[an error occurred while processing this directive]		


<!-- OWNER_NAME="Larry Hoyle, University of Kansas" -->
<!--link rev=made href="mailto:larryhoyle@ku.edu "-->
<!-- OWNER_INFO="University of Kansas, IPSR (785) 864-3701" -->

<h1>
 The Pentium FDIV bug - a Picture<br>
</h1>
Intel Pentium chips manufactured before a certain date have a bug in their floating 
point processor which returns less than full precision results for some combinations 
of divisor and dividend when performing a Floating point DIVision (FDIV). A well 
known operation which exhibits this phenomenon is 4195835/3145727. You can check 
to see if your Pentium has the FDIV bug by entering the following formula in the 
Windows calculator: 
<p>
(4195835 / 3145727) * 3145727 - 4195835  <p>
The image below is a 3d graph of the function x/y in the region of
4195835/3145727. Specifically, the region is: <p>
4195833.0 <= x <= 4195836.4 <p>
3145725.7 <= y <= 3145728.4 <p>
On a 486/66, the function graphs as a monotonically increasing surface
with the low point in the foreground corner (where x is low and y is high)
and a high point in the background corner (where x is high and y is low).
On a Pentium with the FDIV bug there are two triangular areas in the
region where an incorrect result is returned. The correct values all
would round to 1.3338 and the incorrect values all would
round to 1.3337, an error in the 5th significant digit. <p>
An archive of principal papers on the Pentium FDIV bug is available at:
<a href="http://www.mathworks.com/company/pentium/index.shtml">
http://www.mathworks.com/company/pentium/index.shtml</a><p>

<a href=
"pentgrph.gif">
<img align="top" alt="click here to retrieve the GIF file"
src="pentgrph.gif">
</a> <p>
A ZIP file containing
the Microsoft Excel spreadsheet along with an Encapsulated Postscript
copy of this graphic can be retrieved from:
<a href="http://www.ipsr.unit.ku.edu/stafffil/hoyle/pentium_fdiv/pentgrph.zip">http://www.ipsr.unit.ku.edu/stafffil/hoyle/pentium_fdiv/pentgrph.zip</a><p>

Larry Hoyle (larryhoyle@ku.edu) <br>
<a href="http://www.ipsr.unit.ku.edu">
Institute for Policy &amp; Social Research
</a><br>
<a href="http://www.ku.edu">
University of Kansas
</a><br>
Nov. 30, 1994
<div class="hidden">
    <img src="http://ires.ku.edu/~ipsr/cgi-bin/IPSRcounter.pl?pagename=pentium" width="50" height="20" alt="Institute for Policy &amp; Social Research" />
</div>

[an error occurred while processing this directive]