diff options
Diffstat (limited to 'doc/arithmetic.tex')
| -rw-r--r-- | doc/arithmetic.tex | 18 |
1 files changed, 6 insertions, 12 deletions
diff --git a/doc/arithmetic.tex b/doc/arithmetic.tex index 52eae11..527c197 100644 --- a/doc/arithmetic.tex +++ b/doc/arithmetic.tex @@ -187,7 +187,7 @@ can be expressed as a simple formula \vspace{-1em} \[ \hspace*{-0.4cm} a^b = - \prod_{k \in \textbf{Z}_{+} ~:~ \left \lfloor {b \over 2^k} \hspace*{-1ex} \mod 2 \right \rfloor = 1} + \prod_{k \in \textbf{Z}_{+} ~:~ \left \lfloor \frac{b}{2^k} \hspace*{-1ex} \mod 2 \right \rfloor = 1} a^{2^k} \] @@ -212,13 +212,10 @@ The algorithm can be expressed in psuedocode as \hspace{-2.8ex} \begin{minipage}{\linewidth} \begin{algorithmic} - \STATE $r \gets 1$ - \STATE $f \gets a$ + \STATE $r, f \gets 1, a$ \WHILE{$b \neq 0$} - \IF{$b \equiv 1 ~(\textrm{Mod}~ 2)$} - \STATE $r \gets r \cdot f$ - \ENDIF - \STATE $f \gets f^2$ \qquad \textcolor{c}{\{$f \gets f \cdot f$\}} + \STATE $r \gets r \cdot f$ {\bf unless} $2 \vert b$ + \STATE $f \gets f^2$ \textcolor{c}{\{$f \gets f \cdot f$\}} \STATE $b \gets \lfloor b / 2 \rfloor$ \ENDWHILE \RETURN $r$ @@ -234,12 +231,9 @@ expressed as \hspace{-2.8ex} \begin{minipage}{\linewidth} \begin{algorithmic} - \STATE $r \gets 1$ - \STATE $f \gets a$ + \STATE $r, f \gets 1, a$ \WHILE{$b \neq 0$} - \IF{$b \equiv 1 ~(\textrm{Mod}~ 2)$} - \STATE $r \gets r \cdot f \hspace*{-1ex}~ \mod m$ - \ENDIF + \STATE $r \gets r \cdot f \hspace*{-1ex}~ \mod m$ \textbf{unless} $2 \vert b$ \STATE $f \gets f^2 \hspace*{-1ex}~ \mod m$ \STATE $b \gets \lfloor b / 2 \rfloor$ \ENDWHILE |