligibility of a prime, works in a manner of marking off patterns of values that cannot be prime (so, it is composite-focused in approach vs. prime-focused).

In order for it to work, we must store all the values we're processing so we can obtain what is left when done-- what remains are the prime values.

Here is the wikipedia page: https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes

Here is an animated image of this sieve in action (from wikipedia): 

{{:haas:fall2016:discrete:projects:sieve_of_eratosthenes_animation.gif|}}

This YouTube video may also be helpful:

[[https://www.youtube.com/watch?v=V08g_lkKj6Q|Sieve of Eratosthenes]]

A basic outline of the algorithm (again, from the wikipedia page):

===Overview of Algorithm===

To find all the prime numbers less than or equal to a given integer **n** by Eratosthenes' method:

  - Create a list of consecutive integers from 2 through **n**: (2, 3, 4, ..., n).
  - Initially, let p equal 2, the smallest prime number.
  - Enumerate the multiples of p by counting to n from 2p in increments of p, and mark them in the list (these will be 2p, 3p, 4p, ... ; the p itself should not be marked).
  - Find the first number greater than p in the list that is not marked. If there was no such number, stop. Otherwise, let p now equal this new number (which is the next prime), and repeat from step 3.

When the algorithm terminates, the numbers remaining in the list that are not marked are the primes below **n**.

===Program Implementation===
This is a space-constrained algorithm, therefore we will need a chunk of space to store these values. Think about what a lot of this looks like with respect to how you know how to organize data.

=====Optimizations on sieve of Eratosthenes=====

====odds-only processing (primesoeodd)====
Taking the **primesoe** codebase, enhance it to do odds-only processing, ideally considering overall storage used.

====sqrt() trick (primesoesrt)====
Taking the **primesoe** codebase, enhance it to utilize the **sqrt()** (or **sqrt()-less square root**) trick.

Compared to the brute/brk algorithms from the previous projects, the performance differences between using **sqrt()** and approximating the square root should be minimal. You are free to utilize either approach in your implementation for this project.

NOTE: this variant is still to process all values (odd and even).

NOTE: if you are curious in comparing actual performance between sqrt() and approximated square root, **primerun** will recognize the following program names:

  * **primesoesrt**
  * **primesoesrtopt**

====odds-only+sqrt() trick (primesoesrtodd)====
Taking the **primesoe** codebase, enhance it to do odds-only processing AND utilize the **sqrt()** (or **sqrt()-less square root**) trick.

Compared to the brute/brk algorithms from the previous projects, the performance differences between using **sqrt()** and approximating the square root should be minimal. You are free to utilize either approach in your implementation for this project.

NOTE: if you are curious in comparing actual performance between sqrt() and approximated square root for this odds-processing variant, **primerun** will recognize the following program names:

  * **primesoesrtodd**
  * **primesoesrtoptodd**

=====Program=====
It is your task to write four Sieve of Eratosthenes-oriented prime number calculating programs:

  - **primesoe.c**: using the space-oriented sieve algorithm (baseline sieve)
  - **primesoeodd.c**: applying the odds-only processing to the sieve of Eratosthenes
  - **primesoesrt.c**: applying the sqrt() trick to sieve of Eratosthenes
  - **primesoesrtodd.c**: applying BOTH odds-only processing and sqrt() trick to sieve of Eratosthenes

