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	On bit test - libzahl - big integer library
	git clone git://git.suckless.org/libzahl
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	---
	commit d1771305d6b1a548544119ce953c9bb758c6b77a
	parent 5990e4e42754a84edfaed2a31ee5cea3c4c9d9b1
	Author: Mattias Andrée <[email protected]>
	Date: Thu, 2 Jun 2016 12:42:12 +0200

	On bit test

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

	Diffstat:
	M 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