top/green.tex

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   9 \chapter{Green computing with \texorpdfstring{\gls{MTASK}}{mTask}}%
  10 \label{chp:green_computing_mtask}
  11 \begin{chapterabstract}
  12         This chapter demonstrate the energy-saving features of \gls{MTASK} by:
  13         \begin{itemize}
  14                 \item giving an overview of general green computing measures for edge devices;
  15                 \item explaining task scheduling in \gls{MTASK}, and how to tweak it so suit the applications and energy needs;
  16                 \item showing how to use interrupts in \gls{MTASK} to reduce the need for polling.
  17         \end{itemize}
  18 \end{chapterabstract}
  19
  20 The edge layer of the \gls{IOT} contains small devices that sense and interact with the world.
  21 While individual devices consume little energy, the sheer number of devices in total amounts to a lot.
  22 Furthermore, many \gls{IOT} devices operate on batteries and higher energy consumption increases the amount of e-waste as \gls{IOT} edge devices are often hard to reach and consequently hard to replace \citep{nizetic_internet_2020}.
  23 It is therefore crucial to lower their energy consumption.
  24
  25 To reduce the power consumption of an \gls{IOT} edge device, the specialized low-power sleep modes of the microprocessors can be leveraged.
  26 Various sleep mode achieve different power reductions because of their run time characteristics.
  27 These specifics range from disabling or suspending \gls{WIFI}; stop powering (parts) of the \gls{RAM}; disabling peripherals; or even turning off the processor completely, requiring an external signal to wake up again.
  28 Determining exactly when, and for how long it is possible to sleep is expensive in the general case.
  29 In practise it means that either annotations in the source code, a \gls{RTOS}, or a handcrafted or general-purpose scheduler is required.
  30
  31 \Cref{tbl:top_sleep} shows the properties and current consumption of two commonly used microcontrollers in their various sleep modes.
  32 It uncovers that switching the \gls{WIFI} radio off yields the biggest energy savings.
  33 In most \gls{IOT} applications, we need \gls{WIFI} for communications.
  34 It is fine to switch it off, but after switching it on, the \gls{WIFI} protocol needs to transmit a number of messages to re-establish the connection.
  35 This implies that it is only worthwhile to switch the radio off when this can be done for some time.
  36 The details vary per system and situation.
  37 As a rule of thumb, derived from experimentation, it is only worthwhile to switch the \gls{WIFI} off when it is not needed for at least some tens of seconds.
  38
  39 \begin{table}
  40         \centering
  41         \caption{Current use (\unit{\milli\ampere}) of two microprocessor boards in various sleep modes.}%
  42         \label{tbl:top_sleep}
  43         \small
  44         \begingroup
  45         % default is 6pt but this gives an overflow of 4.25816pt
  46         \setlength\tabcolsep{5.5pt}
  47         \begin{tabular}{ccccccccc}
  48                 \toprule
  49                                   & \multicolumn{4}{c}{\Gls{WEMOS} D1 mini}
  50                                   & \multicolumn{4}{c}{Adafruit Feather M0 Wifi} \\
  51                 \midrule
  52                           & active   & modem & light & deep  & active & modem & light & deep\\
  53                           &          & sleep & sleep & sleep &        & sleep & sleep & sleep\\
  54                 \midrule
  55                 \gls{WIFI}& on       & off   & off   & off   & on     & off   & off   & off\\
  56                 CPU       & on       & on    & pend. & off   & on     & on    & idle  & idle\\
  57                 \gls{RAM} & on       & on    & on    & off   & on     & on    & on    & on\\
  58                 \midrule
  59                 current   & \numrange{100}{240} & \num{15} & \num{0.5} & \num{0.002} & \numrange{90}{300} & \num{5} & \num{2} &  \num{0.005}\\
  60                 \bottomrule
  61         \end{tabular}
  62         \endgroup
  63 \end{table}
  64
  65 \section{Green \texorpdfstring{\glsxtrshort{IOT}}{IoT} computing}
  66 The data in \cref{tbl:top_sleep} shows that it is worthwhile to put the system in some sleep mode when there is temporarily no work to be done.
  67 A deeper sleep mode saves more energy, but also requires more work to restore the software to its working state.
  68 A processor like the ESP8266 driving the \gls{WEMOS} D1 mini loses the content of its \gls{RAM} in deep sleep mode.
  69 As a result, after waking up, the program itself is preserved, since it is stored in flash memory, but the program state is lost.
  70 When there is a program state to be preserved, we must either store it elsewhere, limit us to light sleep, or use a microcontroller that keeps the \gls{RAM} intact during deep sleep.
  71
  72 For \gls{IOT} nodes executing a single task, explicit sleeping to save energy can be achieved without too much hassle.
  73 This becomes much more challenging as soon as multiple independent tasks run on the same node.
  74 Sleeping of the entire node induced by one task prevents progress of all tasks.
  75 This is especially annoying when the other tasks are executing time critical parts, like communication protocols.
  76 Such protocols control the communication with sensors and actuators.
  77 Without the help of an \gls{OS}, the programmer is forced to combine all subtasks into one big system that decides if it is safe to sleep for all subtasks.
  78
  79 The \gls{MTASK} language offers abstractions for edge layer-specific details such as the heterogeneity of architectures, platforms and frameworks; peripheral access; and multitasking but also for energy consumption and scheduling.
