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@@ -3073,9 +3073,15 @@ To implement the new logical operations, the comparison \key{eq?}, and
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the \key{if} statement, we need to delve further into the x86
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language. Figure~\ref{fig:x86-ast-b} defines the abstract syntax for a
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larger subset of x86 that includes instructions for logical
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-operations, comparisons, and jumps. The logical instruction
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-\key{notq} is quite similar to the arithmetic instructions, so we
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-focus on the comparison and jump instructions.
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+operations, comparisons, and jumps.
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+
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+In addition to its arithmetic operations, x86 provides bitwise operators
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+that perform a logical operation on every bit of their arguments. We will
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+use these to implement Boolean operations like \code{not}. In particular,
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+the \key{xorq} instruction takes two arguments, performs a pairwise
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+exclusive-or (XOR) operation on the bits of
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+its arguments, and writes the result into its second argument (similar
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+to arithmetic instructions like \key{addq}).
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\begin{figure}[tbp]
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\fbox{
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@@ -3083,7 +3089,7 @@ focus on the comparison and jump instructions.
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\[
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\begin{array}{lcl}
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\Arg &::=& \ldots \mid (\key{byte-reg}\; \itm{register}) \\
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-\Instr &::=& \ldots \mid (\key{notq} \; \Arg)\\
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+\Instr &::=& \ldots \mid (\key{xorq} \; \Arg\;\Arg) \\
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&\mid& (\key{cmpq} \; \Arg\; \Arg) \mid (\key{sete} \; \Arg)
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\mid (\key{movzbq}\;\Arg\;\Arg) \\
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&\mid& (\key{jmp} \; \itm{label}) \mid (\key{je} \; \itm{label}) \mid
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@@ -3150,11 +3156,33 @@ $\Rightarrow$
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\end{lstlisting}
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\end{minipage}
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\end{tabular} \\
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-One further caveat is that the arguments of the \key{cmpq} instruction
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-may not both be immediate values. In that case you must insert another
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-\key{movq} instruction to put one of the immediate values in
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+One further caveat is that the second argument of the \key{cmpq} instruction
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+cannot be an immediate value. If you are comparing two immediates, you must insert another \key{movq} instruction to put the second argument in
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\key{rax}.
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+There is no unary x86 instruction that we can translate \code{(not x)} into.
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+However, we can achieve the same results using the bitwise \key{xor} instruction.
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+
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+% The translation of the \code{not} operator is not quite as simple
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+% as it seems. Recall that \key{notq} is a bitwise operator, not a boolean
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+% one. For example, the following program performs bitwise negation on
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+% the integer 1:
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+%
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+% \begin{tabular}{lll}
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+% \begin{minipage}{0.4\textwidth}
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+% \begin{lstlisting}
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+% (movq (int 1) (reg rax))
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+% (notq (reg rax))
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+% \end{lstlisting}
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+% \end{minipage}
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+% \end{tabular}
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+%
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+% After the program is run, \key{rax} does not contain 0, as you might
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+% hope -- it contains the binary value $111\ldots10$, which is the
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+% two's complement representation of $-2$. We recommend implementing boolean
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+% not by using \key{notq} and then masking the upper bits of the result with
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+% the \key{andq} instruction.
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+
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Regarding \key{if} statements, we recommend that you not lower them in
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\code{select-instructions} but instead lower them in
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\code{patch-instructions}. The reason is that for purposes of
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Jeremy G. Siek