1 Introduction
The purpose of this assignment is to become more familiar with bit-level representations of integers and floating point numbers. 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.
2 Handout Instructions
Download the datalab-floating-point.tar from PLMS. Upload the file to a programming server, move it to the directory you want to work on. Then give the command
unix> tar xvf datalab-floating-point.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 code for each of the 2 programming puzzles about two’s complement and 4 programming puzzles about floating point. See the comments in bits.c for detailed rules and a discussion of the desired coding style.
3 The Puzzles
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.
3.1 Two’s Complement Arithmetic
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:
! ˜ & ˆ | + << >>
Table 1 describes a set of functions that make use of the two’s complement representation of integers. Again, refer to the comments in bits.c and the reference versions in tests.c for more information.
Name Description Rating Max Ops
negate(x) Return -x 2 5
isLess(x,n) Returns 1 if x < y, and return 0 otherwise 3 24
Table 1: Arithmetic Functions
3.2 Floating-Point Operations
Table 2 describes a set of functions that operate on the bit-level representations of floating-point numbers. Refer to the comments in bits.c and the reference versions in tests.c for more information.
Name Description Rating Max Ops
float_abs(uf) Compute absolute value of f 2 10
float_twice(uf) Compute 2 * f 4 30
float_i2f(x) Compute (float) x 4 30
float_f2i(uf) Compute (int) ff 4 30
Table 2: Floating-Point Functions. Value f is the floating-point number having the same bit representation as the unsigned integer uf.
Functions float_abs and float_twice must handle the full range of possible argument values, including not-a-number (NaN) and infinity. The IEEE standard does not specify precisely how to handle NaN’s, and the IA32 behavior is a bit obscure. We will follow a convention that when of these functions is given a NaN value as ab argument, it will return the same value for the results (Refer to the comments in bits.c).
4 Evaluation
Your score will be computed out of a maximum of 19 points.
Correctness points. We will evaluate your functions using the btest and dlc program, which is described in the next section. You will get full credit for a problem if it passes all of the tests performed by btest and verified with dlc, and no credit otherwise.
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 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 bitAnd
You can feed it specific function arguments using the option flags -1, -2, and -3:
unix> ./btest -f bitAnd -1 7 -2 0xf
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
5 Handin Instructions
Upload your bits.c file and report in PLMS with the following format:
• Rename your bits.c file as: [student id].c (e.g., 20231234.c)
• Submit your report with pdf format: [student id].pdf (e.g., 20231234.pdf)
Submissions with incorrect format will not be graded, no exception (i.e., you will get 0 points for this entire lab).
6 Tips & Advice
• We provide a program fshow that will help you to understand the structure of floating point numbers. To compile fshow, switch to the handout directory and type:
unix> make
You can use fshow to see what an arbitrary pattern represents as a floating-point number:
unix> ./fshow 2080374784 Floating point value 2.658455992e+36
Bit Representation 0x7c000000, sign = 0, exponent = f8, fraction = 000000 Normalized. 1.0000000000 X 2ˆ(121)
You can also give fshow hexadecimal and floating point values, and it will decipher their bit structure.
• 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 */
}
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