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	Add exercise: [30] Powers of the golden ratio - libzahl - big integer library
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	---
	commit 802b2b18704f1b04ab3c3195d49333a546dc0ff4
	parent 63bc4e141d2f28fcd11187413966235151a92c84
	Author: Mattias Andrée <[email protected]>
	Date: Mon, 25 Jul 2016 15:13:29 +0200

	Add exercise: [30] Powers of the golden ratio

	Signed-off-by: Mattias Andrée <[email protected]>

	Diffstat:
	M doc/exercises.tex \| 38 +++++++++++++++++++++++++++++…

	1 file changed, 38 insertions(+), 0 deletions(-)
	---
	diff --git a/doc/exercises.tex b/doc/exercises.tex
	@@ -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}


	@@ -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}