Skip to content

Typesetting adjustments #213

New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Merged
conrad-watt merged 5 commits into from
Sep 28, 2023
Merged

Typesetting adjustments #213

Show file tree
Hide file tree
Changes from all commits
Commits
Show all changes
5 commits
Select commit Hold shift + click to select a range
883419e
typesetting fixes
ioannad Sep 13, 2023
c40e969
changed '\normalbaselineskip' to 'ex'
ioannad Sep 15, 2023
71d8722
Add some space and clarifying parentheses.
ioannad Sep 15, 2023
c45b792
Adding line breaks to lines that go off the right edge of the document.
ioannad Sep 15, 2023
11377ad
Add missing store to rules for notify, waitN, and rmw.cmpxchg
ioannad Sep 17, 2023
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
55 changes: 27 additions & 28 deletions document/core/exec/instructions.rst
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -3296,7 +3296,7 @@ The rules are identical to :ref:`non-atomic stores <exec-store>`, except that :m
\begin{array}{lcl@{\qquad}l}
S; F; (\I32.\CONST~i)~(t.\CONST~c_2)~(t.\CONST~c_3)~(t.\ATOMICRMW({N}\K{\_u})^?.\ATCMPXCHG~\memarg)
&\stepto^{(\ARD~a.\LLEN~n)~(\ARMW~a.\LDATA[\X{ea}]~b_{\F{r}}^\ast~b_{\F{w}}^\ast)}&
F; (t.\CONST~c)
S; F; (t.\CONST~c)
\end{array}
\\ \qquad
\begin{array}[t]{@{}r@{~}l@{}}
Expand All @@ -3312,7 +3312,7 @@ The rules are identical to :ref:`non-atomic stores <exec-store>`, except that :m
\begin{array}{lcl@{\qquad}l}
S; F; (\I32.\CONST~i)~(t.\CONST~c_2)~(t.\CONST~c_3)~(t.\ATOMICRMW({N}\K{\_u})^?.\ATCMPXCHG~\memarg)
&\stepto^{(\ARD~a.\LLEN~n)~(\ARD_{\SEQCST}~a.\LDATA[\X{ea}]~b_{\F{r}}^\ast)}&
F; (t.\CONST~c)
S; F; (t.\CONST~c)
\end{array}
\\ \qquad
\begin{array}[t]{@{}r@{~}l@{}}
Expand All @@ -3327,7 +3327,7 @@ The rules are identical to :ref:`non-atomic stores <exec-store>`, except that :m
\begin{array}{lcl@{\qquad}l}
S; F; (\I32.\CONST~i)~(t.\CONST~c_2)~(t.\CONST~c_3)~(t.\ATOMICRMW({N}\K{\_u})^?.\ATCMPXCHG~\memarg)
&\stepto^{(\ARD~a.\LLEN~n)}&
F; \TRAP
S; F; \TRAP
\end{array}
\\ \qquad
\begin{array}[t]{@{}r@{~}l@{}}
Expand Down Expand Up @@ -3404,9 +3404,9 @@ The rules are identical to :ref:`non-atomic stores <exec-store>`, except that :m
.. math::
\begin{array}{l}
\begin{array}{lcl@{\qquad}l}
F; (\I32.\CONST~i)~(\I32.\CONST~k)~\MEMORYATOMICNOTIFY~\memarg
S; F; (\I32.\CONST~i)~(\I32.\CONST~k)~\MEMORYATOMICNOTIFY~\memarg
&\stepto&
F; (\I32.\CONST~0)
S; F; (\I32.\CONST~0)
\end{array}
\\ \qquad
\begin{array}[t]{@{}r@{~}l@{}}
Expand All @@ -3416,40 +3416,40 @@ The rules are identical to :ref:`non-atomic stores <exec-store>`, except that :m
