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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) Both sides previous revision Previous revision 2008/05/07 23:18 giuliano 2008/05/07 23:16 giuliano 2008/05/07 01:08 vkuncak 2008/05/07 01:07 vkuncak 2008/05/07 00:45 vkuncak 2008/05/07 00:17 vkuncak 2008/05/07 00:17 vkuncak 2008/05/07 00:14 vkuncak 2008/05/07 00:09 vkuncak 2008/05/07 00:04 vkuncak 2008/05/07 00:04 vkuncak 2008/05/07 00:03 vkuncak 2008/05/06 23:50 vkuncak 2008/05/06 23:49 vkuncak 2008/05/06 23:48 vkuncak created Next revision Previous revision 2008/05/07 23:18 giuliano 2008/05/07 23:16 giuliano 2008/05/07 01:08 vkuncak 2008/05/07 01:07 vkuncak 2008/05/07 00:45 vkuncak 2008/05/07 00:17 vkuncak 2008/05/07 00:17 vkuncak 2008/05/07 00:14 vkuncak 2008/05/07 00:09 vkuncak 2008/05/07 00:04 vkuncak 2008/05/07 00:04 vkuncak 2008/05/07 00:03 vkuncak 2008/05/06 23:50 vkuncak 2008/05/06 23:49 vkuncak 2008/05/06 23:48 vkuncak created Line 7: Line 7: 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*} ++++ ++++ Line 52: Line 52: \end{tabular} \end{tabular}  + ===== Sign Analysis of Programs ===== ===== Sign Analysis of Programs ===== Line 71: Line 72: ​ - 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