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

A project for C/C++ by Corey Forman during the spring 2012.

This project was begun on 3/15/12 and is anticipated to take 3/16/12 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 numbers 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 accept as a parameter the original number and number to **add**, perform the operation, 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**
  * 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>
 #include <stdio.h>
  2 #include <stdlib.h>
  3 int subtraction(int *a1, int *a2,int);
  4 int *add(int *a1, int *a2,int,  int);
  5 int main()
  6 {
  7     char junk;
  8     int choice;
  9     choice=0;
 10
 11     printf("Thank you for using this program. There are some rules. First no decimals. Second put spaces between each number ... not like this 123 butlike this 1 2 3 for des    ired results. third no letters, the program will error out. please note 0 is a number so if you say you want 4 digits then put 4 0's then your digits it will not see those d    igits. thank you for your time.\n\n\n");
 12     printf("please input which you would like to perform. [1] for adding,[2] for subtraction, [3] for devision, and [4] for multiplication: ");
 13
 14     // above is asking which action they wish to take. bellow will be the unfortunate if statements to see what action they selected.
 15     fscanf(stdin, "%d", &choice);
 16     scanf("%c", &junk);
 17 //  printf("%d is what you chose.\n", choice);
 18 //  a=choice+1;
 19 //  printf("%d is testing to see if it is a number by adding 1 and becomming %d\n",choice,a);
 20
 21     if( choice  == 1 )
 22     {
 23         printf(" you have chosen addition\n");
 24         char junk;
 25         int *arr1, *arr2, sizea,sizeb,i,l,a,b,c,e,f,g,k;
 26         i=-1;e=k=f=0;
 27         a=b=c=sizea=sizeb=0;
 28
 29         printf("please enter the size of the first digit: ");
 30         fscanf(stdin, "%d", &sizea);
 31         scanf("%c", &junk);
 32
 33
 34
 35
 36         arr1 = (int *)malloc( sizeof(int) * (sizea));
 37         arr2 = (int *)malloc( sizeof(int) * (sizea));
 38
 39         printf("now enter your first number: ");
 40         g=0;
 41         while(g!='\n'-48)
 42         {
 43             g = fgetc(stdin);
 44             g = g-48;
 45             arr1[e] = g;
 46             e = e+1;
 47 //          if (e=sizea)
 48 //              break;
 49         }
 50         g=0;
 51         printf("now enter your second number, note that you may have to have 0's infront of your second number to make them both the same size: ");
 52         while(g!='\n'-48)
 53         {
 54             g = fgetc(stdin);
 55             g = g-48;
 56             arr2[f] = g;
 57             f = f + 1;
 58         }
 59
 60         printf("your answere is: ");
 61         for(l=sizea-1;l>=0;l--)
 62         {
 63             if( i == -1)
 64             {
 65                 i = sizea - 1;
 66             }
 67
 68             a = arr1[i];
 69
 70             b = arr2[l];
 71             if( (a+b) < 10 )
 72             {
 73                 a = a + b;
 74
 75             }
 76             else if( ( a + b ) >= 10 )
 77             {
 78                 c = arr1[i-1];
 79
 80                 c = c + 1;
 81
 82                 arr1[i-1] = c;
 83                 a = a + b;
 84
 85                 a = a - 10;
 86
 87             }
 88             arr1[i] = a;
 89             i=i-1;
 90         }
 91         if(arr1[0] >= 10)
 92         {
 93             c = arr1[0];
 94             c = c - 10;
 95             arr1[0] = c;
 96             printf("1");
97         }
 98         for(i=0;i<sizea;i++)
 99         {
100         printf("%d",arr1[i]);
101
102
103         }
104         printf("\n");
105     }
106     if( choice == 2)
107     {
108         printf(" you have chosen subtraction\n");
109         char junk;
110         int *arr1,*arr2,sizea,sizeb,i,l,a,b,c,e,f,g,k;
111         i=-1;e=k=0;f=0;
112         a=b=c=sizea=sizeb=0;
113         printf("please enter how many digets the first number consists of: ");
114         fscanf(stdin, "%d", &sizea);
115
116
117         arr1 = (int *)malloc( sizeof(int) * (sizea));
118
119         arr2 = (int *)malloc( sizeof(int) * (sizea));
120
121         scanf("%c", &junk);
122         printf("please enter now your first number: ");
123         g=0;
124         while(g!='\n'-48)
125         {
126             g = fgetc(stdin);
127             g = g - 48;
128             arr1[e] = g;
129             e = e +1;
130
131         }
132         g=0;
133         printf("please enter your second number set please cushion your number to match the length of the first by adding 0's to the beginning of it: ");
134         while(g!='\n'-48)
135         {
136             g = fgetc(stdin);
137             g = g -48;
138             arr2[f] = g;
139             f = f +1;
