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 artificial, but you’ll find yourself thinking much more about bits in working your way through them.
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 file you submit. Below is the link to the tar file for the assignment.
datalab-handout.tar
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 files to be unpacked in the directory. The only file you will be modifying and turning in is bits.c.
The bits.c file contains a skeleton for each of the 4 programming puzzles. Your assignment is to complete each function skeleton using only straightline code for the integer puzzles (i.e., no loops or conditionals) and a limited number of C arithmetic and logical operators. Specifically, you are only allowed to use the following eight operators:
! ~ & ^ | + << >>
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.
The Puzzles
This section describes the puzzles that you will be solving in bits.c.
Table 1 lists the puzzles in rough order of difficulty from easiest to hardest. The “Rating” field gives the difficulty rating (the number of points) for the puzzle, and the “Max ops” field 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.
Datalab puzzles.
Name Description Rating Max ops
tmin() return minimum two’s complement integer 1 4
negate(x) return -x 2 5
isLess(x, y) if x < y then return 1, else return 0 3 24
logicalNeg(x) implement the ! operator 4 12
Evaluation (Note: point values may be adjusted here to make the assignment worth the same as other projects)
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 difficulty 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 inefficient solutions. You will receive two points for each correct function that satisfies 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.
Grading your work
We have included some grading 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 file.
You’ll find it helpful to work through the functions one at a time, testing each one as you go. You can use the -f flag to instruct btest to test only a single function:
unix> ./btest -f bitXor
You can feed it specific function arguments using the option flags -1, -2, and -3:
unix> ./btest -f bitXor -1 4 -2 5
Check the file README for documentation on running the btest program.
dlc: This is a modified 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.
driver.pl: This is a driver program that uses btest and dlc to compute the correctness and performance points for your solution. It takes no arguments:
unix> ./driver.pl
Your instructors will use driver.pl to evaluate your solution. You solution must work when driver.pl is used. If you code does not run using driver.pl it will score a 0.
Handin Instructions
You will turn in your bits.c to Canvas. We hope to use the grader to score your assignment. But this may have to be done manually and if so we will do this as often as possible.
If you worked with a partner, only one of you needs to submit the file. Make sure both names and PIDs are at the top; if your partner's name is not on the submission, they will not receive a score.
Scoring
The grader will assign up to 68 points. The remaining 12 points will be awarded by the GTAs for comments.
The comments must explain the logic of what your code does. If these are not present you will not receive these points.
Advice
Don’t include the header file in your bits.c file, as it confuses dlc and results in some non-intuitive error messages. You will still be able to use printf in your bits.c file for debugging without including the header, although gcc will print a warning that you can ignore.
The dlc program enforces a stricter form of C declarations than is the case for C++ or that is enforced by gcc. In particular, any declaration must appear in a block (what you enclose in curly braces) before any statement that is not a declaration. For example, it will complain about the following code:
int foo(int x)
{
int a = x;
a *= 3; /* Statement that is not a declaration */
int b = a; /* ERROR: Declaration not allowed here */
}