  80 In \gls{MTASK}, tasks are implemented as a rewrite system, where the work is automatically segmented in small atomic bits and stored as a task tree.
  81 Each cycle, a single rewrite step is performed on all task trees, during rewriting, tasks do a bit of their work and progress steadily, allowing interleaved and seemingly parallel operation.
  82 After a loop, the \gls{RTS} knows which task is waiting on which triggers and is thus able to determine the next execution time for each task automatically.
  83 Utilising this information, the \gls{RTS} can determine when it is possible and safe to sleep and choose the optimal sleep mode according to the sleeping time.
  84 For example, the \gls{RTS} never attempts to sleep during an \gls{I2C} communication because \gls{IO} is always contained \emph{within} a rewrite step.
  85 This is very convenient, since the system can inspect the current state of all \gls{MTASK} expressions after a rewrite and decide if sleeping and how long is possible.
  86 %As a consequence, we cannot have fair multitasking.
  87 %When a single rewrite step would take forever due to an infinite sequence of function calls, this would block the entire IoT node.
  88 Even infinite sequences rewrite steps are perfectly fine.
  89 The \gls{MTASK} system does proper tail-call optimizations to facilitate this.
  90
  91 \section{Rewrite interval}
  92 Some \gls{MTASK} examples contain one or more explicit \cleaninline{delay} primitives, offering a natural place for the node executing it to pause.
  93 However, there are many \gls{MTASK} programs that just specify a repeated set of primitives.
  94 A typical example is the program that reads the temperature for a sensor and sets the system \gls{LED} if the reading is below some given \cleaninline{goal}.
  95
  96 \begin{lstClean}[caption={A basic thermostat task.},label={lst:thermostat}]
  97 thermostat :: Main (MTask v Bool) | mtask, dht v
  98 thermostat = declarePin D8 PMOutput \ledPin->
  99         DHT I2Caddr \dht->
 100         {main = rpeat (temperature dht >>~. \temp->
 101                        writeD ledPin (goal <. temp))}
 102 \end{lstClean}
 103
 104 This program repeatedly reads the \gls{DHT} sensor and sets the on-board \gls{LED} based on the comparison with the \cleaninline{goal} as fast as possible on the \gls{MTASK} node.
 105 The \gls{MTASK} machinery ensures that if there are other tasks running on the node, they will make progress.
 106 However, this solution is far from perfect when we take power consumption into account.
 107 In most applications, it is very unlikely that the temperature changes significantly within one minute, let alone within some milliseconds.
 108 Hence, it is sufficient to repeat the measurement with an appropriate interval.
 109
 110 There are various ways to improve this program.
 111 The simplest solution is to add an explicit delay to the body of the repeat loop.
 112 A slightly more sophisticated option is to add a repetition period to the \cleaninline{rpeat} combinator.
 113 The combinator implementing this is called \cleaninline{rpeatEvery}.
 114 Both solutions rely on an explicit action of the programmer.
 115
 116 Fortunately, \gls{MTASK} also contains machinery to do this automatically.
 117 The key of this solution is to associate dynamically an evaluation interval with each task.
 118 The interval $\rewriterate{low}{high}$ indicates that the evaluation can be safely delayed by any number of milliseconds within that range.
 119 Such an interval is just a hint for the \gls{RTS}.
 120 It is not a guarantee that the evaluation takes place in the given interval.
 121 Other parts of the task expression can force an earlier evaluation of this part of the task.
 122 When the system is very busy with other work, the task might even be executed after the upper bound of the interval.
 123 The system calculates the rewrite rates from the current task expression.
 124 This has the advantage that the programmer does not have to deal with them and that they are available in each and every \gls{MTASK} program.
 125
 126 \subsection{Basic tasks}
 127
 128 We start by assigning default rewrite rates to basic tasks.
 129 These rewrite rates reflect the expected change rates of sensors and other inputs.
 130 Basic tasks to one-shot set a value of a sensor or actuator usually have a rate of $\rewriterate{0}{0}$, this is never delayed, e.g.\ writing to a \gls{GPIO} pin.
 131 Basic tasks that continuously read a value or otherwise interact with a peripheral have default rewrite rates that fit standard usage of the sensor.
 132 \Cref{tbl:rewrite} shows the default values for the basic tasks.
 133 I.e.\ reading \glspl{SDS} and fast sensors such as sound or light aim for a rewrite every \qty{100}{\ms}, medium slow sensors such as gesture sensors every \qty{1000}{\ms} and slow sensors such as temperature or air quality every \qty{2000}{\ms}.
 134
 135 \begin{table}
 136         \centering
 137         \caption{Default rewrite rates of basic tasks.}%
 138         \label{tbl:rewrite}
 139         \begin{tabular}{ll}
 140                 \toprule
 141                 task & default interval\\
 142                 \midrule
 143                 reading \pgls{SDS} & $\rewriterate{0}{2000}$\\
 144                 slow sensor & $\rewriterate{0}{2000}$\\
 145                 medium sensor & $\rewriterate{0}{1000}$\\
 146                 fast sensor & $\rewriterate{0}{100}$\\
 147                 \bottomrule
 148         \end{tabular}
 149 \end{table}
 150
 151 \subsection{Deriving rewrite rates}\label{sec:deriving_rewrite_rates}
 152 Based on these default rewrite rates, the system automatically derives rewrite rates for composed \gls{MTASK} expressions using the function $\mathcal{R}$ as shown in \cref{equ:r}.
