CSE 351 Spring 2011 Lab 1

Manipulating Bits (using C)

Assigned: Friday, April 1, 2011
Due: Friday, April 8, 2011 at 11:59 PM
Turnin: Online

Overview

The purpose of this assignment is to become more familiar with data at the bit-level representation. 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.

Instructions

You can fetch the files required for this homework at http://www.cs.washington.edu/education/courses/cse351/11sp/labs/lab1.tar.gz
(Un-tar'ing [just like you did in homework 0] will create a lab1 directory.)

The lab1 folder contains a number of tools, described later, and a bits.c file. bits.c contains a skeleton for each of the programming puzzles, along with a large comment block that describes exactly what the function must do and what restrictions there are on its implementation. Your assignment is to complete each function skeleton using:

only straightline code (i.e., no loops or conditionals);
a limited number of C arithmetic and logical operators; and
no constants longer than 8 bits.

The intent of the restrictions is to require you to think about the data as bits—because of the restrictions, your solutions won't be the most efficient way to accomplish the function's goal, but the process of working out the solution should make the notion of data as bits completely clear.

Note: The infrastructure for this assignment may require a 32-bit system—it tries to force gcc to generate a 32-bit executable, but we can't guarantee it works. If you use a 64-bit system, verify that your code works on a 32-bit system before turn-in (e.g., using attu.cs).

The Puzzles

This section describes the puzzles that you will be solving in bits.c. More complete (and definitive, should there be any inconsistencies) documentation is found in the bits.c file itself.

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.

Table 1: Bit-Level Manipulation Functions
Name Description Rating Max Ops

bitNor(x,y) x nor y using only & and ~ 1 8

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

thirdBits() return a word with every third bit set 1 8

isNotEqual(x,y) return 0 if x == y, and 1 otherwise 2 6

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

logicalShift(x,n) shift x to the right by n, using a logical shift 3 20

isAsciiDigit(x) return 1 if 0x30 <= x <= 0x39 3 15

conditional(x,y,z) same as x ? y : z (the ternary conditional operator) 3 16

bang(x) Compute !n without using the ! operator. 4 12

Table 1: Bit-Level Manipulation Functions
Name	Description	Rating	Max Ops
`bitNor(x,y)`	`x nor y` using only `&` and `~`	1	8
`bitXor(x,y)`	`x ^ y` using only `&` and `~`	1	14
`thirdBits()`	return a word with every third bit set	1	8
`isNotEqual(x,y)`	return 0 if `x == y`, and 1 otherwise	2	6
`byteSwap(x,n,m)`	swap the `n`th byte and the `m`th byte	2	25
`logicalShift(x,n)`	shift `x` to the right by `n`, using a logical shift	3	20
`isAsciiDigit(x)`	return 1 if `0x30 <= x <= 0x39`	3	15
`conditional(x,y,z)`	same as `x ? y : z` (the ternary conditional operator)	3	16
`bang(x)`	Compute `!n` without using the `!` operator.	4	12

Two's Complement Arithmetic

Table 2 describes 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
Name Description Rating Max Ops

minusOne() return a value of -1 1 2

negate(x) return -x 2 5

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

isPower2(x) return 1 if x is a power of 2, and 0 otherwise 4 20

Table 2: Arithmetic Functions
Name	Description	Rating	Max Ops
`minusOne()`	return a value of -1	1	2
`negate(x)`	return `-x`	2	5
`isPositive(x)`	return 1 if `x > 0`, and 0 otherwise	3	8
`isPower2(x)`	return 1 if `x` is a power of 2, and 0 otherwise	4	20

Checking your work

We have included two tools to help you check the correctness of your work.

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:
```
  $ ./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:
```
  $ ./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.
btest: This program checks the functional correctness of the code in bits.c. To build and use it, type the following two commands:
```
  $ make
  $ ./btest
```
Notice that you must rebuild btest each time you modify your bits.c file. (You rebuild it by typing make.)
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:
```
  $ ./btest -f bitNor
```
You can feed it specific function arguments using the option flags -1, -2, and -3:
```
  $ ./btest -f bitNor -1 7 -2 0xf
```
Check the file README for documentation on running the btest program.

Advice

Do not 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.

You should be able to use the debugger on your code. For example:

  $ make
  gcc -O -Wall -m32 -g -lm -o btest bits.c btest.c decl.c tests.c
  gcc -O -Wall -m32 -g -o fshow fshow.c
  gcc -O -Wall -m32 -g -o ishow ishow.c
  $ gdb ./btest
  GNU gdb (GDB) Fedora (7.1-34.fc13)
  Copyright (C) 2010 Free Software Foundation, Inc.
  License GPLv3+: GNU GPL version 3 or later <http://gnu.org/licenses/gpl.html>
  This is free software: you are free to change and redistribute it.
  There is NO WARRANTY, to the extent permitted by law.  Type "show copying"
  and "show warranty" for details.
  This GDB was configured as "i686-redhat-linux-gnu".
  For bug reporting instructions, please see:
  <http://www.gnu.org/software/gdb/bugs/>.
  Reading symbols from /homes/iws/dvhc/cse351/lab1/src/btest...done.
  (gdb) b bitNor
  Breakpoint 1 at 0x8048717: file bits.c, line 144.
  (gdb) r
  Starting program: /homes/iws/dvhc/cse351/lab1/src/btest 
  Score	Rating	Errors	Function

  Breakpoint 1, bitNor (x=-2147483648, y=-2147483648) at bits.c:144
  144	}
  (gdb) p x
  $1 = -2147483648
  (gdb) p/x x
  $2 = 0x80000000
  (gdb) q
  A debugging session is active.

  	Inferior 1 [process 12728] will be killed.

  Quit anyway? (y or n) y
  $

The dlc program enforces a stricter form of C declarations than is the case for C++ or that is enforced by gcc. In particular, in a block (what you enclose in curly braces) all your variable declarations must appear before any statement that is not a declaration. For example, dlc 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 */
  }
```
Instead, you must declare all your variables first, like this:
```
  int foo(int x)
  {
      int a = x;
      int b;
      a *= 3;
      b = a;
  }
```

Turnin

Please submit just your finished bits.c file using the Catalyst turn-in page for this assignment. The navigation sidebar above also has a link to the main Catalyst 351 turnin page.