====Program Specifications====
Your programs should:
  * obtain 2-4 parameters from the command-line (see **command-line arguments** section below).
    * check to make sure the user indeed supplied enough parameters, and exit with an error message if not.
    * argv[1]: maximum quantity of primes to calculate (your program should run until it discovers **that** many primes).
      * this value should be an integer value, greater than or equal to 0.
        * if argv[1] is 0, disable the quantity check, and rely on provided lower and upper bounds (argv[4] would be required in this case).
    * argv[2]: reserved for future compatibility; for now, assume it is **1**.
    * argv[3]: **conditionally optional** lower bound (starting value). Most of the time, this will probably be **2**, but should be a positive integer greater than or equal to 2. This defines where you program will start its prime quantity check from.
      * if omitted, assume a lower bound of **2**.
      * if you desired to specify an upper bound (argv[4]), you obviously MUST provide the lower bound argument under this scheme.
    * argv[4]: **conditionally optional** upper bound (ending value). If provided, this is the ending value you'd like to check to.
      * If doing a quantity run (argv[1] NOT 0), this value isn't necessary.
      * If doing a quantity run AND you specify an upper bound, whichever condition is achieved first dictates program termination. That is, upper bound could override quantity (if it is achieved before quantity), and quantity can override the upper bound (if it is achieved before reaching the specified upper bound).
    * for each argument: you should do a basic check to ensure the user complied with this specification, and exit with a unique error message (displayed to STDERR) otherwise:
      * for insufficient quantity of arguments, display: **PROGRAM_NAME: insufficient number of arguments!**
      * for invalid argv[1], display: **PROGRAM_NAME: invalid quantity!**
      * for invalid argv[2], display: **PROGRAM_NAME: invalid value!**
      * for invalid argv[3], display: **PROGRAM_NAME: invalid lower bound!**
        * if argv[3] is not needed, ignore (no error displayed not forced exit, as it is acceptable defined behavior).
      * for invalid argv[4], display: **PROGRAM_NAME: invalid upper bound!**
        * if argv[4] is not needed, ignore (no error displayed nor forced exit, as it is acceptable defined behavior).
      * In these error messages, **PROGRAM_NAME** is the name of the program being run; this can be accessed as a string stored in **argv[0]**.
    * please take note in differences in run-time, contemplating the impact the various algorithms/optimizations have on performance.
  * start your stopwatch (see **timing** section below).
  * perform the correct algorithm against the input(s) given.
  * display to STDOUT (file pointer **stdout**) the prime numbers calculated.
  * stop your stopwatch. Calculate the time that has transpired (ending time minus starting time).
  * output the processing run-time to STDERR (file pointer **stderr**).
  * your output **MUST** conform to the example output in the **execution** section below. This is also a test to see how well you can implement to specifications. Basically:
    * as primes are being displayed, they are space-separated (first prime hugs the left margin), and when all said and done, a newline is issued.
    * the timing information will be displayed in accordance to code I will provide below (see the **timing** section).

=====Grabit Integration=====
For those familiar with the **grabit** tool on lab46, I have made some skeleton files and a custom **Makefile** available for this project.

To "grab" it:

<cli>
lab46:~/src/cprog$ grabit cprog pnc2
make: Entering directory '/var/public/SEMESTER/cprog/pnc2'
‘/var/public/SEMESTER/cprog/pnc2/Makefile’ -> ‘/home/USERNAME/src/cprog/pnc2/Makefile’
‘/var/public/SEMESTER/cprog/pnc2/primesoe.c’ -> ‘/home/USERNAME/src/cprog/pnc2/primesoe.c’
‘/var/public/SEMESTER/cprog/pnc2/primesoeodd.c’ -> ‘/home/USERNAME/src/cprog/pnc2/primesoeodd.c’
‘/var/public/SEMESTER/cprog/pnc2/primesoesrt.c’ -> ‘/home/USERNAME/src/cprog/pnc2/primesoesrt.c’
‘/var/public/SEMESTER/cprog/pnc2/primesoesrtodd.c’ -> ‘/home/USERNAME/src/cprog/pnc2/primesoesrtodd.c’
make: Leaving directory '/var/public/SEMESTER/cprog/pnc2'
lab46:~/src/cprog$ cd pnc2
lab46:~/src/cprog/pnc2$ ls
Makefile  primesoe.c  primesoeodd.c  primesoesrt.c  primesoesrtodd.c
lab46:~/src/cprog/pnc2$ 
</cli>

Furthermore, if your **pnc2/** project directory is next to a **pnc1/** and **pnc0/** directory, each containing those project's specific prime variants, you can symlink them into the current project directory with a **make link**:

<cli>
lab46:~/src/cprog/pnc2$ make link
‘./primebrute.c’ -> ‘../pnc0/primebrute.c’
‘./primebrk.c’ -> ‘../pnc0/primebrk.c’
‘./primebrkodd.c’ -> ‘../pnc1/primebrkodd.c’
‘./primebrksrt.c’ -> ‘../pnc1/primebrksrt.c’
‘./primebrkoddsrt.c’ -> ‘../pnc1/primebrkoddsrt.c’
‘./primebrksrtopt.c’ -> ‘../pnc1/primebrksrtopt.c’
‘./primebrkoddsrtopt.c’ -> ‘../pnc1/primebrkoddsrtopt.c’
lab46:~/src/cprog/pnc2$ 
</cli>

And, of course, your basic compile and clean-up operations:

  * **make**: compile everything
  * **make debug**: compile everything with debug support
  * **make clean**: remove all binaries

Just another "nice thing" we deserve.

