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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="SECTION003200000000000000000">A Simplified Model of the Computer</A></H1>
<A NAME="secmodelsimplified"> </A>
<P>
The detailed model of the computer given in the previous section
is based on a number of different timing parameters-- <IMG WIDTH=33 HEIGHT=15 ALIGN=MIDDLE ALT="tex2html_wrap_inline58177" SRC="img7.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/img7.gif" >, <IMG WIDTH=33 HEIGHT=15 ALIGN=MIDDLE ALT="tex2html_wrap_inline58179" SRC="img8.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/img8.gif" >, <IMG WIDTH=16 HEIGHT=16 ALIGN=MIDDLE ALT="tex2html_wrap_inline58189" SRC="img10.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/img10.gif" >, <IMG WIDTH=15 HEIGHT=11 ALIGN=MIDDLE ALT="tex2html_wrap_inline58191" SRC="img11.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/img11.gif" >, <IMG WIDTH=15 HEIGHT=15 ALIGN=MIDDLE ALT="tex2html_wrap_inline58193" SRC="img12.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/img12.gif" >, <IMG WIDTH=15 HEIGHT=15 ALIGN=MIDDLE ALT="tex2html_wrap_inline58195" SRC="img13.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/img13.gif" >,
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While it is true that a model with a large number of parameters
is quite flexible and therefore likely to be a good predictor of performance,
keeping track of the all of the parameters during the analysis
is rather burdensome.
<P>
In this section, we present a simplified model which makes the
performance analysis easier to do.
The cost of using the simplified model is that it is likely to
be a less accurate predictor of performance than the detailed model.
<P>
Consider the various timing parameters in the detailed model.
In a real machine, each of these parameters will be a multiple
of the basic clock period<A NAME=803> </A>
of the machine.
The clock frequency<A NAME=804> </A>
of a modern computers is typically between 100 and 500 MHz.
Therefore, the clock period is typically between 2 and 10 ns.
Let the clock period of the machine be <I>T</I>.
Then each of the timing parameters can be expressed as an integer
multiple of the clock period.
E.g., <IMG WIDTH=103 HEIGHT=24 ALIGN=MIDDLE ALT="tex2html_wrap_inline58613" SRC="img132.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/img132.gif" >, where <IMG WIDTH=66 HEIGHT=24 ALIGN=MIDDLE ALT="tex2html_wrap_inline58615" SRC="img133.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/img133.gif" >, <IMG WIDTH=63 HEIGHT=24 ALIGN=MIDDLE ALT="tex2html_wrap_inline58617" SRC="img134.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/img134.gif" >.
<P>
The simplified model eliminates all of the arbitrary timing parameters
in the detailed model.
This is done by making the following two simplifying assumptions:
<UL><LI> All timing parameters are expressed in units of clock cycles.
In effect, <I>T</I>=1.<LI> The proportionality constant, <I>k</I>, for all timing parameters
is assumed to be the same: <I>k</I>=1.
</UL>
The effect of these two assumptions is that we no longer need to keep
track of the various operations separately.
To determine the running time of a program,
we simply count the total number of cycles taken.
<P>
<BR> <HR>
<UL>
<LI> <A NAME="tex2html2473" HREF="page48.html#SECTION003210000000000000000" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page48.html#SECTION003210000000000000000">An Example-Geometric Series Summation</A>
<LI> <A NAME="tex2html2474" HREF="page49.html#SECTION003220000000000000000" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page49.html#SECTION003220000000000000000">About Arithmetic Series Summation</A>
<LI> <A NAME="tex2html2475" HREF="page50.html#SECTION003230000000000000000" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page50.html#SECTION003230000000000000000">Example-Geometric Series Summation Again</A>
<LI> <A NAME="tex2html2476" HREF="page51.html#SECTION003240000000000000000" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page51.html#SECTION003240000000000000000">About Geometric Series Summation</A>
<LI> <A NAME="tex2html2477" HREF="page52.html#SECTION003250000000000000000" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page52.html#SECTION003250000000000000000">Example-Computing Powers</A>
<LI> <A NAME="tex2html2478" HREF="page53.html#SECTION003260000000000000000" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page53.html#SECTION003260000000000000000">Example-Geometric Series Summation Yet Again</A>
</UL>
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