1   Introduction

The purpose of this assignment is to become more familiar with bit-level representations of integers. You’ll do this by solving a series of programming“puzzles.”Many of these puzzles are quite artiicial, but you’ll ind yourself thinking much more about bits in working your way through them.

2   Logistics

You may work in pairs for this assignment. If you work with a partner, list both names and both PIDs in a comment at the beginning of the bits.c ile you submit.

3   Handout Instructions

Start by downloading the datalab-handout.tar to a (protected) directory on a Linux machine in which you plan to do your work. Then give the command

unix> tar xvf datalab-handout.tar.

This will cause a number of iles to be unpacked in the directory. The only ile you will be modifying and turning in is bits.c.

The bits.c ile contains a skeleton for each of the 13 programming puzzles.  Your assignment is to complete each function skeleton using only straightline code for the integer puzzles (i.e., no loops or con- ditionals) and a limited number of C arithmetic and logical operators. Speciically, you are only allowed to use the following eight operators:

! ˜ & ˆ | + << >>

A few of the functions further restrict this list. Also, you are not allowed to use any constants longer than 8 bits. See the comments in bits.c for detailed rules and a discussion of the desired coding style.

4   The Puzzles

This section describes the puzzles that you will be solving in bits.c.

Table 1 lists the puzzles in rought order of dificulty from easiest to hardest. The“Rating”ield gives the dificulty rating (the number of points) for the puzzle, and the“Max ops”ield gives the maximum number of operators you are allowed to use to implement each function.  See the comments in bits.c for more details on the desired behavior of the functions. You may also refer to the test functions in tests.c. These are used as reference functions to express the correct behavior of your functions, although they don’t satisfy the coding rules for your functions.

Table 1: Datalab puzzles.

5   Evaluation

Your score will be computed out of a maximum of 50 points based on the following distribution:

10 Puzzle 1 Correctness points.

20 Puzzle 2 Correctness points.

20 Puzzle 3 Correctness points.

10 Puzzle 4 Correctness points.

Correctness points. The puzzles you must solve have been given a dificulty rating between 1 and 4, such that their weighted sum totals to 50. We will evaluate your functions using the btest program, which is described in the next section. You will get full credit for a puzzle if it passes all of the tests performed by btest, and no credit otherwise.

Performance points.   Our main concern at this point in the course is that you can get the right answer. However, we want to instill in you a sense of keeping things as short and simple as you can. Furthermore, some of the puzzles can be solved by brute force, but we want you to be more clever. Thus, for each function we’ve established a maximum number of operators that you are allowed to use for each function. This limit is very generous and is designed only to catch egregiously ineficient solutions. You will receive two points for each correct function that satisies the operator limit.

Style points. Finally, we’ve reserved 5 points for a subjective evaluation of the style of your solutions and your commenting. Your solutions should be as clean and straightforward as possible. Your comments should be informative, but they need not be extensive.

Performance and Style points will be manually graded after the assignment is due.

Autograding your work

We have included some autograding tools in the handout directory — btest, dlc, and driver.pl — to help you check the correctness of your work.

 btest: This program checks the functional correctness of the functions in bits.c. To build and

use it, type the following two commands:

unix> make

unix> ./btest

Notice that you must rebuild btest each time you modify your bits.c ile.

You’ll ind it helpful to work through the functions one at a time, testing each one as you go. You can use the -f ag to instruct btest to test only a single function:

unix> ./btest -f bitXor

You can feed it speciic function arguments using the option ags -1, -2, and -3:

unix> ./btest -f bitXor -1 4 -2 5

Check the ile README for documentation on running the btest program.

 dlc: This is a modiied version of an ANSI C compiler from the MIT CILK group that you can use

to check for compliance with the coding rules for each puzzle. The typical usage is:

unix> ./dlc bits.c

The program runs silently unless it detects a problem, such as an illegal operator, too many operators, or non-straightline code in the integer puzzles. Running with the -e switch:

unix> ./dlc -e bits.c

causes dlc to print counts of the number of operators used by each function. Type ./dlc -help for a list of command line options.