Data Lab: Manipulating Bits Solution

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

 

This is an individual project. All handins are electronic. Clarifications and corrections will be posted on the course Web page.

 

3.  Handout Instructions

 

The datalab-handout.tar will be posted on the moodle webpage. Start by copying datalab- handout.tar to a (protected) directory on a Linux machine in which you plan to do your work. Give the command

 

unix module unload soft/gcc

 

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 14 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:

 

! ̃& 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.

 

4.   The Puzzles

 

 

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

 

A.  Bit Manipulations and Two’s complement Arithmetic

 

 

Table 1 describes a set of functions that manipulate and test sets of bits. 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.

 

Name   Description      Rating Max Ops

bitXor(x,y)      x ˆ y using only   and &          1          14

evenBits          return word with all even-numbered bits set to 1       1          8

leastBitPos(x)  Return a mask that marks the position of the least

significant 1 bit. If x == 0, return 0    2          6

isEqual(x, y)    Return 1 if x == y , and 0 otherwise   2          5

fitsBits(x, n)    Return 1 if x can be represented as an n-bit, two's complement integer        2          15

reverseBytes(x)           Reverse the bytes of x            3          25

isPositive(x)    Return 1 if x 0, return 0 otherwise  3          8

multFiveEights(x)       Multiplies by 5/8 rounding toward 0  3          12

isLessOrEqual(x, y)    Return 1 if x <= y, return 0 otherwise            3          24

logicalNeg(x)  Implement the ! operator using all of the legal

operators except !        4          12

tc2sm(x)          Convert from two's complement to sign-magnitude

where the MSB is the sign bit.            4          15

leftBitCount(x)           returns count of number of consective 1's in left-

hand (most significant) end of word  4          50

Table 1: Bit-Level Manipulation Functions.

 

 

B.  Floating-Point Operations

 

For this part of the assignment, you will 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.

 

Name   Description      Rating Max Ops

float_neg(uf)   Compute -f      2          10

float_half(uf)  Compute 0.5*f            4          40

Table 2: Floating-Point Functions. Value f is the floating-point number having the same bit representation as the unsigned integer uf.

 

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

 

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 100 points based on the following distribution:

 

67 Correctness points.

28 Performance points.

5 Style points.

 

Correctness points. The 14 puzzles you must solve have been given a difficulty rating between 1 and 4, such that their weighted sum totals to 38. This is then scaled linearly to 67 points. 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.

 

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 bitXOR

 

You can feed it specific function arguments using the option flags -1, -2, and -3: 4

 

unix ./btest -f bitXOR -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

 

Your instructors will use driver.pl to evaluate your solution.

 

6.  Handin Instructions

 

 

Submit your final bits.c file to the moodle webpage.

 

 

 

7.  Advice

 

 

•     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 */

}