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	<title>Comments on: to divide or to multiply</title>
	<atom:link href="http://laurentschneider.com/wordpress/2007/06/to-divide-or-to-multiply.html/feed/" rel="self" type="application/rss+xml" />
	<link>http://laurentschneider.com/wordpress/2007/06/to-divide-or-to-multiply.html</link>
	<description>Oracle Certified Master</description>
	<pubDate>Mon, 01 Dec 2008 17:29:59 +0000</pubDate>
	<generator>http://wordpress.org/?v=2.6.5</generator>
		<item>
		<title>By: Laurent Schneider</title>
		<link>http://laurentschneider.com/wordpress/2007/06/to-divide-or-to-multiply.html#comment-4081</link>
		<dc:creator>Laurent Schneider</dc:creator>
		<pubDate>Thu, 21 Jun 2007 12:17:47 +0000</pubDate>
		<guid isPermaLink="false">http://laurentschneider.com/wordpress/2007/06/to-divide-or-to-multiply.html#comment-4081</guid>
		<description>&lt;i&gt;
&#62; SQL&#62; exec while (:y&#62;1e-125) loop :y:=:y*:z; end loop
&#62; 
&#62; PL/SQL procedure successfully completed.
&#62; 
&#62; Elapsed: 00:00:00.00
&lt;/i&gt;
00.00 seems a bit fast, are you sure y was set to 1e125 at the beginning of the test?</description>
		<content:encoded><![CDATA[<p><i><br />
&gt; SQL&gt; exec while (:y&gt;1e-125) loop :y:=:y*:z; end loop<br />
&gt;<br />
&gt; PL/SQL procedure successfully completed.<br />
&gt;<br />
&gt; Elapsed: 00:00:00.00<br />
</i><br />
00.00 seems a bit fast, are you sure y was set to 1e125 at the beginning of the test?</p>
]]></content:encoded>
	</item>
	<item>
		<title>By: Laurent Schneider</title>
		<link>http://laurentschneider.com/wordpress/2007/06/to-divide-or-to-multiply.html#comment-4058</link>
		<dc:creator>Laurent Schneider</dc:creator>
		<pubDate>Tue, 19 Jun 2007 10:41:34 +0000</pubDate>
		<guid isPermaLink="false">http://laurentschneider.com/wordpress/2007/06/to-divide-or-to-multiply.html#comment-4058</guid>
		<description>thanks all for your comments... I was sceptic as I saw this tuning hint. By achieving 40% performance I thought it was worth mentioning. Well, since on APC notebook (is it a &lt;a href="http://www.tadpolecomputer.com/products/notebooks/bullfrog.asp" rel="nofollow"&gt;notebook with solaris/sparc&lt;/a&gt;? ) the division is faster, my test is perhaps is meaningless. Or is it due to TextEdit ;-)

It is also dependent from Oracle. Here one more demo with binary_double, which is about 10x faster ... the difference is smaller, here on solaris/10.2

