Architecture of Computer and Network, Spring 2023 Data Lab: Manipulating Bits

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   handout   file   is   avaliable   at   the   course   file   page.   Start   by   copying datalabhandout.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-

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 15 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:

! ~ & ^ | + << >>

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.

4.1 Bit Manipulations

Table 1describes 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.

Table 1: Bit-Level Manipulation Functions.

4.2 Two’s Complement Arithmetic

Table2describes 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.

Table 2: Arithmetic Functions

4.3 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.

Table3describes 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.

Table 3: Floating-Point Functions. Value f is the floating-point number having the same bit representation as the unsigned integer uf.

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:

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, fractio

n = 000000

Normalized.  1.0000000000 X 2^(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:

41

Correctness points.

30

Performance points.

29

Document points.

Correctness points. The 15 puzzles you must solve have been given a difficulty rating   between 1 and 4, such that their weighted sum totals to 41. 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 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

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

6 Handin Instructions

Please submit your project before due date. The project consistes of two parts, the

source file (bits.c) filled with your code and a document file (.pdf) of explaination for the function of your code of each problem. You shall write the document either in English or Chinese.