 153
 154 \begin{equ}
 155         \begin{align}
 156                 \mathcal{R} :: (\mathit{MTask}~v~a)    & \shortrightarrow \rewriterate{\mathit{Int}}{\mathit{Int}} \notag \\
 157                 \mathcal{R} (t_1~{.||.}~t_2)  & = \mathcal{R}(t_1) \cap_{\textit{safe}} \mathcal{R}(t_2) \label{R:or} \\
 158                 \mathcal{R}(t_1~{.\&\&.}~t_2) & = \mathcal{R}(t_1) \cap_{\textit{safe}} \mathcal{R}(t_2) \label{R:and}\\
 159                 \mathcal{R}(t~{>\!\!>\!\!*.}~[a_1 \ldots a_n]) & = \mathcal{R}(t) \label{R:step} \\
 160                 \mathcal{R}(\mathit{rpeat}~t~\mathit{start})   & =
 161                         \left\{\begin{array}{ll}
 162                                 \mathcal{R}(t) & \text{if $t$ is unstable}\\
 163                                 \rewriterate{r_1-\mathit{start}}{r_2-\mathit{start}} & \text{otherwise}\\
 164                         \end{array}\right.\\
 165                 \mathcal{R} (\mathit{waitUntil}~d) & = \rewriterate{e-\mathit{time}}{e-\mathit{time}}\label{R:delay}\\
 166                 \mathcal{R} (t) & =
 167                         \left\{%
 168                                 \begin{array}{ll}
 169                                         \rewriterate{\infty}{\infty}~& \text{if}~t~\text{is Stable} \\
 170                                         \rewriterate{r_l}{r_u} & \text{otherwise}
 171                                 \end{array}
 172                         \right.\label{R:other}
 173         \end{align}
 174         \caption{Function $\mathcal{R}$ for deriving refresh rates.}%
 175         \label{equ:r}
 176 \end{equ}
 177
 178 \subsubsection{Parallel combinators}
 179 For parallel combinators, the \emph{or}-combinator (\cleaninline{.\|\|.}) in \cref{R:or} and the \emph{and}-combinator (\cleaninline{.&&.}) in \cref{R:and}, the safe intersection (see \cref{equ:safe_intersect}) of the rewrite rates is taken to determine the rewrite rate of the complete task.
 180 The conventional intersection does not suffice here because it yields an empty intersection when the intervals do not overlap.
 181 In that case, the safe intersection returns the range with the lowest numbers.
 182 The rationale is that subtasks should not be delayed longer than their rewrite range.
 183 Evaluating a task earlier should not change its result but just consumes more energy.
 184
 185 \begin{equ}
 186         \[
 187                 X \cap_{\textit{safe}} Y = \left\{%
 188                         \begin{array}{ll}
 189                                 X\cap Y & X\cap Y \neq \emptyset\\
 190                                 Y & Y_2 < X_1\\
 191                                 X & \text{otherwise}\\
 192                         \end{array}
 193                         \right.
 194         \]
 195         \caption{Safe intersection operator}\label{equ:safe_intersect}
 196 \end{equ}
 197
 198 \subsubsection{Sequential combinators}
 199 For the step combinator (\cref{R:step})---and all other derived sequential combinators\nobreak---\nobreak\hskip0ptthe refresh rate of the left-hand side task is taken since that is the only task that is rewritten.
 200 Only after stepping, the combinator rewrites to the right-hand side.
 201
 202 \subsubsection{Repeating combinators}
 203 The repeat combinators repeats its argument indefinitely.
 204 As the \cleaninline{rpeat} task tree node already includes a rewrite rate (set to $\rewriterate{0}{0}$ for a default \cleaninline{rpeat}), both \cleaninline{rpeat} and \cleaninline{rpeatEvery} use the same task tree node and thus only one entry is required here.
 205 The derived refresh rate of the repeat combinator is the refresh rate of the child if it is unstable.
 206 Otherwise, the refresh rate is the embedded rate time minus the start time.
 207 In case of the \cleaninline{rpeat} task, the default refresh rate is $\rewriterate{0}{0}$ so the task immediately refreshes and starts the task again.
 208 \todo{netter opschrijven}
 209
 210 \subsubsection{Delay combinators}
 211 Upon installation, a \cleaninline{delay} task is stored as a \cleaninline{waitUntil} task tree containing the time of installation added to the specified time to wait.
 212 Execution wise, it waits until the current time exceeds the time is greater than the argument time.
 213
 214 \subsubsection{Other tasks}
 215 All other tasks are captured by \cref{R:other}.
 216 If the task is stable, rewriting can be delayed indefinitely since the value will not change anyway.
 217 In all other cases, the values from \cref{tbl:rewrite} apply where $r_l$ and $r_u$ represent the lower and upper bound of this rate.
 218
 219 The rewrite intervals associated with various steps of the thermostat program from \cref{lst:thermostat} are given in \cref{tbl:intervals}.
 220 Those rewrite steps and intervals are circular, after step 2 we continue with step 0 again.
 221 Only the actual reading of the sensor with \cleaninline{temperature dht} offers the possibility for a non-zero delay.