&lt;code&gt;
SQL&gt; declare
  2    z number;
  3    y number;
  4  begin
  5    z := power(2,103)*1e-31;
  6    for i in 1..10 loop
  7  	 y := 1e125;
  8  	 while (y&lt;1e-125) loop y:=y/z; end loop;
  9    end loop;
 10  end;
 11  /
Elapsed: 00:00:02.95
SQL&gt; declare
  2    z number;
  3    y number;
  4  begin
  5    z := power(2,-103)*1e31;
  6    for i in 1..10 loop
  7  	 y := 1e125;
  8  	 while (y&gt;1e-125) loop y:=y*z; end loop;
  9    end loop;
 10  end;
 11  /
Elapsed: 00:00:01.54
SQL&gt; declare
  2    z binary_double;
  3    y binary_double;
  4  begin
  5    z := power(2,103)*1e-31;
  6    for i in 1..100 loop
  7  	 y := 1e125;
  8  	 while (y&gt;1e-125) loop y:=y/z; end loop;
  9    end loop;
 10  end;
 11  /
Elapsed: 00:00:02.87
SQL&#62; declare
  2    z binary_double;
  3    y binary_double;
  4  begin
  5    z := power(2,-103)*1e31;
  6    for i in 1..100 loop
  7  	 y := 1e125;
  8  	 while (y&gt;1e-125) loop y:=y*z; end loop;
  9    end loop;
 10  end;
 11  /
Elapsed: 00:00:02.40
&lt;/code&gt;</description>
		<content:encoded><![CDATA[<p>thanks all for your comments&#8230; I was sceptic as I saw this tuning hint. By achieving 40% performance I thought it was worth mentioning. Well, since on APC notebook (is it a <a href="http://www.tadpolecomputer.com/products/notebooks/bullfrog.asp" rel="nofollow">notebook with solaris/sparc</a>? ) the division is faster, my test is perhaps is meaningless. Or is it due to TextEdit <img src='http://laurentschneider.com/wordpress/wp-includes/images/smilies/icon_wink.gif' alt=';-)' class='wp-smiley' /> </p>
<p>It is also dependent from Oracle. Here one more demo with binary_double, which is about 10x faster &#8230; the difference is smaller, here on solaris/10.2</p>
<p><pre><code>
SQL&gt; declare
&nbsp;&nbsp;2&nbsp;&nbsp;&nbsp;&nbsp;z number;
&nbsp;&nbsp;3&nbsp;&nbsp;&nbsp;&nbsp;y number;
&nbsp;&nbsp;4&nbsp;&nbsp;begin
&nbsp;&nbsp;5&nbsp;&nbsp;&nbsp;&nbsp;z := power(2,103)*1e-31;
&nbsp;&nbsp;6&nbsp;&nbsp;&nbsp;&nbsp;for i in 1..10 loop
&nbsp;&nbsp;7&nbsp;&nbsp;&nbsp;&nbsp; y := 1e125;
&nbsp;&nbsp;8&nbsp;&nbsp;&nbsp;&nbsp; while (y&lt;1e-125) loop y:=y/z; end loop;
&nbsp;&nbsp;9&nbsp;&nbsp;&nbsp;&nbsp;end loop;
 10&nbsp;&nbsp;end;
 11&nbsp;&nbsp;/
Elapsed: 00:00:02.95
SQL&gt; declare
&nbsp;&nbsp;2&nbsp;&nbsp;&nbsp;&nbsp;z number;
&nbsp;&nbsp;3&nbsp;&nbsp;&nbsp;&nbsp;y number;
&nbsp;&nbsp;4&nbsp;&nbsp;begin
&nbsp;&nbsp;5&nbsp;&nbsp;&nbsp;&nbsp;z := power(2,-103)*1e31;
&nbsp;&nbsp;6&nbsp;&nbsp;&nbsp;&nbsp;for i in 1..10 loop
&nbsp;&nbsp;7&nbsp;&nbsp;&nbsp;&nbsp; y := 1e125;
&nbsp;&nbsp;8&nbsp;&nbsp;&nbsp;&nbsp; while (y&gt;1e-125) loop y:=y*z; end loop;
&nbsp;&nbsp;9&nbsp;&nbsp;&nbsp;&nbsp;end loop;
 10&nbsp;&nbsp;end;
 11&nbsp;&nbsp;/
Elapsed: 00:00:01.54
SQL&gt; declare
&nbsp;&nbsp;2&nbsp;&nbsp;&nbsp;&nbsp;z binary_double;
&nbsp;&nbsp;3&nbsp;&nbsp;&nbsp;&nbsp;y binary_double;
&nbsp;&nbsp;4&nbsp;&nbsp;begin
&nbsp;&nbsp;5&nbsp;&nbsp;&nbsp;&nbsp;z := power(2,103)*1e-31;
&nbsp;&nbsp;6&nbsp;&nbsp;&nbsp;&nbsp;for i in 1..100 loop
&nbsp;&nbsp;7&nbsp;&nbsp;&nbsp;&nbsp; y := 1e125;
&nbsp;&nbsp;8&nbsp;&nbsp;&nbsp;&nbsp; while (y&gt;1e-125) loop y:=y/z; end loop;
&nbsp;&nbsp;9&nbsp;&nbsp;&nbsp;&nbsp;end loop;
 10&nbsp;&nbsp;end;
 11&nbsp;&nbsp;/
Elapsed: 00:00:02.87
SQL&amp;gt; declare
&nbsp;&nbsp;2&nbsp;&nbsp;&nbsp;&nbsp;z binary_double;
&nbsp;&nbsp;3&nbsp;&nbsp;&nbsp;&nbsp;y binary_double;
&nbsp;&nbsp;4&nbsp;&nbsp;begin
&nbsp;&nbsp;5&nbsp;&nbsp;&nbsp;&nbsp;z := power(2,-103)*1e31;
&nbsp;&nbsp;6&nbsp;&nbsp;&nbsp;&nbsp;for i in 1..100 loop
&nbsp;&nbsp;7&nbsp;&nbsp;&nbsp;&nbsp; y := 1e125;
&nbsp;&nbsp;8&nbsp;&nbsp;&nbsp;&nbsp; while (y&gt;1e-125) loop y:=y*z; end loop;
&nbsp;&nbsp;9&nbsp;&nbsp;&nbsp;&nbsp;end loop;
 10&nbsp;&nbsp;end;
 11&nbsp;&nbsp;/
Elapsed: 00:00:02.40
</code></pre></p>
]]></content:encoded>
	</item>
	<item>
		<title>By: Sidhu</title>
		<link>http://laurentschneider.com/wordpress/2007/06/to-divide-or-to-multiply.html#comment-4055</link>
		<dc:creator>Sidhu</dc:creator>
		<pubDate>Tue, 19 Jun 2007 09:16:11 +0000</pubDate>
		<guid isPermaLink="false">http://laurentschneider.com/wordpress/2007/06/to-divide-or-to-multiply.html#comment-4055</guid>
		<description>BTW if we discuss the reasons for the same...what can be the reasons that multiplication involves lesser processing time than division. One as Laurent said "checking for divide by zero things". Any other hits...

