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日期:2019-04-03 10:02

CS 2505 Spring 2019

Data Lab: Data and Bitwise Operations

Assigned: March 19

Due: Tuesday March 29, 23:59

Ends: Friday April 5, 23:59

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 artificial, but you’ll

find 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 file you submit.

3 Handout Instructions

Download the file datalab-handout.tarfrom the course website to a (protected) directory on a Linux

machine on 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 assigned 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 arithmetic and logical operators:

! & | + << >>

(Of course, you are allowed to use the assignment operator.) A few of the functions further restrict this list.

Also, you are not allowed to use any literal constants longer than 8 bits. See the comments in bits.c for

detailed rules and a discussion of the desired coding style.

1

4 The Puzzles

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

4.1 Bit Manipulations

Table 1 describes a set of functions that manipulate and test sets of bits. The “Rating” field gives the

difficulty rating for the puzzle, the “Max Ops” field gives the maximum number of operators you are allowed

to use to implement each function, and the “Points” field shows how many points a solution to the puzzle is

worth. 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.

Name Description Rating Max

Ops Points

bitAnd(x, y) returns x & y 1 8 30

upperBits(n) pads n upper bits with 1’s 1 10 30

byteSwap(x, n, m) swaps the nth byte and the mth byte of x 2 25 25

isLess(x, y) if x < y then return 1, else return 0 3 24 15

Table 1: Required Functions

5 Evaluation

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 subOK

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

unix> ./btest -f subOK -1 0xFFFFFFFF 0xFAFAFAFA

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

2

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. If your code does not compile

when tested with driver.pl you will receive a 0 for the assignment.

Scoring rules

Your score will be computed out of a maximum of 100 points based on the following distribution:

Correctness points. (maximum 80 points) The 4 puzzles you must solve have been given a difficulty rating

between 1 and 3. Each of the puzzles will be worth the number of points shown in the tables above, but the

5 points for each puzzle will be reserved for performance. 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 driver.pl, and no credit otherwise.

Performance points. (maximum 20 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 5 points for each correct function that satisfies the operator limit.

Explanation and analysis points. (maximum deduction 40 points) You must add to the header comment

for each function an explanation of the logic employed in your solution. This comment must be accurate,

precise and complete. For example:

3

/*

* isNotMultOf4 - returns 0 if x is a multiple of 4,

* non-0 otherwise

* Examples: isMultOf4(0x033B104C) = 0

* isMultOf4(0x033B1046) != 0

* Legal ops: ? & ? |

* Max ops: 5

* Rating: 1

* Logic:

* x is a multiple of 4 if and only if x % 4 = 0. But, since

* x % 4 returns the remainder when x is divided by 4, and

* dividing by 4 will simply chop off the two low bits of x,

* x % 4 will yield the two low bits of the representation

* of x. So, x is a multiple of 4 if and only if its

* representation ends in two 0s.

*

* We can obtain the desired bits by applying the right

* mask to x. The key is to set the 30 high bits to 0,

* so we could do this: x & 0x00000003.

*

*/

int isMultOf4(int x) {

int mask = 0x03; // OK, it’s a one-byte constant ’0011’,

// which will be sign-extended to a

// 32-bit value:

// 00000000 00000000 00000000 00000011.

return x & mask; // 0 if low bits are 00, non-0 otherwise

}

We will evaluate your explanations for some, but not all, of the functions. If your explanation for a function

is unsatisfactory, we will apply a deduction of up to 10 points to your score for that function.

The evaluation of these comments will be performed by the TAs, not by the autograding tools described

below. It is up to you to make sure your explanations are worthy of credit.

6 Handin Instructions

You will submit your bits.c file to the Curator under the heading c06. Like the earlier programming

assignments, this is not autograded at the time of submission. Instead, we will periodically run autograding

code on your submissions, and post the results to the Curator system.

Of course, if you apply the tools btest, dlc, and driver.pl properly, you will already know whether

your solution passes testing.

4

7 Advice

The nature of this assignment requires creating a 32-bit executable. However, 64-bit Linux distributions,

including CentOS, do not include some libraries that are necessary to build a 32-bit executable.

That leaves you with two choices.

You can complete the assignment on a node in the rlogin cluster, which do support 32-bit builds.

Or, you can update your CentOS virtual machine to include the necessary libraries. The following

command may suffice:

> yum install glibc-devel.i686

If not, you may find the discussion below to be helpful:

stackoverflow.com/questions/23638271/how-to-compile-32-bit-apps-on-64-bit-rhel

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 an archaic form of the C Standard. In particular, its rules for declarations

are different than those 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 */

}

The effect will be that dlc will ”zap” the offending code, and it will not compile, or will compile but

not perform correctly. You can avoid lots of disappointment if you make sure you use driver.pl

to do the final testing of your solution.

We will make no accommodations for failing to test your solution with driver.pl; you have been

warned.

5


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