 222
 223 \subsection{Example}
 224 %%\begin{table}[tb]
 225 \begin{table}
 226         \centering
 227         \caption{Rewrite steps of the thermostat from \cref{lst:thermostat} and associated intervals.}%
 228         \label{tbl:intervals}
 229         \begin{tabular}{cp{20em}c}
 230                 \toprule
 231                 Step & Expression & Interval \\
 232                 \midrule
 233                 0  &
 234                 \begin{lstClean}[aboveskip=-2ex,belowskip=-2ex,frame=]
 235 rpeat ( temperature dht >>~. \temp.
 236         writeD builtInLED (goal <. temp)
 237 )\end{lstClean}
 238                    &
 239                    $\rewriterate{0}{0}$ \\
 240                    %\hline
 241                 1  &
 242                 \begin{lstClean}[aboveskip=-2ex,belowskip=-2ex,frame=]
 243 temperature dht >>~. \temp.
 244 writeD builtInLED (goal <. temp) >>|.
 245 rpeat ( temperature dht >>~. \temp.
 246         writeD builtInLED (goal <. temp)
 247 )\end{lstClean}
 248                    & $\rewriterate{0}{2000}$ \\
 249                    %\hline
 250                 2  &
 251                 \begin{lstClean}[aboveskip=-2ex,belowskip=-2ex,frame=]
 252 writeD builtInLED false >>|.
 253 rpeat ( temperature dht >>~. \temp.
 254         writeD builtInLED (goal <. temp)
 255 )\end{lstClean}
 256                 & $\rewriterate{0}{0}$ \\
 257                 \bottomrule
 258         \end{tabular}
 259 \end{table}
 260
 261 \subsection{Tweaking rewrite rates}
 262 A tailor-made \gls{ADT} (see \cref{lst:interval}) determines the timing intervals for which the value is determined at runtime but the constructor is known at compile time.
 263 During compilation, the constructor of the \gls{ADT} is checked and code is generated accordingly.
 264 If it is \cleaninline{Default}, no extra code is generated.
 265 In the other cases, code is generated to wrap the task tree node in a \emph{tune rate} node.
 266 In the case that there is a lower bound, i.e.\ the task must not be executed before this lower bound, an extra \emph{rate limit} task tree node is generated that performs a no-op rewrite if the lower bound has not passed but caches the task value.
 267
 268 \begin{lstClean}[caption={The \gls{ADT} for timing intervals in \gls{MTASK}.},label={lst:interval}]
 269 :: TimingInterval v = Default
 270                     | BeforeMs (v Int)         // yields [+$\rewriterate{0}{x}$+]
 271                     | BeforeS  (v Int)         // yields [+$\rewriterate{0}{x \times 1000}$+]
 272                     | ExactMs  (v Int)         // yields [+$\rewriterate{x}{x}$+]
 273                     | ExactS   (v Int)         // yields [+$\rewriterate{0}{x \times 1000}$+]
 274                     | RangeMs  (v Int) (v Int) // yields [+$\rewriterate{x}{y}$+]
 275                     | RangeS   (v Int) (v Int) // yields [+$\rewriterate{x \times 1000}{y \times 1000}$+]
 276 \end{lstClean}
 277
 278 \subsubsection{Sensors and \texorpdfstring{\glspl{SDS}}{shared data sources}}
 279 In some applications, it is necessary to read sensors or \glspl{SDS} at a different rate than the default rate given in \cref{tbl:rewrite}, i.e.\ to customise the rewrite rate.
 280 This is achieved by calling the access functions with a custom rewrite rate as an additional argument (suffixed with the backtick (\cleaninline{`}))
 281 The adaptions to other classes are similar and omitted for brevity.
 282 \Cref{lst:dht_ext} shows the extended \cleaninline{dht} and \cleaninline{dio} class definition with functions for custom rewrite rates.
 283
 284 \begin{lstClean}[caption={Auxiliary definitions to \cref{lst:gpio,lst:dht} for \gls{DHT} sensors and digital \gls{GPIO} with custom timing intervals.},label={lst:dht_ext}]
 285 class dht v where
 286         ...
 287         temperature` :: (TimingInterval v) (v DHT) -> MTask v Real
 288         temperature  ::                    (v DHT) -> MTask v Real
 289         humidity`    :: (TimingInterval v) (v DHT) -> MTask v Real
 290         humidity     ::                    (v DHT) -> MTask v Real
 291
 292 class dio p v | pin p where
 293         ...
 294         readD` :: (TimingInterval v) (v p) -> MTask v Bool | pin p
 295         readD  ::                    (v p) -> MTask v Bool | pin p
 296 \end{lstClean}
 297
 298 As example, we define an \gls{MTASK} that updates the \gls{SDS} \cleaninline{tempSds} in \gls{ITASK} in a tight loop.
