myriad of typos

[phd-thesis.git] / top / green.tex

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\chapter{Green computing with mTask}%
\label{chp:green_computing_mtask}
\begin{chapterabstract}
        This chapter demonstrates the energy-saving features of \gls{MTASK} by:
        \begin{itemize}
                \item giving an overview of general green computing measures for edge devices;
                \item explaining task scheduling in \gls{MTASK}, and how to tweak it so suit the applications and energy needs;
                \item showing how to use interrupts in \gls{MTASK} to reduce the need for polling.
        \end{itemize}
\end{chapterabstract}

The edge layer of the \gls{IOT} is built from energy-efficient devices that sense and interact with the world.
While individual devices consume little energy, the sheer number of devices in total amounts to a lot.
Furthermore, many of these 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}.
It is therefore crucial to lower their energy consumption.

To reduce the power consumption of an \gls{IOT} edge device, the specialised low-power sleep modes of the microprocessors can be leveraged.
Different sleep mode achieve different power reductions because of their run time characteristics.
These specifics range from disabling or suspending the \gls{WIFI} radio; stop powering (parts) of the \gls{RAM}; disabling peripherals; or even turning off the processor completely, requiring an external signal to wake up again.
Determining exactly when, and for how long it is safe to sleep is expensive in the general case.
In practise, it means that either annotations in the source code, a \gls{RTOS}, or a scheduler is required.

\Cref{tbl:top_sleep} shows the properties and current consumption of two commonly used microcontrollers in their various sleep modes.
It uncovers that switching the \gls{WIFI} radio off yields the biggest energy saving.
In most \gls{IOT} applications, we need \gls{WIFI} for communications.
It is fine to switch it off when not communicating, but after switching it on, the \gls{WIFI} protocol needs to transmit a number of messages to re-establish the connection.
This implies that it is only worthwhile to switch the radio off when this can be done for some time.
The details vary per system and situation.
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.

\begin{table}
        \centering
        \caption{Current use (\unit{\milli\ampere}) of two microprocessor boards in various sleep modes.}%
        \label{tbl:top_sleep}
        \small
        \begingroup
        % default is 6pt but this gives an overflow of 4.25816pt
        \setlength\tabcolsep{5.5pt}
        \begin{tabular}{ccccccccc}
                \toprule
                                  & \multicolumn{4}{c}{\Gls{WEMOS} D1 mini}
                                  & \multicolumn{4}{c}{Adafruit Feather M0 \gls{WIFI}} \\
                \midrule
                          & active   & modem & light & deep  & active & modem & light & deep\\
                          &          & sleep & sleep & sleep &        & sleep & sleep & sleep\\
                \midrule
                \gls{WIFI}& on       & off   & off   & off   & on     & off   & off   & off\\
                CPU       & on       & on    & pend. & off   & on     & on    & idle  & idle\\
                \gls{RAM} & on       & on    & on    & off   & on     & on    & on    & on\\
                \midrule
                current   & \numrange{100}{240} & \num{15} & \num{0.5} & \num{0.002} & \numrange{90}{300} & \num{5} & \num{2} &  \num{0.005}\\
                \bottomrule
        \end{tabular}
        \endgroup
\end{table}

\section{Green \IOT{} computing}
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.
A deeper sleep mode saves more energy, but also requires more work to restore the software to its working state.
A processor like the ESP8266 driving the \gls{WEMOS} D1 mini loses the content of its \gls{RAM} in deep sleep mode.
As a result, after waking up, the program itself is preserved, since it is stored in flash memory, but the program state is lost.
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.

For edge devices executing a single task, explicit sleeping to save energy can be achieved without too much hassle.
This becomes much more challenging as soon as multiple independent tasks run on the same device.
Sleeping of the device induced by one task prevents progress of all tasks.
This is especially annoying when the other tasks are executing time critical parts, like communication protocols.
Such protocols control the communication with sensors and actuators.
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.

