libzahl

big integer library
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commit d1771305d6b1a548544119ce953c9bb758c6b77a
parent 5990e4e42754a84edfaed2a31ee5cea3c4c9d9b1
Author: Mattias Andrée <maandree@kth.se>
Date:   Thu,  2 Jun 2016 12:42:12 +0200

On bit test

Signed-off-by: Mattias Andrée <maandree@kth.se>

Diffstat:
doc/bit-operations.tex | 37+++++++++++++++++++++++++++++++++++--
1 file changed, 35 insertions(+), 2 deletions(-)

diff --git a/doc/bit-operations.tex b/doc/bit-operations.tex @@ -209,7 +209,7 @@ divide-and-conquer algorithms. The function \begin{alltt} - zbset(z_t r, z_t a, size_t bit, int mode); + void zbset(z_t r, z_t a, size_t bit, int mode); \end{alltt} \noindent @@ -233,7 +233,40 @@ $mode < 0$ ($-1$): flip \section{Bit test} \label{sec:Bit test} -TODO % zbtest +libzahl provides a function for testing whether a bit +in a big integer is set: + +\begin{alltt} + int zbtest(z_t a, size_t bit); +\end{alltt} + +\noindent +it will return 1 if the bit with the index {\tt bit} +is set in {\tt a}, counting from the least significant +bit, starting at zero. 0 is returned otherwise. The +sign of {\tt a} is ignored. + +We can think of this like so: consider + +$$ \lvert a \rvert = \sum_{i = 0}^\infty k_i 2^i,~ k_i \in \{0, 1\}, $$ + +\noindent +{\tt zbtest(a, b)} returns $k_b$. Equivalently, we can think +that {\tt zbtest(a, b)} return whether $b \in B$ where $B$ +is defined by + +$$ \lvert a \rvert = \sum_{b \in B} 2^b,~ B \subset \textbf{Z}_+, $$ + +\noindent +or as right-shifting $a$ by $b$ bits and returning whether the +least significant bit is set. + +{\tt zbtest} always returns 1 or 0, but for good code quality, you +should avoid testing against 1, rather you should test whether the +value is a truth-value or a falsehood-value. However, there is +nothing wrong with depending on the value being restricted to being +either 1 or 0 if you want to sum up returned values or otherwise +use them in new values. \newpage