cs270 Programming Assignment PAx - Floating Point math


Due: xx/xx/xxxx @ 11:59PM
Key: Use the key PAx for checkin

About The Assignment

This assignment is designed to teach you how to do several floating point point operations in C without using either the float or double types. Rather, you will manipulate the bits of the floating point values using the field code you wrote in a previous assignment. You will also learn simple pointer operations using C's address-of operator (&) and dereference operator (*).

When you have completed this assignment you will understand how floating point values are stored in the computer, and how to perform several operations in the case where the underlying hardware/software does not provide floating point support. For example, the LC3 computer you will use later in this course has no floating point support.

First read the Getting Started section below and then study the documentation for flt32.h in the Files tab to understand the details of the assignment.

Getting Started

Perform the following steps
  1. Create a directory for this assignment. A general scheme might be to have a directory for each CS class you are taking and beneath that, a directory for each assignment. The name of the directory is arbitrary, but you may find it useful to name it for the assignment (e.g. PAx).
  2. Copy six files into this directory. It is easiest to right click on the link, and do a Save Target As.. for each of the files.
  3. Open a terminal and make sure you are in the directory you created in step 1. The cd command can be used for this.
  4. In the terminal type the following command to build the executable.
    You should see the following output:
        /usr/bin/gcc -g -Wall -c -std=c11 field.c
        /usr/bin/gcc -g -Wall -c -std=c11 flt32.c
        /usr/bin/gcc -g -Wall -c -std=c11 testFlt32.c
        /usr/bin/gcc -g -o testFlt32 field.o flt32.o testFlt32.o
  5. In the terminal type testFlt32 and read how to run the the program.
  6. In the terminal type testFlt32 bin -3.625 and you should see the output:
        dec: -1066926080  hex: 0xC0680000  bin: 1100-0000-0110-1000-0000-0000-0000-0000
    What you are seeing it the internal bit pattern of the floating point value -3.625 expressed as an integer, as hex, and as binary.

You now have a functioning program. All the commands work, however, only bin will produce correct results at this point.

Completing the Code

Before attempting to write any of the functions of flt32.c, study the documentation in found in the files tab. Plan what you need to do before writing code.

The best way to complete the code is to follow a write/compile/test sequence. Do not attempt to write everything at once. Rather choose one function and do the following steps.

  1. Write some/all of one function in flt32.c using your favorite editor.
  2. Save your changes and recompile field.c using make. You will find it convenient to work with both a terminal and editor window at the same time.
  3. Repeat steps 1 and 2 until there are no errors or warnings.
  4. Test the function you have been working on. Do not attempt to move on until you complete and thoroughly test a function.
  5. Repeat steps 1 thru 5 for the remaining functions.

You may work on the functions in any order, but most are very simple and are support functions for the meat of the code. A sample solution prepared by the author contained the following:

Your code may be a little longer, but in every case, these methods are quite simple. If you find any of your solution is much longer that stated, you will want to think about how you are approaching the problem. Remember to take advantage of the methods you wrote for field.c. Simply call those methods from your code. Do NOT copy code from field.c into this file.

Floating Point Addition

The single function flt32_add() is the only complex function in this assignment. Many of the things you need to do can be done by calling the support methods you have already written and thoroughly tested.

The general algorithm for floating point addition is as follws:

  1. Extract the sign, exponent, and value for each of the numbers
  2. Allign the decimal points using shift operations. When this is complete both numbers have the same exponent which is the initial value for the exponent of the sum.
  3. Convert the sign/magnitude representation to two's complement
  4. Do an integer addition
  5. Convert the two's complement back to sign/magnitude
  6. Normalize the result using shift operations and increment/decrement the exponent appropriately.
  7. Reassemble the sign, exponent and value into a 32 bit value.

Checking in Your Code

You will submit the single file flt32.c using the checkin program. Use the name PAx. At the terminal type:

    ~cs270/bin/checkin PAx flt32.c

The above command submits your assignment. For a sanity check, type the following to get the file you checked in and make sure it compiles and runs properly with the provided files:

    mkdir sanityCheck
    cd sanityCheck
    ~cs270/bin/peek PAx flt32.c > flt32.c
    cp ../field.h ../field.c ../flt32.h ../testFlt32.c ../Makefile .
    // Do LOTS of test cases.
Relax, you are done with your assignment!