NOTE: You do NOT want to do this on a populated pnc2/ project directory-- it will overwrite files. Only do this on an empty directory.

=====Command-Line Arguments=====
To automate our comparisons, we will be making use of command-line arguments in our programs. As we have yet to really get into arrays, I will provide you same code that you can use that will allow you to utilize them for the purposes of this project.

====header files====
We don't need any extra header files to use command-line arguments, but we will need an additional header file to use the **atoi(3)** function, which we'll use to quickly turn the command-line parameter into an integer, and that header file is **stdlib.h**, so be sure to include it with the others:

<code c>
#include <stdio.h>
#include <stdlib.h>
</code>

====setting up main()====
To accept (or rather, to gain access) to arguments given to your program at runtime, we need to specify two parameters to the main() function. While the names don't matter, the types do.. I like the traditional **argc** and **argv** names, although it is also common to see them abbreviated as **ac** and **av**.

Please declare your main() function as follows:

<code c>
int main(int argc, char **argv)
</code>

The arguments are accessible via the argv array, in the order they were specified:

  * **argv[0]**: program invocation (path + program name)
  * **argv[1]**: our maximum / upper bound

====Simple argument checks====
Although I'm not going to require extensive argument parsing or checking for this project, we should check to see if the minimal number of arguments has been provided:

<code c>
    if (argc < 2)  // if less than 2 arguments have been provided
    {
        fprintf(stderr, "Not enough arguments!\n");
        exit(1);
    }
</code>

====Grab and convert max====
Finally, we need to put the argument representing the maximum value into a variable.

I'd recommend declaring a variable of type **int**.

We will use the **atoi(3)** function to quickly convert the command-line arguments into **int** values:

<code c>
    max  = atoi(argv[1]);
</code>

And now we can proceed with the rest of our prime implementation.

=====Allocating large arrays=====
Being new to arrays, you may not know it yet, but there is an upper bound to how big you can declare an array at **compile time**.

That is, using the conventional array declaration:

<code c>
data_type arrayname[size];
</code>

It is likely dependent on some combination of the execution environment (32-, 64-bit?) and the compiler, but in practice I've found things generally get unhappy if we try to request array sizes at some point beyond 1-4million elements (which makes sense, most processes in modern operating systems allocate a default stack size of 4-8MiB... if a short int is 2 bytes, how many consecutive short ints before you hit 4MiB?)

As we'll be needing array sizes considerably larger than this for the project (will we? If I could drop a hint: **yes, we will**), how do we get around this?

The answer: **runtime memory allocation**

We can allocate memory at run-time, which gives us the benefit of populating variables and performing equations to derive more specific values. This is also a rather powerful programming technique/ability to deploy in more complex programs, so keep it handy in your toolkits.

To do so, we ignore the fake facade that is the array, and treat it like it actually exists to the computer: **a pointer**.

So when you declare your array, instead of using the square bracket notation, do it as a pointer instead:

<code c>
datatype *array_name  = NULL;
</code>

THEN, later on in your program when it comes time to allocate the array, we use a memory allocation function, of which for our current purposes one of the following 2 could suit our needs:

  * **malloc(size)**
    * allocates **size** bytes and returns the address
  * **calloc(count, size)**
    * allocates count * size bytes and returns the address; it also will scrub the memory, making sure everything is set to zero (**malloc()** does not do this; **malloc()** is also faster because of this, something to keep in mind to differentiate the two).

So, if we wanted a 32768 element integer array, to show examples allocating with each function (you'd obviously only use one, whichever best fit your usage scenario):

<code c>
int *array_name  = NULL;

// using malloc()
array_name = (int *) malloc (sizeof(int) * 32768);

// using calloc()
array_name = (int *) calloc (32768, sizeof(int));
</code>

What else is going on here? What's with the parenthesis and the integer pointer?

That's a typecast, and is a way of telling the compiler to contort data IN THAT INSTANCE to a certain type (because it is a different type, other than what we want).

As it turns out, **malloc()** and **calloc()** both return //raw memory//, which in C is manifested as type **<nowiki>void *</nowiki>**; if our array is an integer pointer, we should be nice and cast it (apply the rules of an integer pointer to the raw memory, allowing the assignment to take place without the compiler whining-- some compilers, depending on settings in place, may whine more than others).

With this, we can get around the compile time array limits, because by allocating memory at runtime, we're getting additional memory given to us, vs. trying to fit within the default initial allotment.

