HP-91 or

HP-22?

Background: Dennis Harm's article "

The New Accuracy: Making 2^3=8" (HP Journal, October 1976, pages 16-17) explains why the original HP calculators get 8.000000003 for 2^3, and how the

HP-91 (and later models) get exactly 8.

This implies that the HP-91 was the first HP calculator to have "the new accuracy". The HP-91 was introduced in

March 1976. However, the

CCE33 emulator of the

HP-22 also gets exactly 8 for 2^3, and the HP-22 was introduced in

September 1975 (only one month after the HP-25, which returns 8.000000003 for 2^3). Is the CCE33 emulator of the HP-22 faulty (I don't see how that's possible, since it uses the original HP microcode), or was the HP-22 the first calculator with "the new accuracy"?

Request: If you own a real, physical HP-22 that is working, please calculate 2^3 on it, then press Shift 9, and tell us what is displayed. Thanks!

Checked in my physical HP-22 - displays 8.000000000

S/N 1708S

BTW: Was a wonderful opportunity to look for that machine in my pile :-)

Hi Joe, Hi Andy, I read the Dennis Harm's article and the post.

The 35 (three versions) and all the classic calculators return 8.000000002 for 2^3 and not 8.000000003, as written, where am I wrong?

the same result on the woodstocks up to the 25

My HP-22 s/n 1602A1****

2^3 = 8.000000000

Dave

The bible "

A Guide to HP handheld calculators and Computers" also mentions the HP-91 as the first to have the more accurate algorithms.

Could it be possible that the HP-22 was updated at some point?

Anybody with a HP-22 made in 1975?

J-F

[Edit: The HP-22 was the first to get the improvement according to this

source :-) ]

(06-21-2020 07:07 PM)J-F Garnier Wrote: [ -> ]Anybody with a HP-22 made in 1975?

J-F

Close!

My HP-22 is S/N 1601A... and displays 8.000000000

I think Joe was just testing us....

(06-21-2020 05:48 PM)aurelio Wrote: [ -> ]Hi Joe, Hi Andy, I read the Dennis Harm's article and the post.

The 35 (three versions) and all the classic calculators return 8.000000002 for 2^3 and not 8.000000003, as written, where am I wrong? the same result on the woodstocks up to the 25

Oops! You're quite right. Let's call it a typo (even though it was more accurately a braino).

(06-21-2020 07:07 PM)J-F Garnier Wrote: [ -> ][Edit: The HP-22 was the first to get the improvement according to this source :-) ]

OH NO! We covered all this just 3 years ago, but I don't remember having done so AT ALL. The conclusion is undeniable: I'm now officially OLD... two months before my 65th birthday.

But I *DO* remember that I enjoy playing with HP calculators, so at least I still have that.

(06-21-2020 08:37 PM)aurelio Wrote: [ -> ] (06-21-2020 08:01 PM)rprosperi Wrote: [ -> ]I think Joe was just testing us....

I think so, Bob

No, all the replies above say that their HP-22 returns exactly 8, which disagrees with the commonly told story that the first HP with the new accuracy was the HP-91. That common misconception should be corrected. But now please excuse me, I need a nap.

It's possible that the code really was originally developed for the HP-91 (the first TopCat), and then it was also used for the HP-22 (both use Woodstock technology), which was likely much quicker to market.

The 91 was the first machine in a totally new line with many innovations such as case, layout and keyboard design, thermal printer, adding ENG notation, etc. while the HP-22 was just another Woodstock which had been out for many months already, so not unreasonable that they wrote it for the 91, copied it in the 22 and the 22 simply were produced 6 months earlier. Just speculation, but it does explain the observed facts and stories.

In the article of the HP Journal introducing the HP21/22/25 (reproduced

here) we can read this:

"To improve the final results given by the HP-22, improvements were made to the standard HP-21- family arithmetic subroutines. The y^x algorithm was extended to handle negative numbers to integer powers--for example (-2)^2 or (-2)^-2--and a subroutine was developed to calculate the expression (1 +y)^x, which occurs frequently in financial equations. "
J-F

Hi all,

my HP22 (S/N 1512S...) return 8,0000000.

Cheers.

I'm just a little worried by a test case that involves small integers like this.

Another example given by Kahan as an accuracy test is this:

729^33.5 / 3^201 -1

It would be interesting to me to see this calculation done on an HP-22, or HP-91, or both, or any other in

Joe's timeline of accuracy.

Here are my results:

HP-15C LE: zero

HP-25: -9.99E-08 (same as HP-35 with V4 ROM)

(06-22-2020 09:51 AM)EdS2 Wrote: [ -> ]I'm just a little worried by a test case that involves small integers like this. Another example given by Kahan as an accuracy test is this:

729^33.5 / 3^201 -1

It would be interesting to me to see this calculation done on an HP-22, or HP-91, or both, or any other in Joe's timeline of accuracy.