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.
In the \gls{MTASK} system, tasks are implemented as a rewrite system, where the work is automatically segmented in small atomic bits and stored as a task tree.
Each cycle, a single rewrite step is performed on all task trees.
During rewriting, each step, tasks do a bit of their work and progress steadily, allowing interleaved and seemingly parallel operation.
Atomic blocks, such as \gls{IO}, are always contained within a rewrite step.
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.
After each loop, the \gls{RTS} knows which task is waiting on which triggers and is thus determines when it is possible and safe to sleep and choose the optimal sleep mode according to the sleeping time.
%As a consequence, we cannot have fair multitasking.
%When a single rewrite step would take forever due to an infinite sequence of function calls, this would block the entire \gls{IOT} node.
%Even infinite sequences rewrite steps are perfectly fine.
%The \gls{MTASK} system does proper tail-call optimisations to facilitate this.

\section{Rewrite interval}
Some \gls{MTASK} programs contain one or more explicit \cleaninline{delay} primitives, offering a natural place a pause.
However, there are many \gls{MTASK} programs that just specify a repeated set of primitives.
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}.

\begin{lstClean}[caption={A basic thermostat task.},label={lst:thermostat}]
thermostat :: Main (MTask v Bool) | mtask, dht v
thermostat = declarePin D8 PMOutput \ledPin->
        DHT (DHT_DHT (i2c 0x36)) \dht->
        {main = rpeat (temperature dht >>~. \temp->
                       writeD ledPin (goal <. temp))}
\end{lstClean}

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.
The \gls{MTASK} machinery ensures that if there are other tasks running on the device, they make progress.
However, this solution is far from perfect when we take power consumption into account.
In most applications, it is very unlikely that the temperature changes significantly within one minute, let alone within some milliseconds.
Hence, it is sufficient to repeat the measurement with an appropriate interval.

There are various ways to improve this program.
The simplest solution is to add an explicit delay to the body of the repeat loop.
A slightly more sophisticated option is to add a repetition period to the \cleaninline{rpeat} combinator.
The combinator implementing this is called \cleaninline{rpeatEvery}.
Both solutions rely on an explicit action of the programmer.

Fortunately, \gls{MTASK} also contains machinery to do this automatically.
The key of this solution is to associate an evaluation interval with each task dynamically.
The interval $\rewriterate{low}{high}$ indicates that the evaluation can be safely delayed by any number of milliseconds within that range.
Such an interval is just a hint for the \gls{RTS}.
It is not a guarantee that the evaluation takes place in the given interval.
For example, other parts of the task expression can force an earlier evaluation of this part of the task.
On the other hand, when the system is very busy with other work, the task might even be executed after the upper bound of the interval.
The system calculates the rewrite rates from the current state of the task, i.e.\ the task tree.
This has the advantage that the programmer does not have to deal with them explicitly and that they are available in each and every \gls{MTASK} program.

\subsection{Basic tasks}
We start by assigning default rewrite rates to basic tasks.
These rewrite rates reflect the expected change rates of sensors and other inputs.
Basic tasks to set a value of a sensor or actuator have a rate of $\rewriterate{0}{0}$, this is never delayed.
An example of such a one-shot task in the task that writes to a \gls{GPIO} pin.
Basic tasks that continuously read a sensor or otherwise interact with a peripheral have default rewrite rates that fit standard usage of the sensor.
\Cref{tbl:rewrite} shows the default values for the basic tasks.
Reading \glspl{SDS} and measuring fast sensors such as sound or light aim for a rewrite every \qty{100}{\ms}.
Medium slow sensors such as gesture sensors are expected to rewrite every \qty{1000}{\ms}.
Slow sensors such as temperature or air quality have an upper bound of \qty{2000}{\ms}.

\begin{table}
        \centering
        \caption{Default rewrite rates of basic tasks.}%
        \label{tbl:rewrite}
        \begin{tabular}{ll}
                \toprule
                task & default interval\\
                \midrule
                reading \pgls{SDS} & $\rewriterate{0}{2000}$\\
                slow sensor & $\rewriterate{0}{2000}$\\
                medium sensor & $\rewriterate{0}{1000}$\\
                fast sensor & $\rewriterate{0}{100}$\\
                \bottomrule
        \end{tabular}
\end{table}

