Floating Point Representation and Operations_Project 6 Solution

Computer Project #6 -- Floating Point Representation and Operations

Assignment Overview:
For this assignment, you will develop a C function which adds single
precision floating point values without the use of floating point hardware.

It is worth 40 points (4% of course grade)

Assignment Specifications:

1) Some computer systems do not have floating point hardware (they have an
Integer Unit, but not a Floating Point Unit). Thus, floating point
operations on those systems must be performed using software.

You will develop the C function listed below:

float add( float, float );

The two arguments are the single precision floating point values to be
added, and the return value is the sum of those two values.

Arguments which are denormal will be processed as the value zero.

If either argument is the floating point value "not-a-number", function
"add" will return that value. Otherwise, if either argument is the floating
point value "infinity", function "add" will return that value.

The value returned from function "add" will be as accurate as possible.

Function "add" (and any associated "helper" functions which you develop)
will constitute a module named "proj06.support.c". The functions in that
support module will not call any C library functions, and they will not use
any floating point operations. There is one exception: the functions may
use the assignment operation to copy a floating point value from one
variable to another.

2) You will develop a driver module to test your implementation of function
"add" in your support module. The source code for the driver module must be
in a separate file. All output will be appropriately labeled.

Your driver module will not be interactive. If it accepts any input, you
will supply that input in a text file named "proj06.tests".

Assignment Deliverables:

The deliverables for this assignment are:

proj06.makefile -- the makefile which produces "proj06"
proj06.support.c -- the source code for your support module
proj06.driver.c -- the source code for your driver module
proj06.tests -- the input to your driver module, if needed

Be sure to use the specified file names, and to submit your files for
grading via the "handin" program.



Assignment Notes:

1) Please note that your driver module may not be written as an interactive
program, where the user supplies input in response to prompts. Instead,
your test cases will either be included in the source code as literal
constants, or will be supplied as inputs to the driver module in a file
named "proj06.tests".

If your driver requires no inputs, your solution will be executed using:

proj06

If your driver does require inputs, your solution will be executed using:

proj06 < proj06.tests

2) The Murdocca and Heuring text contains information about floating point
representation and operations (particularly pages 45-48 and pages 74-76).

Please note that infinity, not-a-number, zero and denormal numbers are
special cases in IEEE floating point notation.

3) An outline of one method for computing C = A + B is given below:

Extract sign, exponent, and fraction fields of both A and B.
Place leading bit in both significands.
Determine exponent of C based on exponents of A and B; shift
significand of A or B (based on the difference between exponents).
Compute significand of C = significand of A + significand of B.
Normalize significand of C.
Insert sign, exponent, and fraction fields of C.

Note that this outline does not describe special cases, such as operands
which are infinity, not-a-number, zero or denormal numbers.

4) In order to work with a 32-bit item as both a floating point value and an
integer value, you might consider using a union. For example:

#include <stdio.h

union sp_item
{
float frep;
unsigned irep;
};

int main()
{
union sp_item num;

num.frep = 1.5;

printf( "Real: %f Hex integer: %08x \n", num.frep, num.irep );
}

When compiled and executed, that program produces the following:

Real: 1.500000 Hex integer: 3fc00000

Note that the four-byte memory location "num" can be referenced as both an
object of type "float" and an object of type "unsigned int".