Sidhu</description>
		<content:encoded><![CDATA[<p>BTW if we discuss the reasons for the same&#8230;what can be the reasons that multiplication involves lesser processing time than division. One as Laurent said &#8220;checking for divide by zero things&#8221;. Any other hits&#8230;</p>
<p>Sidhu</p>
]]></content:encoded>
	</item>
	<item>
		<title>By: Sidhu</title>
		<link>http://laurentschneider.com/wordpress/2007/06/to-divide-or-to-multiply.html#comment-4054</link>
		<dc:creator>Sidhu</dc:creator>
		<pubDate>Tue, 19 Jun 2007 09:14:31 +0000</pubDate>
		<guid isPermaLink="false">http://laurentschneider.com/wordpress/2007/06/to-divide-or-to-multiply.html#comment-4054</guid>
		<description>Right Andrew

I too did some RnD on the net. At many places, there are talks about this thing (ie multiplication is faster than division). As you said ultimately it depends upon how the same thing is being done at the resigters' level.

So can we conclude that its independent of Oracle ? (I mean its entirely dependent on hardware, no way related with Oracle)

Sidhu</description>
		<content:encoded><![CDATA[<p>Right Andrew</p>
<p>I too did some RnD on the net. At many places, there are talks about this thing (ie multiplication is faster than division). As you said ultimately it depends upon how the same thing is being done at the resigters&#8217; level.</p>
<p>So can we conclude that its independent of Oracle ? (I mean its entirely dependent on hardware, no way related with Oracle)</p>
<p>Sidhu</p>
]]></content:encoded>
	</item>
	<item>
		<title>By: APC</title>
		<link>http://laurentschneider.com/wordpress/2007/06/to-divide-or-to-multiply.html#comment-4053</link>
		<dc:creator>APC</dc:creator>
		<pubDate>Tue, 19 Jun 2007 07:51:17 +0000</pubDate>
		<guid isPermaLink="false">http://laurentschneider.com/wordpress/2007/06/to-divide-or-to-multiply.html#comment-4053</guid>
		<description>I was discussing this with some colleagues and the consensus is that it really comes down to chip architecture.  Different chips will implement the instructions in different fashions.  As it happens I have just read this on the &lt;a href="http://worsethanfailure.com/Articles/OMGWTF-Finalist-01-The-Buggy-4Function-Calculator.aspx" rel="nofollow"&gt;WorseThanFailure&lt;/a&gt; site:

"Stephen writes primarily C code .... for tiny devices called “Nodes” that have a whopping 512K of memory, a 2x20 display, and a RISC processor that can’t divide. Really: their compiler treats “%” and “/” as syntactical sugar that gets replaced with a call to a library function which, in turn, uses a series of bitshifts and subtractions to perform division."

