In the old days it was unquestioned that HP made the best calculators from hardware to software. I've been away from calculators for a long time and I understand HP has been farming out stuff to Kinpo for a while already. I understand Kinpo also makes TI's calculators. Because of RPL and RPN, HP remains my choice in calculators. I can't imagine anything better.

But I am curious, are there any competitors in terms of numerical accuracy or is HP still the best in that too? It would be interesting to compare results with different brands.

WP 34S.

Head and shoulders above all the non-symbolic machines.

Of course, I'm biased

- Pauli

Ok, that may be true. But I was wondering about regular production stuff rather than specialty projects.

Well... For what its worth, you can see a relative figure of merit for "accuracy" using a specific metric [ arcsin (arccos (arctan (tan (cos (sin (9) ) ) ) ) ) ] at Calculator Forensics.

The results table is shown at :

http://www.rskey.org/~mwsebastian/miscprj/models.htm
Oddly enough the only production HP models to achieve a perfect result of 9 (with 10 digit resolution) are the Kinpo made HP-9S and HP-30s models which where not designed by HP at all.

Thanks, that's the kind of info I was looking for. That's extremely interesting. The late model TIs do pretty well and some of the Casios are surprising too.

He only reports that for trig functions. I wonder if there is a site with info on a wider range of functions. Lots of good stuff on rskey. I have seen it before but have not seen every page.

(02-17-2014 10:28 AM)Steve Simpkin Wrote: [ -> ]Oddly enough the only production HP models to achieve a perfect result of 9 (with 10 digit resolution) are the Kinpo made HP-9S and HP-30s models which where not designed by HP at all.

Watch it! A result of 9 doesn't have to be perfect in this case. For finite precision calculators (as all of the test objects are), the perfect result depends on their precision. IIRC, Dieter posted once about that topic.

d:-/

This question raised my interest and I have just checked this on the HP Prime.

First, this is the result you get in R (Angle Measure: Radians)

(

The R Project for Statistical Computing):

Code:

> sprintf("%.16f",asin(acos(atan(tan(cos(sin(9)))))))

[1] "0.4247779607693797"

These are the results I get on the HP Prime:

Angle Measure: Radians
CAS:

0.424777960769

Home:

0.424777960769

Angle Measure: Degrees
CAS:

9.00000000591

Home:

8.99999864267

It is interesting to see that you get the same results in Radians mode but slightly different ones in Degrees mode.

All the best,

Dominik

Interesting. An HP 48 also gets much better accuracy in this test in radians rather than degrees. The error is only 2.0E-12!

(02-17-2014 03:09 PM)HP67 Wrote: [ -> ]Interesting. An HP 48 also gets much better accuracy in this test in radians rather than degrees. The error is only 2.0E-12!

The test is designed to be worthwhile in degrees only. It produces an intermediate result that stresses the precision of the calculator (cos returns a result close to 1). The test is not designed to evaluate the quality of the algorithms, it's just a convenient way to distinguish various machines and/or the built-in chips.

Thank you Walter and Marcus for explaining the results of this "benchmark test" better than I could.

Thanks, Marcus. I never liked radians much anyway

(02-17-2014 11:59 AM)walter b Wrote: [ -> ]Watch it! A result of 9 doesn't have to be perfect in this case. For finite precision calculators (as all of the test objects are), the perfect result depends on their precision. IIRC, Dieter posted once about that topic.

Looked it up and found an interesting post from Rodger Rosenbaum:

"It appears that whenever the digits after the decimal point are greater than .9999999995 or less than .0000000005, they get dropped--at least as a result of a trig calculation [...]"

From:

http://www.hpmuseum.org/cgi-sys/cgiwrap/...read=85973
(02-18-2014 12:54 PM)Tugdual Wrote: [ -> ]http://www.rskey.org/~mwsebastian/miscprj/models.htm

Very surprised to see that the "Canon Canola F-11 37" returns the same value as most HP products. Does it mean that HP sold some source code or Canon stole their patent?

No. The Canola F-11 returns 9,000417403 just as many HP calculators, simply because that's the exact "forensic" result for a perfectly accurate 10-digit calculator. The result simply shows that Canon did their homework as well as HP.

As already pointed out: the "perfect" result is

not 9. For a calculator with 10 digit precision it's actually 9,000417403. A perfect 12-digit device should return 8,99999864267.

Dieter