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======Project: BIG NUM======

A project for COURSENAME by YOUR NAME during the SEMESTER YEAR.

This project was begun on DATE and is anticipated to take TIME UNIT to complete. Project was completed on MONTH DAY, YEAR.

=====Objectives=====
State the purpose of this project. What is the point of this project? What do we hope to accomplish by undertaking it?

=====Prerequisites=====
In order to successfully accomplish/perform this project, the listed resources/experiences need to be consulted/achieved:

  * successful completion of project #1 and solid understanding of pertinent topics
  * familiarity with memory allocation via **malloc(3)**
  * familiarity with memory, accessing data via pointer dereferencing, and address calculation
  * familiarity with looking up C function parameters/information in the manual
  * familiarity with functions, their parameters and return types

=====Background=====
State the idea or purpose of the project. What are you attempting to pursue?

Upon approval, you'll want to fill this section out with more detailed background information. DO NOT JUST PROVIDE A LINK.

Providing any links to original source material, such as from a project page, is a good idea.

You'll want to give a general overview of what is going to be accomplished (for example, if your project is about installing a web server, do a little write-up on web servers. What is it, why do we need one, how does it work, etc.)

=====Scope=====
This project will have you implementing code to support the storage and manipulation of numbers outside of the established data types.

In C, from our first project (Project #0), we explored the various established data types, and determined their various sizes and representational ranges.

From that, we should know the largest value we can store in a variable using the biggest data type size (**unsigned long long int**), which is: **18,446,744,073,709,551,615**

That's a 20-digit number.

But this project will have us creating the ability to store and manipulate largers much larger than that. We'll start with a target of 4 and 24 digits (if you write your code effectively, the number of digits should ultimately not matter).

Why 4? Can't we already easily store values of 4 digits?

Yes, but looking to implement the ability to store and manipulate a 4 digit number will help us to better realize the logic and code necessary to scale our solution to support any number of digits.

While there are many approaches to this problem, follow through this example to get some insight. You don't have to take this approach, but it will cover some important concepts you will need to implement in your solution, whether or not you take this approach.

Let's look at a 4 digit number not as a side-effect of being able to be stored in a quantity of appropriate size, but as 4 literal stored digits in memory. To wit:

<code c>
    unsigned char *value;
    value = (unsigned char *) malloc (sizeof(unsigned char) * 4);
    *(value+0) = *(value+1) = *(value+2) = *(value+3) = 0;
</code>

What just happened here? Make sure you understand, or ask questions and get clarification before attempting to continue.

Essentially, we have just allocated 4 bytes of memory (of type **unsigned char**), which are located consecutively in memory. To draw a picture, we'd have this:

^  0  ^  0  ^  0  ^  0  ^
|  *(value+0)  |  *(value+1)  |  *(value+2)  |  *(value+3)  |

4 bytes of memory, each containing a single digit of our 4 digit number. Let's assume we are attacking this as a decimal (base 10) value, and we'll maintain our assumption that the left-most value is the **most significant digit**, and the right-most value is the **least significant digit**.

For example, let's say we wanted to store the 4-digit number 8192 in memory using this scheme. The code and resulting "picture" would be as follows:

<code c>
    *(value+0) = 8;
    *(value+1) = 1;
    *(value+2) = 9;
    *(value+3) = 2;
</code>

^  8  ^  1  ^  9  ^  2  ^
|  *(value+0)  |  *(value+1)  |  *(value+2)  |  *(value+3)  |

Make sense?

Be aware that *(value+0), the first memory address of our sequence, is at the left side of our value... therefore it stores the **most significant digit**. You are free to do it the other way, just make sure that whatever approach you take, you maintain your logic.

Now, what if we wanted to perform an addition?

8192+4 = 8196

Pretty easy right?

4 in our memory scheme would be represented as "0004", and we'd accomplish the addition as follows:

<code c>
    *(value+0) = *(value+0) + 0;
    *(value+1) = *(value+1) + 0;
    *(value+2) = *(value+2) + 0;
    *(value+3) = *(value+3) + 4;
</code>

As you can see, the value of "4" was added only to the last (**least significant**) digit stored in our value. Displaying it should should the expected answer:

^  8  ^  1  ^  9  ^  6  ^
|  *(value+0)  |  *(value+1)  |  *(value+2)  |  *(value+3)  |

There's actually two situations that occur with adding... what we just saw was the straight "sum". In this case, the sum was the only meaningful result generated.

