Online calculator simulators?

[pier4r]

I mean for example https://www.numworks.com/simulator/ rathert than emulator/simulators that one has to download extra. Something integrated in the browser.

(screenshot: https://postimg.cc/sMH00NZr)

Numworks offers one, are there any for HP, Casio, TI and the like? (even if not official)

It is quite a marketing tool because one can get a feel of the functions of a system.

[Thomas Klemm]

From sydneysmith.com:

• HP-21
• HP-25C
• HP-29C
• HP-65
• HP-67
  

From stendec.io:

• HP-10C
• HP-11C
• HP-12C
• HP-15C
• HP-16C
  

[Maximilian Hohmann]

Two google search results from many selected at random:

Ti-89: https://ti89-simulator.com/
HP-15C: https://hp15c.com/web/hp15c.html

[Thomas Klemm]

(07-07-2022 07:24 PM)Maximilian Hohmann Wrote:  Ti-89

I forgot about this: TI-57 Programmable Calculator

Quote:HP-15C

Announced here: New HP-15C simulator

---

And finally one for the HP-48.

[pauln]

For the TI-57, I really like this version: https://www.pcjs.org/machines/ti/ti57/rev0/

For the HP-15C, I notice that pressing "1" 25 times and then "Enter" produces "1.1111 24" instead of "1,111,111,111".

I haven't used an HP-15C in a very long time. Is that the behavior of an actual HP-15C?

[Thomas Klemm]

(07-07-2022 07:42 PM)pauln Wrote:  Is that the behavior of an actual HP-15C?

No. But that happens only with Greg Hewgill's simulator.

Both simulators of the HP-15C return 9.000000000 as a result of the calculator forensic test:

9
SIN COS TAN
TAN^-1 COS^-1 SIN^-1

However an emulator or the real calculator returns:

9.000417403

[rprosperi]

(07-07-2022 08:03 PM)Thomas Klemm Wrote:  Both simulators of the HP-15C return 9.000000000 as a result of the calculator forensic test:

9
SIN COS TAN
TAN^-1 COS^-1 SIN^-1

So, not simulations of high fidelity. If this is faked, what else is wrong???

Funny how an accurate answer can make one immediately suspicious of a calculating tool...

[Wes Loewer]

The Cemetech calculator site has the jsTIfied online TI-83+/84+ emulator (not simulator) but you have to supply your own ROM.

https://www.cemetech.net/projects/jstified/

[Thomas Klemm]

(07-07-2022 10:18 PM)rprosperi Wrote:  If this is faked, what else is wrong???

I don't think that they put effort into faking the result.
It's probably just calculated with more than 10 digits and then rounded for the display.

We can see that once 9 is subtracted from the result:

-1.674305-10 (1674305139)
-4.377387-10 (4377387341)

Interestingly enough the second is the exact same result we get from the simulator by Torsten Manz.

For comparison: Free42 Decimal returns just 9 with ALL display format.
But if the result is copied we get:

8.999999999999999999999999999937534

This is also displayed with SHOW.
However the HP-15C lacks a two line display.
Thus this can't be done.

I'm fine with this behaviour as long as I know it is a simulator.

[Thomas Okken]

Also, it's using binary floating point.
Try 1 ENTER .2 - .2 - .2 - .2 - .2 -

[jonmoore]

(07-07-2022 10:18 PM)rprosperi Wrote:  

(07-07-2022 08:03 PM)Thomas Klemm Wrote:  Both simulators of the HP-15C return 9.000000000 as a result of the calculator forensic test:

9
SIN COS TAN
TAN^-1 COS^-1 SIN^-1

So, not simulations of high fidelity. If this is faked, what else is wrong???

Funny how an accurate answer can make one immediately suspicious of a calculating tool...

For fun, I did the calculation in a bunch of calculators I had close to hand.



All of HP's post Voyager calculators agree on their result, and as one one expect the 11C and DM41x agree with the 15C. The TI Voyage 200 is different again.

And then I thought, what the hell, lets input the the calculation on the Casio CG50 - 8.999999998, Casio fx-991ex - 9.000000007, and the TI-nspire CX II - 8.99999998177 (this agrees with the TI Voyage 200).

I know that the TI and Casio hardware calculate trigonometric functions internally to 15 significant digits. As for post-Voyager HP calculators, I had presumed they calculate trigonometric functions internally to 15 significant digits but maybe they only use 13 significant digits.