 299 The \cleaninline{temperature`} reading requires that this happens at least once per minute.
 300 Without other tasks on the \gls{IOT} node, the temperature \gls{SDS} is updated once per minute.
 301 Other tasks can cause a slightly more frequent update.
 302
 303 \begin{lstClean}[caption={Updating \pgls{SDS} in \gls{ITASK} at least once per minute.},label={lst:updatesds2}]
 304 delayTime :: TimingInterval v | mtask v
 305 delayTime = BeforeS (lit 60) // 1 minute in seconds
 306
 307 devTask :: Main (MTask v Real) | mtask, dht, liftsds v
 308 devTask =
 309         DHT (DHT_DHT pin DHT11) \dht =
 310         liftsds \localSds = tempSds
 311         In {main = rpeat (temperature` delayTime dht >>~. setSds localSds)}
 312 \end{lstClean}
 313
 314 \subsubsection{Repeating tasks}
 315 The task combinator \cleaninline{rpeat} restarts the child task in the evaluation if the previous produced a stable result.
 316 However, in some cases it is desirable to postpone the restart of the child.
 317 For this, the \cleaninline{rpeatEvery} task is introduced which receives an extra argument, the rewrite rate, as shown in \cref{lst:rpeatevery}.
 318 Instead of immediately restarting the child once it yields a stable value, it checks whether the lower bound of the provided timing interval has passed since the start of the task\footnotemark.
 319 \footnotetext{In reality, it also compensates for time drift by taking into account the upper bound of the timing interval.
 320 If the task takes longer to stabilise than the upper bound of the timing interval, this upper bound is taken as the start of the task instead of the actual start.}
 321
 322 \begin{lstClean}[caption={Repeat task combinator with a timing interval.},label={lst:rpeatevery}]
 323 class rpeat v where
 324         rpeat :: (MTask v t) -> MTask v t
 325         rpeatEvery v :: (TimingInterval v) (MTask v t) -> MTask v t
 326 \end{lstClean}
 327
 328 \Cref{lst:rpeateveryex} shows an example of an \gls{MTASK} task utilising the \cleaninline{rpeatEvery} combinator that would be impossible to create with the regular \cleaninline{rpeat}.
 329 The \cleaninline{timedPulse} function creates a task that sends a \qty{50}{\ms} pulse to the \gls{GPIO} pin 0 every second.
 330 The task created by the \cleaninline{timedPulseNaive} functions emulates the behaviour by using \cleaninline{rpeat} and \cleaninline{delay}.
 331 However, this results in a time drift because rewriting tasks trees takes some time and the time it takes can not always be reliably predicted due to external factors.
 332 E.g.\ writing to \gls{GPIO} pins takes some time, interrupts may slow down the program (see \cref{lst:interrupts}), or communication may occur in between task evaluations.
 333
 334 \begin{lstClean}[caption={Example program for the repeat task combinator with a timing interval.},label={lst:rpeateveryex}]
 335 timedPulse :: Main (MTask v Bool) | mtask v
 336 timedPulse = declarePin D0 PMOutput \d0->
 337         in {main = rpeatEvery (ExactSec (lit 1)) (
 338                      writeD d0 true
 339                 >>|. delay (lit 50)
 340                 >>|. writeD d0 false
 341                 )
 342         }
 343
 344 timedPulseNaive :: Main (MTask v Bool) | mtask v
 345 timedPulseNaive = declarePin D0 PMOutput \d0->
 346         {main = rpeat (
 347                      writeD d0 true
 348                 >>|. delay (lit 50)
 349                 >>|. writeD d0 false
 350                 >>|. delay (lit 950))
 351         }
 352 \end{lstClean}
 353
 354 \section{Task scheduling in the \texorpdfstring{\gls{MTASK}}{mTask} engine}\label{sec:scheduling}
 355 The rewrite rates from the previous section only tell us how much the next evaluation of the task can be delayed.
 356 In the \gls{MTASK} system, an \gls{IOT} edge devices can run multiple tasks.
 357 In addition, it has to communicate with a server to collect new tasks and updates of \glspl{SDS}.
 358 Hence, the rewrite intervals cannot be used directly to let the microcontroller sleep.
 359 Our scheduler has the following objectives.
 360 \begin{itemize}
 361         \item
 362                 Meet the deadline whenever possible, i.e.\ the system tries to execute every task before the end of its rewrite interval.
 363                 Only too much work on the device might cause an overflow of the deadline.
 364         \item
 365                 Achieve long sleep times. Waking up from sleep consumes some energy and takes some time.
 366                 Hence, we prefer a single long sleep over splitting this interval into several smaller pieces.
 367         \item
 368                 The scheduler tries to avoid unnecessary evaluations of tasks as much as possible.
 369                 A task should not be evaluated now when its execution can also be delayed until the next time that the device is active.
 370                 That is, a task should preferably not be executed before the start of its rewrite interval.
 371                 Whenever possible, task execution should even be delayed when we are inside the rewrite interval as long as we can execute the task before the end of the interval.
 372         \item
 373                 The optimal power state should be selected.
 374                 Although a system uses less power in a deep sleep mode, it also takes more time and energy to wake up from deep sleep.
 375                 When the system knows that it can sleep only a short time it is better to go to light sleep mode since waking up from light sleep is faster and consumes less energy.
 376 \end{itemize}
 377
 378 The algorithm $\mathcal{R}$ from \cref{sec:deriving_rewrite_rates} computes the evaluation rate of the current tasks.
 379 For the scheduler, we transform this interval to an absolute evaluation interval; the lower and upper bound of the start time of that task measured in the time of the \gls{IOT} edge device.
 380 We obtain those bounds by adding the current system time to the bounds of the computed rewrite interval by algorithm $\mathcal{R}$.