But there's also another situation we can have, and that is a carry. A carry is when the result is too big to be stored in a single digit (ie a 2 digit number). So we react by storing the least significant digit and **carry**ing the most significant digit to the next placevalue.

Let's take our 8196 and add 1024 to it. What do we get? **9220**

Illustrated, we have:

^Carry:  |  0  |  1  |  1  |  0  |
^Value:  |  8  |  1  |  9  |  6  |
^Addend:  |  1  |  0  |  2  |  4  |
^Sum:  ^  9  ^  2  ^  2  ^  0  ^
|  ^  *(value+0)  ^  *(value+1)  ^  *(value+2)  ^  *(value+3)  ^

So, for this project I'd like for you to write a set of functions and a test program that:

  * have a function that will allocate space to store a value of desired length (at least 4 and 24, but feel free to test it with larger numbers: 32, 40, 64, etc.) and return the address (so we can assign it to one of our pointers).
  * have a function that will **zero** your value, running through each position and setting it to 0.
  * have a function that will **increment** a given bignum
  * have a function that will **decrement** a given bignum
  * have a function that will accept as a parameter the original number and number to **add**, perform the operation (using **increment** as a base), and place the result in the original number
  * implement a function to tackle **subtraction** being mindful of the carry
  * implement a function to perform **multiplication** (using **add** as a base)
  * implement a function to perform **division**
  * implement a function that accepts as two arguments two of our dynamically allocated "numbers", compares them, and returns a -1 if the left parameter is greater, 0 if they are equal, and 1 if the right parameter is greater.
  * implement a sample program that:
    * prompts the user to enter a the number length (4 digits, 24 digits, 32 digits, etc.)
    * prompts the user for actual values (you'll have to rig up a way to convert the user's input into the appropriate values to place in your managed data type
    * gives the user a choice (perhaps via a menu) that lets them select from all the available functions (even resetting and starting over with new digit-lengths).

=====Code=====

The encipher code:

<code c>
/*
 * encipher.c - program that encodes a message according to a key
 *
 *
 * Compile with: gcc -o encipher encipher.c
 *
 * Place key value in: key.txt
 * Place message to encipher in: plain.txt
 * Enciphered message placed in: cipher.txt
 *
 * Execute with: ./encipher    or    ./encipher KEYVAL
 *
 */
 
#include <stdio.h>
 
int main(int argc, char **argv)
{
    printf("Hello, World!\n");
    
    if(argc == 2)
    {
        printf("%s was called with the following argument: %d\n", argv[0], atoi(argv[1]));
    }
    else
    {
        printf("No argument was provided. Get value from file.\n");
    }
    return(0);
}
</code>

Don't forget your deciphering code as well.
=====Execution=====

An example run of the enciphering process:

<cli>
lab46:~/src/cprog/project1$ ./encipher 7
Cipher key provided on command line: 7

Message is: Traveling the world is the best way to study geography.
 Cipher is: Ayhclspun aol dvysk pz aol ilza dhf av zabkf nlvnyhwof.

lab46:~/src/cprog/project1$ cat cipher.txt
Ayhclspun aol dvysk pz aol ilza dhf av zabkf nlvnyhwof.
lab46:~/src/cprog/project1$ 
</cli>

Now, we switch gears and decipher a different (previously enciphered) message:

<cli>
lab46:~/src/cprog/project1$ echo "12" > key.txt
lab46:~/src/cprog/project1$ echo "Ftq yagzfmuz mfq ftq pas, MZP TAI!" > cipher.txt
lab46:~/src/cprog/project1$ ./decipher
Cipher key found in key.txt: 12

 Cipher is: Ftq yagzfmuz mfq ftq pas, MZP TAI!
Message is: The mountain ate the dog, AND HOW!

lab46:~/src/cprog/project1$ cat plain.txt
The mountain ate the dog, AND HOW!
lab46:~/src/cprog/project1$ 
</cli>
=====Reflection=====
Comments/thoughts generated through performing the project, observations made, analysis rendered, conclusions wrought. What did you learn from doing this project?

=====References=====
In performing this project, the following resources were referenced:

  * URL1
  * URL2
  * URL3 (provides useful information on topic)
  * URL4

Generally, state where you got informative and useful information to help you accomplish this project when you originally worked on it (from Google, other wiki documents on the Lab46 wiki, etc.)
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