Here are my results:

HP-15C LE: zero

HP-25: -9.99E-08 (same as HP-35 with V4 ROM)

Using the emulator, only 32e, 37e, 38e/c give 0 as result.

cheers

Tony

(06-22-2020 01:07 AM)Joe Horn Wrote: [ -> ]OH NO! We covered all this just 3 years ago, but I don't remember having done so AT ALL. The conclusion is undeniable: I'm now officially OLD... two months before my 65th birthday.

But I *DO* remember that I enjoy playing with HP calculators, so at least I still have that.

Don't worry Joe, +1

even if I'm just a bit younger...

it happens, this forum is the "wikipedia" of the calculators and you, like most of the other pioneer members, are the "relators" of the encyclopedia, thank-you for that

(06-22-2020 01:07 AM)Joe Horn Wrote: [ -> ] (06-21-2020 08:37 PM)aurelio Wrote: [ -> ]I think so, Bob

No, all the replies above say that their HP-22 returns exactly 8, which disagrees with the commonly told story that the first HP with the new accuracy was the HP-91. That common misconception should be corrected. But now please excuse me, I need a nap.

I was just jocking Joe. of course, don't take it for true

(06-22-2020 12:04 PM)aurelio Wrote: [ -> ] (06-22-2020 01:07 AM)Joe Horn Wrote: [ -> ]OH NO! We covered all this just 3 years ago, but I don't remember having done so AT ALL. The conclusion is undeniable: I'm now officially OLD... two months before my 65th birthday.

But I *DO* remember that I enjoy playing with HP calculators, so at least I still have that.

Don't worry Joe, +1 even if I'm just a bit younger...

Yes, me too, and I'm not 60 yet.

I just tried the

29C in emulation and was surprised to see a different answer - was there another change in HP's arithmetic?

Here are my results:

HP-25: -9.99E-08 (same as emulated HP-35 with V4 ROM)

HP-67: 1E-09 (microcode emulation)

HP 29C: 1E-09 (microcode emulation)

HP 35s: zero

HP 30b: zero

HP-15C LE: zero

(I think the LE uses the same algorithms as the original 15C)

Real HP-22 gives the same result as Tony's CCE33: 1.0000000 E-09 (for 729^33.5 / 3^201 - 1)

(06-22-2020 01:53 PM)EdS2 Wrote: [ -> ]HP-15C LE: zero

(I think the LE uses the same algorithms as the original 15C)

Quite possibly. A DM15L (using the HP-15C ROM) makes 2^3 precisely 8.

Hmm, I see that if we subtract the two powers instead of dividing them, we learn a little more:

HP-35 (v4 ROM) -7.96E88

HP-25C -7.96E88

HP-29C 5E86

HP-15C (LE) 2E86

HP 30b 2E84

HP 35s 2E84

Also, it occurred to me that if we're seeking families of machines which use the same algorithms and machinery, we should expect the calculator forensics test to produce a related grouping - perhaps a slightly coarser one. (Instead of measuring log and exp, we're measuring trig, so it might not be coarser, just different.)

From

the results page:

9.004076901

HP-35v3

9.004076644

HP-45, HP-46, HP-65

9.004076898

HP-55

9.004076649

HP-21, HP-25, HP-25C

9.000417403

HP-27

HP-19C

HP-29C

HP-41C

HP-41CV

HP-67

HP-91

HP-97, HP-97S

HP-10C, HP-11C, HP-15C (Voyager)

HP-31E, HP-32E, HP-33E, HP-34C (Spice)

(06-22-2020 09:51 AM)EdS2 Wrote: [ -> ]I'm just a little worried by a test case that involves small integers like this. Another example given by Kahan as an accuracy test is this:

729^33.5 / 3^201 -1

It would be interesting to me to see this calculation done on an HP-22, or HP-91, or both, or any other in Joe's timeline of accuracy.

Here are my results:

HP-15C LE: zero

HP-25: -9.99E-08 (same as HP-35 with V4 ROM)

Hi,

I've tested on my HP10bII+, too

pi * e - e * pi

--> gives 0 [ in Algebric mode with Л x e^1 - e^1 x Л = ]

729^33.5 / 3^201 -1

--> gives 0 [ with 729^33.5 ÷ ( 3^201 ) - 1 = ]

But, LN 729 x 33.5 ÷ ( LN 3 x 201 ) - 1 = gives -5E-12 (and curiously 1,00000000 in DISP . mode before applying - 1 = )

(06-22-2020 03:05 PM)AndiGer Wrote: [ -> ]Real HP-22 gives the same result as Tony's CCE33: 1.0000000 E-09 (for 729^33.5 / 3^201 - 1)

Same result on my HP-67 s/n 1610S