Cheers, APC</description>
		<content:encoded><![CDATA[<p>I was discussing this with some colleagues and the consensus is that it really comes down to chip architecture.  Different chips will implement the instructions in different fashions.  As it happens I have just read this on the <a href="http://worsethanfailure.com/Articles/OMGWTF-Finalist-01-The-Buggy-4Function-Calculator.aspx" rel="nofollow">WorseThanFailure</a> site:</p>
<p>&#8220;Stephen writes primarily C code &#8230;. for tiny devices called “Nodes” that have a whopping 512K of memory, a 2&#215;20 display, and a RISC processor that can’t divide. Really: their compiler treats “%” and “/” as syntactical sugar that gets replaced with a call to a library function which, in turn, uses a series of bitshifts and subtractions to perform division.&#8221;</p>
<p>Cheers, APC</p>
]]></content:encoded>
	</item>
	<item>
		<title>By: Eriks</title>
		<link>http://laurentschneider.com/wordpress/2007/06/to-divide-or-to-multiply.html#comment-4052</link>
		<dc:creator>Eriks</dc:creator>
		<pubDate>Tue, 19 Jun 2007 06:06:59 +0000</pubDate>
		<guid isPermaLink="false">http://laurentschneider.com/wordpress/2007/06/to-divide-or-to-multiply.html#comment-4052</guid>
		<description>That's a bold statement, knowing that oracle runs not only on windows. 

On 

Oracle9i Enterprise Edition Release 9.2.0.7.0 - 64bit Production
PL/SQL Release 9.2.0.7.0 - Production
CORE    9.2.0.7.0       Production
TNS for HPUX: Version 9.2.0.7.0 - Production
NLSRTL Version 9.2.0.7.0 - Production

results are the same for division and multiply.</description>
		<content:encoded><![CDATA[<p>That&#8217;s a bold statement, knowing that oracle runs not only on windows. </p>
<p>On </p>
<p>Oracle9i Enterprise Edition Release 9.2.0.7.0 - 64bit Production<br />
PL/SQL Release 9.2.0.7.0 - Production<br />
CORE    9.2.0.7.0       Production<br />
TNS for HPUX: Version 9.2.0.7.0 - Production<br />
NLSRTL Version 9.2.0.7.0 - Production</p>
<p>results are the same for division and multiply.</p>
]]></content:encoded>
	</item>
	<item>
		<title>By: Francois</title>
		<link>http://laurentschneider.com/wordpress/2007/06/to-divide-or-to-multiply.html#comment-4051</link>
		<dc:creator>Francois</dc:creator>
		<pubDate>Tue, 19 Jun 2007 05:39:57 +0000</pubDate>
		<guid isPermaLink="false">http://laurentschneider.com/wordpress/2007/06/to-divide-or-to-multiply.html#comment-4051</guid>
		<description>Hello,
I think that this can derive from a single question: How basic (processor operations) steps a division takes inside the processor ? Probably much more than for a multiplication.
Francois</description>
		<content:encoded><![CDATA[<p>Hello,<br />
I think that this can derive from a single question: How basic (processor operations) steps a division takes inside the processor ? Probably much more than for a multiplication.<br />
Francois</p>
]]></content:encoded>
	</item>
	<item>
		<title>By: Sidhu</title>
		<link>http://laurentschneider.com/wordpress/2007/06/to-divide-or-to-multiply.html#comment-4049</link>
		<dc:creator>Sidhu</dc:creator>
		<pubDate>Mon, 18 Jun 2007 17:27:41 +0000</pubDate>
		<guid isPermaLink="false">http://laurentschneider.com/wordpress/2007/06/to-divide-or-to-multiply.html#comment-4049</guid>
		<description>Laurent

Interesting post

Here are my findings on 10gr2 in my laptop (windows XP)...pretty much in line with you. I ran the same example:

SQL&#62; var z number
SQL&#62; var y number
SQL&#62; exec :z := power(2,102)*2e-31;

PL/SQL procedure successfully completed.

SQL&#62; exec :y := 1e125;

PL/SQL procedure successfully completed.

