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  $Header: /home/ff/cs61c/cvsroot/assignments/lab/06.float/index.rst,v 1.6 2005/11/30 23:42:29 cs61c-tc Exp $

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CS61C Lab 6
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Floating Point and Number Rep
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Background
==========

Goals
-----

This lab shoul help you examine how computers store integer and floating 
point values.

Reading
-------

* P&H Sections on floating point

Info
----

Recall that the single precision floating point number is stored as::

	SEEE EEEE EIII IIII IIII IIII IIII IIII

where:

S is the sign bit, 0 for positive, 1 for negative
E is the exponent, bias 127
I is the significant, with an implicit 1

For example, the floating point representation of 1.0 would be 
0x3F800000. Verify to yourself that this is correct.

Exercises
=========

Setup
-----

Copy the contents of ~cs61c/labs/06 to a suitable location in
your home directory.

::

	$ mkdir -p ~/lab
	$ cp -R ~cs61c/labs/06/ ~/lab

Exercise 1: Integers
--------------------

Find the shortest sequence of MIPS instructions to determine if there is 
a carry out from the addition of two registers, say $t3 and $t4. Place a 
0 or 1 in register $t2 if the carry out is 0 or 1, respectively. (This 
can be done in just two instructions). Verify that your code works for 
the following values:

========== ========== ==========
Operand    Operand    Carry out?
========== ========== ==========
0x7fffffff 0x80000000 no
0xffffffff 0          no
0xffffffff 1          yes
========== ========== ==========

Exercise 2: Floating Point
--------------------------

Find a positive floating point value x, for which x+1.0=x. Verify your 
result in a MIPS assembly language program, and determine the stored 
exponent and fraction for your x value (either on the computer or on 
paper).

Note: The provided MIPS program `p2.s`_ will allow you to experiment with 
adding floating point values. It leaves the output in $f12 and also $s0, 
so you can examine the hex representation of the floating point value by 
printing out $s0.

.. _`p2.s`: p2.s

Exercise 3: Floating Point
--------------------------

Next, find the smallest positive floating point value x for which 
x+1.0=x. Again, determine the stored exponent and fraction for x.

Exercise 4: Floating Point Associativity
----------------------------------------

Finally, using what you have learned from the last two parts, determine 
a set of positive floating point numbers such that adding these numbers 
in a different order can yield a different value. You can do this using 
only three numbers. (Hint: Experiment with adding up different amounts 
of the x value you determined in part 3, and the value 1.0).

This shows that for three floating point numbers a, b, and c, a+b+c does 
not necessarily equal c+b+a.

If time permits, you should write a program to add these three values in 
different orders. It should be a straightforward modification of the 
program from part 2-3.