Align comments in listings

chapters/synchronous.tex

@@ -423,8 +423,8 @@ \section{Clock Constructors}\label{clock-constructors}
 
 \begin{example}
 \begin{lstlisting}[language=modelica]
-Clock c = Clock(angle > 0, 0.1) // before first tick of c:
-                                // interval(c) = 0.1
+Clock c = Clock(angle > 0, 0.1); // before first tick of c:
+                                 // interval(c) = 0.1
 \end{lstlisting}
 \end{example}
 
@@ -443,9 +443,9 @@ \section{Clock Constructors}\label{clock-constructors}
 
 \begin{example}
 \begin{lstlisting}[language=modelica]
-Clock c1 = Clock(1, 10) // 100 ms, no solver
+Clock c1 = Clock(1, 10);                   // 100 ms, no solver
 Clock c2 = Clock(c1, "ImplicitTrapezoid"); // 100 ms, ImplicitTrapezoid solver
-Clock c3 = Clock(c2, ""); // 100 ms, no solver
+Clock c3 = Clock(c2, "");                  // 100 ms, no solver
 \end{lstlisting}
 \end{example}
 \end{semantics}
@@ -601,7 +601,7 @@ \subsection{Base-clock conversion operators}\label{base-clock-conversion-operato
   Real y(start=1), yc;
 equation
   der(y) + y = 2;
-  yc = sample (y, Clock(0.1));
+  yc = sample(y, Clock(0.1));
 initial equation
   der(y) = 0;
 \end{lstlisting}
@@ -679,7 +679,7 @@ \subsection{Sub-clock conversion operators}\label{sub-clock-conversion-operators
 Clock u = Clock(x > 0);
 Clock y1 = subSample(u, 4);
 Clock y2 = superSample(y1, 2); // fine; y2 = subSample(u, 2)
-Clock y3 = superSample(u, 2); // error
+Clock y3 = superSample(u, 2);  // error
 Clock y4 = superSample(y1, 5); // error
 \end{lstlisting}
 \end{example}
@@ -703,14 +703,14 @@ \subsection{Sub-clock conversion operators}\label{sub-clock-conversion-operators
 Note, due to the restriction of \lstinline!superSample! on event clocks, \lstinline!shiftSample! can only shift the number of ticks of the event clock, but cannot introduce new ticks.  Example:
 \begin{lstlisting}[language=modelica]
 // Rational interval clock
-Clock u  = Clock(3, 10); // ticks: 0, 3/10, 6/10, ..
-Clock y1 = shiftSample(u, 1, 3); // ticks: 1/10, 4/10,
-...
+Clock u  = Clock(3, 10);            // ticks: 0, 3/10, 6/10, ..
+Clock y1 = shiftSample(u, 1, 3);    // ticks: 1/10, 4/10,
+$\ldots$
 // Event clock
-Clock u = Clock(sin(2 * pi * time) > 0, startInterval = 0.0)
-// ticks: 0.0, 1.0, 2.0, 3.0, ...
-Clock y1 = shiftSample(u, 2); // ticks: 2.0, 3.0, ...
-Clock y2 = shiftSample(u, 2, 3); // error (resolution must be 1)
+Clock u = Clock(sin(2 * pi * time) > 0, startInterval = 0.0);
+                                    // ticks: 0.0, 1.0, 2.0, 3.0, ...
+Clock y1 = shiftSample(u, 2);       // ticks: 2.0, 3.0, ...
+Clock y2 = shiftSample(u, 2, 3);    // error (resolution must be 1)
 \end{lstlisting}
 \end{nonnormative}
 \end{semantics}
@@ -729,20 +729,20 @@ \subsection{Sub-clock conversion operators}\label{sub-clock-conversion-operators
 \begin{lstlisting}[language=modelica]
 // Rational interval clock 1
 
