Add exercice: [▶10] Modular powers of 2 - libzahl - big integer library
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 (DIR) commit b8f83987b190e282fd25c24e1c251678ad757765
 (DIR) parent faaa7dc980a80895b703775d18132eb6db105021
 (HTM) Author: Mattias Andrée <maandree@kth.se>
       Date:   Wed, 27 Jul 2016 03:58:35 +0200
       
       Add exercice: [▶10] Modular powers of 2
       
       Signed-off-by: Mattias Andrée <maandree@kth.se>
       
       Diffstat:
         M doc/exercises.tex                   |      17 +++++++++++++++++
       
       1 file changed, 17 insertions(+), 0 deletions(-)
       ---
 (DIR) diff --git a/doc/exercises.tex b/doc/exercises.tex
       @@ -38,6 +38,14 @@ which calculates $r = a \dotminus b = \max \{ 0,~ a - b \}$.
        
        
        
       +\item {[$\RHD$\textit{10}]} \textbf{Modular powers of 2}
       +
       +What is the advantage of using \texttt{zmodpow}
       +over \texttt{zbset} or \texttt{zlsh} in combination
       +with \texttt{zmod}?
       +
       +
       +
        \item {[\textit{M10}]} \textbf{Convergence of the Lucas Number ratios}
        
        Find an approximation for
       @@ -219,6 +227,15 @@ void monus(z_t r, z_t a, z_t b)
        \end{alltt}
        
        
       +\item \textbf{Modular powers of 2}
       +
       +\texttt{zbset} and \texttt{zbit} requires $\Theta(n)$
       +memory to calculate $2^n$. \texttt{zmodpow} only
       +requires $\mathcal{O}(\min \{n, \log m\})$ memory
       +to calculate $2^n \text{ mod } m$. $\Theta(n)$
       +memory complexity becomes problematic for very
       +large $n$.
       +
        
        \item \textbf{Convergence of the Lucas Number ratios}