For the first assignment, we will look at how Racket (Scheme) handles big numbers.

Consider the following Java program (available in Test.java).

  public class Test {
    public void main(String[] args) {
      System.out.println(999999999999999999999 * 2);
    }
  }

You could easily calculate 999999999999999999999 * 2 with pencil and paper;
Java cannot handle it.

  $ javac Test.java
  Test.java:3: error: integer number too large: 999999999999999999999
      System.out.println(999999999999999999999 * 2);
                         ^
  1 error

With Racket, there is no problem:

  $ racket
  Welcome to Racket v6.0.1.
  > (* 999999999999999999999 2)
  1999999999999999999998
  >

So how does Racket handle these numbers?
We will implement a simplified big-num module to understand it better.

In our implementation, a number will be a list of "blocks" of numbers from 0-999,
stored with the least significant "block" first. So 9,873,201 will be
stored as:

  '(201 873 9)

Your job is to complete big-num.rkt.  The breakdown of points is as follows:
* 10 points -- Complete big-add1
*  5 points -- Complete big-subtract1
*  3 points -- Complete big-eq
*  1 points -- Complete big-multiply
*  1 points -- Complete big-power-of


Starter code is available at http://cs.sjsu.edu/~austin/cs152-fall15/hw/hw1/.
The files include:
* big-num.rkt -- You will modify this file (only).
* bc.rkt -- A (very) simple calculator that relies on your big-num module.
* test.rkt -- A number of test cases that use big-num.
* input -- A number of cases that bc.rkt should handle correctly.
* output_EXPECTED -- the expected results of calling (from the command line):
  $racket test.rkt
  $racket bc.rkt < input

Note that negative numbers are not supported, so
  (big-subtract '(9) '(10))
may give an error.

Submit big-num.rkt through Canvas.  If you submit additional files, you will lose 2 points.

Some notes on this assignment:

*Your solution must be recursive.
*You cannot use Scheme's "set!" function.
*You must work by yourself.
*Your code cannot call string->bignum or number->bignum.

If you violate any of these rules, you will get a 0 for the assignment.