\subsection{Deriving rewrite rates}\label{sec:deriving_rewrite_rates}
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}.

\begin{equ}
        \begin{align}
                \mathcal{R} :: (\mathit{MTask}~v~a)    & \shortrightarrow \rewriterate{\mathit{Int}}{\mathit{Int}} \notag \\
                \mathcal{R} (t_1~{.||.}~t_2)  & = \mathcal{R}(t_1) \cap_{\textit{safe}} \mathcal{R}(t_2) \label{R:or} \\
                \mathcal{R}(t_1~{.\&\&.}~t_2) & = \mathcal{R}(t_1) \cap_{\textit{safe}} \mathcal{R}(t_2) \label{R:and}\\
                \mathcal{R}(t~{>\!\!>\!\!*.}~[a_1 \ldots a_n]) & = \mathcal{R}(t) \label{R:step} \\
                \mathcal{R}(\mathit{rpeat}~t~\mathit{start})   & =
                        \left\{\begin{array}{ll}
                                \mathcal{R}(t) & \text{if $t$ is unstable}\\
                                \rewriterate{r_1-\mathit{start}}{r_2-\mathit{start}} & \text{otherwise}\\
                        \end{array}\right.\\
                \mathcal{R} (\mathit{waitUntil}~d) & = \rewriterate{e-\mathit{time}}{e-\mathit{time}}\label{R:delay}\\
                \mathcal{R} (t) & =
                        \left\{%
                                \begin{array}{ll}
                                        \rewriterate{\infty}{\infty}~& \text{if}~t~\text{is Stable} \\
                                        \rewriterate{r_l}{r_u} & \text{otherwise}
                                \end{array}
                        \right.\label{R:other}
        \end{align}
        \caption{Function $\mathcal{R}$ for deriving refresh rates.}%
        \label{equ:r}
\end{equ}

\subsubsection{Parallel combinators}
For parallel combinators, the disjunction combinator (\cleaninline{.\|\|.}) in \cref{R:or} and the conjunction 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.
The conventional intersection does not suffice here because it yields an empty intersection when the intervals do not overlap.
In that case, the safe intersection returns the range with the lowest numbers.
The rationale is that subtasks should preferably not be delayed longer than their rewrite range.
Evaluating a task earlier should not change its result but just consumes more energy.

\begin{equ}
        \[
                X \cap_{\textit{safe}} Y = \left\{%
                        \begin{array}{ll}
                                X\cap Y & X\cap Y \neq \emptyset\\
                                Y & Y_2 < X_1\\
                                X & \text{otherwise}\\
                        \end{array}
                        \right.
        \]
        \caption{Safe intersection operator}\label{equ:safe_intersect}
\end{equ}

\subsubsection{Sequential combinators}
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 during evaluation.
Only after stepping, the combinator rewrites to the result of evaluating the right-hand side expression.

\subsubsection{Repeating combinators}
The repeat combinator repeats its argument indefinitely.
There are two repeating combinators, \cleaninline{rpeat} and \cleaninline{rpeatEvery} that both use the same task tree node.
The \cleaninline{rpeat} task combinator is a special type of \cleaninline{rpeatEvery}, i.e.\ the rewrite rate is fixed to $\rewriterate{0}{0}$.
The derived refresh rate of the repeat combinator is the refresh rate of the child if it is unstable.
Otherwise, the refresh rate is the embedded rate time minus the start time.
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.

\subsubsection{Delay combinators}
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.
Execution wise, it waits until the current time exceeds the time is greater than the argument time.

\subsubsection{Other tasks}
All other tasks are captured by \cref{R:other}.
If the task is stable, rewriting can be delayed indefinitely since the value will not change anyway.
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.

\subsection{Example}
The rewrite intervals associated with various steps of the thermostat program from \cref{lst:thermostat} are given in \cref{tbl:intervals}.
The rewrite steps and intervals are circular, after step 2 we continue with step 0 again.
Only the actual reading of the sensor with \cleaninline{temperature dht} offers the possibility for a non-zero delay.

