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HYP, ARC and the rest
Message #1 Posted by Antonio Maschio (Italy) on 4 June 2007, 6:07 a.m.

On modern (and less modern) calculators, you have the trig functions on three separate and contiguous keys, with their arc functions on the same shifted key (e.g. arcsin on sin). The hyp key is generally shifted, so you have to digit (typically):

shift hyp shift sin

to get arcsinh. This configuration, while common, uses three keys and four shifted keys, totallying seven key-positions.

No one, as far as I know, has ever thought to a simpler way to accomplish the same task:

HYP ARC SIN COS TAN

on five adjacent keys which can perform every trig and hyp function:

SIN for sin

ARC SIN for arcsin

HYP SIN for sinh

HYP ARC SIN (or ARC HYP SIN) for arcsinh.

This configuration uses five main keys, but nothing else, leaving two extra key-positions with respect to the previous configuration.

I think (but you may have a very different opinion) that trig (and possibly hyp) functions are those that are far more used after LN, EXP, LOG, and the other classics (the four basics, root, square, and so forth), that usually are more or less in an easy position and don't need any help, while trigs and hyps would (and deserve).

And, thinking to some older TI model, the ARC function could even be used in conjunction with LOG (or LN) to get EXP or vice-versa, or to root to get square, and so forth, making more room for other functions, or to put more functions on the main keys, or to reduce the total keys amount. People who need a scientific calculator should easily understand and use such ARC key!

I'd want your opinion on this subject, which is a minor subject, I know.

-- Antonio

      
Re: HYP, ARC and the rest
Message #2 Posted by Maximilian Hohmann on 4 June 2007, 7:47 a.m.,
in response to message #1 by Antonio Maschio (Italy)

Hello!

Quote:
No one, as far as I know, has ever thought to a simpler way to accomplish the same task:

HYP ARC SIN COS TAN

on five adjacent keys which can perform every trig and hyp function:

I have just recently added an "MBO Alpha 2000" calculator (ca. 1978, green VFD tube) to my collection, that has exactly these five keys :-) I could not find a picture on the internet, but if you wish to see it, I will post an image when I'h home tonight!

Greetings, Max

NB: Try this link, as long as it works, it's from the eBay auction: http://i12.ebayimg.com/07/i/000/93/ab/01ef_1.JPG

Edited: 4 June 2007, 7:49 a.m.

      
Re: HYP, ARC and the rest
Message #3 Posted by DaveJ on 4 June 2007, 9:06 a.m.,
in response to message #1 by Antonio Maschio (Italy)

Quote:
On modern (and less modern) calculators, you have the trig functions on three separate and contiguous keys, with their arc functions on the same shifted key (e.g. arcsin on sin). The hyp key is generally shifted, so you have to digit (typically):

shift hyp shift sin

to get arcsinh. This configuration, while common, uses three keys and four shifted keys, totallying seven key-positions.

No one, as far as I know, has ever thought to a simpler way to accomplish the same task:

HYP ARC SIN COS TAN

on five adjacent keys which can perform every trig and hyp function:

SIN for sin

ARC SIN for arcsin

HYP SIN for sinh

HYP ARC SIN (or ARC HYP SIN) for arcsinh.

This configuration uses five main keys, but nothing else, leaving two extra key-positions with respect to the previous configuration.

What is the difference between ARC SIN and INV SIN using the normal inverse key? Exact same number of presses and you save one key. Seems silly to have a dedicated ARC key, INV is more logical in my opinion, and is already on practically every calc.

Quote:
I think (but you may have a very different opinion) that trig (and possibly hyp) functions are those that are far more used after LN, EXP, LOG, and the other classics (the four basics, root, square, and so forth), that usually are more or less in an easy position and don't need any help, while trigs and hyps would (and deserve).

And, thinking to some older TI model, the ARC function could even be used in conjunction with LOG (or LN) to get EXP or vice-versa, or to root to get square, and so forth, making more room for other functions, or to put more functions on the main keys, or to reduce the total keys amount. People who need a scientific calculator should easily understand and use such ARC key!

I'd want your opinion on this subject, which is a minor subject, I know.

The HYP key is one of my pet hates, to me it is the most useless key on a scientific calculator. I have never used it. But hey, that's just me.

Now there are just some keys that simply *must* be on dedicated keys on a good scientific calculator in my opinion. My list of keys (with there INV functions) is: EXP +/- ENG (INV ENG) Log (INV 10^X) Ln (INV e^X) SQRT X^2 1/X X^Y (X SQRT) X<->Y STO (or Min) RCL (or MR)

Note that I didn't list X^2 as an inverse function to SQRT, both are vital to have on their own key.

Any calc that expands those INV functions onto their own keys gets extra bonus points in my book.

Other silly keys that often get their own key are the fraction key and the Sexagesimal key. I would not shed a tear on any calc that lost those keys.

Dave.

