| Assigned: | Friday, August 29 |
| Due: | Friday, September 12, 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 an implementation of increment, addition and multiplication of nonnegative integers, stored in binary, in either Java or C++. Design your functions as shown in one of the following pages.
Follow the designs as shown, since otherwise your program will not link correctly with the tester.Please keep track, as best you can, of the number of hours that you spend on this. In the 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. Include all of the time, including time spent testing and debugging, but not time spent submitting it.
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 should meet the following requirements. (And yes, I will grade down for failure to meet these requirements, even if you have not been asked to meet such stringent requirements in the past.)
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 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 they 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, or if it is 0, and has 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 positive number that starts with a 0.
Your functions must not have requirements that are not stated in the contracts. For example, for the C++ implementation, it is unacceptable to insist that array R be set to all zeros by the caller before calling sum or product, since the contract does not say anything about that.
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 program.
Test your functions. In order to do the testing, you will want a function that prints a binary number. That is not part of the assignment, and should not be turned in, but software designers often find that they need to write extra functions to aid in testing.
If you do not test your functions, you can rest assured that they do not work, and they will fare poorly when graded. Test them thoroughly. Do not be satisfied with one or two tests.
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). (x means times.)
You can use any system that you like. The systems in the lab have changed. The Windows lab has Eclipse. Austin 218 has machines that log into a Linux server. You can use g++ or javac/java on that. It also has Eclipse. If you nave any questions about this, or if you have trouble using a system, please let me know.
Because of system changes, it is not yet clear how you will submit your work. I will let you know later.