%%\begin{table}[tb]
\begin{table}
        \centering
        \caption{Rewrite steps of the thermostat from \cref{lst:thermostat} and associated intervals.}%
        \label{tbl:intervals}
        \begin{tabular}{cp{20em}c}
                \toprule
                Step & Expression & Interval \\
                \midrule
                0  &
                \begin{lstClean}[aboveskip=-2ex,belowskip=-2ex,frame=]
rpeat ( temperature dht >>~. \temp.
        writeD builtInLED (goal <. temp)
)\end{lstClean}
                   &
                   $\rewriterate{0}{0}$ \\
                   %\hline
                1  &
                \begin{lstClean}[aboveskip=-2ex,belowskip=-2ex,frame=]
temperature dht >>~. \temp.
writeD builtInLED (goal <. temp) >>|.
rpeat ( temperature dht >>~. \temp.
        writeD builtInLED (goal <. temp)
)\end{lstClean}
                   & $\rewriterate{0}{2000}$ \\
                   %\hline
                2  &
                \begin{lstClean}[aboveskip=-2ex,belowskip=-2ex,frame=]
writeD builtInLED false >>|.
rpeat ( temperature dht >>~. \temp.
        writeD builtInLED (goal <. temp)
)\end{lstClean}
                & $\rewriterate{0}{0}$ \\
                \bottomrule
        \end{tabular}
\end{table}

\subsection{Tweaking rewrite rates}
A tailor-made \gls{ADT} (see \cref{lst:interval}) is used to tweak the timing intervals.
The value is determined at runtime, but the constructor is known at compile time.
During compilation, the constructor of the \gls{ADT} is checked and code is generated accordingly.
If it is \cleaninline{Default}, no extra code is generated.
In the other cases, code is generated to wrap the task tree node in a \emph{tune rate} node.
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.

\begin{lstClean}[caption={The \gls{ADT} for timing intervals in \gls{MTASK}.},label={lst:interval}]
:: TimingInterval v = Default
                    | BeforeMs (v Int)         // yields [+$\rewriterate{0}{x}$+]
                    | BeforeS  (v Int)         // yields [+$\rewriterate{0}{x \times 1000}$+]
                    | ExactMs  (v Int)         // yields [+$\rewriterate{x}{x}$+]
                    | ExactS   (v Int)         // yields [+$\rewriterate{0}{x \times 1000}$+]
                    | RangeMs  (v Int) (v Int) // yields [+$\rewriterate{x}{y}$+]
                    | RangeS   (v Int) (v Int) // yields [+$\rewriterate{x \times 1000}{y \times 1000}$+]
\end{lstClean}

\subsubsection{Sensors and shared data sources}
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.
This is achieved by calling the access functions with a custom rewrite rate as an additional argument (suffixed with the backtick (\cleaninline{`}))
The adaptions to other classes are similar and omitted for brevity.
\Cref{lst:dht_ext} shows the extended \cleaninline{dht} and \cleaninline{dio} class definition with functions for custom rewrite rates.

\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}]
class dht v where
        ...
        temperature` :: (TimingInterval v) (v DHT) -> MTask v Real
        temperature  ::                    (v DHT) -> MTask v Real
        humidity`    :: (TimingInterval v) (v DHT) -> MTask v Real
        humidity     ::                    (v DHT) -> MTask v Real

class dio p v | pin p where
        ...
        readD` :: (TimingInterval v) (v p) -> MTask v Bool | pin p
        readD  ::                    (v p) -> MTask v Bool | pin p
\end{lstClean}

As an example, we define an \gls{MTASK} that updates the \gls{SDS} \cleaninline{tempSds} in \gls{ITASK} in a tight loop.
The \cleaninline{temperature`} reading dictates that this happens at least once per minute.
Without other tasks on the device, the temperature \gls{SDS} is updated once per minute.
Other tasks can cause a slightly more frequent update.

\begin{lstClean}[caption={Updating \pgls{SDS} in \gls{ITASK} at least once per minute.},label={lst:updatesds2}]
delayTime :: TimingInterval v | mtask v
delayTime = BeforeS (lit 60) // 1 minute in seconds

devTask :: Main (MTask v Real) | mtask, dht, lowerSds v
devTask =
        DHT (DHT_DHT pin DHT11) \dht =
        lowerSds \localSds = tempSds
        In {main = rpeat (temperature` delayTime dht >>~. setSds localSds)}
\end{lstClean}

