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# Computer Systems Data Lab: Manipulating Bit

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CSCI 2400 – Computer Systems
Data Lab: Manipulating Bit
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 Logistics
All handins are electronic. Clarifications and corrections will be posted on the course Moodle page. Grading
will be done through interviews.
3 Handout Instructions
Start by copying datalab-handout.tar to a (protected) directory on a Linux machine in which you
plan to do your work. We recommend the desktop or home directory of your virtual machine. 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 programming puzzles. Your assignment is to complete
each function skeleton using only straightline (no if/while/etc) 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 | + << >>
A few of the functions further restrict this list. Also, you are not allowed to use any constants longer than
8 bits, but you can construct larger constants using 8 bit constants and operators. See the comments in
bits.c for detailed rules and a discussion of the desired coding style.
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4 The Puzzles
This section describes the puzzles that you will be solving in bits.c.
Some of the puzzle are bit manipulations (treating the data as a vector of bits), some are focused on two’s
complement artihmetic, teaching bits as numbers. There are some extra credit problems that treat the bits as
floating point numbers.
Each problem has a Difficulty Rating and maximum number of operations. 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 – each one describes the intended semantics, the rating and
the allowed number of operations. 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
4.1 Floating-Point Operations
For Extra Credit, you can implement some common single-precision floating-point operations. In this section, you are allowed to use standard control structures (conditionals, loops), and you may use both int and
unsigned data types, including arbitrary unsigned and integer constants. You may not use any unions,
structs, or arrays. Most significantly, you may not use any floating point data types, operations, or constants.
Instead, any floating-point operand will be passed to the function as having type unsigned, and any returned floating-point value will be of type unsigned. Your code should perform the bit manipulations that
implement the specified floating point operations.
Table 1 describes a set of functions that operate on the bit-level representations of floating-point numbers.
Name Description Rating Max Ops
float_abs(uf) Compute |f| 2 10
float_f2i(f) Compute (int) f 4 30
float_half(uf) Compute f/2 4 30
Table 1: 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_half 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:
unix> make
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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
This section only includes evaluation for the standard section, not the extra credit.
The assignment is scored in two parts – you will receive 40 percent of the overall score for having correctly functioning functions handed in on time and 60 percent for being able to correctly explain how your
To compute the 40% for the correctness score, your correctness score will be computed out of a maximum
of 62 points based on the following distribution:
34 of 62 points correct output
28 of 62 points not exceeding the maximum operations
Correctness points. The 12 puzzles you must solve have been given a difficulty rating between 1 and 4, such
that their weighted sum totals to 29. 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.
Extra Credit
You can receive up to 10% extra credit for this assignment by completing all of the floating point problems.
You will have to read ahead to learn about floating point, because we’re going to cover it later; however,
you’re going to have to learn it someday…
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We have included some autograding tools in the handout directory — btest, dlc, and driver.pl —
Note that the autograding script produces a report about ’points’ – this doesn’t align with what we’ve described above (which is what holds). This happens in part because of the presence of the extra problems.
• 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 bitOr
You can feed it specific function arguments using the option flags -1, -2, and -3:
unix> ./btest -f bitOr -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
The default driver.pl script uses simple tests to check if your code is likely correct. A more
comprehensive test is to involve driver.pl -b, which will use a BDD library to prove that your
code handles all cases. This is what the TA’s will use during interview grading, but this can be more
time consuming. You should be fine just using driver.pl without the -b flag for testing.
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6 Handin Instructions
and we encourage you upload often so you don’t run into problems at the last minute or lose
• Don’t include the <stdio.h> 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 <stdio.h> 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 */
b *= a; // ERROR — this comment style causes errors
}
8 The “Beat the Prof” Contest
For fun, we’re offering an optional “Beat the Prof” contest that allows you to compete with other students
and the instructor to develop the most efficient puzzles. The goal is to solve each Data Lab puzzle using the
fewest number of operators. Students who match or beat the instructor’s operator count for each puzzle are
winners!
To submit your entry to the contest, type: