For some reason, we have decided that n = 2499 is appropriate for benchmarking our calculators.
There is nothing magic about this number. As I will show later, the relative accuracy is strongly
dependent on n, even over a relatively narrow range. This makes the relative accuracy after n
iterations a poor measure of performance. Faster computers typically use n = 100,000 or 250,000. If
the computer (or calculator) does not have built-in timer facilities, then the timing must be done by
hand. In this case, a large value for n reduces relative uncertainty from human reaction time in starting
and stopping the stopwatch.
This table shows the relative error and execution time for a variety of calculators and languages. I
cannot vouch for the accuracy, since most results were culled from posts on the HP and TI discussion
groups.
Doug Burkett-3.081E-9187TI Basic, AMS 2.05TI-92+ HW2
Doug Burkett1.011E-996C (GCC compiler) AMS 2.05TI-92+ HW2
Jacek Marchel-3.081E-97268K assemblerTI-92+
Jacek Marchel-3.081E-9255TI Basic (HW1? AMS?)TI-92+
Doug Burkett-3.081E-9272TI Basic, AMS 2.05TI-89 HW1
Doug Burkett1.011E-9138C (GCC compiler), AMS 2.05TI-89 HW1
Ralf Fritzsch-3.081E-9328Z80 assemblerTI-86
Ralf Fritzsch-3.081E-9433TI BasicTI-86
Mike Morrow-3.08E-9368TI-85
Doug Burkett-1.022E-547 minOPL BasicPsion XPII
Ralf Fritzsch-3.572E-9138SysRPL, 15-digitHP-49G
Thomas Rast-2.054E-787SysRPL, 12-digit, Display offHP-49G
Ralf Fritzsch-2.054E-796SysRPL, 12-digit, Display onHP-49G
Ralf Fritzsch-2.054E-7120UserRPLHP-49G
Jonathon Busby-3.572E-962Saturn ASM, display off, 15-digitHP-48GX
Jonathon Busby-3.572E-970Saturn ASM, display on, 15-digitHP-48GX
Mike Morrow-2.054E-7112UserRPL?HP-48GX
Mike Morrow-2.054E-7199UserRPL?HP-48SX
Mike Morrow-2.054E-7602HP-42S
Mike Morrown/a~45 minHP-41CX
Mike Morrow-2.054E-7451HP-32Sii
Mike Morrow-2.054E-7255HP-28S
Mike Morrow-2.054E-7369HP-20S
Mike Morrown/a~45 minHP-15C
Reported by:
Relative
accuracy
Execution
time, secLanguageModel
The best relative accuracy is returned with the TI-89 / TI-92 Plus, with the GCC C compiler program.
The best execution time is returned by the HP-48GX with an ASM program and the display turned off.
So what can we conclude from these results? Very little, actually. We can conclude, for this very
synthetic problem, that the relative accuracies range from less than 7 to nearly 9 significant digits. We
see that newer hardware is more accurate and has faster execution times. We see that the choice of
programming language has a strong effect on the execution time. None of this is news; there are no
surprises here. Instead, what cannot be concluded is more significant:
! We cannot conclude that the HP-48GX is, in general, faster at numeric computation, because we
have only tested a tiny subset of all the functions.
! We cannot conclude that the TI-89 / TI-92 Plus is, in general, more accurate, because again, only a
tiny subset of the functions has been tested.
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