\subsubsection{Repeating tasks}
The task combinator \cleaninline{rpeat} restarts the child task in the evaluation if the previous produced a stable result.
However, in some cases it is desirable to postpone the restart of the child.
For this, the \cleaninline{rpeatEvery} task is introduced which receives an extra argument, the rewrite rate, as shown in \cref{lst:rpeatevery}.
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.
\footnotetext{In reality, it also compensates for time drift by taking into account the upper bound of the timing interval.
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.}

\begin{lstClean}[caption={Repeat task combinator with a timing interval.},label={lst:rpeatevery}]
class rpeat v where
        rpeat :: (MTask v t) -> MTask v t
        rpeatEvery v :: (TimingInterval v) (MTask v t) -> MTask v t
\end{lstClean}

\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}.
The \cleaninline{timedPulse} function creates a task that sends a \qty{50}{\ms} pulse to the \gls{GPIO} pin 0 every second.
The task created by the \cleaninline{timedPulseNaive} functions emulates the behaviour by using \cleaninline{rpeat} and \cleaninline{delay}.
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.
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.

\begin{lstClean}[caption={Example program for the repeat task combinator with a timing interval.},label={lst:rpeateveryex}]
timedPulse :: Main (MTask v Bool) | mtask v
timedPulse = declarePin D0 PMOutput \d0->
        in {main = rpeatEvery (ExactSec (lit 1)) (
                     writeD d0 true
                >>|. delay (lit 50)
                >>|. writeD d0 false
                )
        }

timedPulseNaive :: Main (MTask v Bool) | mtask v
timedPulseNaive = declarePin D0 PMOutput \d0->
        {main = rpeat (
                     writeD d0 true
                >>|. delay (lit 50)
                >>|. writeD d0 false
                >>|. delay (lit 950))
        }
\end{lstClean}

\section{Task scheduling in the mTask engine}\label{sec:scheduling}
The rewrite rates from the previous section only tell us how much the next evaluation of the task can be delayed.
In the \gls{MTASK} system, an \gls{IOT} edge devices can run multiple tasks.
In addition, it has to communicate with a server to collect new tasks and updates of \glspl{SDS}.
Hence, the rewrite intervals cannot be used directly to let the microcontroller sleep, so a scheduler is involved.
Our scheduler has the following objectives.

\begin{itemize}
        \item
                Meet the deadline whenever possible, i.e.\ the system tries to execute every task before the end of its rewrite interval.
                Only too much work on the device might cause an overflow of the deadline.
        \item
                Achieve long sleep times. Waking up from sleep consumes some energy and takes some time.
                Hence, we prefer a single long sleep over splitting the sleep interval into several smaller pieces.
        \item
                The scheduler tries to avoid unnecessary evaluations of tasks as much as possible.
                A task should not be evaluated now when its execution can also be delayed until the next time that the device is active.
                That is, a task should preferably not be executed before the start of its rewrite interval.
                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.
        \item
                The optimal power state should be selected.
                Although a system uses less power in a deep sleep mode, it also takes more time and energy to wake up from deep sleep.
                When the system knows that it can sleep only for a short time it is better to go to light sleep mode since waking up from light sleep is faster and consumes less energy.
\end{itemize}

The algorithm $\mathcal{R}$ from \cref{sec:deriving_rewrite_rates} computes the evaluation rate of the current tasks.
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.
We obtain those bounds by adding the current system time to the bounds of the computed rewrite interval by algorithm $\mathcal{R}$.

