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Re: PowerPCs

> In posting timing comparisons for Mathematica operations, 
> please be careful to use ACTUAL ELAPSED TIME 
> from pressing enter key until completion of operation.
> Do *NOT* use the Timing command without explicitly saying so.
> Do *NOT* trust the front end timings -- verify them with a stop watch.
> Do *NOT* give comparisons of your times with others unless others have
> stated explicitly their timing methods so you can be sure they are comparable.
> Richard Mercer

I am not an expert on computer timing comparisons, but here are a few
remarks that people doing timing comparisons of may find useful.

1) The Mathematica Timing function uses, and consequently inherits
   the reliability (or lack of reliability) of the C library times
   function.  The times function (according to the UNIX man page)
   gives "the CPU time used while executing  instructions in the
   user space of the calling process."  The time reported is the
   time used by the Mathematica kernel process for evaluating an
   expression.  It does not include the time for parsing the input,
   formatting the output, or the time used by child processes.

2) The time given by the front end when you select "Display
   timing after each evaluation" reports the change in the
   system tick count, as reported by TickCount (on the Macintosh),
   GetTickCount (under Windows), or a similar function.
   It is basically an electronic stopwatch.  This time includes
   such things as the time used by processes unrelated to
   Mathematica, time used by the operating system for memory
   management, and the time used by the operating system for
   switching between processes.  If you are trying to measure
   time used by the Mathematica kernel, this time is subject to
   arbitrarily large error.

3) A stopwatch operated by a human independent of the computer
   is subject to the same effects as (2), plus error due to
   human reaction time and due to individual definitions of things
   like "press enter key" and especially "completion of operation".  

The best method to use depends on what you are trying to measure.

If you are trying to measure time used by the kernel for evaluation,
and you trust the C library, then Timing is the easiest function
to use.  If you don't trust the C library, and know enough about
operating systems to ensure that the Mathematica kernel gets the
full attention of the cpu, then you can use stopwatch time.  If
neither of these cases applies to you, then you are stuck.

Parsing and output formatting is done largely by the kernel.
Timing[ToExpression[<input>]] causes <input> to be parsed during
evaluation, so the result will include the time needed for
parsing.  Similarly, Timing[ToString[<input>]] will include the
time needed for formatting output.

PostScript interpreters and graphics renderers are either separate
processes or are part of the front end.  As with parsing and
output formatting, there is no separate function for timing
these things.  You can get a rough estimate of the time needed
to render graphics by subtracting the stopwatch time from the
result returned by Timing, assuming of course that nothing
else on your computer is using the cpu.

If you want to estimate the time needed to do things in an
environment with some typical set of other processes running
and some typical amount time used for memory management and
other operating system processes, then front end "Display timing
after each evaluation" time or stopwatch time are probably
appropriate.  I do not know of anything that could cause a
significant difference between front end time and stopwatch time.

Dave Withoff
Research and Development
Wolfram Research

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