-Clock u  = Clock(3, 10); // ticks: 0, 3/10, 6/10, ..
-Clock y1 = shiftSample(u, 3); // ticks: 9/10, 12/10, ..
-Clock y2 = backSample(y1, 2); // ticks: 3/10, 6/10,
-...
-Clock y3 = backSample(y1, 4); // error (ticks before u)
-Clock y4 = shiftSample(u, 2, 3); // ticks: 2/10, 5/10,
-...
-Clock y5 = backSample(y4, 1, 3); // ticks: 1/10, 4/10,
-...
+Clock u  = Clock(3, 10);          // ticks: 0, 3/10, 6/10, ..
+Clock y1 = shiftSample(u, 3);     // ticks: 9/10, 12/10, ..
+Clock y2 = backSample(y1, 2);     // ticks: 3/10, 6/10,
+$\ldots$
+Clock y3 = backSample(y1, 4);     // error (ticks before u)
+Clock y4 = shiftSample(u, 2, 3);  // ticks: 2/10, 5/10,
+$\ldots$
+Clock y5 = backSample(y4, 1, 3);  // ticks: 1/10, 4/10,
+$\ldots$
 // Event clock
-Clock u = Clock(sin(2 * pi * time) > 0, startInterval=xx)
-// ticks: 0, 1.0, 2.0, 3.0, ....
-Clock y1 = shiftSample(u, 3); // ticks: 3.0, 4.0, ...
-Clock y2 = backSample(y1, 2); // ticks: 1.0, 2.0, ...
+Clock u = Clock(sin(2 * pi * time) > 0, startInterval = xx)
+                                  // ticks: 0, 1.0, 2.0, 3.0, ....
+Clock y1 = shiftSample(u, 3);     // ticks: 3.0, 4.0, ...
+Clock y2 = backSample(y1, 2);     // ticks: 1.0, 2.0, ...
 \end{lstlisting}
 \end{example}
 \end{semantics}
@@ -762,7 +762,7 @@ \subsection{Sub-clock conversion operators}\label{sub-clock-conversion-operators
 
 Let $a$ and $b$ be positive integers with $a < b$, and
 \begin{lstlisting}[language=modelica]
-yb = backSample (u, $a$, $b$)
+yb = backSample(u, $a$, $b$)
 ys = shiftSample(u, $b-a$, $b$)
 \end{lstlisting}
 
@@ -787,7 +787,7 @@ \subsection{Sub-clock conversion operators}\label{sub-clock-conversion-operators
     x = previous(x) + 0.1;
   end when;
   when clk2 then
-    y = noClock(x); // most recent value of x
+    y = noClock(x);      // most recent value of x
     z = sample(hold(x)); // left limit of x (infinitesimally delayed)!
   end when;
 end NoClockVsSampleHold;
@@ -928,20 +928,20 @@ \subsection{Base-clock Partitioning}\label{base-clock-partitioning}
 
 After base clock partitioning, the following partitions are identified:
 \begin{lstlisting}[language=modelica]
-// Base partition 1 // clocked partition
-ud1 = sample (y,c1); // incidence(e) = {ud1}
-0 = f1(yd1, ud1, previous(ud1)); // incidence(e) = {yd1,ud1}
-ud2 = superSample (yd1,2); // incidence(e) = {ud2, yd1}
-0 = f2(yd2, ud2); // incidence(e) = {yd2, ud2}
-
-// Base partition 2 // continuous-time partition
-u = hold (yd2); // incidence(e) = {u}
-0 = f3(der(x1), x1, u); // incidence(e) = {x1,u}
-0 = f4(der(x2), x2, x1); // incidence(e) = {x2,x1}
-0 = f6(y, x1, u); // incidence(e) = {y,x1,u}
+// Base partition 1 -- clocked partition
+ud1 = sample(y, c1);             // incidence(e) = {ud1}
+0 = f1(yd1, ud1, previous(ud1)); // incidence(e) = {yd1, ud1}
+ud2 = superSample(yd1, 2);       // incidence(e) = {ud2, yd1}
+0 = f2(yd2, ud2);                // incidence(e) = {yd2, ud2}
+
+// Base partition 2 -- continuous-time partition
+u = hold(yd2);                   // incidence(e) = {u}
+0 = f3(der(x1), x1, u);          // incidence(e) = {x1, u}
+0 = f4(der(x2), x2, x1);         // incidence(e) = {x2, x1}
+0 = f6(y, x1, u);                // incidence(e) = {y, x1, u}
 
