CS60 Homework 10
---------------------

Due: Mon. Nov 3rd at 1:00pm

Complex Number Arithmetic Library
-----------------------------------

The task of homework 10 is to write a simple library that performs
arithmetic on complex numbers.  Complex numbers are numbers that
consist of a real part and imaginary part such that they can be used
as points on the imaginary plane. We can think of a pair of integers
(x,y) as the complex number (x+yi) where i is the square root of -1.

There is a a pre-written header file, on the website, that contains
the definition of a complex number type:

struct complex_t {
	int x;
	int y;
};

Also on the website there is an code file that I have written and
that needs implementation of the following functions:

int addcomplex(struct complex_t *result, struct complex_t *a, struct complex_t *b);

int mulcomplex(struct complex_t *result, struct complex_t *a, struct complex_t *b);

the prototypes of which are also in the included header file.  Your
task is to implement these two functions and create a library called
libcomplex.a which contains the complied object code of the function
implementation.  Finally, you need to create a Makefile that compiles
your code and my code, creates a library, and finally links the object
file 'hw10.o' with your library to create and executable.  You must
explicitly create a library file called 'libcomplex.a' that is used in
linking using the '-lcomplex' directive to gcc, it is not sufficient
to simply link your code's .o file with hw10.o.  You may NOT edit the
hw10.c file that I have written, the goal of this project is to write
a complex number library which does not require editing hw10.c.

Complex Arithmetic
------------------

Assuming we have two complex numbers representations (a,b) and (c,d)
(which correspond to the complex numbers a+bi and c+di), arithmetic is
performed in the following manner:

(a,b) + (c,d) = (a+c, b+d)

and

(a,b) * (c,d) = (a*c - b*d, a*d + b*c)


The program hw10.o performs the following operations in the following
order:

(10,1) + (10,1)
(500,40) + (0,0)
(12,11) * (3,10)
(100,43) * (1,0)
(0,1) * (0,1)


Turnin
---------------

The turnin tag for this assignment is 'hw10' and must include the code
for the complex number arithmetic functions, a Makefile, and a
typescript showing compilation using make (gcc must have -ansi
-pedantic flags as usual) and execution of the resulting binary.


Sample Output
----------------

[nurmi@localhost hw10]$ ls
Makefile     complex.h    hw10.c       typescript
complex.c    hw10         hw10.outline
[nurmi@localhost hw10]$ make clean
rm -f complex.o libcomplex.a hw10.o
[nurmi@localhost hw10]$ make
cc -I./   -c -o complex.o complex.c
making libcomplex
ar rs libcomplex.a complex.o 
ar: creating archive libcomplex.a
cc -I./   -c -o hw10.o hw10.c
making all
gcc -ansi -pedantic hw10.o -o hw10 -L./ -lcomplex
[nurmi@localhost hw10]$ ./hw10
Res1: 20 + 2i
Res2: 500 + 40i
Res3: -74 + 153i
Res4: 100 + 43i
Res5: -1 + 0i
[nurmi@localhost hw10]$ ls
Makefile     complex.h    hw10         hw10.o       libcomplex.a
complex.c    complex.o    hw10.c       hw10.outline typescript
[nurmi@localhost hw10]$ make clean
rm -f complex.o libcomplex.a hw10.o
[nurmi@localhost hw10]$ ls
Makefile     complex.h    hw10.c       typescript
complex.c    hw10         hw10.outline
[nurmi@localhost hw10]$