Interestingly, the TI Voyage 200 and TI nspire CX II actually shows the 15 significant digits as you copy paste the last value via ANS.



If you look at the results statistically, it's the Voyager calculators that are the outliers and if this was indeed a "calculator forensic test", one could suggest they are the least accurate.

As expected, the one post Voyager HP calculator that had a different result was the HP35s - 8.99999986001. This is most probably due to the fact that the HP35s has issues with trigonometric calculations close to zero. As much as it's in the same ball park as the other HP calculators, it's only in agreement up to the 5th decimal place. For some applications, that's a world of difference, and of course for others it's close enough (many engineering applications only require precision of between 4 and 6 decimal places). It really all depends on how the round-off errors stack up in a chain of calculations of this nature.

And seeing as this train of inquiry started off as criticism of the precision capabilities of certain HP-15C emulators, I thought I'd compare the chain of calculations with Mathematica. And here the results agreed with the TI Voyage 200/Nspire all the way until the last two calculations. The ArcCos result varied slightly in the final 4 decimal places and the final result after the ArcSin, resulted back at 9. Which is in fact, the correct answer if all of the calculations are done symbolically - three trigonometric functions, followed by their inverses should resolve back to the original number. It looks a little too convenient that Mathematica still resolves to 9 even though all previous calculations are only accurate to 15 significant digits, but it's bang on the nose.



In conclusion, the older HP hardware is still pretty accurate considering their lower precision, but the fact remains that they begin to deviate from 9 at the 4th decimal place, the post Voyager HP's begin to deviate at the 6th decimal place, and the TI's come out second from best by only deviating from 9 at the 8th decimal place. But it's the Casio's that win in this particular accuracy test, by only beginning to deviate from 9 at the 9th decimal place. Both the Casios calculate all functions to 15 significant digits under the hood, even though they only display 10 significant digits.

There's nothing particularly scientific or robust in these findings but I do find it interesting in terms of some of the 'truths' we hold onto ref Mr Kahan and BCD, which aren't necessarily as true as they once were in 2022.

[Massimo Gnerucci]

Full calculator forensics results sorted by model

[Steve Simpkin]

Jonmoore, Showing all of those calculators with slightly different answers reminds me of Segal's law
"A man with a watch knows what time it is. A man with two watches is never sure."

[Albert Chan]

(07-09-2022 02:15 PM)jonmoore Wrote:  The ArcCos result varied slightly in the final 4 decimal places and the final result after the ArcSin, resulted back at 9. Which is in fact, the correct answer if all of the calculations are done symbolically - three trigonometric functions, followed by their inverses should resolve back to the original number. It looks a little too convenient that Mathematica still resolves to 9 even though all previous calculations are only accurate to 15 significant digits, but it's bang on the nose.

9. really meant 9.00000 (6 sig. diigts)

To get what is actually stored, try Numberform[%]

[rprosperi]

(07-09-2022 02:15 PM)jonmoore Wrote:  All of HP's post Voyager calculators agree on their result, and as one one expect the 11C and DM41x agree with the 15C.

All HP (made) calculators that came after the 71B (1983) used the same low-level Saturn math libraries, essentially unchanged. These were indeed created with heavy influence by (if not actual involvement of) Dr. Kahan, and initially comprised the first IEEE FP math standards. This does not apply to machines that were re-implemented by Kinpo, etc. for 33S, 35S, etc.

(07-09-2022 02:15 PM)jonmoore Wrote:  And then I thought, what the hell, lets input the the calculation on the Casio CG50 - 8.999999998, Casio fx-991ex - 9.000000007, and the TI-nspire CX II - 8.99999998177 (this agrees with the TI Voyage 200).
[snip]
There's nothing particularly scientific or robust in these findings but I do find it interesting in terms of some of the 'truths' we hold onto ref Mr Kahan and BCD, which aren't necessarily as true as they once were in 2022.

I don't disagree but do recall that all of these machines are 30+ years newer, so it's not surprising that they eventually improved things. I still hold his contributions as unique, significant and insightful, and likely the very impetus for competitors to try harder. Of course the ever-dropping price of silicon made it somewhat easier by simply growing the CPU, memory, etc.

[jonmoore]

(07-09-2022 06:16 PM)rprosperi Wrote:  I don't disagree but do recall that all of these machines are 30+ years newer, so it's not surprising that they eventually improved things. I still hold his contributions as unique, significant and insightful, and likely the very impetus for competitors to try harder. Of course the ever-dropping price of silicon made it somewhat easier by simply growing the CPU, memory, etc.