 // Identified as separate partition, but belonging to partition 2
-0 = f5(der(x3), x3); // incidence(e) = {x3}
+0 = f5(der(x3), x3);             // incidence(e) = {x3}
 \end{lstlisting}
 \end{example}
 
@@ -980,15 +980,15 @@ \subsection{Sub-clock Partitioning}\label{sub-clock-partitioning}
 \begin{lstlisting}[language=modelica]
 // Base partition 1 (clocked partition)
 // Sub-clock partition 1.1
-ud1 = sample (y,c1); // incidence(e) = {ud1}
-0 = f1(yd1,ud1,previous(yd1)); // incidence(e) = {yd1,ud1}
+ud1 = sample(y, c1);             // incidence(e) = {ud1}
+0 = f1(yd1, ud1, previous(yd1)); // incidence(e) = {yd1,ud1}
 
 // Sub-Clock partition 1.2
-ud2 = superSample (yd1,2); // incidence(e) = {ud2}
-0 = f2(yd2,ud2); // incidence(e) = {yd2,ud2}
+ud2 = superSample(yd1, 2);       // incidence(e) = {ud2}
+0 = f2(yd2, ud2);                // incidence(e) = {yd2,ud2}
 
 // Base partition 2 (no sub-clock partitioning, since continuous-time)
-u = hold (yd2);
+u = hold(yd2);
 0 = f3(der(x1), x1, u);
 0 = f4(der(x2), x2, x1);
 0 = f5(der(x3), x3);
@@ -1008,10 +1008,10 @@ \subsection{Sub-clock Inferencing}\label{sub-clock-inferencing}
 It must be possible to determine that the constraint set is valid at compile time.  However, in certain cases, it could be possible to defer providing actual numbers until run-time.
 \end{nonnormative}
 
-It is required that accumulated sub- and super sampling factors in the range of 1 to 2\textsuperscript{63} can be handled.
+It is required that accumulated sub- and supersampling factors in the range of 1 to 2\textsuperscript{63} can be handled.
 
 \begin{nonnormative}
-64 bit internal representation of numerator and denominator with sign can be used and gives minimum resolution 1.08E-19 seconds and maximum range 9.22E+18 seconds = 2.92E+11 years.
+64 bit internal representation of numerator and denominator with sign can be used and gives minimum resolution $1.08\times 10^{-19}$ seconds and maximum range $9.22\times 10^{18}$~seconds = $2.92\times 10^{11}$~years.
 \end{nonnormative}
 
 \section{Continuous-Time Equations in Clocked Partitions}\label{continuous-time-equations-in-clocked-partitions}
@@ -1220,16 +1220,16 @@ \subsection{Solver Methods}\label{solver-methods}
 Assume the differential equation
 \begin{lstlisting}[language=modelica]
   input Real u;
-  Real x(start=1, fixed=true);
+  Real x(start = 1, fixed = true);
 equation
   der(x) = -x + u
 \end{lstlisting}
 shall be transformed to a clocked discretized continuous-time partition with the \lstinline!"ExplicitEuler"! method.  The following model is a manual implementation:
 \begin{lstlisting}[language=modelica]
   input Real u;
   parameter Real x_start = 1;
-  Real x(start=x_start); // previous(x) = x_start at first clock tick
-  Real der_x(start=0); // previous(der_x) = 0 at first clock tick
+  Real x(start = x_start); // previous(x) = x_start at first clock tick
+  Real der_x(start = 0);   // previous(der_x) = 0 at first clock tick
 protected
   Boolean first(start=true);
 equation
@@ -1240,8 +1240,7 @@ \subsection{Solver Methods}\label{solver-methods}
       x = previous (x);
     else
       // second and further clock tick
-      x = previous (x) +
-      interval()*previous(der_x);
+      x = previous(x) + interval() * previous(der_x);
     end if;
     der_x = -x + u;
   end when;