 381
 382 For the implementation, it is important to note that the evaluation of a task takes time.
 383 Some tasks are extremely fast, but other tasks require long computations and time-consuming communication with peripherals as well as with the server.
 384 These execution times can yield a considerable and noticeable time drift in \gls{MTASK} programs.
 385 For instance, a task like \cleaninline{rpeatEvery (ExactMs 1) t} should repeat \cleaninline{t} every millisecond.
 386 The programmer might expect that \cleaninline{t} will be executed for the ${(N+1)}^{th}$ time after $N$ milliseconds.
 387 Uncompensated time drift might make this considerably later.
 388 The \gls{MTASK} \gls{RTS} does not pretend to be a hard real-time \gls{OS}, and cannot give firm guarantees with respect to evaluation time.
 389 Nevertheless, we try to make time handling as reliable as possible.
 390 This is achieved by adding the start time of this round of task evaluations rather than the current time to compute absolute execution intervals.
 391
 392 \subsection{Scheduling Tasks}
 393 Apart from the task to execute, the \gls{IOT} device has to maintain the connection with the server and check there for new tasks and updates of \gls{SDS}.
 394 When the microcontroller is active, it checks the connection and updates from the server and executes the task if it is in its execution window.
 395 Next, the microcontroller goes to light sleep for the minimum of a predefined interval and the task delay.
 396
 397 In general, the microcontroller node executes multiple \gls{MTASK} tasks at the same time.
 398 The \gls{MTASK} node repeatedly check for inputs from servers and execute all tasks that cannot be delayed to the next evaluation round one step.
 399 The tasks are stored in a priority queue to check efficiently which of them need to be stepped.
 400 The \gls{MTASK} tasks are ordered at their absolute latest start time in this queue; the earliest deadline first.
 401 We use the earliest deadline to order tasks with equal latest deadline.
 402
 403 It is very complicated to make an optimal scheduling algorithm for tasks to minimize the energy consumption.
 404 We use a simple heuristic to evaluate tasks and determine sleep time rather than wasting energy on a fancy evaluation algorithm.
 405 \Cref{lst:evalutionRound} gives this algorithm in pseudo code.
 406 First the \gls{MTASK} node checks for new tasks and updates of \glspl{SDS}.
 407 This communication adds any task to the queue.
 408 The \cleaninline{stepped} set contains all tasks evaluated in this evaluation round.
 409 Next, we evaluate tasks from the queue until we encounter a task that has an evaluation interval that is not started.
 410 This might evaluate tasks earlier than required, but maximizes the opportunities to sleep after this evaluation round.
 411 %Using the \prog{stepped} set ensures that we evaluate each task at most once during an evaluation round.
 412 Executed tasks are temporarily stored in the \cleaninline{stepped} set instead of inserted directly into the queue to ensure that they are evaluated at most once in a evaluation round to ensure that there is frequent communication with the server.
 413 A task that produces a stable value is completed and is not queued again.
 414
 415 \begin{algorithm}
 416 %\DontPrintSemicolon
 417 \SetKwProg{Repeatt}{repeat}{}{end}
 418 \KwData{queue = []\;}
 419 \Begin{
 420         \Repeatt{}{
 421                 time = currentTime()\;
 422                 queue += communicateWithServer()\;
 423                 stepped = []\tcp*{tasks stepped in this round}
 424                 \While{$\neg$empty(queue) $\wedge$ earliestDeadline(top(queue)) $\leq$ time}{
 425                         (task, queue) = pop(queue)\;
 426                         task2 = step(task)\tcp*{computes new execution interval}
 427                         \If(\tcp*[f]{not finished after step}){$\neg$ isStable(task2)}{
 428                                 stepped += task2\;
 429                         }
 430                 }
 431                 queue = merge(queue, stepped)\;
 432                 sleep(queue)\;
 433         }
 434 }
 435 \caption{Pseudo code for the evaluation round of tasks in the queue.}
 436 \label{lst:evalutionRound}
 437 \end{algorithm}
 438
 439 The \cleaninline{sleep} function determines the maximum sleep time based on the top of the queue.
 440 The computed sleep time and the characteristics of the microprocessor determine the length and depth of the sleep.
 441 For very short sleep times it is not be worthwhile to put the processor in sleep mode.
 442 In the current \gls{MTASK} \gls{RTS}, the thresholds are determined by experimentation but can be tuned by the programmer.
 443 On systems that lose the content of their \gls{RAM} it is not possible to go to deep sleep mode.
 444
 445 \section{Interrupts}\label{lst:interrupts}
 446 Most microcontrollers have built-in support for processor interrupts.
 447 These interrupts are hard-wired signals that can interrupt the normal flow of the program to execute a small piece of code, the \gls{ISR}.
 448 While the \glspl{ISR} look like regular functions, they do come with some limitations.
 449 For example, they must be very short, in order not to miss future interrupts; can only do very limited \gls{IO}; cannot reliably check the clock; and they operate in their own stack, and thus communication must happen via global variables.
 450 After the execution of the \gls{ISR}, the normal program flow is resumed.
 451 Interrupts are heavily used internally in the \gls{RTS} of the microcontrollers to perform timing critical operations such as \gls{WIFI}, \gls{I2C}, or \gls{SPI} communication; completed \gls{ADC} conversions; software timers; exception handling; \etc.