\end{array}
\\[1ex]
\begin{array}{lcl@{\qquad}l}
F; (\I32.\CONST~i)~(\I32.\CONST~k)~\MEMORYATOMICNOTIFY~\memarg
S; F; (\I32.\CONST~i)~(\I32.\CONST~k)~\MEMORYATOMICNOTIFY~\memarg
&\stepto&
F; \TRAP
S; F; \TRAP
\end{array}
\\ \qquad
\begin{array}[t]{@{}r@{~}l@{}}
(\iff & \X{mem}.\MITYPE = \limits~\UNSHARED \\
\wedge & \X{ea} + N/8 > |\X{mem}.\MIDATA| \vee \X{ea} \mod N/8 \neq 0) \\
\wedge & (\X{ea} + N/8 > |\X{mem}.\MIDATA| ~\vee~ \X{ea} \mod~N/8 \neq 0)) \\
\end{array}
\\
%
~\\
\begin{array}{lcl@{\qquad}l}
F; (\I32.\CONST~i)~(\I32.\CONST~k)~\MEMORYATOMICNOTIFY~\memarg
&\stepto^{(\ARD~a.\LLEN~n)~(\ANOTIFY~a.\LDATA[\X{ea}]~j~k)}&
F; (\I32.\CONST~j)
S; F; (\I32.\CONST~i)~(\I32.\CONST~k)~\MEMORYATOMICNOTIFY~\memarg && \\
\qquad\qquad \stepto^{(\ARD~a.\LLEN~n)~(\ANOTIFY~a.\LDATA[\X{ea}]~j~k)}
\quad S; F; (\I32.\CONST~j) &&
\end{array}
\\ \qquad
\begin{array}[t]{@{}r@{~}l@{}}
(\iff & \X{mem}.\MITYPE = \limits~\SHARED \\ord
(\iff & \X{mem}.\MITYPE = \limits~\SHARED \\
\wedge & \X{ea} + N/8 \leq n \\
\wedge & j \leq k \\
\wedge & \X{ea} \mod N/8 = 0) \\[1ex]
\end{array}
\\[1ex]
\begin{array}{lcl@{\qquad}l}
F; (\I32.\CONST~i)~(\I32.\CONST~k)~\MEMORYATOMICNOTIFY~\memarg
S; F; (\I32.\CONST~i)~(\I32.\CONST~k)~\MEMORYATOMICNOTIFY~\memarg
&\stepto^{(\ARD~a.\LLEN~n)}&
F; \TRAP
S; F; \TRAP
\end{array}
\\ \qquad
\begin{array}[t]{@{}r@{~}l@{}}
(\iff & \X{mem}.\MITYPE = \limits~\SHARED \\
\wedge & \X{ea} + N/8 > n \vee \X{ea} \mod N/8 \neq 0) \\
\wedge & (\X{ea} + N/8 > n ~\vee~ \X{ea} \mod N/8 \neq 0)) \\
\end{array}
\\
%
Expand Down Expand Up @@ -3523,9 +3523,8 @@ The rules are identical to :ref:`non-atomic stores <exec-store>`, except that :m
.. math::
\begin{array}{l}
\begin{array}{lcl@{\qquad}l}
F; (\I32.\CONST~i)~(\iN.\CONST~c)~(\I64.\CONST~k)~\MEMORYATOMICWAIT{N}~\memarg
&\stepto&
F; \TRAP
S; F; (\I32.\CONST~i)~(\iN.\CONST~c)~(\I64.\CONST~k)~\MEMORYATOMICWAIT{N}~\memarg && \\
\qquad\qquad \stepto \quad S; F; \TRAP &&
\end{array}
\\ \qquad
\begin{array}[t]{@{}r@{~}l@{}}
Expand All @@ -3535,9 +3534,9 @@ The rules are identical to :ref:`non-atomic stores <exec-store>`, except that :m
%
~\\
\begin{array}{lcl@{\qquad}l}
F; (\I32.\CONST~i)~(\iN.\CONST~c)~(\I64.\CONST~k)~\MEMORYATOMICWAIT{N}~\memarg
&\stepto^{(\ARD~a.\LLEN~n)~(\ARD_{\SEQCST}~a.\LDATA[\X{ea}]~b^\ast)~(\AWAIT~a.\LDATA[\X{ea}]~t)}&
F; (\WAITX~a.\LDATA[\X{ea}]~k)
S; F; (\I32.\CONST~i)~(\iN.\CONST~c)~(\I64.\CONST~k)~\MEMORYATOMICWAIT{N}~\memarg &&\\
