<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
</head>
<body text="#000000" bgcolor="#FFFFFF">
<p>Just digging a bit further in julia:</p>
<p>println("2.0^53+2.0^1 : $(bits(2.0^53+2.0^1))")<br>
println("2.0^53+2.0^1+1 : $(bits(2.0^53+2.0^1+1))")<br>
println("")<br>
println("2.0^53+2.0^2 : $(bits(2.0^53+2.0^2))")<br>
println("2.0^53+2.0^2+1 : $(bits(2.0^53+2.0^2+1))")</p>
<p>gives:<br>
</p>
<p><tt>2.0^53+2.0^1 :
0100001101000000000000000000000000000000000000000000000000000001</tt><tt><br>
</tt><tt>2.0^53+2.0^1+1 :
0100001101000000000000000000000000000000000000000000000000000010</tt><tt><br>
</tt><tt><br>
</tt><tt>2.0^53+2.0^2 :
0100001101000000000000000000000000000000000000000000000000000010</tt><tt><br>
</tt><tt>2.0^53+2.0^2+1 :
0100001101000000000000000000000000000000000000000000000000000010</tt><br>
</p>
<p>So the first two are different while the last two are bit
identical.</p>
<p>I anyone can point to the specific bit in IEEE spec for this,
I'll be happy!</p>
<p><br>
</p>
Antoine<br>
<br>
<div class="moz-cite-prefix">Le 19/09/2017 à 08:58, antoine
monmayrant a écrit :<br>
</div>
<blockquote type="cite"
cite="mid:73ce2d3c-4b16-f4ef-526b-c7a0a5c8e315@laas.fr">
<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
<p>Houps, my bad, julia does exactly the same when using Float64,
not Int64:</p>
<p><br>
</p>
<p>println((2.0^53 + 2.0^2) + 1.0 == (2.0^53 + 2.0^2))</p>
<p>true</p>
<p>println((2.0^53 + 2.0^1) + 1.0 == (2.0^53 + 2.0^1))</p>
<p>false</p>
<p><br>
</p>
<p>It has to be some normal IEEE thing but I did not manage to
find the proper reference for it.</p>
<p><br>
</p>
<p>Antoine</p>
<p><br>
</p>
<div class="moz-cite-prefix">Le 18/09/2017 à 20:54, Samuel Gougeon
a écrit :<br>
</div>
<blockquote type="cite"
cite="mid:03a6b389-083a-0dad-b6ab-b8a9a29ecf44@free.fr">
<meta http-equiv="content-type" content="text/html;
charset=utf-8">
<p><font face="Arial">Dear co-Scilabers,</font></p>
<p>I met a strange Scilab's bug this week-end. But today, i
tried with Octave, Matlab2016 and R, and i found the same
strange behavior. So, either i am missing something, or the
bug affects all these languages in the same way. It is
reported @ <a class="moz-txt-link-freetext"
href="http://bugzilla.scilab.org/15276"
moz-do-not-send="true">http://bugzilla.scilab.org/15276</a><br>
</p>
<p>In a few words, here it is:</p>
<p>The mantissa of any decimal number is recorded on 53 bits
(numbered #0 to #52) + 1 bit for the sign.<br>
This relative absolute accuracy sets the value of the
epsilon-machine :<br>
<tt>--> %eps == 2^0 / 2^52</tt><tt><br>
</tt><tt> ans =</tt><tt><br>
</tt><tt> T</tt><br>
From here, it comes, as expected:</p>
<p><tt>--> 2^52 + 1 == 2^52</tt><tt><br>
</tt><tt> ans =</tt><tt><br>
</tt><tt> F</tt><tt><br>
</tt><tt><br>
</tt><tt>--> 2^53 - 1 == 2^53<br>
ans =<br>
F<br>
<br>
--> 2^53 + 1 == 2^53</tt><tt> // (A)<br>
</tt><tt> ans =</tt><tt><br>
</tt><tt> T</tt><tt><br>
</tt><br>
Now comes the issue:<br>
In (A), the relative difference 1/2^53 is too small (<
%eps) to be recorded and to change the number. OK.<br>
Since 1 / (2^53 +2) is even smaller than 1 / (2^53), it should
nor make a difference. Yet, it does:</p>
<p><tt>--> (2^53 + 2^1) + 1 == (2^53 + 2^1)</tt><tt><br>
</tt><tt> ans =</tt><tt><br>
</tt><tt> F</tt><tt><br>
</tt><br>
How is this possible ??!<br>
But this occurs only when THIS bit #0 is set. For higher bits
(hebelow the #1 one), we get back to the expected behavior:<br>
<tt>--> (2^53 + 2^2) + 1 == (2^53 + 2^2)</tt><tt><br>
</tt><tt> ans =</tt><tt><br>
</tt><tt> T</tt><tt><br>
</tt><br>
So, when the bit #0 is set and we add a value on the bit
"#-1", the language somewhat behaves as if there was a
"withholding" value on the bit #0, and seems to toogle it.<br>
Is is a part of any IEEE floating point convention, or am i
missing anything, or is it a true bug?<br>
Again, R, Octave and Matlab behave exactly in the same way...</p>
<span id="result_box" class="short_text" lang="en"><span
class="">Looking forward to reading your thoughts,<br>
<br>
</span></span>Samuel<br>
<br>
<p><br>
</p>
<p><br>
</p>
<p><br>
</p>
<br>
<fieldset class="mimeAttachmentHeader"></fieldset>
<br>
<pre wrap="">_______________________________________________
users mailing list
<a class="moz-txt-link-abbreviated" href="mailto:users@lists.scilab.org" moz-do-not-send="true">users@lists.scilab.org</a>
<a class="moz-txt-link-freetext" href="http://lists.scilab.org/mailman/listinfo/users" moz-do-not-send="true">http://lists.scilab.org/mailman/listinfo/users</a>
</pre>
</blockquote>
<br>
<br>
<fieldset class="mimeAttachmentHeader"></fieldset>
<br>
<pre wrap="">_______________________________________________
users mailing list
<a class="moz-txt-link-abbreviated" href="mailto:users@lists.scilab.org">users@lists.scilab.org</a>
<a class="moz-txt-link-freetext" href="http://lists.scilab.org/mailman/listinfo/users">http://lists.scilab.org/mailman/listinfo/users</a>
</pre>
</blockquote>
<br>
</body>
</html>