 452
 453 Using interrupts in \gls{MTASK} task offer two substantial benefits: fewer missed events and better energy usage.
 454 Sometimes an external event such as a button press only occurs for a very small duration, making it possible to miss it due to it happening right between two polls.
 455 Using interrupts is not a fool-proof way of never missing an event.
 456 Events may still be missed if they occur during the execution of an \gls{ISR} or while the microcontroller is still in the process of waking up from a triggered interrupt.
 457 There are also some sensors, such as the CCS811 air quality sensor, with support for triggering interrupts when a value exceeds a critical limit.
 458
 459 There are several different types of interrupts possible.
 460 \begin{table}
 461         \centering
 462         \caption{Overview of \gls{GPIO} interrupt types.}%
 463         \label{tbl:gpio_interrupts}
 464         \begin{tabular}{ll}
 465                 \toprule
 466                 type    & triggers\\
 467                 \midrule
 468                 change  & input changes\\
 469                 falling & input becomes low\\
 470                 rising  & input becomes high\\
 471                 low     & input is low\\
 472                 high    & input is high\\
 473                 \bottomrule
 474         \end{tabular}
 475 \end{table}
 476
 477 \subsection{\Gls{ARDUINO} platform}
 478 \Cref{lst:arduino_interrupt} shows an exemplatory program utilising interrupts written in \gls{ARDUINO}'s \gls{CPP} dialect.
 479 The example shows a debounced light switch for the built-in \gls{LED} connected to \gls{GPIO} pin 13.
 480 When the user presses the button connected to \gls{GPIO} pin 11, the state of the \gls{LED} changes.
 481 As buttons sometimes induce noise shortly after pressing, events within \qty{30}{\ms} after pressing are ignored.
 482 In between the button presses, the device goes into deep sleep using the \arduinoinline{LowPower} library.
 483
 484 \Crefrange{lst:arduino_interrupt:defs_fro}{lst:arduino_interrupt:defs_to} defines the pin and debounce constants.
 485 \Cref{lst:arduino_interrupt:state} defines the current state of the \gls{LED}, it is declared \arduinoinline{volatile} to exempt it from compiler optimisations because it is accessed in the interrupt handler.
 486 \Cref{lst:arduino_interrupt:cooldown} flags whether the program is in debounce state, i.e.\ events should be ignored for a short period of time.
 487
 488 In the \arduinoinline{setup} function (\crefrange{lst:arduino_interrupt:setup_fro}{lst:arduino_interrupt:setup_to}), the pinmode of the \gls{LED} and interrupt pins are set.
 489 Furthermore, the microcontroller is instructed to wake up from sleep mode when a \emph{rising} interrupt occurs on the interrupt pin and to call the \gls{ISR} at \crefrange{lst:arduino_interrupt:isr_fro}{lst:arduino_interrupt:isr_to}.
 490 This \gls{ISR} checks if the program is in cooldown state.
 491 If this is not the case, the state of the \gls{LED} is toggled.
 492 In any case, the program goes into cooldown state afterwards.
 493
 494 In the \arduinoinline{loop} function, the microcontroller goes to low-power sleep immediately and indefinitely.
 495 Only when an interrupt triggers, the program continues, writes the state to the \gls{LED}, waits for the debounce time, and finally disables the \arduinoinline{cooldown} state.
 496
 497 \begin{lstArduino}[numbers=left,label={lst:arduino_interrupt},caption={Light switch using interrupts.}]
 498 #define LEDPIN 13[+\label{lst:arduino_interrupt:defs_fro}+]
 499 #define INTERRUPTPIN 11
 500 #define DEBOUNCE 30[+\label{lst:arduino_interrupt:defs_to}+]
 501
 502 volatile int state = LOW;[+\label{lst:arduino_interrupt:state}+]
 503 volatile bool cooldown = true;[+\label{lst:arduino_interrupt:cooldown}+]
 504
 505 void setup() {[+\label{lst:arduino_interrupt:setup_fro}+]
 506         pinMode(LEDPIN, OUTPUT);
 507         pinMode(INTERRUPTPIN, INPUT);
 508         LowPower.attachInterruptWakeup(INTERRUPTPIN, buttonPressed, RISING);
 509 }[+\label{lst:arduino_interrupt:setup_to}+]
 510
 511 void loop() {[+\label{lst:arduino_interrupt:loop_fro}+]
 512         LowPower.sleep();
 513         digitalWrite(LEDPIN, state);
 514         delay(DEBOUNCE);
 515         cooldown = false;
 516 }[+\label{lst:arduino_interrupt:loop_to}+]
 517
 518 void buttonPressed() {[+\label{lst:arduino_interrupt:isr_fro}+]
 519         if (!cooldown)
 520                 state = !state;
 521         cooldown = true;
 522 }[+\label{lst:arduino_interrupt:isr_to}+]
 523 \end{lstArduino}
 524
 525 \subsection{The \texorpdfstring{\gls{MTASK}}{mTask} language}
 526 \Cref{lst:mtask_interrupts} shows the interrupt interface in \gls{MTASK}.
 527 The \cleaninline{interrupt} class contains a single function that, given an interrupt mode and a \gls{GPIO} pin, produces a task that represents this interrupt.
