path: root/vol1/1.4.1.lyx

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\begin_layout Standard
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exerc1[10]
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State the characteristics of subroutine (5),
 just as (4) gives the characteristics of Subroutine 1.3.2M.
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answer 
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\begin_inset Formula 
\[
\left.\begin{array}{ll}
\text{Calling sequences:} & \text{\texttt{JMP MAX100} if \ensuremath{n=100}, or \texttt{JMP MAXN}}.\\
\text{Entry conditions:} & \text{For \texttt{MAXN}, }\text{rI3}=n;\ n\geq1.\\
\text{Exit conditions:} & \text{rA}=\max_{k=1}^{n}\mathtt{CONTENTS(X}+k\mathtt{)}=\mathtt{CONTENTS(X}+\text{rI2}\mathtt{)};\\
 & \text{rI3}=0.
\end{array}\right\} 
\]

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exerc2[10]
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Suggest code to substitute for (6) without using the 
\family typewriter
JSJ
\family default
 instruction.
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answer
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MAX50   ENT3 50
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        STJ  EXIT
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\begin_layout Plain Layout

        JMP  MAXN
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EXIT    JMP  *
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rexerc4[21]
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White a subroutine that generalizes 
\family typewriter
MAXN
\family default
 by finding the maximum value of 
\begin_inset Formula $\mathtt{X[}a\mathtt{]},\mathtt{X[}a+r\mathtt{]},\mathtt{X[}a+2r\mathtt{]},\dots,\mathtt{X[}n\mathtt{]}$
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,
 where 
\begin_inset Formula $r$
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 and 
\begin_inset Formula $n$
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 are parameters and 
\begin_inset Formula $a$
\end_inset

 is the smallest positive number with 
\begin_inset Formula $a\equiv n\pmod r$
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,
 namely 
\begin_inset Formula $a=1+(n-1)\bmod r$
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.
 Give a special entrance for the case 
\begin_inset Formula $r=1$
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.
 List the characteristics of your subroutine,
 as in (4).
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answer
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MAXIMUM ENT1 1
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MAXMOD  STJ  9F
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        JMP  2F
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1H      CMPA X,3
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        JGE  3F
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2H      ENT2 0,3
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        LDA  X,3
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3H      DEC3 0,1
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        J3P  1B
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9H      JMP  *
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\begin_inset Formula 
\[
\left.\begin{array}{ll}
\text{Calling sequences:} & \text{\texttt{JMP MAXIMUM} if \ensuremath{r=1}, or \texttt{JMP MAXMOD}}.\\
\text{Entry conditions:} & \text{rI3}=n;\text{ for \texttt{MAXMOD}, }\text{rI1}=r;\ n,r\geq1.\\
\text{Exit conditions:} & \text{rA}=\max_{k=1}^{\lfloor(n-1)/r\rfloor}\mathtt{CONTENTS(X}+n-kr\mathtt{)}=\mathtt{CONTENTS(X}+\text{rI2}\mathtt{)};\\
 & \text{rI3}\leq0.
\end{array}\right\} 
\]

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rexerc7[20]
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Why is self-modifying code now frowned upon?
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answer 
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Modern computers have separate instruction and data caches for efficiency,
 and typically several instructions are being processed at once,
 so modifying one of these instructions means emptying the instruction cache and pipeline,
 severely degrading performance.
 
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These computers also support a security measure that works by preventing pieces of code intended to be executed from being written to,
 in order to avoid attackers executing code by overriding some buffer due to a bug in the application,
 and self-modifying code would need to have that protection disabled.
 
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Third,
 typically these computers are running several processes or threads which may share code,
 and if the code is self-modifying we would need to keep several copies of it,
 which wastes memory.
 
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Finally,
 self-modifying code is difficult to reason about unless it is restricted to a few well known patterns,
 but these patterns can be easily replaced by constructions like stacks which do not suffer from the problems above and allow techniques like recursion.
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