For the implementation, it is important to note that the evaluation of a task takes time.
Some tasks are extremely fast, but other tasks require longer computations and time-consuming communication with peripherals as well as with the server.
These execution times can yield a considerable and noticeable time drift in \gls{MTASK} programs.
For instance, a task like \cleaninline{rpeatEvery (ExactMs 1) t} should repeat \cleaninline{t} every millisecond.
The programmer might expect that \cleaninline{t} will be executed for the ${(N+1)}$th time after $N$ milliseconds.
Uncompensated time drift makes this considerably later.
The \gls{MTASK} \gls{RTS} does not pretend to be a hard \gls{RTOS}, and gives no firm guarantees with respect to evaluation time.
Nevertheless, we try to make time handling as reliable as possible.
This is achieved by adding the start time of this round of task evaluations rather than the current time to compute absolute execution intervals.

\subsection{Scheduling Tasks}
Apart from the task to execute, the device maintains the connection with the server and check there for new tasks and updates of \gls{SDS}.
When the microcontroller is active, the connection is checked and updates from the server are processed.
After that, the tasks that are within the execution window are executed.
Next, the microcontroller goes to light sleep for the minimum of a predefined interval and the task delay.

In general, the microcontroller executes multiple \gls{MTASK} tasks at the same time.
The \gls{MTASK} device repeatedly check for inputs from the server and executes all tasks that cannot be delayed to the next evaluation round one step.
The tasks are stored in a priority queue to check efficiently which of them need to be stepped.
The \gls{MTASK} tasks are ordered at their absolute latest start time in this queue; earliest deadline first.
We use the earliest deadline to order tasks with equal latest deadline.

It is very complicated to make an optimal scheduling algorithm for tasks to minimise the energy consumption.
We use a simple heuristic to evaluate tasks and determine sleep time rather than wasting energy on a fancy evaluation algorithm.
\Cref{lst:evalutionRound} gives this algorithm in pseudo code.
First the edge device checks for new tasks and updates of \glspl{SDS}.
This communication adds the new task to the queue, if there where any.
The \cleaninline{stepped} set contains all tasks evaluated in this evaluation round.
Next, we evaluate tasks from the queue until we encounter a task that has an evaluation interval that has not started.
This may result in evaluating tasks earlier than required, but maximises the opportunities to sleep after this evaluation round.
%Using the \prog{stepped} set ensures that we evaluate each task at most once during an evaluation round.
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.
A task that produces a stable value is completed and is not queued again.

\begin{algorithm}
%\DontPrintSemicolon
\SetKwProg{Repeatt}{repeat}{}{end}
\KwData{queue = []\;}
\Begin{
        \Repeatt{}{
                time = currentTime()\;
                queue += communicateWithServer()\;
                stepped = []\tcp*{tasks stepped in this round}
                \While{$\neg$empty(queue) $\wedge$ earliestDeadline(top(queue)) $\leq$ time}{
                        (task, queue) = pop(queue)\;
                        task2 = step(task)\tcp*{computes new execution interval}
                        \If(\tcp*[f]{not finished after step}){$\neg$ isStable(task2)}{
                                stepped += task2\;
                        }
                }
                queue = merge(queue, stepped)\;
                sleep(queue)\;
        }
}
\caption{Pseudo code for the evaluation round of tasks in the queue.}
\label{lst:evalutionRound}
\end{algorithm}

The \cleaninline{sleep} function determines the maximum sleep time based on the top of the queue.
The computed sleep time and the characteristics of the microprocessor determine the length and depth of the sleep.
For very short sleep times it is not be worthwhile to put the processor in sleep mode.
In the current \gls{MTASK} \gls{RTS}, the thresholds are determined by experimentation but can be tuned by the programmer.
On systems that lose the content of their \gls{RAM} it is not possible to go to deep sleep mode.

\section{Interrupts}\label{lst:interrupts}
Most microcontrollers have built-in support for processor interrupts.
These interrupts are hard-wired signals that interrupts the normal flow of the program in order to execute a small piece of code, the \gls{ISR}.
While the \glspl{ISR} look like regular functions, they do come with some limitations.
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.
After the execution of the \gls{ISR}, the normal program flow is resumed.
Interrupts are heavily used internally in the firmware of 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.