 528 Lowercase variants of the various interrupt modes such as \cleaninline{change :== lit Change} are available as convenience macros (see \cref{sec:expressions}).
 529
 530 \begin{lstClean}[label={lst:mtask_interrupts},caption={The interrupt interface in \gls{MTASK}.}]
 531 class interrupt v where
 532         interrupt :: (v InterruptMode) (v p) -> MTask v Bool | pin p
 533
 534 :: InterruptMode = Change | Rising | Falling | Low | High
 535 \end{lstClean}
 536
 537 When the \gls{MTASK} device executes this task, it installs an \gls{ISR} and sets the rewrite rate of the task to infinity, $\rewriterate{\infty}{\infty}$.
 538 The interrupt handler is set up in such a way that the rewrite rate is changed to $\rewriterate{0}{0}$ once the interrupt triggers.
 539 As a consequence, the task is executed on the next execution cycle.
 540
 541 The \cleaninline{pirSwitch} function in \cref{lst:pirSwitch} creates, given an interval in \unit{\ms}, a task that reacts to motion detection by a \gls{PIR} sensor (connected to \gls{GPIO} pin 0) by lighting the \gls{LED} connected to \gls{GPIO} pin 13 for the given interval.
 542 The system lightens the \gls{LED} again when there is still motion detected after this interval.
 543 By changing the interrupt mode in this program text from \cleaninline{High} to \cleaninline{Rising} the system lights the \gls{LED} only one interval when it detects motion no matter how long this signal is present at the \gls{PIR} pin.
 544
 545 \begin{lstClean}[caption={Example of a toggle light switch using interrupts.},label={lst:pirSwitch}]
 546 pirSwitch :: Int -> Main (MTask v Bool) | mtask v
 547 pirSwitch =
 548         declarePin D13 PMOutput \ledpin->
 549         declarePin D0 PMInput \pirpin->
 550         {main = rpeat (     interrupt high pirpin
 551                        >>|. writeD ledpin false
 552                        >>|. delay (lit interval)
 553                        >>|. writeD ledpin true) }
 554 \end{lstClean}
 555
 556 \subsection{The \texorpdfstring{\gls{MTASK}}{mTask} engine}
 557
 558 While interrupt tasks have their own node type in the task tree, they differ slightly from other node types because they require a more elaborate setup and teardown.
 559 Enabling and disabling interrupts is done in a general way in which tasks register themselves after creation and deregister after deletion.
 560 Interrupts should be disabled when there are no tasks waiting for that kind of interrupt because unused interrupts can lead to unwanted wake ups, and only one kind of interrupt can be attached to a pin.
 561
 562 \subsubsection{Event registration}
 563 The \gls{MTASK} \gls{RTS} contains an event administration to register which task is waiting on which event.
 564 During the setup of an interrupt task, the event administration in the \gls{MTASK} \gls{RTS} is checked to determine whether a new \gls{ISR} for the particular pin needs to be registered.
 565 Furthermore, this registration allows for a quick lookup in the \gls{ISR} to find the tasks listening to the events.
 566 Conversely, during the teardown, the \gls{ISR} is disabled again when the last interrupt task of that kind is deleted.
 567 The registration is light-weight and consists only of an event identifier and task identifier.
 568 This event registration is stored as a linked list of task tree nodes so that the garbage collector can clean them up when they become unused.
 569
 570 Registering and deregistering interrupts is a device specific procedure, although most supported devices use the \gls{ARDUINO} \gls{API} for this.
 571 Which pins support which interrupt differs greatly from device to device but this information is known at compile time.
 572 At the time of registration, the \gls{RTS} checks whether the interrupt is valid and throws an \gls{MTASK} exception if it is not.
 573 Moreover, an exception is thrown if multiple types of interrupts are registered on the same pin.
 574
 575 \subsubsection{Triggering interrupts}
 576 Once an interrupt fires, tasks registered to that interrupt are not immediately evaluated because it is usually not safe to do.
 577 For example, the interrupt could fire in the middle of a garbage collection process, resulting in incorrect pointers.
 578 Furthermore, as the \gls{ISR} is supposed to be be very short, just a flag in the event administration is set.
 579 Interrupt event flags are processed at the beginning of the event loop, before tasks are executed.
 580 For each subscribed task, the task tree is searched for nodes listening for the particular interrupt.
 581 When found, the node is flagged and the pin status is written.
 582 Afterwards, the evaluation interval of the task is set to $\rewriterate{0}{0}$ and the task is reinsterted at the front of the scheduling queue to ensure rapid evaluation of the task.
 583 Finally, the event is removed from the registration and the interrupt is disabled.
 584 The interrupt can be disabled as all tasks waiting for the interrupt become stable after firing.
 585 More occurrences of the interrupts do not change the value of the task as stable tasks keep the same value forever.
 586 Therefore, it is no longer necessary to keep the interrupt enabled, and it is relatively cheap to enable it again if needed in the future.
 587 Evaluating interrupt task node in the task tree is trivial because all of the work was already done when the interrupt was triggered.
 588 The task emits the status of the pin as a stable value if the information in the task shows that it was triggered.
 589 Otherwise, no value is emitted.
 590
 591 \section{Conclusion}
 592 \todo[inline]{Conclusion}
 593
 594 \input{subfilepostamble}
 595 \end{document}