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Add notes on li psudo-instruiction details.

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John Winans 2020-11-25 08:20:17 -06:00
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book/programs/chapter.tex
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@ -384,7 +384,7 @@ Introduce and present subroutines but not nesting until introduce stack operatio
\section{Pseudo Operations}
\enote{Explain why we have pseudo ops. These mappings are lifted from the ISM, Vol 1, V2.2}%
\enote{Explain why we have pseudo ops. Most of these mappings are lifted from the ISM, Vol 1, V2.2}%
\begin{verbatim}
la rd, symbol
auipc rd, symbol[31:12]
@ -410,5 +410,52 @@ Introduce and present subroutines but not nesting until introduce stack operatio
tail offset auipc x6, offset[31:12] # same as call but no x1
jalr x0, x6, offset[11:0]
mv rd,rs addi rd,rs,0
li rd,number lui rd,(number >>U 12)+(number&0x00000800 ? 1 : 0)
addi rd,rd,(number&0xfff)
\end{verbatim}
\subsection{The {\tt li} Pseudo Instruction}
Note that the {\tt li} pseudo instruction includes a conditional addition of 1 to the operand
in the {\tt lui} instruction. This is because the immediate operand in the
{\tt addi} instruction is sign-extended before it is added to rd.
If the immediate operand to the {\tt addi} has its most-significant-bit set to 1 then
it will have the effect of subtracting 1 from the most significant 20-bits in {\tt rd}.
Consider putting the value {\tt 0x12345800} into register {\tt x5} using the following
naive example code:
\begin{verbatim}
lui x5,0x12345 // x5 = 0x12345000
addi x5,x5,0x800 // x5 = 0x12345000 + sx(0x800) = 0x12345000 + 0xfffff800 = 0x12344800
\end{verbatim}
Therefore, in order to put the value {\tt 0x12345800} into register {\tt x5}, the value
used in the {\tt lui} instruction will altered to compensate for the sign-extention
in the {\tt addi} instruction:
\begin{verbatim}
lui x5,0x12346 // x5 = 0x12346000
addi x5,x5,0x800 // x5 = 0x12346000 + sx(0x800) = 0x12346000 + 0xfffff800 = 0x12345800
\end{verbatim}
Keep in mind that the {\em only} time that this altering of the operand in the {\tt lui}
instruction will take place is when the most-significant-bit of the operand in the
{\tt addi} is set to one.
Consider the case where we wish to put the value {\tt 0x12345700} into register {\tt x5}:
\begin{verbatim}
lui x5,0x12345 // x5 = 0x12345000
addi x5,x5,0x700 // x5 = 0x12345000 + sx(0x700) = 0x12345000 + 0x00000700 = 0x12345700
\end{verbatim}
This time, the sign-extension performed by the {\tt addi} instruction will sign-extend the
{\tt 0x700} to {\tt 0x00000700} before the addition.
Therefore, the {\tt li} pseudo-instruction will {\em only} increment the operand of the
{\tt lui} instruction when it is known that the operand of the {\tt addi} instruction
will end up being treated as a negative number.