Lecture 10 – Sep 25th, 2019

Setup

Log in to clyde.
Create a directory and cd into it.
Copy ~steve/ex/rand.h and ~steve/ex/rand.c into the directory.

Task

Take a look at rand.h and look at the function declared there. What arguments does it take? What does it return?
Write a file printfloat.c. Include rand.h and stdio.h. Your main function should call random_value() one time, storing the result in a variable of type double. Print that value out three times using printf with the %e, %f, and %g format specifiers.
Compile the program using
```
$ clang -std=c11 -Wall -o printfloat printfloat.c rand.c
```
and then run it a few times. Do the printed values match what you expected? If not, check out the man page for printf(3) (you’ll need to run $ man 3 printf because printf(1) is the manual page for the shell command printf and we want the library function).
Modify printfloat.c to change the precision used to print the floats. E.g., try %.1e, %.2e, %.3e. Recompile and run the program a few times each.
Each time we recompile, we’re forcing the compiler to recompile rand.c even though it hasn’t changed. This isn’t a big deal with such a small program, but imagine a program with 100 files. This could take a long time for each small change.
Compile each of printfloat.c and rand.c separately and then link them together.
```
$ clang -std=c11 -Wall -c -o printfloat.o printfloat.c
$ clang -std=c11 -Wall -c -o rand.o rand.c
$ clang -o printfloat printfloat.o rand.o
```
Now modify printfloat.c in some way (any way you want), recompile just printfloat.o and then do the final linking step.
```
$ clang -std=c11 -Wall -c -o printfloat.o printfloat.c
$ clang -o printfloat printfloat.o rand.o
```
What do you think the average distance between two uniformly random numbers in the range [0, 1] is? There are two ways we can figure this out. The hard way: we could compute the integral $\int_0^1\int_0^1|x-y|\,dx\,dy.$
But this isn’t calculus class, so let’s do it the easy way: Monte–Carlo simulation. That’s just a fancy way of saying, let’s run a bunch of random trials and see what we get on average.
Write a new file mc.c. Include rand.h and stdio.h as before. Use #define to define a constant NUM_TRIALS. E.g., something like
```
#define NUM_TRIALS 10
```
In the main function, define a variable double total = 0.0;. Next, loop NUM_TRIALS times (a for loop works well here) and use random_value() to get two random numbers x and y. Use the fabs function (read its man page to see what header you need and how to call it) to compute the absolute value of x-y. Add the result to total.
After the loop, print out the average value of $|x-y|$ by dividing total by NUM_TRIALS.
Compile your program by compiling mc.c to mc.o and then linking mc.o and rand.o as a program called mc. Run ./mc a few times.
Increase the value of NUM_TRIALS and recompile and run. Try the values 100, 1000, and 10000.
Does the answer match what you’d expect? (I find it kind of surprising!) Let’s double check our results by asking a much more complicated computer program than the one we just wrote to work a lot harder and solve the double integral above. Check out the result on Wolfram|Alpha.