140         }
141     printf("your answere is: ");
142         for(l=sizea-1;l>=0;l--)
143         {
144             if(i == -1)
145             {
146                 i = sizea -1;
147             }
148             a = arr1[i];
149             b = arr2[l];
150             if( a >= b )
151             {
152                 a = a - b;
153             }
154             else if( a < b)
155             {
156                 c = arr1[i-1];
157                 c = c - 1;
158                 arr1[i-1] = c;
159                 a = a + 10;
160                 a = a - b;
161             }
162             arr1[i] = a;
163             i=i-1;
164         }
165
166         for(i=0;i<sizea;i++)
167         {
168         printf("%d",arr1[i]);
169
170
171         }
172
173
174         printf("\n");
175
176
177     }
178     if( choice == 3)
179     {
180         printf(" you have chosen devision\n");
181         char junk;
182         int *arr1, *arr2, sizea,i,l,a,b,c,e,f,g,k;
183         i=-1;e=k=f=0;
184         a=b=c=sizea=0;
185
186         printf("please enter the size of your first digit: ");
187         fscanf(stdin,"%d", &sizea);
188         scanf("%c", &junk);
189
190
191
192         arr1 = (int *)malloc( sizeof(int) * (sizea));
193         arr2 = (int *)malloc( sizeof(int) * (sizea));
194
195         printf("now enter your first number: ");
196         g=0;
197         while(g!='\n'-48)
198         {
199             g = fgetc(stdin);
200             g = g-48;
201             arr1[e] = g;
202             e = e+1;
203         }
204
205         g=0;
206         printf("now enter your second number. please cushion it with 0's to insure they are the same size ... 0's before the number you wish to enter: ");
207         while(g!='\n'-48)
208         {
209             g = fgetc(stdin);
210             g = g -48;
211             arr2[f] = g;
212             f = f +1;
213         }
214
215         fprintf(stdout,"your answere is %d \n",subtraction(arr1,arr2,sizea));
216     }
217     if( choice == 4)
218     {
219         printf(" you have chosen multiplication\n");
220
221         char junk;
222         int *arr1,*arr2,sizea,sizeb,i,l,a,b,c,e,f,g,k,times;
223         i=-1;e=k=0;f=0;
224         a=b=c=sizea=sizeb=times=0;
225         printf("please enter how many digets the first number consists of: ");
226         fscanf(stdin, "%d", &sizea);
227
228
229         arr1 = (int *)malloc( sizeof(int) * (sizea));
230
231         arr2 = (int *)malloc( sizeof(int) * (sizea));
232
233         scanf("%c", &junk);
234         printf("please enter now your number: ");
235         g=0;
236         while(g!='\n'-48)
237         {
238             g = fgetc(stdin);
239             g = g - 48;
240             arr1[e] = g;
241             arr2[e] = g;
242             e = e +1;
243         }
244
245         printf("now enter what you are multiplying it by: ");
246         fscanf(stdin, "%d", &times);
247
248         printf("your answer is ");
249         add(arr1,arr2,times,sizea);
250
251         for(i=0;i<sizea;i++)
252         {
253         printf("%d",arr1[i]);
254         }
255         printf("\n");
256     }
257     if( (choice != 1) && (choice !=2) && (choice != 3) && (choice != 4));   {
258         printf("you failed to enter in one of the choices\n");
259         exit(1);
260     }
261
262     return(0);
263 }
264
265
266 int subtraction(int *arr1, int *arr2,int sizea)
267 {
268     int l,i,a,b,c,p;
269     l=i=a=b=c=p=0;
270     while(!(*arr1 <= 0))
271     {
272         i=sizea-1;
273         for(l=sizea-1;l>=0;l--)
274         {
275
276             a = arr1[i];
277             b = arr2[l];
278             if( a >= b )
279             {
280                 a = a - b;
281             }
282             else if( (a < b)&&(arr1[i-1]>0))
283             {
284                 c = arr1[i-1];
285                 c = c - 1;
286                 arr1[i-1] = c;
287                 a = a + 10;
288                 a = a - b;
289             }
290             arr1[i] = a;
291             i=i-1;
292         }
293         p=p+1;
294     }
295     return(p);
296 }
297
298 int *add(int *arr1, int *arr2,int times, int sizea)
299 {
300     int l,i,a,b,c,p;
301     l=i=a=b=c=0;
302     p=1;
303     while( p != times)
304     {
305         i=sizea-1;
306         for(l=sizea-1;l>=0;l--)
307         {
308
309             a = arr1[i];
310
311             b = arr2[l];
312             if( (a+b) < 10 )
313             {
314                 a = a + b;
315
316             }
317             else if( ( a + b ) >= 10 )
318             {
319                 c = arr1[i-1];
320
321                 c = c + 1;
322
323                 arr1[i-1] = c;
324                 a = a + b;
325
326                 a = a - 10;
327
328             }
329             arr1[i] = a;
330             i=i-1;
331         }
332         p = p + 1;
333     }
334     return(arr1);
335 }