You should then be able to access it using regular array notation, or my preference: pointer arithmetic.

<code c>
// C array syntax for accessing 3rd element of array:
array_name[2]

// C pointer arithmetic syntax for accessing 3rd element of array:
*(array_name+2)
</code>

=====Approximating array size=====
The nature of utilizing an array for the sieves, as you will likely discover quickly, is that the sheer quantity of elements needed increments drastically as the desired quantity goes up.

For example, if we were seeking the first 32 primes:

<cli>
lab46:~/src/cprog/pnc2$ ./primebrk 32 1
2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 127 131
</cli>

... we would see that the 32nd prime is 131. For the Sieve of Eratosthenes to successfully work in this case, we'd need an array size of at least 132 (if we do the standard mapping of array element to actual number, where element 0 would correspond with the number 0, and element 131 would correspond with number 131; 0-131 = 132 elements).

But that number isn't immediately known (indeed, the nature of the distribution of prime numbers is the subject of considerable mathematical exploration, with many various proofs demonstrating different aspects of their distribution-- don't believe me? Just google "**distribution of primes**" and read up for yourself). And short of some impressive looking and very calculus-requiring integral, there doesn't (at least from some of my searches) seem to be a decent algebraic expression we can use to come close.

And without this knowledge of the largest prime in the desired quantity, our sieve implementation (with the requirements as I have specified) is sort of at a standstill.

So how do we get around this? I propose a combination of accepting knowledge from a more aware source (me), and a little algebraic ingenuity. Let's hack ourselves an array size equation! (Do I hear a "heck yeah!" ? "HECK YEAH!")

First, you can actually produce a lot of this data, from your **pnc1** programs (technically **pnc0** as well, but you'll be waiting a whole heck of a lot longer).

Let's take one of the purportedly best-running programs from **pnc1** (**primebrksrtoptodd**) and contort it into giving us the information that we need.

With a little bit of UNIX shell magic (again, I'm not expecting you to know this, so I'm just giving it to you, but from the abstract/conceptual level, you should be able to recognize things here like loops and output statements, and with some informed knowledge of shell syntax, see variables as well), we have the following:

<code bash 1>
# clear the screen
clear

# loop for a powers of 2 progression 32-4194304 (inclusive)
for((qty=32; qty<=4194304; qty*=2)); do

    # display the quantity lead-in information
    printf "[%7s] %7sth prime: " "${qty}" "${qty}"
    
    # obtain the last/largest prime in the specified quantity
    value=$(./primebrksrtoptodd ${qty} 1 2>/dev/null | tr ' ' '\n' | tail -2 | head -1)

    # display it, along with calculating its approximate multiplier
    printf "%8s (x%s)\n" "${value}" $(echo "(${value}/${qty})+1" | bc -q)
done
</code>

We start with **qty** of 32, as that is the default starting point of **primerun** (so why not; makes sense to work with what we've got). But there's still an unknown: the //MAXIMUM// quantity we'll need to deal with, especially in relation to primerun (focus on primerun execution, not to infinity). This is less available to you, short of just guessing some possible maximum.

I'm going to drop a hint: you'll very likely not be going beyond a quantity of **4194304** (at least with a primerun cut-off limit of 2 seconds), so use THAT as your upper bound of quantity, and that is why I use that number in the shell script given above.

You don't have to worry about running said shell script, as the output is right here:

<cli>
[     32]      32th prime:      131 (x5)
[     64]      64th prime:      311 (x5)
[    128]     128th prime:      719 (x6)
[    256]     256th prime:     1619 (x7)
[    512]     512th prime:     3671 (x8)
[   1024]    1024th prime:     8161 (x8)
[   2048]    2048th prime:    17863 (x9)
[   4096]    4096th prime:    38873 (x10)
[   8192]    8192th prime:    84017 (x11)
[  16384]   16384th prime:   180503 (x12)
[  32768]   32768th prime:   386093 (x12)
[  65536]   65536th prime:   821641 (x13)
[ 131072]  131072th prime:  1742537 (x14)
[ 262144]  262144th prime:  3681131 (x15)
[ 524288]  524288th prime:  7754077 (x15)
[1048576] 1048576th prime: 16290047 (x16)
[2097152] 2097152th prime: 34136029 (x17)
[4194304] 4194304th prime: 71378569 (x18)
</cli>

What we have is the following:

  * first column is the specified quantity we are going to (as instantiated by primerun; I just have us doing a simple powers of 2 progression)
  * the next column (the N-th prime), is the last prime in that quantity sequence (131 IS the 32nd prime, starting from 2)
  * the last column, the xNUMBER, is the approximate multiplier we get by dividing the N-th prime by the quantity (and taking the ceiling (I just added one, since we're doing integer division and it'll truncate anyway), since it likely will NOT be a clean division)

So from the data given above, we can see that a rough approximation of space needed for 32 primes would be <nowiki>32*5</nowiki> or 160 elements (131 falls nicely into 160).

