Misc corrections (#120)

* Definitions: Put some numbers in for gas limits.

* PVM Invocations: Make clearer the fallthrough repercussion.

* PVM Invocations: Correct fallback condition

* PVM Hostcalls: d should be mu

* Version

VERSION

@@ -1 +1 @@
-0.4.3
+0.4.4

preamble.tex

@@ -179,7 +179,7 @@
 \newcommand*{\registers}{\omega}
 \newcommand*{\memory}{\mu}
 
-\newcommand*{\jamdraftversion}{\input{VERSION}\!\!\!}
+\newcommand*{\jamdraftversion}{\input{VERSION}\!\!\!\! Bangkok}
 \newcommand*{\jamdraftversionstring}{\jamdraftversion}
 
 \newcommand*{\makegpbackground}{

text/definitions.tex

@@ -259,10 +259,10 @@ \subsubsection{Constants}
   \item[$\mathsf{D} = 28,800$] The period in timeslots after which an unreferenced preimage may be expunged.
   \item[$\mathsf{E} = 600$] The length of an epoch in timeslots.
   \item[$\mathsf{F} = 2$] The audit bias factor, the expected number of additional validators who will audit a work-report in the following tranche for each no-show in the previous.
-  \item[$\mathsf{G}_A$] The total gas allocated to a core for Accumulation.
-  \item[$\mathsf{G}_I$] The gas allocated to invoke a work-package's Is-Authorized logic.
-  \item[$\mathsf{G}_R$] The total gas allocated for a work-package's Refine logic.
-  \item[$\mathsf{G}_T$] The total gas allocated across all cores for Accumulation. May be no smaller than $\mathsf{G}_A\cdot\mathsf{C} + \sum_{g \in \mathcal{V}(\chi_\mathbf{g})}(g)$.
+  \item[$\mathsf{G}_A = 100,000$] The total gas allocated to a core for Accumulation.
+  \item[$\mathsf{G}_I = 1,000,000$] The gas allocated to invoke a work-package's Is-Authorized logic.
+  \item[$\mathsf{G}_R = 500,000,000$] The total gas allocated for a work-package's Refine logic.
+  \item[$\mathsf{G}_T = 341,000,000$] The total gas allocated across all cores for Accumulation. Should be no smaller than $\mathsf{G}_A\cdot\mathsf{C} + \sum_{g \in \mathcal{V}(\chi_\mathbf{g})}(g)$.
   \item[$\mathsf{H} = 8$] The size of recent history, in blocks.
   \item[$\mathsf{I} = 4$] The maximum amount of work items in a package.
   \item[$\mathsf{J} = 8$] The maximum sum of dependency items in a work-report.