\qquad\qquad \stepto^{(\ARD~a.\LLEN~n)~(\ARD_{\SEQCST}~a.\LDATA[\X{ea}]~b^\ast)~(\AWAIT~a.\LDATA[\X{ea}]~t)}
\quad S; F; (\WAITX~a.\LDATA[\X{ea}]~k) && \\
\end{array}
\\ \qquad
\begin{array}[t]{@{}r@{~}l@{}}
Expand All @@ -3549,9 +3548,9 @@ The rules are identical to :ref:`non-atomic stores <exec-store>`, except that :m
\end{array}
\\[1ex]
\begin{array}{lcl@{\qquad}l}
F; (\I32.\CONST~i)~(\iN.\CONST~c)~(\I64.\CONST~k)~\MEMORYATOMICWAIT{N}~\memarg
&\stepto^{(\ARD~a.\LLEN~n)~(\ARD_{\SEQCST}~a.\LDATA[\X{ea}]~b^\ast)}&
F; (\I32.\CONST~1)
S; F; (\I32.\CONST~i)~(\iN.\CONST~c)~(\I64.\CONST~k)~\MEMORYATOMICWAIT{N}~\memarg &&\\
\qquad\qquad \stepto^{(\ARD~a.\LLEN~n)~(\ARD_{\SEQCST}~a.\LDATA[\X{ea}]~b^\ast)}
\quad S; F; (\I32.\CONST~1)
\end{array}
\\ \qquad
\begin{array}[t]{@{}r@{~}l@{}}
Expand All @@ -3562,14 +3561,14 @@ The rules are identical to :ref:`non-atomic stores <exec-store>`, except that :m
\end{array}
\\[1ex]
\begin{array}{lcl@{\qquad}l}
F; (\I32.\CONST~i)~(\iN.\CONST~c)~(\I64.\CONST~k)~\MEMORYATOMICWAIT{N}~\memarg
&\stepto^{(\ARD~a.\LLEN~n)}&
F; \TRAP
S; F; (\I32.\CONST~i)~(\iN.\CONST~c)~(\I64.\CONST~k)~\MEMORYATOMICWAIT{N}~\memarg &&\\
\qquad\qquad \stepto^{(\ARD~a.\LLEN~n)}
\quad S; F; \TRAP
\end{array}
\\ \qquad
\begin{array}[t]{@{}r@{~}l@{}}
(\iff & \X{mem}.\MITYPE = \limits~\SHARED \\
\wedge & (\X{ea} + N/8 > n \vee \X{ea} \mod N/8 \neq 0)) \\
\wedge & (\X{ea} + N/8 > n ~\vee~ \X{ea} \mod N/8 \neq 0)) \\
\end{array}
\\
%
Expand Down
114 changes: 58 additions & 56 deletions document/core/exec/relaxed.rst
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -22,40 +22,46 @@ Preliminary Definitions
.. math::
\begin{array}{rcl}
\timeevt(\act^\ast~\AT~\time_p~\time) & = & \time \\
\\
&&\\
\locact(\ARD_{\ord}~\loc~\byte^\ast~\NOTEARS^?) & = & \loc \\
\locact(\AWR_{\ord}~\loc~\byte^\ast~\NOTEARS^?) & = & \loc \\
\locact(\ARMW~\loc~{\byte_1}^\ast~{\byte_2}^\ast) & = & \loc \\
\\
&&\\
\ordact(\ARD_{\ord}~\loc~\byte^\ast~\NOTEARS^?) & = & \ord \\
\ordact(\AWR_{\ord}~\loc~\byte^\ast~\NOTEARS^?) & = & \ord \\
\ordact(\ARMW~\loc~{\byte_1}^\ast~{\byte_2}^\ast) & = & \SEQCST \\
\\
\overlapact(\act_1, \act_2) & = & \rangeact(\act_1) \cup \rangeact(\act_2) \neq \epsilon \\
\sameact(\act_1, \act_2) & = & \rangeact(\act_1) = \rangeact(\act_2) \\
\\
\readingact(\act) & = & \readact(\act) \neq \epsilon \\
\writingact(\act) & = & \writeact(\act) \neq \epsilon \\
\\
&&\\
\overlapact(\act_1, \act_2) & = & (\rangeact(\act_1) \cup \rangeact(\act_2) \neq \epsilon) \\
\sameact(\act_1, \act_2) & = & (\rangeact(\act_1) = \rangeact(\act_2)) \\
&&\\
