CS2011 - Data Lab: Manipulating Bits  - Solved

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.

 

 
     
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 con- ditionals) 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, and some have fewer restrictions. 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.

Note: For this assignment, we will always use 32-bit numbers. Bits are numbered from the right, counting from zero. So, the rightmost (least-significant) bit is bit 0, and the leftmost is bit 31.

 

 

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 (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.

 


oddBits(void) Return word with all odd-numbered bits set to 1 using    only !, ˜, &, ˆ, |, +, <<, and >>.

isTmin(x) Returns 1 if x is the minimum, two’s complement  10 number, and 0 otherwise.

     bitXor(x,y)        xˆy using only ˜ and &.                                                               14

                                                           Same as x ? y : z.                                                                     16

 greatestBitPos(x) Return a mask that marks the position of the most  70 significant 1 bit. If  x  ==  0, return 0.  greatestBitPos(96) = 0x40.

 

Table 1: Bit-Level Manipulation Functions.

 

4.2 Two’s Complement Arithmetic
For this part of the assignment, you will implement some common single-precision floating-point opera- tions. 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 3 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.

 

 Name Description  Rating Max Ops float_neg(uf) Compute -f  2 10 float_i2f(x) Compute (float) x 4 30 float_twice(uf) Compute 2*f  4 30

 

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, in- cluding 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, 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.

 


 

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 43. 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 7 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

 

•  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.

 

 


 
        Notes and Advice
 

•  This is an individual assignment. You may discuss general strategy for solving any puzzle, but you may not copy or even look at anyone else’s code, including solutions found online. In previous terms, several students were found to have identical code for a number of the puzzles, all copied from the same online source.

•  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 */ 



 
 
 

} 

 

 

        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:

 

unix> ./driver.pl -u ‘‘Your Nickname’’