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Sign Analysis of Expressions and Programs
Suppose we want to test quickly whether the result of an expression is positive, negative or zero.
What is (quickly) the sign of
\[
(31283321 + 8629184) \times (-34234) \times (-4 + (123123 \times (-3)))
\]
Why?
\[
(pos \oplus pos) \otimes neg \otimes (neg \oplus (pos \otimes neg)) = pos \otimes neg \otimes neg = pos
\]
What is (quickly) the sign of
\[
(28166461706 + (723497 \times (- 38931))) \times 42
\]
\[
(pos \oplus (pos \otimes neg)) \otimes pos = (pos \oplus neg) \otimes pos = \bottom \otimes pos = \bottom
\]