\readingact(\act) & = & (\readact(\act) \neq \epsilon) \\
\writingact(\act) & = & (\writeact(\act) \neq \epsilon) \\
&&\\
\readact(\ARD_{\ord}~\loc~\byte^\ast~\NOTEARS^?) & = & \byte^\ast \\
\readact(\ARMW~\loc~{\byte_1}^\ast~{\byte_2}^\ast) & = & {\byte_1}^\ast \\
\readact(\act) & = & \epsilon \qquad \otherwise \\
\readact(\act) & = & \epsilon \qquad (\otherwise) \\
&&\\
\writeact(\AWR_{\ord}~\loc~\byte^\ast~\NOTEARS^?) & = & \byte^\ast \\
\writeact(\ARMW~\loc~{\byte_1}^\ast~{\byte_2}^\ast) & = & {\byte_2}^\ast \\
\writeact(\act) & = & \epsilon \qquad \otherwise \\
\writeact(\act) & = & \epsilon \qquad (\otherwise) \\
&&\\
\offsetact(\act) & = & \u32 \qquad (\iff~\locact(\act) = \reg[\u32]) \\
&&\\
\syncact(\act_1,\act_2) & = & (\sameact(\act_1,\act_2) \wedge \\
&& \qquad \ordact(\act_1) = \ordact(\act_2) = \SEQCST) \\
\rangeact(\act) & = & [\u32 \ldots \u32 + n - 1] \\
&& (\iff~\locact(\act) = \reg[\u32] \wedge \\
&& \quad n = \F{max}(|\readact(\act)|,|\writeact(\act)|)) \\
&&\\
\offsetact(\act) & = & \u32 \qquad \iff \locact(\act) = \reg[\u32] \ \\
\\
\syncact(\act_1,\act_2) & = & \sameact(\act_1,\act_2) \wedge \ordact(\act_1) = \ordact(\act_2) = \SEQCST \\
\rangeact(\act) & = & [\u32 \ldots \u32 + n - 1] \qquad \iff \locact(\act) = \reg[\u32] \qquad n = \F{max}(|\readact(\act)|,|\writeact(\act)|) \\
\\
\tearfreeact(\ARD_{\ord}~\loc~\byte^\ast) & = & \bot \qquad \iff \ord = \UNORD \vee \ord = \INIT \\
\tearfreeact(\AWR_{\ord}~\loc~\byte^\ast) & = & \bot \qquad \iff \ord = \UNORD \vee \ord = \INIT \\
\tearfreeact(\act) & = & \top \qquad \otherwise \\
\\
\X{func}_{\reg}(\act_1^\ast~\act~\act_2^\ast~\AT~\time_p~\time) & = & \X{func}(\act) \qquad \iff \locact(\act) = \reg[\u32] \\
\X{func}_{\reg}(\act_1^\ast~\act~\act_2^\ast~\AT~\time_p~\time, \act_3^\ast~\act'~\act_4^\ast~\AT~\time'_p~\time') & = & \X{func}(\act.\act') \qquad \iff \locact(\act) = \locact(\act') = \reg[\u32] \\
\tearfreeact(\ARD_{\ord}~\loc~\byte^\ast) & = & \bot \qquad (\iff~\ord = \UNORD \vee \ord = \INIT) \\
\tearfreeact(\AWR_{\ord}~\loc~\byte^\ast) & = & \bot \qquad (\iff~\ord = \UNORD \vee \ord = \INIT) \\
\tearfreeact(\act) & = & \top \qquad (\otherwise) \\
&&\\
\X{func}_{\reg}(\act_1^\ast~\act~\act_2^\ast~\AT~\time_p~\time) & = & \X{func}(\act) \\
&& (\iff~\locact(\act) = \reg[\u32]) \\
\X{func}_{\reg}(\act_1^\ast~\act~\act_2^\ast~\AT~\time_p~\time, \quad &&\\
\qquad \act_3^\ast~\act'~\act_4^\ast~\AT~\time'_p~\time') & = & \X{func}(\act,\act') \\
&& (\iff~\locact(\act) = \locact(\act') = \reg[\u32]) \\
\end{array}

