Programming Assignment PA4: CS 270 Computer Organization

Programming Assignment PA4 - Floating Point Math

Programming due Sunday, February 15 at 10:00pm, no late submission.

This assignment has four objectives:

to learn floating path representation and math,
to write more C code that directly manipulates numbers,
to appreciate what floating point hardware does, and
to see if you can follow directions!

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 code in field.c that you wrote for PA3.

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 or software does not provide floating point support. This understanding will be crucial later in the semester because you will write similar programs for the LC3 computer, which has no support for floating point.

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

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. PA3).
Copy five files into this directory. It is easiest to right click on the link, and do a Save Target As.. for each of the files.
- field.h (do not modify)
- field.o (do not modify)
- flt32.c (complete this file)
- flt32.h (do not modify)
- testFlt32.c (do not modify)
- Makefile (do not modify)
Open a terminal and make sure you are in the directory you created in step 1. The cd command can be used for this.

In the terminal type the following command to build the executable.


    make

You should see the following output:


    c99 -g -Wall -c flt32.c
    c99 -g -Wall -c testFlt32.c
    c99 -g -o testFlt32 field.o flt32.o testFlt32.o

In the terminal type ./testFlt32 and read how to run the the program.
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.

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

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

flt32_get_sign(): 1 line of code
flt32_get_exp(): 1 line of code
flt32_get_val(): 1 line of code
flt32_abs(): 1 line of code
flt32_sub(): 1 line of code
flt32_negate(): 3 lines of code
flt32_get_sve(): 4 lines of code
flt32_leftmost_1(): 10 lines of code
flt32_add(): 60 lines of code

Your code may be a little longer, but in most every case, these functions 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 functions you wrote that are documented in field.h. Simply call those functions from your code.

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 functions you have already written and thoroughly tested.

The general algorithm for floating point addition is as follows:

Extract the sign, exponent, and mantissa for each of the numbers.
Adjust the number with the smaller exponent so that it has the same exponent as the other one. This is done by shifting the mantissa and and incrementing the exponent. When this is complete both numbers should have the same exponent. This will be the initial value for the exponent of the sum.
Convert the sign/magnitude representation to 2’s complement.
Do an integer addition.
Convert the two’s complement back to sign/magnitude
Normalize the result using shift operations and increment/decrement the exponent appropriately.
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 page on the course webpage.

Specifications

Your program must meet the following specifications:

Work on your own, as always.
The name of the source code file must be exactly flt32.c.
Name the file exactly - upper and lower case matters!
Comments at the top as shown above.
Make sure your code runs on machines in the COMCS 120 lab.
Submit your program to the Checkin tab as you were shown in the recitation.
Read the syllabus for the late policy.
We will be checking programs for plagiarism, so please don't copy from anyone else.

Grading Criteria

100 points for perfect submission.
0 points for no submission, will not compile, submitted class file, etc.
Each test can make multiple calls to the function being tested, with different values.
Preliminary Tests
- testCompile: checks that program compiles. (0 points)
- test1: calls testFlt32 with sign to check flt32_get_sign (positive number). (5 points)
- test2: calls testFlt32 with sign to check flt32_get_sign (negative number). (5 points)
- test3: calls testFlt32 with exp to check flt32_get_exp. (5 points)
- test4: calls testFlt32 with val to check flt32_get_val. (5 points)
- test5: calls testFlt32 with abs to check flt32_abs (positive number). (5 points)
- test6: calls testFlt32 with abs to check flt32_abs (negative number). (5 points)
- test7: calls testFlt32 with neg to check flt32_negate (positive number). (5 points)
- test8: calls testFlt32 with neg to check flt32_negate (negative number). (5 points)
- test9: calls testFlt32 with lm1 to check flt32_leftmost_1. (10 points)

Submit the single file flt32.c to the Checkin tab on the course website, as you were shown in the recitation, and read the syllabus for the late policy (if necessary).