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  83. Undocumented Features of VSA
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  101. <time datetime="2012-09-07T13:57:00-04:00" pubdate data-updated="true">Sep 7<span>th</span>, 2012</time>
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  102.          &bull; <a rel="bookmark" href="/blog/2012/09/07/undocumented-features-of-vsa/">&infin;</a>
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  106. 

  107. <div class="entry-content"><p>As I&#8217;ve written about recently, I&#8217;ve been hacking on VSA.  I&#8217;ve been
    108. 

  108. trying to get to the point where the example in Balakrishnan&#8217;s
    109. 

  109. dissertation works.  I chose this example because I don&#8217;t know of any
    110. 

  110. others!  Below is a snapshot of the example that I started with.</p>
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  111. 

  112. <p><img src="/images/vsa-example.png"></p>
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  113. 

  114. <p>And here are the results that VSA is supposed to be able to infer:</p>
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  115. 

  116. <p><img src="/images/vsa-results.png"></p>
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  117. 

  118. <p>There are several interesting things about these results.  First, note
    119. 

  119. that %edx is bounded, even though it is incremented in a loop.  In
    120. 

  120. contrast, %eax grows to its maximum value.  Although %eax approaches
    121. 

  121. the maximum positive integer, VSA infers that it does not overflow.
    122. 

  122. That sounds kind of weird, doesn&#8217;t it?</p>
    123. 

  123. 

  124. <p>My VSA implementation does not yield the same results.  It notices
    125. 

  125. that %eax is incremented without a direct bound on line 9, and widens
    126. 

  126. %eax to <code>2^31 - 8</code> at line 7.  On line 9, the computation %eax + 8
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  127. overflows, and represents any value on the stack.  The next loop
    128. 

  128. iteration, we see weak updates to the whole stack at L1 and line 8,
    129. 

  129. since %eax represents any stack address.</p>
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  130. 

  131. <p>Somewhere there&#8217;s a hidden assumption in addition of value-sets that
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  132. says adding values in non-global regions cannot overflow.  This kind
    133. 

  133. of makes sense, if regions are separated, since the program might
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  134. crash.  I do not consider this to be a sound assumption, however.
    135. 

  135. (Programs can handle exceptions&#8230;)  Perhaps that is why this
    136. 

  136. assumption is not explicitly mentioned, or if it is, is so buried that
    137. 

  137. I could not find it.  I expected it to be in the definition of
    138. 

  138. addition for value-sets, but it&#8217;s not there.</p>
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  139. 

  140. <p>With this assumption/hack, we get the same results as the example
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  141. above.</p>
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  164. <time datetime="2012-09-07T13:57:00-04:00" pubdate data-updated="true">Sep 7<span>th</span>, 2012</time>
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