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From: <git_AT_suckless.org>
Date: Mon, 25 Jul 2016 16:57:13 +0200 (CEST)

commit 802b2b18704f1b04ab3c3195d49333a546dc0ff4
Author: Mattias Andrée <maandree_AT_kth.se>
AuthorDate: Mon Jul 25 15:13:29 2016 +0200
Commit: Mattias Andrée <maandree_AT_kth.se>
CommitDate: Mon Jul 25 15:13:29 2016 +0200

    Add exercise: [30] Powers of the golden ratio
    
    Signed-off-by: Mattias Andrée <maandree_AT_kth.se>

diff --git a/doc/exercises.tex b/doc/exercises.tex
index cebff1c..23b8ef4 100644
--- a/doc/exercises.tex
+++ b/doc/exercises.tex
_AT_@ -188,6 +188,14 @@ than or equal to a preselected number.
 
 
 
+\item {[\textit{30}]} \textbf{Powers of the golden ratio}
+
+Implement function that returns $\varphi^n$ rounded
+to the nearest integer, where $n$ is the input and
+$\varphi$ is the golden ratio.
+
+
+
 \end{enumerate}
 
 
_AT_@ -477,5 +485,35 @@ the set of pseudoprimes.
 
 
 
+\item \textbf{Powers of the golden ratio}
+
+This was an information gathering exercise.
+For $n \ge 1$, $L_n = [\varphi^n]$, where
+$L_n$ is the $n^\text{th}$ Lucas number.
+
+\( \displaystyle{
+ L_n \stackrel{\text{\tiny{def}}}{\text{=}} \left \{ \begin{array}{ll}
+ 2 & \text{if} ~ n = 0 \\
+ 1 & \text{if} ~ n = 1 \\
+ L_{n - 1} + L_{n + 1} & \text{otherwise}
+ \end{array} \right .
+}\)
+
+\noindent
+but for efficiency and briefness, we will use
+\texttt{lucas} from \secref{sec:Lucas numbers}.
+
+\vspace{-1em}
+\begin{alltt}
+void golden_pow(z_t r, z_t p)
+\{
+ if (zsignum(p) <= 0)
+ zsetu(r, zzero(p));
+ else
+ lucas(r, p);
+\}
+\end{alltt}
+
+
 
 \end{enumerate}
Received on Mon Jul 25 2016 - 16:57:13 CEST