            
Re: HYP, ARC and the rest
Message #4 Posted by Gene on 4 June 2007, 10:28 a.m.,
in response to message #3 by DaveJ

Quote:
The HYP key is one of my pet hates, to me it is the most useless key on a scientific calculator. I have never used it. But hey, that's just me. Dave.

Gene: But that's just silly. Hyperbolic functions have many uses and it is not wise to leave it off a scientific calculator in this day and age.

Applications for hyperbolic functions include: catenary curves, design of many structures (nuclear cooling towers, buildings at Dulles, etc), gears with skewed axes, even the shape of a shadow cast on a wall by a lampshade, etc, etc, etc.

http://www.pen.k12.va.us/Div/Winchester/jhhs/math/lessons/calc2004/apphyper.html

Giving a scientific calculator the abilities to do these things at the expense of one shift key location seems very reasonable.

Saying "I don't like it because I have never used it" is short-sighted, IMO. What if I never use base conversions? Should I have the inclusion of BASE and LOGIC as a pet peeve? Or should I recognize that many people DO use them?

                  
Re: HYP, ARC and the rest
Message #5 Posted by DaveJ on 4 June 2007, 5:10 p.m.,
in response to message #4 by Gene

Quote:

Gene: But that's just silly. Hyperbolic functions have many uses and it is not wise to leave it off a scientific calculator in this day and age.

Applications for hyperbolic functions include: catenary curves, design of many structures (nuclear cooling towers, buildings at Dulles, etc), gears with skewed axes, even the shape of a shadow cast on a wall by a lampshade, etc, etc, etc.

http://www.pen.k12.va.us/Div/Winchester/jhhs/math/lessons/calc2004/apphyper.html

Giving a scientific calculator the abilities to do these things at the expense of one shift key location seems very reasonable.

Saying "I don't like it because I have never used it" is short-sighted, IMO. What if I never use base conversions? Should I have the inclusion of BASE and LOGIC as a pet peeve? Or should I recognize that many people DO use them?

Sorry, I should have been clearer, I didn't mean leave HYP off the calculator completely, just not give it a dedicated key. A shift function is perfectly adequate. The thing I hate it that probably the majority of scientific calcs I've seen dedicate a key to HYP.

Dave.

                  
Re: HYP, ARC and the rest
Message #6 Posted by DaveJ on 4 June 2007, 5:36 p.m.,
in response to message #4 by Gene

Quote:

Gene: But that's just silly. Hyperbolic functions have many uses and it is not wise to leave it off a scientific calculator in this day and age.

Applications for hyperbolic functions include: catenary curves, design of many structures (nuclear cooling towers, buildings at Dulles, etc), gears with skewed axes, even the shape of a shadow cast on a wall by a lampshade, etc, etc, etc.

http://www.pen.k12.va.us/Div/Winchester/jhhs/math/lessons/calc2004/apphyper.html

Giving a scientific calculator the abilities to do these things at the expense of one shift key location seems very reasonable.

Saying "I don't like it because I have never used it" is short-sighted, IMO. What if I never use base conversions? Should I have the inclusion of BASE and LOGIC as a pet peeve? Or should I recognize that many people DO use them?

Sorry, I should have been clearer. I am not saying leaving off the HYP function altogether, just don't dedicate a key to it.

I am sure there are a far greater number of calculator uses who do *not* use HYP on a regular basis than those who do. Yet probably the majority of scientific calcs have a dedicated HYP key. Casio are famous for it, and indeed in the older models it is a such a protected and revered key that it often does not have any other shift function associated with it.

Dave.

      
Re: HYP, ARC and the rest
Message #7 Posted by Jean-Michel on 4 June 2007, 9:11 a.m.,
in response to message #1 by Antonio Maschio (Italy)

CASIO fx-602p (about '83)

5 Keys (3rd/4th row) :

INV hyp

sin/sin-1 cos/cos-1 tan/tan-1

            
Re: HYP, ARC and the rest
Message #8 Posted by DaveJ on 4 June 2007, 9:32 a.m.,
in response to message #7 by Jean-Michel

Quote:
CASIO fx-602p (about '83)

5 Keys (3rd/4th row) :

INV hyp

sin/sin-1 cos/cos-1 tan/tan-1

The majority of Casio calcs operate the same way, and have a dedicated HYP key next to the TRIG keys. And all the ones I have accept the HYP and INV in any order, so you can use either: INV HYP SIN or HYP INV SIN

And come to think of it, it's probably the reason why most of the older Casio calcs don't have any extra shift function on the HYP key.

Dave.

                  
Re: HYP, ARC and the rest
Message #9 Posted by Palmer O. Hanson, Jr. on 7 June 2007, 10:09 a.m.,
in response to message #8 by DaveJ

Quote:

The majority of Casio calcs operate the same way, and have a dedicated HYP key next to the TRIG keys. And all the ones I have accept the HYP and INV in any order, so you can use either: INV HYP SIN or HYP INV SIN

And come to think of it, it's probably the reason why most of the older Casio calcs don't have any extra shift function on the HYP key.

Dave.