For 1024 we have a multiplier of 8 (<nowiki>1024*8</nowiki> = 8192, which 8161 safely fits into).

Okay, so we've got some raw numbers, we know the array size needed for the smallest quantity (<nowiki>32*5</nowiki>), we also know the array size needed for the likely largest quantity (<nowiki>4194304*18</nowiki>). So how do we handle the intermediaries?

As you can see, there is no a clean progression at play here, so no simple patterns we can play off of. I offer a few suggestions (and for the purposes of this project, any are acceptable):

  * just go with the max size (x18): **<nowiki>array_size = qty * 18;</nowiki>**
  * deploy some **if()** statements and do a stepped progression.

For example, we see that since our max multiplier is 18, what if we did some factoring of 18? Say: 6, 12, 18?

We could rig up something like this:

<code c>
if (qty <= 128)
    array_size = qty * 6;
else if (qty <= 32768)
    array_size = qty * 12;
else
    array_size = qty * 18;
</code>

In general, though, this is just a mild annoyance in our quest to implement the sieve of Eratosthenes, so if you just hard code an 18, while certainly dirty, will get the job done for our current purposes (I will most certainly NOT hold it against you).

Make sense? Hopefully. And moreso, if you've been able to follow this, it is also indicative of your general level of comprehension: if you understand the overall problem, the specific issue, and can interact conceptually, that makes you a better problem solver/Computer Scientist/programmer.

And please, ASK QUESTIONS if something doesn't make sense.

=====Timing=====
Often times, when checking the efficiency of a solution, a good measurement (especially for comparison), is to time how long the processing takes.

In order to do that in our prime number programs, we are going to use C library functions that obtain the current time, and use it as a stopwatch: we'll grab the time just before starting processing, and then once more when done. The total time will then be the difference between the two (end_time - start_time).

We are going to use the **gettimeofday(2)** function to aid us in this, and to use it, we'll need to do the following:

====header file====
In order to use the **gettimeofday(2)** function in our program, we'll need to include the **sys/time.h** header file, so be sure to add it in with the existing ones:

<code c>
#include <stdio.h>
#include <stdlib.h>
#include <sys/time.h>
</code>

====timeval variables====
**gettimeofday(2)** uses a **struct timeval** data type, of which we'll need to declare two variables in our programs (one for storing the starting time, and the other for the ending time).

Please declare these with your other variables, up at the top of main() (but still WITHIN main()-- you do not need to declare global variables).

<code c>
    struct timeval time_start; // starting time
    struct timeval time_end;   // ending time
</code>

====Obtaining the time====
To use **gettimeofday(2)**, we merely place it at the point in our code we wish to take the time.

For our prime number programs, you'll want to grab the start time **AFTER** you've declared variables and processed arguments, but **JUST BEFORE** starting the driving loop doing the processing.

That call will look something like this:

<code c>
    gettimeofday(&time_start, 0);
</code>

The ending time should be taken immediately after all processing (and prime number output) is completed, and right before we display the timing information to STDERR:

<code c>
    gettimeofday(&time_end, 0);
</code>

====Displaying the runtime====
Once we having the starting and ending times, we can display this to STDERR. You'll want this line:

<code c>
    fprintf(stderr, "%10.6lf\n", time_end.tv_sec - time_start.tv_sec + ((time_end.tv_usec - time_start.tv_usec) / 1000000.0));
</code>

For clarity sake, that format specifier is "%10.6lf", where the "lf" is "long float", that is **NOT** a number one but a lowercase letter 'ell'.

And with that, we can compute an approximate run-time of our programs. The timing won't necessarily be accurate down to that level of precision, but it will be informative enough for our purposes.

=====Execution=====
Your program output should be as follows (given the specified range):

<cli>
lab46:~/src/cprog/pnc2$ ./primesoe 32 1
2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 127 131
  0.000088
lab46:~/src/cprog/pnc2$ 
</cli>

The execution of the programs is short and simple- grab the parameters, do the processing, produce the output, and then terminate.

