| Assigned: | Tuesday, August 26 |
| Due: | Tuesday, September 9, 11:59pm |
Arithmetic on large integers can be done by storing an integer in an array, in binary notation. Each member of the array is either 0 or 1. Functions can be written to perform operations such as addition and multiplication.
Write a Java class called Arithmetic, in a file called Arithmetic.java, with static methods to increment, add and multiply nonnegative integers. The integers must be represented in binary as arrays of bits, with the low order bit at index 0. Use the following template.
// Author: ***
// Date: ***
// Tabs: *** (indicate where the tab stops are)
// Time
// Learning language : ***
// Writing function definitions: ***
// Testing function definitions: ***
public class Arithmetic
{
//=================================================================
// inc(A) returns an array of bits representing A+1.
//=================================================================
public static byte[] inc(byte[] A)
{
...
}
//=================================================================
// sum(A,B) returns an array of bits representing A+B.
//=================================================================
public static byte[] sum(byte[] A, byte[] B)
{
...
}
//=================================================================
// product(A,B) returns an array of bits representing A*B.
//=================================================================
public static byte[] product(byte[] A, byte[] B)
{
...
}
}
You can add any number of private static methods.
**Note** Please do not include a package line. If there is a package line, then I must either put your file into a directory whose name matches your package name or I must remove the package line. If your IDE (such as Eclipse) puts in a package line, just remove it in the version that you submit.
Please keep track, as best you can, of the number of hours that you spend on this. In the source file that you submit, write a comment at the top telling your name, and just below that your estimate of the number of hours used for: (1) learning the language or library; (2) writing the module; (3) testing and debugging. Try to be as honest and accurate as possible and reasonable.
You are not asked to write a complete application here. Only three functions (or methods) are to be provided. They are for use in other programs. I will test them by using them in another program. Do not include a main function or method.
Your functions must meet the following requirements.
You are not allowed to trivialize the problem by using a library that performs arithmetic on large integers. The idea is to program the algorithms.
Your functions must implement something close to the standard addition and multiplication algorithms. It is not acceptable, for example, to add x and y by starting at x and doing y increments. That is extremely slow. Similarly, it is not acceptable to multiply x and y by adding y to itself x times. That is also much too slow.
The multiplication algorithm that you learned in grade shool has you write down all of the intermediate products before adding them all up. It is not necessary to do that. Just accumulate the sum as you generate each intermediate product. Be sure to shift over an appropriate amount.
Your functions must not make any assumptions about how large the arrays are, other than those explicitly stated. You cannot assume that the numbers fit into a 64-bit integer. It is unacceptable to assume that the numbers have no more than 100 bits in them. It must be possible to compile your class or functions and put them into a library, and find that they can be used for arbitrarily large integers without recompiling them.
Say that a binary number is normalized if its most significant bit is 1. As a special case, a normalized representation of the number 0 is an array if 0 bits. Your functions must produce normalized results. They cannot presume, however, that their parameter arrays are normalized. For example, a parameter to the addition function might be a number whose high-order bit is 0.
Your functions must not have requirements that have not been stated. For example, they cannot require that the caller perform some initialization.
Your functions must not have any visible actions not stated in the contracts. For example, the contracts do not indicate that anything is being read or written, so nothing should be read or written. Your functions cannot change any of the parameter arrays.
Strive for simplicity and elegance in your definitions. Try to make them clear and readable. Do not be excessively concerned with efficiency.
Test your functions thoroughly. Do not be satisfied with one or two tests of each function.
Test your class by writing a separate class ArithmeticTest that does the testing. It will have at least a main method and a method that prints a binary number.
Here are some recommended tests. You would be well advised to do others as well. All numbers are in standard binary notation (high order bit first).
You can use any system that you like. If you have any questions about this, or if you have trouble using a system, please let me know.
To submit your work you will need to log into one of the Linux computers in Austin 208, or log into xlogin.cs.ecu.edu remotely (using ssh or putty or NX client). Be sure that your files are on that computer, and that your current directory is the one that contains those files.
Then, in a terminal, issue command
~abrahamsonk/3675/bin/submit 1 Arithmetic.java ArithmeticTest.javaCommand
~abrahamsonk/3675/bin/submit 1will tell you what you have submitted.