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\chapter[SCOPE: Source code optimisation package]
{SCOPE: REDUCE source code optimisation package}
\label{SCOPE}
\typeout{{SCOPE: REDUCE source code optimisation package}}

{\footnotesize
\begin{center}
J.A. van Hulzen \\
University of Twente, Department of Computer Science \\
P.O. Box 217, 7500 AE Enschede \\
The Netherlands \\[0.05in]
e--mail: infhvh@cs.utwente.nl
\end{center}
}

SCOPE is a package to produce optimised versions of algebraic
expressions.  It can be used in two distinct fashions, as an adjunct
to numerical code generation (using GENTRAN, described in
chapter~\ref{GENTRAN}) or as a stand alone way of investigating
structure in an expression.

When used with GENTRAN\ttindex{GENTRAN} it is sufficient to set the
switch {\tt GENTRANOPT}\ttindex{GENTRANOPT} on, and GENTRAN will then
use SCOPE internally.  This is described in its internal detail in the
GENTRAN manual and the SCOPE documentation.

As a stand-alone package SCOPE provides the operator {\tt OPTIMIZE}.

\ttindex{OPTIMIZE}
A SCOPE application is easily performed and based on the use of
the following syntax:

{\small
\begin{flushleft}
\begin{tabular}{lcl}
$<$SCOPE\_application$>$ & $\Rightarrow$ & {\tt OPTIMIZE} $<$object\_seq$>$
[{\tt INAME} $<$cse\_prefix$>$]\\
$<$object\_seq$>$ & $\Rightarrow$ & $<$object$>$[,$<$object\_seq$>$]\\
$<$object$>$ & $\Rightarrow$ & $<$stat$>~\mid~<$alglist$>~\mid~<$alglist\_production$>$ \\
$<$stat$>$ & $\Rightarrow$ & $<$name$>~<$assignment operator$>~<$expression$>$\\
$<$assignment operator$>$ & $\Rightarrow$ & $:=~\mid~::=~\mid~::=:~\mid~:=:$\\
$<$alglist$>$ & $\Rightarrow$ & \{$<$eq\_seq$>$\}\\
$<$eq\_seq$>$ & $\Rightarrow$ & $<$name$>~=~<$expression$>$[,$<$eq\_seq$>$]\\
$<$alglist\_production$>$ & $\Rightarrow$ & $<$name$>~\mid~<$function\_application$>$\\
$<$name$>$ & $\Rightarrow$ & $<$id$>~\mid~<$id$>(<$a\_subscript\_seq$>)$\\
$<$a\_subscript\_seq$>$ & $\Rightarrow$ & $<$a\_subscript$>$[,$<$a\_subscript\_seq$>$]\\
$<$a\_subscript$>$ & $\Rightarrow$ & $<$integer$>~\mid~<$integer infix\_expression$>$\\
$<$cse\_prefix$>$ & $\Rightarrow$ & $<$id$>$
\end{tabular}
\end{flushleft}}

A SCOPE action can be applied on one assignment statement, or to a
sequence of such statements, separated by commas, or a list of expressions.

\index{SCOPE option ! {\tt INAME}}
The optional use of the {\tt INAME} extension in an {\tt OPTIMIZE}
command is introduced to allow the user to influence the generation of
cse-names.  The cse\_prefix is an identifier, used to generate
cse-names, by extending it with an integer part. If the cse\_prefix
consists of letters only, the initially selected integer part is 0.
If the user-supplied cse\_prefix ends with an integer its value
functions as initial integer part.

\begin{verbatim}
z:=a^2*b^2+10*a^2*m^6+a^2*m^2+2*a*b*m^4+2*b^2*m^6+b^2*m^2;

      2  2       2  6    2  2          4      2  6    2  2
z := a *b  + 10*a *m  + a *m  + 2*a*b*m  + 2*b *m  + b *m

OPTIMIZE z:=:z ;


G0 := b*a
G4 := m*m
G1 := G4*b*b
G2 := G4*a*a
G3 := G4*G4
z := G1 + G2 + G0*(2*G3 + G0) + G3*(2*G1 + 10*G2)

\end{verbatim}
it can be desirable
to rerun an optimisation request with a restriction on the minimal size of
the righthandsides. The command

\index{SCOPE function ! {\tt SETLENGTH}}
\hspace*{1cm} {\tt SETLENGTH} $<$integer$>$\$

can be used to produce rhs's with a minimal arithmetic complexity,
dictated by the value of
its integer argument. Statements, used to rename function applications, are
not affected by the {\tt SETLENGTH} command. The default setting is restored
with the command

\hspace*{1cm} {\tt RESETLENGTH}\$
\index{SCOPE function ! {\tt RESETLENGTH}}

{\em Example:}
\begin{verbatim}
SETLENGTH 2$

OPTIMIZE z:=:z INAME s$

       2  2
s1 := b *m
       2  2
s2 := a *m
               4                       4
z := (a*b + 2*m )*a*b + 2*(s1 + 5*s2)*m  + s1 + s2

\end{verbatim}

Details of the algorithm used is given in the Scope User's Manual.