Using interrupts in \gls{MTASK} task offer two substantial benefits: fewer missed events and better energy usage.
Sometimes an external event such as a button press only occurs for a small duration, making it possible to miss it due to it happening right between two polls.
Using interrupts is not a fool-proof way of never missing an event.
Events could still be missed if they occur during the execution of an \gls{ISR} or while the microcontroller was in the process of waking up from a triggered interrupt.
There are also some sensors, such as the CCS811 air quality sensor, with support for triggering interrupts when a measurement exceeds a critical limit.

There are several different types of interrupts possible that each fire in slightly different circumstances (see \cref{tbl:gpio_interrupts}).

\begin{table}
        \centering
        \caption{Overview of \gls{GPIO} interrupt types.}%
        \label{tbl:gpio_interrupts}
        \begin{tabular}{ll}
                \toprule
                type    & triggers\\
                \midrule
                change  & input changes\\
                falling & input becomes low\\
                rising  & input becomes high\\
                low     & input is low\\
                high    & input is high\\
                \bottomrule
        \end{tabular}
\end{table}

\subsection{\Gls{ARDUINO} platform}
\Cref{lst:arduino_interrupt} shows an exemplatory program utilising interrupts written using the \ccpp{} dialect of \gls{ARDUINO}.
The example shows a debounced light switch for the built-in \gls{LED} connected to \gls{GPIO} pin 13.
When the user presses the button connected to \gls{GPIO} pin 11, the state of the \gls{LED} changes.
As buttons sometimes induce noise shortly after pressing, events within \qty{30}{\ms} after pressing are ignored.
In between the button presses, the device goes into deep sleep using the \arduinoinline{LowPower} library.

\Crefrange{lst:arduino_interrupt:defs_fro}{lst:arduino_interrupt:defs_to} defines the pin and debounce constants.
\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.
\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.

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.
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}.
This \gls{ISR} checks if the program is in cooldown state.
If this is not the case, the state of the \gls{LED} is toggled.
In any case, the program goes into cooldown state afterwards.

In the \arduinoinline{loop} function, the microcontroller goes to low-power sleep immediately and indefinitely.
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.

\begin{lstArduino}[numbers=left,label={lst:arduino_interrupt},caption={Light switch using interrupts.}]
#define LEDPIN 13[+\label{lst:arduino_interrupt:defs_fro}+]
#define INTERRUPTPIN 11
#define DEBOUNCE 30[+\label{lst:arduino_interrupt:defs_to}+]

volatile int state = LOW;[+\label{lst:arduino_interrupt:state}+]
volatile bool cooldown = true;[+\label{lst:arduino_interrupt:cooldown}+]

void setup() {[+\label{lst:arduino_interrupt:setup_fro}+]
        pinMode(LEDPIN, OUTPUT);
        pinMode(INTERRUPTPIN, INPUT);
        LowPower.attachInterruptWakeup(INTERRUPTPIN, buttonPressed, RISING);
}[+\label{lst:arduino_interrupt:setup_to}+]

void loop() {[+\label{lst:arduino_interrupt:loop_fro}+]
        LowPower.sleep();
        digitalWrite(LEDPIN, state);
        delay(DEBOUNCE);
        cooldown = false;
}[+\label{lst:arduino_interrupt:loop_to}+]

void buttonPressed() { /* ISR */ [+\label{lst:arduino_interrupt:isr_fro}+]
        if (!cooldown)
                state = !state;
        cooldown = true;
}[+\label{lst:arduino_interrupt:isr_to}+]
\end{lstArduino}

\subsection{The mTask language}
\Cref{lst:mtask_interrupts} shows the interrupt interface in \gls{MTASK}.
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.
Lowercase variants of the various interrupt modes such as \cleaninline{change :== lit Change} are available as convenience macros (see \cref{sec:expressions}).

\begin{lstClean}[label={lst:mtask_interrupts},caption={The interrupt interface in \gls{MTASK}.}]
class interrupt v where
        interrupt :: (v InterruptMode) (v p) -> MTask v Bool | pin p

:: InterruptMode = Change | Rising | Falling | Low | High
\end{lstClean}

When the \gls{MTASK} device executes this task, it installs an \gls{ISR} and sets the rewrite rate of the task to infinity, $\rewriterate{\infty}{\infty}$.
The interrupt handler is set up in such a way that the rewrite rate is changed to $\rewriterate{0}{0}$ once the interrupt triggers.
As a consequence, the task is executed on the next execution cycle.

