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rom/generalities/binarities.tex

Lines changed: 7 additions & 4 deletions
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@@ -4,13 +4,16 @@
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\item \romColumnPadding{}
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\item \romColumnClaimedByPush{}
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\item \PFB{}
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\item \romColumnOpcodeIsPush{} \quad (\trash)
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\item \romColumnOpcodeIsJumpDest{} \quad (\trash)
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\item[\vspace{\fill}]
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\item \romColumnEmptyCode {}
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\item \romColumnNonemptyCode {}
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\item \done {}
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\item \romColumnOpcodeIsPush{} (\trash)
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\item \romColumnOpcodeIsJumpDest{} (\trash)
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\item[\vspace{\fill}]
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\end{enumerate}
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\end{multicols}
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\saNote{}
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both \romColumnOpcodeIsPush{} and \romColumnOpcodeIsJumpDest{} are instruction decoded, see section~(\ref{rom: instruction decoding}); their ``binary-ness'' is thus a given.
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both \romColumnOpcodeIsPush{} and \romColumnOpcodeIsJumpDest{} are instruction decoded,
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see section~(\ref{rom: instruction decoding});
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their ``binary-ness'' is thus a given,
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whence the (\trash).

rom/generalities/cfi.tex

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@@ -1,14 +1,21 @@
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We impose
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\begin{enumerate}
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\item $\romColumnCfi _{0} = 0$ (\sanityCheck)
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\item $\romColumnCfi _{i + 1} \in \{ \romColumnCfi _{i}, 1 + \romColumnCfi _{i} \}$ (\sanityCheck)
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\item\label{rom: generalities: cfi constraints: 0/1 increments} $\romColumnCfi _{i + 1} \in \{ \romColumnCfi _{i}, 1 + \romColumnCfi _{i} \}$
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\item \If $\romColumnCfi _{i} = 0$ \Then $\flagSum _{i} = 0$
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\item \If $\romColumnCfi _{i} \neq 0$ \Then $\flagSum _{i} = 1$
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\item \If $\romColumnCfi _{i} \neq 0$ \Then $\romColumnCfi _{i + 1} = \romColumnCfi _{i} + \done _{i}$
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\item\label{rom: generalities: cfi constraints: exact increments} \If $\romColumnCfi _{i} \neq 0$ \Then $\romColumnCfi _{i + 1} = \romColumnCfi _{i} + \done _{i}$
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\end{enumerate}
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\saNote{}
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It follows from the above and
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section~(\ref{rom: generalities: flag sum constraints})
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that $\romColumnCfi \equiv 0 \iff \flagSum \equiv 0$
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and once $\romColumnCfi$ is nonzero it is required to remain so until the end of the trace,
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allowing for $0/1$ increments only.
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allowing for $0/1$ increments only,
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(\ref{rom: generalities: cfi constraints: exact increments}).
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\saNote{}
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Constraint~(\ref{rom: generalities: cfi constraints: 0/1 increments})
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doesn't follow from
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constraint~(\ref{rom: generalities: cfi constraints: exact increments})
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since that constraint applies to non-padding-rows.

rom/generalities/wght_sum.tex

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@@ -8,9 +8,9 @@
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\]
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We impose
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\begin{enumerate}
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\item \weightedFlagSum{} is \textbf{code-fragment-context-constant}
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\item \weightedFlagSum{} is \textbf{\cfi{}-constant}
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\end{enumerate}
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\saNote{}
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It follows that both
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\romColumnEmptyCode{} and \romColumnNonemptyCode{} are
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\textbf{code-fragment-context-constant}.
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\textbf{\cfi{}-constant}.

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