\label{tab:CellLib_binary}
\end{table}
+The {\tt \$shl} and {\tt \$shr} cells implement logical shifts, whereas the {\tt \$sshl} and
+{\tt \$sshr} cells implement arithmetic shifts. The {\tt \$shl} and {\tt \$sshl} cells implement
+the same operation. All four of these cells interpret the second operand as unsigned, and require
+\B{B\_SIGNED} to be zero.
+
+Two additional shift operator cells are available that do not directly correspond to any operator
+in Verilog, {\tt \$shift} and {\tt \$shiftx}. The {\tt \$shift} cell performs a right logical shift
+if the second operand is positive (or unsigned), and a left logical shift if it is negative.
+The {\tt \$shiftx} cell performs the same operation as the {\tt \$shift} cell, but the vacated bit
+positions are filled with undef (x) bits, and corresponds to the Verilog indexed part-select expression.
+
+For the binary cells that output a logical value ({\tt \$logic\_and}, {\tt \$logic\_or},
+{\tt \$eqx}, {\tt \$nex}, {\tt \$lt}, {\tt \$le}, {\tt \$eq}, {\tt \$ne}, {\tt \$ge},
+{\tt \$gt}), when the \B{Y\_WIDTH} parameter is greater than 1, the output is zero-extended,
+and only the least significant bit varies.
+
+\subsection{Multiplexers}
+
+Multiplexers are generated by the Verilog HDL frontend for {\tt
+?:}-expressions. Multiplexers are also generated by the {\tt proc} pass to map the decision trees
+from RTLIL::Process objects to logic.
+
+The simplest multiplexer cell type is {\tt \$mux}. Cells of this type have a \B{WIDTH} parameter
+and data inputs \B{A} and \B{B} and a data output \B{Y}, all of the specified width. This cell also
+has a single bit control input \B{S}. If \B{S} is 0 the value from the \B{A} input is sent to
+the output, if it is 1 the value from the \B{B} input is sent to the output. So the {\tt \$mux}
+cell implements the function \lstinline[language=Verilog]; Y = S ? B : A;.
+
+The {\tt \$pmux} cell is used to multiplex between many inputs using a one-hot select signal. Cells
+of this type have a \B{WIDTH} and a \B{S\_WIDTH} parameter and inputs \B{A}, \B{B}, and \B{S} and
+an output \B{Y}. The \B{S} input is \B{S\_WIDTH} bits wide. The \B{A} input and the output are both
+\B{WIDTH} bits wide and the \B{B} input is \B{WIDTH}*\B{S\_WIDTH} bits wide. When all bits of
+\B{S} are zero, the value from \B{A} input is sent to the output. If the $n$'th bit from \B{S} is
+set, the value $n$'th \B{WIDTH} bits wide slice of the \B{B} input is sent to the output. When more
+than one bit from \B{S} is set the output is undefined. Cells of this type are used to model
+``parallel cases'' (defined by using the {\tt parallel\_case} attribute or detected by
+an optimization).
+
+The {\tt \$tribuf} cell is used to implement tristate logic. Cells of this type have a \B{WIDTH}
+parameter and inputs \B{A} and \B{EN} and an output \B{Y}. The \B{A} input and \B{Y} output are
+\B{WIDTH} bits wide, and the \B{EN} input is one bit wide. When \B{EN} is 0, the output \B{Y}
+is not driven. When \B{EN} is 1, the value from \B{A} input is sent to the \B{Y} output. Therefore,
+the {\tt \$tribuf} cell implements the function \lstinline[language=Verilog]; Y = EN ? A : 'bz;.
+
+Behavioural code with cascaded {\tt if-then-else}- and {\tt case}-statements
+usually results in trees of multiplexer cells. Many passes (from various
+optimizations to FSM extraction) heavily depend on these multiplexer trees to
+understand dependencies between signals. Therefore optimizations should not
+break these multiplexer trees (e.g.~by replacing a multiplexer between a
+calculated signal and a constant zero with an {\tt \$and} gate).
+
\subsection{Registers}
- D-Type Flip-Flops are represented by {\tt \$dff} cells. These cells have a clock port \B{CLK},
- an input port \B{D} and an output port \B{Q}. The following parameters are available for \$dff
+ D-type flip-flops are represented by {\tt \$dff} cells. These cells have a clock port \B{CLK},
+ an input port \B{D} and an output port \B{Q}. The following parameters are available for {\tt \$dff}
cells:
\begin{itemize}
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