Astro 503
Homework #2, due Jan 24, 2006
1.  Write a complex.cpp file that implements all the subroutines
declared in the following complex.h file.  Then write a
textComplex.cpp program that has a main() that tests each of these
routines. 

//// begin complex.h
typedef struct {
	double real;
	double imag;
} Complex;

Complex
add(Complex z1, Complex z2);
Complex
subtract(Complex z1, Complex z2);
Complex
multiply(Complex z1, Complex z2);
Complex
divide(Complex z1, Complex z2);
void
conjugate(Complex& z);
double
norm(Complex z);
//// end complex.h

2. a) Write subroutines and a header file stopwatch.cpp/stopwatch.h to
   make a "stopwatch" out of  the following two subroutines:

void stopwatchReset();
double stopwatchRead();

These should work in the following way: first you call
stopwatchReset().  Any successive call to stopwatchRead() returns the
number of seconds since you last called stopwatchReset().  To get
started on this, look up the C standard library routines "difftime"
and "time."  On UNIX, just type "man difftime" and "man 3 time" at
your command line.

b)  Write a program called "speed.cpp" that does the following:
  * Creates three arrays a,b, and c of 20,000 double precision numbers each.
  * Fills the arrays a and b with positive numbers of your choosing.
  * Uses the stopwatch functions to determine how long it takes to
  place the (element-wise) product of a and b into c, then prints out
  the number of seconds.
  * Repeats previous step, but using a pointer-index loop instead of
  the natural (for i=0; i<20000; i++) loop.
  * Reports how long it takes to calculate the sqrt of every element
  of a.
  * Reports how long it takes to calculate the arctangent of every
  element of b.

c) Now recompile speed.cpp by telling your compiler to optimize (on
   GNU and Intel compilers, you say "g++ -O -c" or "icc -O -c" instead
   of just "g++ -c" etc.  Report the speeds of your programs with and
   without optimization on your machine.

3.  Write a subroutine NthPrime.cpp that will determine and return the
    value of the Nth prime number, where N<=10,000.  Write the code so
    that the determination of the Mth prime is done only once, no
    matter how many times the routine is called or what the sequence
    of N's is for the call.  Extra credit for the one whose program
    runs most quickly on Reiko's machine!

4. Write a subroutine that reverses the characters in a string.  Then
   create a driver program called reverseit.cpp that will print back to the
   screen all of the words on its command line, but with each word's
   characters reversed.  You may do this with either C-style
   null-terminated strings, or with the C++ string class, as you
   please. Sample:

garyb%  reverseit steelers over colts
sreleets revo stloc