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	On bit-splitting - libzahl - big integer library
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	---
	commit 12c7344ec6770c692094456bc81e7ed4322552aa
	parent bc8390c7615cf9a466420aa05130322488d54d7b
	Author: Mattias Andrée <[email protected]>
	Date: Sat, 14 May 2016 20:51:30 +0200

	On bit-splitting

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

	Diffstat:
	M doc/bit-operations.tex \| 46 +++++++++++++++++++++++++++++…

	1 file changed, 45 insertions(+), 1 deletion(-)
	---
	diff --git a/doc/bit-operations.tex b/doc/bit-operations.tex
	@@ -110,7 +110,51 @@ $r = \phantom{10001}1000_2$ after calling
	\section{Split}
	\label{sec:Split}

	-TODO % zsplit
	+In \secref{sec:Shift} and \secref{sec:Truncation}
	+we have seen how bit operations can be used to
	+calculate division by a power of two and
	+modulus a power of two efficiently using
	+bit-shift and bit-truncation operations. libzahl
	+also has a bit-split operation that can be used
	+to efficently calculate both division and
	+modulus a power of two efficiently in the same
	+operation, or equivalently, storing low bits
	+in one integer and high bits in another integer.
	+This function is
	+
	+\begin{alltt}
	+ void zsplit(z_t high, z_t low, z_t a, size_t b);
	+\end{alltt}
	+
	+\noindent
	+Unlike {\tt zdivmod}, it is not more efficient
	+than calling {\tt zrsh} and {\tt ztrunc}, but
	+it is more convenient. {\tt zsplit} requires
	+that {\tt high} and {\tt low} are from each
	+other distinct references.
	+
	+Calling {\tt zsplit(high, low, a, b)} is
	+equivalent to
	+
	+\begin{alltt}
	+ ztrunc(low, a, delim);
	+ zrsh(high, a, delim);
	+\end{alltt}
	+
	+\noindent
	+assuming {\tt a} and {\tt low} are not the
	+same reference (reverse the order of the
	+functions if they are the same reference.)
	+
	+{\tt zsplit} copies the lowest {\tt b} bits
	+of {\tt a} to {\tt low}, and the rest of the
	+bits to {\tt high}, with the lowest {\tt b}
	+removesd. For example, if $a = 1010101111_2$,
	+then $high = 101010_2$ and $low = 1111_2$
	+after calling {\tt zsplit(high, low, a, 4)}.
	+
	+{\tt zsplit} is especially useful in
	+divide-and-conquer algorithms.


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