Assignment 5

Goal



To get hands on experience with algorithms to perform mathematical operations on large integers.


High-level description



You will be writing a replacement for Java's BigInteger Euclidean algorithm on integer values that would overflow


to perform multiplications and to run the extended long .


Specifications



1. You are provided with the start of a class to process arbitrarily-sized integers called HeftyInteger . HeftyInteger objects are represented internally as two's-complement raw integers using byte arrays

(i.e., instances of    byte[] ).


1.  Currently,    HeftyInteger  has the following operations implemented:


A constructor that creates a new    HeftyInteger  object based on a provided  byte[] .


A method to compute the sum of two    HeftyInteger  objects.


A method to determine the negation of a    HeftyInteger  object.


A method to compute the difference of two    HeftyInteger  objects.


Several other helper methods.


2.    Due to the use of a two's complement representation of the integers, positive HeftyInteger objects should always have at least one leading 0 bit (indicating that the integer is positive) in their

byte[] representation. This property may cause the array to be bigger than expected (e.g., a 1024-bit positive integer will be represented using a length 129 byte array).

    3. HeftyIntegers are represented using a big-endian byte-order, so the most significant byte is at index 0 of the byte[] .

4.  You will further need to implement the following functions:

HeftyInteger multiply(HeftyInteger other)


HeftyInteger[] XGCD(HeftyInteger other)


Any additional helper functions that you deem necessary.


5.  You may not use any calls the Java API class    java.math.BigInteger  or any other JCL class


within  HeftyInteger .

2.  Once  HeftyInteger  is complete, make sure your implementation of
HeftyInteger  can be used
to run the driver programs contained in  MultiplicationTest.java
and  XgcdTest.java . To get

full credit, your implementation should be efficient enough to complete multiplication or XGCD given 200-digit inputs within 3 minutes.

Submission Guidelines



DO NOT upload any IDE package files.


You must be able to compile the driver programs by running javac MultiplicationTest.java and javac XgcdTest.java , respectively.

You must be able to run the driver program by running java MultiplicationTest and java XgcdTest , respectively.


You must fill out    info_sheet.txt .


The project is due at the precise date and time stated above. Upload your progress to Box frequently, even far in advance of this deadline. No late assignments will be accepted. At the deadline, your Box folder will automatically be changed to read-only, and no more changes will be accepted. Whatever is present in your Box folder at that time will be considered your submission for this assignment—no other submissions will be considered.


Grading Rubric



HeftyInteger



Feature    Points

multiply    40

XGCD
55
Assignment info sheet/submission
5