Description

1 Introduction
The purpose of this assignment is to become more familiar with bit-level representations of floating point numbers. Youll solve six problems in the presentation.
2 Logistics
This is an individual project. All handins are electronic. Clarifications and corrections will be posted on PLMS. If you have any question, please use Q & A board. Submitted codes are assumed to be runnable on programming server.
3 Handout Instructions
Start by copying datalab-floating-point.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-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 for each of the 6 programming problems.
4 The Problems
4.1 Two’s Complement Arithmetic
Your assignment is to complete each function skeleton using only straightline code for the integer problems (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 | + << >>
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.
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) -x without negation 2 5
isLess(x,y) x < y? 3 24
Table 1: Arithmetic Functions
4.2 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.
Functions float_neg 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 for any function returning a NaN value, it will return the one with bit representation 0x7FC00000.
The included program fshow helps you understand the structure of floating point numbers. To compile fshow, switch to the handout directory and type:
Name Description Rating Max Ops
float_abs(uf) Compute absolute value of f 2 10
float_twice(uf) Computer 2*f 4 30
float_i2f(x) Compute (float) x 4 30
float_f2i(uf) Compute (int) f 4 30
Table 2: Floating-Point Functions. Value f is the floating-point number having the same bit representation as the unsigned integer uf.
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.
5 Evaluation
Your score will be computed out of a maximum of 19 points.
Correctness points. We will evaluate your functions using the btest 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 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.
6 Handin Instructions
Upload your source file bits.c and report in PLMS. You need to explain your answer in the report. The format of file is (student number) (your name).c / .doc.
7 Advice
• 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 */
}