text/pvm_invocations.tex

@@ -45,7 +45,7 @@ \subsection{Is-Authorized Invocation}\label{sec:isauthorizedinvocation}
     (\N, \N_G, \regs, \ram) &\to (\Z_G, \regs, \ram)\\
     (n, \gascounter, \registers, \memory) &\mapsto \begin{cases}
       \Omega_G(\gascounter, \registers, \memory) &\when n = \mathtt{gas} \\
-      (\gascounter - 10, [\mathtt{WHAT}, \registers_8, \dots], \memory) &\otherwise
+      (\gascounter - 10, [\registers_0, \dots, \registers_6, \mathtt{WHAT}, \registers_8, \dots], \memory) &\otherwise
     \end{cases}
   \end{aligned}
   \right.
@@ -96,7 +96,7 @@ \subsection{Refine Invocation}\label{sec:refineinvocation}
       \Omega_O(\gascounter, \registers, \memory, (\mathbf{m}, \mathbf{e})) &\when n = \mathtt{poke}\\
       \Omega_K(\gascounter, \registers, \memory, (\mathbf{m}, \mathbf{e})) &\when n = \mathtt{invoke}\\
       \Omega_X(\gascounter, \registers, \memory, (\mathbf{m}, \mathbf{e})) &\when n = \mathtt{expunge}\\
-      (\gascounter - 10, [\mathtt{WHAT}, \registers_8, \dots], \memory) &\otherwise
+      (\gascounter - 10, [\registers_0, \dots, \registers_6, \mathtt{WHAT}, \registers_8, \dots], \memory) &\otherwise
     \end{cases}
   \end{aligned}
   \right.
@@ -162,7 +162,7 @@ \subsection{Accumulate Invocation}\label{sec:accumulateinvocation}
     \Omega_Q(\gascounter, \registers, \memory, (\mathbf{x}, \mathbf{y})) &\when n = \mathtt{quit} \\
     \Omega_S(\gascounter, \registers, \memory, (\mathbf{x}, \mathbf{y}), \mathbf{H}_t) &\when n = \mathtt{solicit} \\
     \Omega_F(\gascounter, \registers, \memory, (\mathbf{x}, \mathbf{y}), \mathbf{H}_t) &\when n = \mathtt{forget} \\
-    (\gascounter - 10, [\mathtt{WHAT}, \registers_8, \dots], \memory, \mathbf{x}) &\otherwise\\
+    (\gascounter - 10, [\registers_0, \dots, \registers_6, \mathtt{WHAT}, \registers_8, \dots], \memory, \mathbf{x}) &\otherwise\\
     \quad \where \mathbf{d} = (\mathbf{x}_\mathbf{u})_\mathbf{d}\cup\mathbf{x}_\mathbf{d}\;,\ \mathbf{s} = (\mathbf{x}_\mathbf{u})_\mathbf{d}[\mathbf{x}_s]\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!& \\
   \end{cases} \\
   G((\gascounter, \registers, \memory, \mathbf{s}), (\mathbf{x}, \mathbf{y})) &\equiv (\gascounter, \registers, \memory, (\mathbf{x}^*, \mathbf{y}))\ \where \mathbf{x}^* = \mathbf{x} \exc (\mathbf{x}^*_\mathbf{u})_\mathbf{d}[(\mathbf{x}^*_\mathbf{u})_s] = \mathbf{s} \\
@@ -220,7 +220,7 @@ \subsection{On-Transfer Invocation}\label{sec:ontransferinvocation}
     \Omega_W(\gascounter, \registers, \memory, \mathbf{s}, s) &\when n = \mathtt{write} \\
     \Omega_G(\gascounter, \registers, \memory) &\when n = \mathtt{gas} \\
     \Omega_I(\gascounter, \registers, \memory, s, \mathbf{d}) &\when n = \mathtt{info} \\
-    (\gascounter - 10, [\mathtt{WHAT}, \registers_8, \dots], \memory, \mathbf{s}) &\otherwise
+    (\gascounter - 10, [\registers_0, \dots, \registers_6, \mathtt{WHAT}, \registers_8, \dots], \memory, \mathbf{s}) &\otherwise
   \end{cases}
 \end{align}
 
@@ -409,7 +409,7 @@ \subsection{Accumulate Functions}\label{sec:accumulatefunctions}
   $\begin{aligned}
     \using [m, a, v, o, n] &= \registers_{7 \dots 12} \\
     \using \mathbf{g} &= \begin{cases}
-      \left\{ (s \mapsto g) \ \where \se_4(s) \concat \se_8(g) = \mathbf{d}_{o+12i\dots+12} \mid i \in \N_n \right\} &\when \mathbb{Z}_{o \dots+ 12n} \subset \mathbb{V}_{\memory} \\
+      \left\{ (s \mapsto g) \ \where \se_4(s) \concat \se_8(g) = \memory_{o+12i\dots+12} \mid i \in \N_n \right\} &\when \mathbb{Z}_{o \dots+ 12n} \subset \mathbb{V}_{\memory} \\
       \error &\otherwise
     \end{cases} \\
     (\registers'_7, (\mathbf{x}'_\mathbf{u})_\mathbf{x}) &= \begin{cases}