Homework 3

This is a continuation of your work from assignment 2. Implement the subtract() and bitwise_and() methods. Feel free to reuse your earlier code (translating into C++ if necessary, obviously). Write good tests covering all corner cases and also be careful about wraparound conditions. Write a main function that calls the tests. Each test should bomb the program with an assertion violation when an operation returns the wrong interval. You don't need to provide test cases for the logic that detects invalid intervals.

Please do not hand in brute force transfer functions that concretize their arguments, run the concrete operation in the cross product of the resulting sets, and then lift the resulting set back into the abstract domain. This implementation is suitable for testing but not for production.

Unlike C and C++, where signed overflow is undefined, this abstract domain models wrapping integers. Assuming the inputs to a transfer function are valid intervals, no undefined behaviors exist.

You may add whatever utility methods (constructors, equality operators, etc.) you like to the interval class.

class interval {
  // 5-bit signed intervals: valid values for lo and hi are -16..15 and it is
  // required that hi >= lo. the bounds are inclusive.
  int lo, hi;

public:
  // these functions must trigger an assertion violation when presented with any
  // invalid interval, and must never return an invalid interval

  // requirement: be sound and fully precise
  // the second argument is to be subtracted from the first
  static interval subtract(interval, interval);

  // requirement: be sound and don't always return top
  static interval bitwise_and(interval, interval);
};