</code>


=====Execution=====

ADDITION
<cli>
lab46:~/src/cprog/c++/project2$ ./bignum
Thank you for using this program. There are some rules. First no decimals. Second put spaces between each number ... not like this 123 butlike this 1 2 3 for desired results. third no letters, the program will error out. please note 0 is a number so if you say you want 4 digits then put 4 0's then your digits it will not see those digits. thank you for your time.


please input which you would like to perform. [1] for adding,[2] for subtraction, [3] for devision, and [4] for multiplication: 1
 you have chosen addition
please enter the size of the first digit: 4
now enter your first number: 4321
now enter your second number, note that you may have to have 0's infront of your second number to make them both the same size: 0043
your answere is: 4364

</cli>

SUBTRACTION

<cli>
 you have chosen subtraction
please enter how many digets the first number consists of: 5
please enter now your first number: 64326
please enter your second number set please cushion your number to match the length of the first by adding 0's to the beginning of it: 03452
your answere is: 60874

</cli>

DEVISION

<cli>
 you have chosen devision
please enter the size of your first digit: 3
now enter your first number: 555
now enter your second number. please cushion it with 0's to insure they are the same size ... 0's before the number you wish to enter: 055
your answere is 9
</cli>

MULTIPLICATION

<cli>
 you have chosen multiplication
please enter how many digets the first number consists of: 3
please enter now your number: 025
now enter what you are multiplying it by: 005
your answer is 125
</cli>

=====Reflection=====
This was a super difficult but super fun to do program. It took many hours and much help but it was also a great learning experience. One key thing i learned is to read every letter of my programs because more often then not my mistakes lay in the fact that i put one letter into a variable or something just wrong so my program decides to have a spazz attack on me. Other then that issue it was amazing and im glad it is finished. 
=====References=====
In performing this project, the following resources were referenced:

  * class