.. todo:: add loc for wait/woken/timeout/notify
Expand All @@ -78,9 +84,9 @@ A trace is a coinductive set of :ref:`events <syntax-evt>`. A trace is considere

.. math::
\begin{array}{c}
\config \stepto^{\evt} \config' \qquad \vdash \config' : \trace \qquad \timeevt(\evt) \notin \timeevt^\ast(\trace) \\[0.2\normalbaselineskip]
\hline \\[-0.8\normalbaselineskip]
\hline \\[-0.8\normalbaselineskip]
\config \stepto^{\evt} \config' \qquad \vdash \config' : \trace \qquad \timeevt(\evt) \notin \timeevt^\ast(\trace) \\[0.2ex]
\hline \\[-0.8ex]
\hline \\[-0.8ex]
\vdash \config : \evt~\trace
\end{array}

Expand All @@ -96,54 +102,50 @@ Consistency

.. math::
\frac{
\forall \reg, \, \vdash_{\reg} \trace \consistentwith
\forall \reg,~ \vdash_{\reg} \trace~\consistentwith
}{
\vdash \trace \consistent
\vdash \trace~\consistent
}

.. math::
\frac{
\begin{array}[b]{@{}c@{}}
\vdash_{\reg} \trace \suspensionsconsistentwith \\
\vdash_{\reg} \trace~\suspensionsconsistentwith \\
\forall \evt_R \in \readingact_{\reg}(\trace), \exists \evt_W^\ast,
\trace \vdash_{\reg} \evt_R \readseachfrom \evt_W^\ast \\
\trace \vdash_{\reg} \evt_R~\readseachfrom~\evt_W^\ast \\
\forall \evt_I, \evt \in \trace, \,
\ordact_{\reg}(\evt_I) = \INIT \wedge
\evt_I \neq \evt \wedge
\overlapact(\evt_I, \evt) \Rightarrow \evt_I \prechb \evt
\end{array}
}{
\vdash_{\reg} \trace \consistentwith
\vdash_{\reg} \trace~\consistentwith
}

.. math::
\frac{
\begin{array}[b]{@{}c@{}}
\left|\evt_W^\ast\right| = |\readact_{\reg}(\evt_R)| \\
\forall i < |\evt_W^\ast|,
\trace \vdash_{\reg}^i \evt_R \readsfrom \left(\evt_W^\ast[i]\right)
\trace \vdash_{\reg}^i \evt_R~\readsfrom~\left(\evt_W^\ast[i]\right)
\\
\vdash_{\reg} \evt_R \notear \evt_W^\ast
\vdash_{\reg} \evt_R~\notear~\evt_W^\ast
\end{array}
}{
\trace \vdash_{\reg} \evt_R \readseachfrom \evt_W^\ast
\trace \vdash_{\reg} \evt_R~\readseachfrom~\evt_W^\ast
}

