Some comparisons of Algebraic Manipulation on different hardware.

As of June 25, 1987.

Times are elapsed (with cpu times in parenthes for machines where
this was substantially different eg suns).
Note by elapsed time I wall clock
Main culprit was page faults).
All times were average of several cycles to get gc information.
The large problem gc'd a number of times on the small sun, and 
so only one computation was performed.  All machines were with
only one user running at normal priority.

Machine.         Factor((x+y+z)^10)       Factor((x+y+z)^20)

sun3/50             27.3 (cpu 9.7)         243.0 (cpu 63.7)       
too many users to judge: sun3/180          ?16.0(cpu 10.9)         ?
sun3/260             3.08(cpu 3.08)         19.33(cpu 19.5)
TI Explorer          3.4                    14.2           
Symbolics 3640       5.6                    21.3
withIFU  




For comparsion the old version using maclisp on dec-20:
Quite fast on small problems.  
Dec20(maclisp)      (cpu 5.5)               Problem Too Big



Notes: The times all are elapsed, and include time for gc.  On the
lisp machine only ephemeral gc was included.  The SUN suffered greatly
from page faults: for example the actual run time was 8.05 for the
first one, and with a gc every two or three times costing 5 seconds.
The rest of the time was spent in page faults, particularly costly
during the gc.

Executing on a sun-3/50 with 4meg memory and shoe box.  sun operating
system 3.2 c compiling of system with debugging on.  The common lisp
version is by Bill Schelter running in KCL, and running inside gnuemacs.
Page faulting was extremely expensive.  We have included an appendix for
the 3/50 to show the vagaries of the timings due to poor paging.

The Maxima in all cases was a full version including lisp compiler
and the Maxima to lisp translation facility.  Approximately 120 files
were loaded.  On the very small machine reducing the size of the 
system, would probably prove beneficial.

In all cases the code was the Common Lisp version by Bill Schelter at
University of Texas, and distributed by National Energy Software
Foundation at Argonne Illinois.  KCL is available free of charge by
anonymous ftp from University of Texas on rascal.ics.utexas.edu
[128.83.144.1] Login as ftp, with no password.  See the message
kcl.broadcast in the ftp directory for instructions.  You must mail in
a copy of the form in that message to validate your free license.
Both Maxima and KCL include ALL sources.

The GCD switch used was SPMOD.  

Note this is not meant to be a comparison of factoring algorithms, but
rather just a simple easily quantified test of complex polynomial
manipulation, which has been found to be a good point of comparison
when considering different hardware for large algebraic manipulation
problems.

The Explorer was running release 3.0, and the Symbolics release 7.
Note there has been a dramatic improvement in the TI timing with 
the advent of an efficient ephemeral GC in release 3.0, and new
function calling.  The time for TI is one half what it was in release 2.0
on the same machine.


Appendix Sun3/50
Here is the actual transcript.  You can see how the times varied:
(C3) expand((x+y+z)^10)$
(C9) factor(d3);

Evaluation took 8.20 seconds (17.93 elapsed)
					    10
(D9) 				 (Z + Y + X)
(C10) ''c3;

Evaluation took 7.98 seconds (16.98 elapsed)
					    10
(D10) 				 (Z + Y + X)
(C11) ''c3;


GBC invoked
GBC finished
Evaluation took 13.98 seconds (50.25 elapsed)
					    10
(D11) 				 (Z + Y + X)
(C12) ''c3;

Evaluation took 8.02 seconds (16.57 elapsed)
					    10
(D12) 				 (Z + Y + X)
(C13) ''c3;


GBC invoked
GBC finished
Evaluation took 13.90 seconds (52.20 elapsed)
					    10
(D13) 				 (Z + Y + X)
(C14) ''c3;

Evaluation took 8.05 seconds (16.65 elapsed)
					    10
(D14) 				 (Z + Y + X)
(C15) ''c3;


GBC invoked
GBC finished
Evaluation took 13.90 seconds (56.88 elapsed)
					    10
(D15) 				 (Z + Y + X)
(C16) 
(C16) expand((x+y+z)^20)$

Evaluation took 10.10 seconds (13.20 elapsed)
(C17) 1;
(D17) 				       1          
(C18) factor(d16);


GBC invoked
GBC finished

GBC invoked
GBC finished

GBC invoked
GBC finished

GBC invoked
GBC finished
Evaluation took 63.77 seconds (243.45 elapsed)
					    20
(D18) 				 (Z + Y + X)