SQL&#62; set timi on
SQL&#62; exec while (:y&#62;1e-125) loop :y:=:y/:z; end loop

PL/SQL procedure successfully completed.

Elapsed: 00:00:00.10
SQL&#62; set timi off
SQL&#62; print y

         Y
----------
9.988E-126

SQL&#62; exec :z := power(2,-104)*2e31;

PL/SQL procedure successfully completed.

SQL&#62; exec :y := 1e125;

PL/SQL procedure successfully completed.

SQL&#62; set timi on
SQL&#62; exec while (:y&#62;1e-125) loop :y:=:y*:z; end loop

PL/SQL procedure successfully completed.

Elapsed: 00:00:00.04
SQL&#62; set timi off
SQL&#62; print y

         Y
----------
9.988E-126

SQL&#62; 


Sidhu</description>
		<content:encoded><![CDATA[<p>Laurent</p>
<p>Interesting post</p>
<p>Here are my findings on 10gr2 in my laptop (windows XP)&#8230;pretty much in line with you. I ran the same example:</p>
<p>SQL&gt; var z number<br />
SQL&gt; var y number<br />
SQL&gt; exec :z := power(2,102)*2e-31;</p>
<p>PL/SQL procedure successfully completed.</p>
<p>SQL&gt; exec :y := 1e125;</p>
<p>PL/SQL procedure successfully completed.</p>
<p>SQL&gt; set timi on<br />
SQL&gt; exec while (:y&gt;1e-125) loop :y:=:y/:z; end loop</p>
<p>PL/SQL procedure successfully completed.</p>
<p>Elapsed: 00:00:00.10<br />
SQL&gt; set timi off<br />
SQL&gt; print y</p>
<p>         Y<br />
&#8212;&#8212;&#8212;-<br />
9.988E-126</p>
<p>SQL&gt; exec :z := power(2,-104)*2e31;</p>
<p>PL/SQL procedure successfully completed.</p>
<p>SQL&gt; exec :y := 1e125;</p>
<p>PL/SQL procedure successfully completed.</p>
<p>SQL&gt; set timi on<br />
SQL&gt; exec while (:y&gt;1e-125) loop :y:=:y*:z; end loop</p>
<p>PL/SQL procedure successfully completed.</p>
<p>Elapsed: 00:00:00.04<br />
SQL&gt; set timi off<br />
SQL&gt; print y</p>
<p>         Y<br />
&#8212;&#8212;&#8212;-<br />
9.988E-126</p>
<p>SQL&gt; </p>
<p>Sidhu</p>
]]></content:encoded>
	</item>
	<item>
		<title>By: APC</title>
		<link>http://laurentschneider.com/wordpress/2007/06/to-divide-or-to-multiply.html#comment-4048</link>
		<dc:creator>APC</dc:creator>
		<pubDate>Mon, 18 Jun 2007 15:58:11 +0000</pubDate>
		<guid isPermaLink="false">http://laurentschneider.com/wordpress/2007/06/to-divide-or-to-multiply.html#comment-4048</guid>
		<description>Laurent

Are you sure about this?  Optimization by wallclock is notoriously flaky.  Certainly 9.2 on my laptop the results look a bit different:
&lt;code&gt;
SQL&#62; var z number
SQL&#62; var y number
SQL&#62; exec :z := power(2,102)*2e-31;

PL/SQL procedure successfully completed.

SQL&#62; exec :y := 1e125;

PL/SQL procedure successfully completed.

SQL&#62; set timi on
SQL&#62; exec while (:y&#62;1e-125) loop :y:=:y/:z; end loop

PL/SQL procedure successfully completed.

Elapsed: 00:00:00.03
SQL&#62; set timi off
SQL&#62; print y
         Y
----------
9.988E-126

SQL&#62; 
SQL&#62; exec :z := power(2,-104)*2e31;

PL/SQL procedure successfully completed.

SQL&#62; exec :y := 1e125;

PL/SQL procedure successfully completed.

SQL&#62; set timi on
SQL&#62; exec while (:y&#62;1e-125) loop :y:=:y*:z; end loop

PL/SQL procedure successfully completed.