.. math::
\frac{
\begin{array}[b]{@{}l@{}}
\evt_R \neq \evt_W \\
\evt_W \in \writingact_{\reg}(\trace)
\end{array}
\qquad
\begin{array}[b]{@{}r@{}}
\trace \vdash_{\reg}^{i,k} \evt_R \valueconsistent \evt_W \\
\trace \vdash_{\reg}^k \evt_R \hbconsistent \evt_W
\begin{array}[b]{@{}c}
\evt_R \neq \evt_W \\
\evt_W \in \writingact_{\reg}(\trace) \\
\trace \vdash_{\reg}^{i,k} \evt_R~\valueconsistent~\evt_W \\
\trace \vdash_{\reg}^k \evt_R~\hbconsistent~\evt_W \\
\trace \vdash_{\reg} \evt_R~\sclastvisible~\evt^\ast_W
\end{array}
\qquad
\trace \vdash_{\reg} \evt_R \sclastvisible \evt^\ast_W
}{
\trace \vdash_{\reg}^i \evt_R \readsfrom \evt_W
\trace \vdash_{\reg}^i \evt_R~\readsfrom~\evt_W
}

.. math::
Expand All @@ -153,22 +155,18 @@ Consistency
k = \offsetact_{\reg}(\evt_R) + i &=& \offsetact_{\reg}(\evt_W) + j
\end{array}
}{
\trace \vdash_{\reg}^{i,k} \evt_R \valueconsistent \evt_W
\trace \vdash_{\reg}^{i,k} \evt_R~\valueconsistent~\evt_W
}

.. math::
\frac{
\begin{array}[b]{@{}c}
\neg (\evt_R \prechb \evt_W) \\
\syncact_{\reg}(\evt_W, \evt_R) \Rightarrow \evt_W \prechb \evt_R
\end{array}
\qquad
\begin{array}[b]{@{}l@{}}
\forall \evt'_W \in \writingact_{\reg}(\trace),\\
\quad \evt_W \prechb \evt'_W \prechb \evt_R \Rightarrow k \notin \rangeact_{\reg}(\evt'_W)
\syncact_{\reg}(\evt_W, \evt_R) \Rightarrow \evt_W \prechb \evt_R \\
\forall \evt'_W \in \writingact_{\reg}(\trace), \evt_W \prechb \evt'_W \prechb \evt_R \Rightarrow k \notin \rangeact_{\reg}(\evt'_W)
\end{array}
}{
\trace \vdash_{\reg}^k \evt_R \hbconsistent \evt_W
\trace \vdash_{\reg}^k \evt_R~\hbconsistent~\evt_W
}

.. math::
Expand All @@ -180,23 +178,27 @@ Consistency
\quad \evt_W \prectot \evt'_W \prechb \evt_R \Rightarrow \neg\syncact_{\reg}(\evt_W, \evt'_W)
\end{array}
}{
\trace \vdash_{\reg} \evt_R \sclastvisible \evt_W
\trace \vdash_{\reg} \evt_R~\sclastvisible~\evt_W
}

.. math::
\frac{
\tearfreeact_{\reg}(\evt_R) \Rightarrow |\{\evt_W \in \evt_W^\ast ~|~ \sameact_{\reg}(\evt_R, \evt_W) \wedge \tearfreeact_{\reg}(\evt_W)\}| \leq 1
\begin{array}[b]{l@{}}
\tearfreeact_{\reg}(\evt_R) \Rightarrow \\
\quad |\{\evt_W \in \evt_W^\ast ~|~ \sameact_{\reg}(\evt_R, \evt_W) \wedge \tearfreeact_{\reg}(\evt_W)\}| \leq 1
\end{array}
}{
\vdash_{\reg} \evt_R \notear \evt_W^\ast
\vdash_{\reg} \evt_R~\notear~\evt_W^\ast
}

.. math::
\frac{
TODO
}{
\vdash_{\reg} \trace \suspensionsconsistentwith
\vdash_{\reg} \trace~\suspensionsconsistentwith
}


.. todo:: pull out the trace events which denote wait/wake actions as a timestamped list, check queue behaviour


Expand Down