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Fix PVM page size constant usage #152

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Fix PVM page size constant usage #152

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2 changes: 1 addition & 1 deletion text/overview.tex
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Expand Up @@ -180,7 +180,7 @@ \subsection{The Virtual Machine and Gas}\label{sec:virtualmachineandgas}
\mathsf{Z}_P &= 2^{12}
\end{align}

The \textsc{pvm} assumes a simple pageable \textsc{ram} of 32-bit addressable octets situated in pages of $2^p = 4096$ octets where each page may be either immutable, mutable or inaccessible. The \textsc{ram} definition $\mathbb{M}$ includes two components: a value $\mathbf{V}$ and access $\mathbf{A}$. If the component is unspecified while being subscripted then the value component may be assumed. Within the context of the virtual machine, $\memory \in \mathbb{M}$ is typically used to denote \textsc{ram}.
The \textsc{pvm} assumes a simple pageable \textsc{ram} of 32-bit addressable octets situated in pages of $\mathsf{Z}_P = 4096$ octets where each page may be either immutable, mutable or inaccessible. The \textsc{ram} definition $\mathbb{M}$ includes two components: a value $\mathbf{V}$ and access $\mathbf{A}$. If the component is unspecified while being subscripted then the value component may be assumed. Within the context of the virtual machine, $\memory \in \mathbb{M}$ is typically used to denote \textsc{ram}.
\begin{align}
\mathbb{V}_{\memory} &\equiv \{i \mid \memory_\mathbf{A}[\floor{\nicefrac{i}{\mathsf{Z}_P}}] \ne \none \} \\
\mathbb{V}^*_{\memory} &\equiv \{i \mid \memory_\mathbf{A}[\floor{\nicefrac{i}{\mathsf{Z}_P}}] = \text{W} \}
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10 changes: 5 additions & 5 deletions text/pvm.tex
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Expand Up @@ -698,13 +698,13 @@ \subsection{Standard Program Initialization}\label{sec:standardprograminit}
With conditions:
\begin{align}\label{eq:conditions}
&\using \mathcal{E}_3(|\mathbf{o}|) \concat \mathcal{E}_3(|\mathbf{w}|) \concat \mathcal{E}_2(z) \concat \mathcal{E}_3(s) \concat \mathbf{o} \concat \mathbf{w} \concat \mathcal{E}_4(|\mathbf{c}|) \concat \mathbf{c} = \mathbf{p}\\
&\mathsf{Z}_P = 2^{14}\ ,\quad\mathsf{Z}_Q = 2^{16}\ ,\quad\mathsf{Z}_I = 2^{24}\\
&\using \rnp{x \in \N} \equiv \mathsf{Z}_P\left\lceil \frac{x}{\mathsf{Z}_P} \right\rceil\quad,\qquad\rnq{x \in \N} \equiv \mathsf{Z}_Q\left\lceil \frac{x}{\mathsf{Z}_Q} \right\rceil\\
&5\mathsf{Z}_Q + Q(|\mathbf{o}|) + Q(|\mathbf{w}| + z\mathsf{Z}_P) + Q(s) + \mathsf{Z}_I \leq 2^{32}
&\mathsf{Z}_G = 2^{14}\ ,\quad\mathsf{Z}_Q = 2^{16}\ ,\quad\mathsf{Z}_I = 2^{24}\\
&\using \rnp{x \in \N} \equiv \mathsf{Z}_G\left\lceil \frac{x}{\mathsf{Z}_G} \right\rceil\quad,\qquad\rnq{x \in \N} \equiv \mathsf{Z}_Q\left\lceil \frac{x}{\mathsf{Z}_Q} \right\rceil\\
&5\mathsf{Z}_Q + Q(|\mathbf{o}|) + Q(|\mathbf{w}| + z\mathsf{Z}_G) + Q(s) + \mathsf{Z}_I \leq 2^{32}
\end{align}
Thus, if the above conditions cannot be satisfied with unique values, then the result is $\none$, otherwise it is a tuple of $\mathbf{c}$ as above and $\mem$, $\registers$ such that:
\begin{equation}\label{eq:memlayout}
\forall i \in \N_{2^{32}} : ((\mem_\mathbf{V})_i, (\mem_\mathbf{A})_{\floor{\nicefrac{i}{\mathsf{Z}_P}}}) = \left\{\begin{alignedat}{5}
\forall i \in \N_{2^{32}} : ((\mem_\mathbf{V})_i, (\mem_\mathbf{A})_{\floor{\nicefrac{i}{\mathsf{Z}_G}}}) = \left\{\begin{alignedat}{5}
&\tup{\is{\mathbf{V}}{\mathbf{o}_{i - \mathsf{Z}_Q}}\ts\is{\mathbf{A}}{R}} &&\ \when
\mathsf{Z}_Q
&\ \leq i < \ &&
Expand All @@ -720,7 +720,7 @@ \subsection{Standard Program Initialization}\label{sec:standardprograminit}
&(0, W) &&\ \when
2\mathsf{Z}_Q + \rnq{|\mathbf{o}|} + |\mathbf{w}|
&\ \leq i < \ &&
2\mathsf{Z}_Q + \rnq{|\mathbf{o}|} + \rnp{|\mathbf{w}|} + z\mathsf{Z}_P\\
2\mathsf{Z}_Q + \rnq{|\mathbf{o}|} + \rnp{|\mathbf{w}|} + z\mathsf{Z}_G\\
&(0, W) &&\ \when
2^{32} - 2\mathsf{Z}_Q - \mathsf{Z}_I - \rnp{s}
&\ \leq i < \ &&
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