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<b>Data Structures and Algorithms 
with Object-Oriented Design Patterns in C++</b><br>
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<H1><A NAME="SECTION003100000000000000000">A Detailed Model of the Computer</A></H1>
<A NAME="secmodeldetailed">&#160;</A>
<P>
In this section we develop a detailed model
of the running time performance of C++ programs.
The model developed is independent of the underlying
hardware and system software.
Rather than analyze the performance of a particular,
arbitrarily chosen physical machine,
we consider the implementation of the C++ programming language 
as a kind a ``virtual C++ machine'' (see Figure&nbsp;<A HREF="page35.html#figcppvm" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page35.html#figcppvm"><IMG  ALIGN=BOTTOM ALT="gif" SRC="cross_ref_motif.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/icons/cross_ref_motif.gif"></A>).
<P>
A direct consequence of this approach is that we lose some fidelity--the resulting model will not be able to accurately predict the
performance of all possible hardware/software systems.
On the other hand, we shall see that the resulting model
is still rather complex and rich in detail.
<P>
<P><A NAME="283">&#160;</A><A NAME="figcppvm">&#160;</A> <IMG WIDTH=575 HEIGHT=399 ALIGN=BOTTOM ALT="figure239" SRC="img6.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/img6.gif"  ><BR>
<STRONG>Figure:</STRONG> Virtual C++ Machine<BR>
<P><BR> <HR>
<UL> 
<LI> <A NAME="tex2html2322" HREF="page36.html#SECTION003110000000000000000" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page36.html#SECTION003110000000000000000">The Basic Axioms</A>
<LI> <A NAME="tex2html2323" HREF="page37.html#SECTION003120000000000000000" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page37.html#SECTION003120000000000000000">A Simple Example-Arithmetic Series Summation</A>
<LI> <A NAME="tex2html2324" HREF="page38.html#SECTION003130000000000000000" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page38.html#SECTION003130000000000000000">Array Subscripting Operations</A>
<LI> <A NAME="tex2html2325" HREF="page39.html#SECTION003140000000000000000" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page39.html#SECTION003140000000000000000">Another Example-Horner's Rule</A>
<LI> <A NAME="tex2html2326" HREF="page40.html#SECTION003150000000000000000" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page40.html#SECTION003150000000000000000">Analyzing Recursive Functions</A>
<LI> <A NAME="tex2html2327" HREF="page42.html#SECTION003160000000000000000" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page42.html#SECTION003160000000000000000">Yet Another Example-Finding the Largest Element of an Array</A>
<LI> <A NAME="tex2html2328" HREF="page43.html#SECTION003170000000000000000" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page43.html#SECTION003170000000000000000">Average Running Times</A>
<LI> <A NAME="tex2html2329" HREF="page44.html#SECTION003180000000000000000" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page44.html#SECTION003180000000000000000">About Harmonic Numbers</A>
<LI> <A NAME="tex2html2330" HREF="page45.html#SECTION003190000000000000000" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page45.html#SECTION003190000000000000000">Best-Case and Worst-Case Running Times</A>
<LI> <A NAME="tex2html2331" HREF="page46.html#SECTION0031100000000000000000" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page46.html#SECTION0031100000000000000000">The Last Axiom</A>
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