The \cleaninline{pirSwitch} function in \cref{lst:pirSwitch} creates, given an interval in milliseconds, 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.
The system turns on the \gls{LED} again when there is still motion detected after this interval.
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.

\begin{lstClean}[caption={Example of a toggle light switch using interrupts.},label={lst:pirSwitch}]
pirSwitch :: Int -> Main (MTask v Bool) | mtask v
pirSwitch =
        declarePin D13 PMOutput \ledpin->
        declarePin D0 PMInput \pirpin->
        {main = rpeat (     interrupt high pirpin
                       >>|. writeD ledpin false
                       >>|. delay (lit interval)
                       >>|. writeD ledpin true) }
\end{lstClean}

\subsection{The mTask engine}

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.
Enabling and disabling interrupts is done in a general way in which tasks register themselves after creation and deregister after deletion.
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 at the time.

\subsubsection{Event registration}
The \gls{MTASK} \gls{RTS} contains an event administration to register which task is waiting on which event.
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.
Furthermore, this registration allows for a quick lookup in the \gls{ISR} to find the tasks listening to the events.
Conversely, during the teardown, the \gls{ISR} is disabled again when the last interrupt task of that kind is deleted.
The registration is light-weight and consists only of an event identifier and task identifier.
This event registration is stored as a linked list of task tree nodes so that the garbage collector cleans them up when they become unused.

Registering and deregistering interrupts is a device-specific procedure, although most supported devices use the \gls{ARDUINO} \gls{API} for this.
Which pins support which interrupt differs greatly from device to device, but this information is known at compile time.
At the time of registration, the \gls{RTS} checks whether the interrupt is valid and throws an \gls{MTASK} exception if it is not.
Moreover, an exception is thrown if multiple types of interrupts are registered on the same pin.

\subsubsection{Triggering interrupts}
Once an interrupt fires, tasks registered to that interrupt are not immediately evaluated because it is usually not safe to do.
For example, the interrupt could fire in the middle of a garbage collection process, resulting in corrupt memory.
Furthermore, to insure the \gls{ISR} to be very short, just a flag in the event administration is set to be processed later.
Interrupt event flags are processed at the beginning of the event loop, before tasks are executed.
For each subscribed task, the task tree is searched for nodes listening for the particular interrupt.
When found, the node is flagged and the pin status is written.
Afterwards, the evaluation interval of the task is set to $\rewriterate{0}{0}$ and the task is reinserted at the front of the scheduling queue to ensure rapid evaluation of the task.
Finally, the event is removed from the registration and the interrupt is disabled.
The interrupt can be disabled as all tasks waiting for the interrupt become stable after firing.
More occurrences of the interrupts do not change the value of the task as stable tasks keep the same value forever.
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.
Evaluating interrupt task node in the task tree is trivial because all the work was already done when the interrupt was triggered.
The task emits the status of the pin as a stable value if the information in the task shows that it was triggered.
Otherwise, no value is emitted.

\section{Conclusion}
This chapter show how we can automatically associate execution intervals to tasks.
Based on these intervals, we can delay the executions of those tasks.
When all task executions can be delayed, the microprocessor executing those tasks can go to sleep mode to reduce its energy consumption.
This is a rather difficult problem that must be solved dynamically, since we make no assumptions on the number and nature of the tasks that will be allocated to an \gls{IOT} device.
Furthermore, the execution intervals offer an elegant and efficient way to add interrupts to the language.
Those interrupts offer a more elegant and energy efficient implementation of watching an input than polling this input.

The actual reduction of the energy is of course highly dependent on the number and nature of the task shipped to the edge device.
Our examples show a reduction in energy consumption of two orders of magnitude.
Those reductions are a necessity for edge devices running of battery power.
Given the exploding number of \gls{IOT} edge devices, such savings are also mandatory for other devices to limit the total power consumption of the \gls{IOT}.

\input{subfilepostamble}
\end{document}