Based on specifications, it should also be able to do the following (override quantity with lower/upper bounds):

<cli>
lab46:~/src/cprog/pnc2$ ./primesoe 48 1 4 18
5 7 11 13 17
  0.000080
lab46:~/src/cprog/pnc2$ 
</cli>

And (shift the lower bound, but still count out 32 primes):

<cli>
lab46:~/src/cprog/pnc2$ ./primesoe 32 1 16
17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 127 131 137 139 149 151 157 163
  0.000087
lab46:~/src/cprog/pnc2$ 
</cli>

And of course the same for the 3 variants, and the same error message reporting if invalid values are given.
====Performance changes====
You may notice a change with the sieves as compared to the other algorithms you've implemented with respect to performance- there will likely be a lower bound of performance, ie you have to exceed a certain threshold before the algorithm truly enters its power band, and then it may truly be a step-up in terms of performance.

=====Check Results=====
To verify your program's correctness and view your implementation's performance, **primerun** will recognize the indicated program names listed above.

I'll hold off from posting actual primerun output; I want you to see the results without any expectations. Do know that the arrangement of programs (from left to right) is in order of worst to best performance based on my implementations.

If/when the runtime of a particular prime variant exceeds an upper threshold (likely to be set at 2 seconds), it will be omitted from further tests, and a series of dashes will instead appear in the output.

If you don't feel like waiting, simply hit **CTRL-c** and the script will terminate.

If the check is successful, you will see "OK" displayed beneath in the appropriate column; if unsuccessful, you will see "MISMATCH".

=====Submission=====
To successfully complete this project, the following criteria must be met:

  * Code must compile cleanly (no warnings or errors)
  * Output must be correct, and match the form given in the sample output above.
  * Code must be nicely and consistently indented (you may use the **indent** tool)
  * Code must utilize the algorithm(s) presented above.
    * **primesoe.c**
    * **primesoeodd.c**
    * **primesoesrt.c**
    * **primesoesrtodd.c**
  * Code must be commented
    * have a properly filled-out comment banner at the top
      * be sure to include any compiling instructions
    * have at least 20% of your program consist of **<nowiki>//</nowiki>**-style descriptive comments
  * Output Formatting (including spacing) of program must conform to the provided output (see above).
  * Track/version the source code in a repository
  * Submit a copy of your source code to me using the **submit** tool.

To submit this program to me using the **submit** tool, run the following command at your lab46 prompt:

<cli>
$ submit cprog pnc2 primesoe.c primesoeodd.c primesoesrt.c primesoesrtodd.c
Submitting cprog project "pnc2":
    -> primesoe.c(OK)
    -> primesoeodd.c(OK)
    -> primesoesrt.c(OK)
    -> primesoesrtodd.c(OK)

SUCCESSFULLY SUBMITTED
</cli>

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.

What I will be looking for:

<code>
78:pnc2:final tally of results (78/0)
*:pnc2:submit all programs correctly perform argument checking [2/2]
*:pnc2:primesoe.c no negative compiler messages [2/2]
*:pnc2:primesoe.c implements only specified algorithm [8/8]
*:pnc2:primesoe.c adequate indentation and comments [3/3]
*:pnc2:primesoe.c output conforms to specifications [3/3]
*:pnc2:primesoe.c primerun runtime tests succeed [3/3]
*:pnc2:primesoeodd.c no negative compiler messages [2/2]
*:pnc2:primesoeodd.c implements only specified algorithm [8/8]
*:pnc2:primesoeodd.c adequate indentation and comments [3/3]
*:pnc2:primesoeodd.c output conforms to specifications [3/3]
*:pnc2:primesoeodd.c primerun runtime tests succeed [3/3]
*:pnc2:primesoesrt.c no negative compiler messages [2/2]
*:pnc2:primesoesrt.c implements only specified algorithm [8/8]
*:pnc2:primesoesrt.c adequate indentation and comments [3/3]
*:pnc2:primesoesrt.c output conforms to specifications [3/3]
*:pnc2:primesoesrt.c primerun runtime tests succeed [3/3]
*:pnc2:primesoesrtodd.c no negative compiler messages [2/2]
*:pnc2:primesoesrtodd.c implements only specified algorithm [8/8]
*:pnc2:primesoesrtodd.c adequate indentation and comments [3/3]
*:pnc2:primesoesrtodd.c output conforms to specifications [3/3]
*:pnc2:primesoesrtodd.c primerun runtime tests succeed [3/3]
</code>