saying numbers

report/src/report.tex

@@ -9,8 +9,12 @@
 \usepackage{siunitx}
 \usepackage{ragged2e}
 \usepackage{booktabs}
+\usepackage{algorithm}
+\usepackage{algpseudocodex}
 \usepackage{hyperref}
 
+\newcommand{\algorithmautorefname}{Algorithm}
+
 \title{Solar Pump Control}
 \subtitle{Arduino Project for the Arduino Block Course 2022}
 \author{Engelmann, Mario\and Gehr, Stefan}
@@ -94,7 +98,64 @@ and increments the queue.
 Both index variables get set back to zero in case they reach the the end of the queue.
 
 \section{Saying Numbers}
-
+As our ``client'' only speaks German, we needed to implement the way numbers are read in that language.
+First we implemented a function sayDigit(\(d\)) that plays the corresponding sound of the digit \(d\).
+So ``eins'' for \(d=1\),  ``zwei'' for \(d=2\), and so on.
+Then for a few special cases we needed to create the function
+sayPreNumber(\(n\)) that only says ``ein'' instead of ``eins'' for \(n=1\) and just calls our normal sayNumber(\(n\)) function otherwise.
+This is necessary for cases like \(n=31\) which is read as ``EINunddreißig'' instead of ``EINSunddreißig''.
+Another special fucntion is sayAftNumber(\(n\)) which only our normal sayNumber(\(\n\)) function if \(n\ne 0\).
+It is necessary for numbers like 100, 200, 300, \dots,
+as we want to say ``zweihundert'' for \(n=200\) and not ``zweihundertnull''.
+\begin{algorithm}
+	\caption{Pseudocode implementation of the sayNumber function}
+	\label{alg:saynumber}
+\begin{algorithmic}[1]
+\Function{sayNumber}{\(n\)}
+	\If{\(n<0\)}
+	\Comment{negative number}
+		\State say(minus)
+		\State sayNumber(\(-n\))
+	\ElsIf{\(n < 10\)}
+	\Comment{1-digit number}
+		\State sayDigit(\(n\))
+	\ElsIf{\(n < 100\)}
+	\Comment{2-digit number}
+		\If{\(n=11\)}
+		\Comment{special case ELF}
+			\State say(elf)
+		\ElsIf{\(n=12\)}
+		\Comment{special case ZWÖLF}
+			\State say(zwölf)
+		\Else
+			\State tens \(\gets \lfloor n / 10 \rfloor\)
+			\State ones \(\gets n - 10 \times \text{tens}\)
+			\If{\(\text{ones}\ne 0\)}
+			\Comment{say the 1-digit first}
+				\State sayPreNumber(ones)
+				\If{\(\text{tens}\ge 2\)}
+				\Comment{UND only for numbers \(> 20\)}
+					\State say(und)
+				\EndIf
+			\EndIf
+			\If{\(\text{tens}=1\)}
+				\State say(zehn)
+			\ElsIf{\(\text{tens}=2\)}
+				\State say(zwanzig)
+			\ElsIf{\(\hdots\)}
+			\State \(\vdots\)
+			\EndIf
+		\EndIf
+	\Else
+	\Comment{3-digit number}
+		\State hundreds \(\gets \lfloor n / 100 \rfloor\)
+		\State sayPreNumber(hundreds)
+		\State sayAftNumber(\(n - 100 \times \text{hundreds}\)
+	\EndIf
+\end{algorithmic}
+\end{algorithm}
+Finally our main function sayNumber(\(n\)) goes thorugh all the possible cases.
+A peudocode implementation of it can be seen in \autoref{alg:saynumber}.
 \section{Temperature}
 
 %\listoffigures