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sav08:sign_analysis_of_expressions_and_programs [2008/05/07 23:16]
giuliano
sav08:sign_analysis_of_expressions_and_programs [2015/04/21 17:30] (current)
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What is (quickly) the sign of What is (quickly) the sign of
-$+\begin{equation*} (31283321 + 8629184) \times (-34234) \times (-4 + (123123 \times (-3))) (31283321 + 8629184) \times (-34234) \times (-4 + (123123 \times (-3))) -$+\end{equation*}
Why? Why?
++++| ++++|
-$+\begin{equation*} (pos \oplus pos) \otimes neg \otimes (neg \oplus (pos \otimes neg)) = pos \otimes neg \otimes neg = pos (pos \oplus pos) \otimes neg \otimes (neg \oplus (pos \otimes neg)) = pos \otimes neg \otimes neg = pos -$+\end{equation*}
++++ ++++

What is (quickly) the sign of What is (quickly) the sign of
-$+\begin{equation*} (28166461706 + (723497 \times (- 38931))) \times 42 (28166461706 + (723497 \times (- 38931))) \times 42 -$+\end{equation*}
++++| ++++|
-$+\begin{equation*} (pos \oplus (pos \otimes neg)) \otimes pos = (pos \oplus neg) \otimes pos = \top \otimes pos = \top (pos \oplus (pos \otimes neg)) \otimes pos = (pos \oplus neg) \otimes pos = \top \otimes pos = \top -$+\end{equation*}
++++ ++++

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\end{tabular} \end{tabular}

+

===== Sign Analysis of Programs ===== ===== Sign Analysis of Programs =====
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</​code>​ </​code>​

-Abstract state: map each variable to element of $A$.+Abstract state: map each variable to element of $A$. Here we have $|A|^3$ possible states.

* computation over control-flow graph   * computation over control-flow graph