No dissing William Kahan's contributions to the world of numerical analysis in general, and post HP-45 to Voyager series calculators specifically intended. Without him, awareness of floating point precision issues in the nascent world of late seventies/early eighties computer science would not have been anywhere near as widespread. The point I was making was exactly the fact that things move on. It's a real pity that Dr Kahan wasn't involved in post Voyager HP calculator hardware.

https://www.wikiwand.com/en/William_Kahan

@Albert, my bad, I should have shown the final value with NumberForm, 14.



Which is very close to the result given by both the TI machines.

I'm quite obviously a fan of HP calculators, but I do get annoyed by the evangelical tone that's often associated with opinions in the HP community. I remember the drubbing the TI 92, 98 & Voyage 200 got on the 48 mail-list back in the day, which was completely unfair because they werein fact more accurate than 48, 49 & 50, and up to the 50g, the Derive based CAS in the TI hardware was superior (even with Erable and ALG). I still prefer my RPL hardware by a country mile, but the TI 92 product line had the benefit that it was effectively Derive in calculator form (which was already finely tuned by the time the 92 came out). I like many run DOS Derive on my HP 200LX but I prefer the calculator translation as it has a far better UX for a handheld device.

I'm primarily a collector of computing devices. I never intended this, I just happen to be a terrible horder of tech I purchased from the 80's onward (I'm 10 years younger than the average hardcore HP collector), although I have purchased a few 70's examples where the price has been right.

The reason I prefer classic HP calculators to classic TI's is simply the fact that HP were pretty much the Apple of it's day in terms of marrying the best in industrial design with superior software engineering. My preference for RPL hardware is that I love the language. Emacs is my text editor of choice and has been for decades, and I've used Emacs Lisp for decades too (although these days I use Doom Emacs, which is Emacs but with VIM key bindings!) - with that in mind, RPL is actually pretty intuitive. However, I do love my Nspire and Voyage 200 for CAS workflows (which I often do with the kids). When I was studying, Derive was the main computer algebra system in the labs, so that's where the bias probably started.

[Steve Simpkin]

(07-09-2022 07:22 PM)jonmoore Wrote:  ...
No dissing William Kahan's contributions to the world of numerical analysis in general, and post HP-45 to Voyager series calculators specifically intended. Without him, awareness of floating point precision issues in the nascent world of late seventies/early eighties computer science would not have been anywhere near as widespread. The point I was making was exactly the fact that things move on. It's a real pity that Dr Kahan wasn't involved in post Voyager HP calculator hardware.
...

Dr. Kahan blames HP marketing for that.

"The HP 12C was successful enough that they were willing to take my advice about building the 15C, but not take my advice about how many to build. They wanted a third of my figure, and Harms did half again what they wanted, and that’s what they were doing. They were producing half of my number. The marketing people had a third of my number. I shouldn’t have said a half. The marketing people had a third of my number, and Harms ended up with the production line producing half of my target number, and then these calculators were disappearing off the shelves as fast as they could be supplied. MIT, for example, for a couple of years was telling its freshmen that they should buy the calculator, and it had a special deal with HP that would get them involved in a somewhat lower price.
HAIGH: What year did the calculator appear?
KAHAN: I think it was 1982, give or take. We could probably look at the manuals and find out exactly when it appeared. Well, HP never produced an advertisement for the 15C in its own right in any Western language. It might have had advertisements that listed the 15C and the 16C and the 11C and so on, but never for the 15C in its own right except for one in Japanese. I saw an advertisement in Japanese. They were selling them by word of mouth as fast as they could produce them, and when my friends and I who had worked on this went to the marketing people and tried to persuade them, “Look, set up another production line, because you want to gather your flowers while you may,” they said, “No, if we set up another production line, we may end up with inventory after all. You know how sales go. The sales rise to a peak and then they go down,” and these guys thought that they must be hitting the peak. They weren’t hitting a peak. They were hitting a ceiling. It’s a different thing. So they never did set up another production line. In consequence, the market was starved. There were waiting lists, and that window closed, and so I never did get the calculators into the hands of sufficiently many students to change the ways in which professors would issue assignments, and that was a bitter disappointment. It colored my relations with this particular group at HP. I continued to work with them for a couple of years, but my heart just wasn’t in it anymore."

