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\hypertarget{JUMP}{JUMP}, \hypertarget{JUMPI}{JUMPI} and \label{eq:mu_pc} #470

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Jan 30, 2018
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\hypertarget{JUMP}{JUMP}, \hypertarget{JUMPI}{JUMPI} and \label{eq:mu_pc} #470

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\hypertarget{JUMP}{JUMP} \hypertarget{JUMPI}{JUMPI} \label{eq:mu_pc}
jamesray1 Jan 23, 2018
70c4734
Update Paper.tex
jamesray1 Jan 24, 2018
6c00c74
hypertarget: move to the same line as the targeted text, change to li…
jamesray1 Jan 30, 2018
63ff7e0
Remove {JUMPI}
jamesray1 Jan 30, 2018
0437001
Readd JUMPI
jamesray1 Jan 30, 2018
58e57a2
Append {} after \linkdest{JUMP}, remove JUMP in second braces
jamesray1 Jan 30, 2018
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9 changes: 5 additions & 4 deletions Paper.tex
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Original file line number Diff line number Diff line change
Expand Up @@ -951,7 +951,8 @@ \subsubsection{Exceptional Halting}
\boldsymbol{\mu}_g < C(\boldsymbol{\sigma}, \boldsymbol{\mu}, I) \quad \vee \\
\mathbf{\delta}_w = \varnothing \quad \vee \\
\lVert\boldsymbol{\mu}_\mathbf{s}\rVert < \mathbf{\delta}_w \quad \vee \\
( w \in \{ \text{\small JUMP}, \text{\small JUMPI} \} \quad \wedge \\ \quad \boldsymbol{\mu}_\mathbf{s}[0] \notin D(I_\mathbf{b}) ) \quad \vee \\
( w \in \{ \text{\small JUMP}, \text{\small
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Why did JUMPI disappear?

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Must be an oversight.

} \} \quad \wedge \\ \quad \boldsymbol{\mu}_\mathbf{s}[0] \notin D(I_\mathbf{b}) ) \quad \vee \\
( w = \text{\small RETURNDATACOPY} \wedge \\ \quad \boldsymbol{\mu}_\mathbf{s}[1] + \boldsymbol{\mu}_\mathbf{s}[2] > \lVert\boldsymbol{\mu}_\mathbf{o}\rVert) \quad \vee \\
\lVert\boldsymbol{\mu}_\mathbf{s}\rVert - \mathbf{\delta}_w + \mathbf{\alpha}_w > 1024 \quad \vee \\
\neg I_w \wedge W(w, \boldsymbol{\mu})
Expand Down Expand Up @@ -1020,7 +1021,7 @@ \subsection{The Execution Cycle}

The gas is reduced by the instruction's gas cost and for most instructions, the program counter increments on each cycle, for the three exceptions, we assume a function $J$, subscripted by one of two instructions, which evaluates to the according value:
\begin{eqnarray}
\quad \boldsymbol{\mu}'_{g} & \equiv & \boldsymbol{\mu}_{g} - C(\boldsymbol{\sigma}, \boldsymbol{\mu}, I) \\
\quad \boldsymbol{\mu}'_{g} & \equiv & \boldsymbol{\mu}_{g} - C(\boldsymbol{\sigma}, \boldsymbol{\mu}, I) \label{eq:mu_pc}\\
\quad \boldsymbol{\mu}'_{pc} & \equiv & \begin{cases}
J_{\text{JUMP}}(\boldsymbol{\mu}) & \text{if} \quad w = \text{\small JUMP} \\
J_{\text{JUMPI}}(\boldsymbol{\mu}) & \text{if} \quad w = \text{\small JUMPI} \\
Expand Down Expand Up @@ -2080,11 +2081,11 @@ \subsection{Instruction Set}
&&&& $A'_{r} \equiv A_{r} + \begin{cases}
R_{sclear} & \text{if} \quad \boldsymbol{\mu}_\mathbf{s}[1] = 0 \; \wedge \; \boldsymbol{\sigma}[I_a]_\mathbf{s}[\boldsymbol{\mu}_\mathbf{s}[0]] \neq 0 \\
0 & \text{otherwise}
\end{cases}$ \\
\end{cases}$ \hypertarget{JUMP}{JUMP} \\
\midrule
0x56 & {\small JUMP} & 1 & 0 & Alter the program counter. \\
&&&& $J_{\text{\tiny JUMP}}(\boldsymbol{\mu}) \equiv \boldsymbol{\mu}_\mathbf{s}[0] $ \\
&&&& This has the effect of writing said value to $\boldsymbol{\mu}_{pc}$. See section \ref{ch:model}. \\
&&&& This has the effect of writing said value to $\boldsymbol{\mu}_{pc}$. See section \ref{ch:model}. \hypertarget{JUMPI}{JUMPI}\\
\midrule
0x57 & {\small JUMPI} & 2 & 0 & Conditionally alter the program counter. \\
&&&& $J_{\text{\tiny JUMPI}}(\boldsymbol{\mu}) \equiv \begin{cases} \boldsymbol{\mu}_\mathbf{s}[0] & \text{if} \quad \boldsymbol{\mu}_\mathbf{s}[1] \neq 0 \\ \boldsymbol{\mu}_{pc} + 1 & \text{otherwise} \end{cases} $ \\
Expand Down