Elapsed: 00:00:00.00
SQL&#62; set timi off
SQL&#62; print y
         Y
----------
9.988E-126

SQL&#62; 
&lt;/code&gt;
I really wouldn't want to have to live on that difference.  And on 9.2 on Solaris division is apparently faster ...
&lt;code&gt;
SQL&#62; var z number
SQL&#62; var y number
SQL&#62; exec :z := power(2,102)*2e-31;

PL/SQL procedure successfully completed.

SQL&#62; exec :y := 1e125;

PL/SQL procedure successfully completed.

SQL&#62; set timi on
SQL&#62; exec while (:y&#62;1e-125) loop :y:=:y/:z; end loop

PL/SQL procedure successfully completed.

Elapsed: 00:00:00.04
SQL&#62; set timi off
SQL&#62; print y
         Y
----------
9.988E-126

SQL&#62; 
SQL&#62; exec :z := power(2,-104)*2e31;

PL/SQL procedure successfully completed.

SQL&#62; exec :y := 1e125;

PL/SQL procedure successfully completed.

SQL&#62; set timi on
SQL&#62; exec while (:y&#62;1e-125) loop :y:=:y*:z; end loop

PL/SQL procedure successfully completed.

Elapsed: 00:00:00.05
SQL&#62; set timi off
SQL&#62; print y
         Y
----------
9.988E-126

SQL&#62; 
&lt;/code&gt;


Cheers, APC</description>
		<content:encoded><![CDATA[<p>Laurent</p>
<p>Are you sure about this?  Optimization by wallclock is notoriously flaky.  Certainly 9.2 on my laptop the results look a bit different:<br />
<pre><code>
SQL&amp;gt; var z number
SQL&amp;gt; var y number
SQL&amp;gt; exec :z := power(2,102)*2e-31;

PL/SQL procedure successfully completed.

SQL&amp;gt; exec :y := 1e125;

PL/SQL procedure successfully completed.

SQL&amp;gt; set timi on
SQL&amp;gt; exec while (:y&amp;gt;1e-125) loop :y:=:y/:z; end loop

PL/SQL procedure successfully completed.

Elapsed: 00:00:00.03
SQL&amp;gt; set timi off
SQL&amp;gt; print y
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Y
----------
9.988E-126

SQL&amp;gt; 
SQL&amp;gt; exec :z := power(2,-104)*2e31;

PL/SQL procedure successfully completed.

SQL&amp;gt; exec :y := 1e125;

PL/SQL procedure successfully completed.

SQL&amp;gt; set timi on
SQL&amp;gt; exec while (:y&amp;gt;1e-125) loop :y:=:y*:z; end loop

PL/SQL procedure successfully completed.

Elapsed: 00:00:00.00
SQL&amp;gt; set timi off
SQL&amp;gt; print y
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Y
----------
9.988E-126

SQL&amp;gt; 
</code></pre><br />
I really wouldn&#8217;t want to have to live on that difference.  And on 9.2 on Solaris division is apparently faster &#8230;<br />
<pre><code>
SQL&amp;gt; var z number
SQL&amp;gt; var y number
SQL&amp;gt; exec :z := power(2,102)*2e-31;

PL/SQL procedure successfully completed.

SQL&amp;gt; exec :y := 1e125;

PL/SQL procedure successfully completed.

SQL&amp;gt; set timi on
SQL&amp;gt; exec while (:y&amp;gt;1e-125) loop :y:=:y/:z; end loop

PL/SQL procedure successfully completed.

Elapsed: 00:00:00.04
SQL&amp;gt; set timi off
SQL&amp;gt; print y
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Y
----------
9.988E-126

SQL&amp;gt; 
SQL&amp;gt; exec :z := power(2,-104)*2e31;

PL/SQL procedure successfully completed.

SQL&amp;gt; exec :y := 1e125;

PL/SQL procedure successfully completed.

SQL&amp;gt; set timi on
SQL&amp;gt; exec while (:y&amp;gt;1e-125) loop :y:=:y*:z; end loop

PL/SQL procedure successfully completed.

Elapsed: 00:00:00.05
SQL&amp;gt; set timi off
SQL&amp;gt; print y
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Y
----------
9.988E-126

SQL&amp;gt; 
</code></pre></p>
<p>Cheers, APC</p>
]]></content:encoded>
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</channel>
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