[jonmoore]

(07-09-2022 07:41 PM)Steve Simpkin Wrote:  

(07-09-2022 07:22 PM)jonmoore Wrote:  ...
No dissing William Kahan's contributions to the world of numerical analysis in general, and post HP-45 to Voyager series calculators specifically intended. Without him, awareness of floating point precision issues in the nascent world of late seventies/early eighties computer science would not have been anywhere near as widespread. The point I was making was exactly the fact that things move on. It's a real pity that Dr Kahan wasn't involved in post Voyager HP calculator hardware.
...

Dr. Kahan blames HP marketing for that.

"... I continued to work with them for a couple of years, but my heart just wasn’t in it anymore."

That's a really great interview segment Steve. You can understand why his heart wasn't in it anymore.

[Steve Simpkin]

(07-09-2022 08:15 PM)jonmoore Wrote:  

(07-09-2022 07:41 PM)Steve Simpkin Wrote:  Dr. Kahan blames HP marketing for that.

"... I continued to work with them for a couple of years, but my heart just wasn’t in it anymore."

That's a really great interview segment Steve. You can understand why his heart wasn't in it anymore.

Yes, unfortunately not his first disagreement with HP marketing and management.

HP-92 (Price)
"It was just marvelous, and it was going to be priced at $450. And the executives, especially those in marketing said, “Hey, there are people who would pay $750 for this. We should price it at $750.” “No, no!” came up a voice from below. “$450 is the right price.” “What the hell do you guys know?” said the more senior marketing people. “This is going to be value price. $750 is well worth it. We’ve shown it to various bigwigs, and they’ve said, ‘Oh yes, absolutely. I would be happy to pay $750 for this.’’’ And it came out with that price."

HP-34C (Solve key)
"He had forwarded this suggestion to the marketing people and characteristically, alas, the marketing people had come back and said, “We’ve asked if anyone wants a solve key, and no one has ever heard of such a thing. They don’t say they want it.”"

HP-34C (Additional explanation of the Solve/Integrate functions in the manual)
"They agreed to do it, and then like a thunderclap, they were appalled when I said, “You know, we’re going to have to put some guidance into the manual because people who use these keys, especially the integrate key, they can fool themselves. These things cannot be foolproof. There will be situations where people will get misleading answers, and they need a little bit of guidance about that.” “Kahan, you just told us to do this stuff, and now you tell us that you’re going to get wrong answers! I mean, all this time, we’ve been listening to you tell us how to get the right answer, invariably, every time!” Well, the difficulty was then that I’d have to go to the manual writers. But there was a Hewlett-Packard policy which said, “We are professionals, and we sell to professionals. We tell them what the device does, and they figure out how to use it. We’re not writing tutorial material in our manuals.” And I tried to explain, “Look—this time you’ve got to put some tutorial material in the manuals. You really must. Otherwise, folks are going to fool themselves."

[Albert Chan]

(07-09-2022 02:15 PM)jonmoore Wrote:  In conclusion, the older HP hardware is still pretty accurate considering their lower precision, but the fact remains that they begin to deviate from 9 at the 4th decimal place, the post Voyager HP's begin to deviate at the 6th decimal place, and the TI's come out second from best by only deviating from 9 at the 8th decimal place. But it's the Casio's that win in this particular accuracy test, by only beginning to deviate from 9 at the 9th decimal place. Both the Casios calculate all functions to 15 significant digits under the hood, even though they only display 10 significant digits.

This has less to do with calculators, and more to do with math.

sin(9°) = sin(pi/20) ≈ pi/20
cos(sin(9°)°) ≈ cos(pi/20 * pi/180) ≈ 1 - (pi^2/3600)^2 / 2! ≈ 0.999996

We had lost 5+ digits precision, due to catastrophic cancellation.
That's why all calculator forensic test will lose 5 to 6 digits precisions.
This is true even if all calculations produce correctly rounded results!

Example, HP Prime CAS side work with 48 bits (truncation mode)
48 bits ≈ 14 decimal digits, we expected 8 to 9 decimals accuracy.

CAS> AAngle := 2; // Degree mode
CAS> asin(acos(atan(tan(cos(sin(9.))))))-9

5.91438720221e−9

If we replace cos(x) with versin(x), the issue goes away.

CAS> versin(x) := 2*sin(x/2)^2; // = 1 - cos(x)
CAS> aversin(y) := 2*asin(sqrt(y/2)); // = acos(1 - y)

CAS> asin(aversin(atan(tan(versin(sin(9.))))))-9

−1.70530256582e−13