You can get the same thing at Wal-Mart for twenty dollars by buying their Durabrand Graphing calculator. And, if you happen to get the second version you get sixteen digit arithmetic.

      
Re: HYP, ARC and the rest
Message #10 Posted by Walter B on 4 June 2007, 10:34 a.m.,
in response to message #1 by Antonio Maschio (Italy)

The very first scientific handheld (HP35) was the only HP I know of with an ARC key as you propose. The very first programmable scientific handheld, the HP65, used a prefix f^(-1) to invert f-shifted functions. These keys were never observed again in an HP pocket calc thereafter.

One reason may be these are very specialized keys: ARC (and HYP as well) makes sense only for SIN, COS, TAN. But they will take 5 keys! INV sounds more flexible, but eventually is rather restricted compared to an universal shift key.

Todays calcs are so packed with functions, keyspace is a major issue. Take the HP35s, for example: it has 43 keys. Sounds a lot. But: You need 16 dedicated keys just for the basic inputs (ON/OFF, digits, ., ENTER, E, +/-, <-), 3 for stack and memory handling (x<>y, RDOWN, RCL), 4 for arithmetic, 6 for transient functions, 4 cursors and 2 prefixes, 3 keys for programming incl. program execution, and one each for MODE, statistical summing, complex input, EQN, and (). This sums up to 43 (surprise!). So, if you want ARC and HYP unshifted, you have to take 2 keys off the list to become shifted instead. Sounds easy. Try it!

IMHO proper function grouping on small keyboards is not easy at all. And a block of 5 adjacent keys will not make it easier.

Just my 0,02 Euro.

Edited: 4 June 2007, 10:38 a.m.

            
Re: HYP, ARC and the rest
Message #11 Posted by htom on 4 June 2007, 10:50 a.m.,
in response to message #10 by Walter B

One keytop, "Trig" that leads to the menu: Hyp Inv Sin Cos Tan.

I don't know if I'd like it, though. It could be argued that the hyperbolic functions should be with the other exponentials, and powers and roots with the trigs.

ln log hsin hcos htan

x^2 y^x sin cos tan

            
Re: HYP, ARC and the rest
Message #12 Posted by Gene on 4 June 2007, 10:55 a.m.,
in response to message #10 by Walter B

Having INV or ARC keys is more associated with the Dark Empire (TI) than with HP.

HP adopted a more direct "key for each function" approach when compared to TI. In general, on most HP scientifics until recently, if you wanted a function, there was a place on a keyboard to press it. The HP41 developed the catalog idea, but you could still assign a function to a key to directly press it. Later, menus gave the ability to get to a function fairly quickly.

Compare that to the TI models. The TI 58/59 series took this to an extreme with 40 OP Codes enterable using the OP function. Mean was available with 2nd x-bar, but to get standard deviation, TI adopted the terrible INV 2nd x-bar!

That obtuse thinking is something HP never went for and I'm very glad.

I really don't like having an INV key that applies to many many functions. Perhaps it is ok for the trig functions, perhaps not. But I really dont' think we want to go back to the ways of the DARK EMPIRE to do INV LN to get e^x, as was the case on the SR-52 model.

                  
Re: HYP, ARC and the rest
Message #13 Posted by GE on 5 June 2007, 5:41 a.m.,
in response to message #12 by Gene

Well on the HP65 the [f-1] key performs the 'inverse' function, and it seems easy to understand. It applies to trigonometrics, logs, square root, fractional part, and probably others (can you guess what [f-1][+] could be ?).

On the HP15C, you don't have a [HYP] key, which makes sense as these are not used that much, but instead a row of :

 HYP
[   ] [Sin] [Cos] [Tan]
HYP-1 Sin-1 Cos-1 Tan-1
Which give :
- direct access to sin, cos, tan
- inverse trigonometry with [g]
- hyperbolics with [f][HYP]
- inverse hyperbolics with [g][HYP]
It sounds almost optimal (direct hyperbolics couls be done with only one prefix key if there was an [HYP] key, which is not desirable).
So I think this solution is optimal in practice.
                        
Re: HYP, ARC and the rest
Message #14 Posted by Antonio Maschio (Italy) on 5 June 2007, 8:58 a.m.,
in response to message #13 by GE

...as usual, the 15C is, definitely, the best calculator! ;-)

Yes, I forgot this when considering the 15C. It has a wonderful feature, the "Abbreviated Key Sequences", that makes obvious, after a prefix, what a user would press, avoiding pressing other (annoying) prefix keys.

I thank you and all others for your observations. Mine was a first thought, and probably more experience in calculators (like yours) and more thinking by my side would prevent me from starting topics like this.

Thanks again.

-- Antonio

                              
Re: HYP, ARC and the rest
Message #15 Posted by Walter B on 5 June 2007, 10:02 a.m.,
in response to message #14 by Antonio Maschio (Italy)

Quote:
more thinking by my side would prevent me from starting topics like this.
Do not be afraid! IMO a good part of this forum is for the questions you (and me) always wanted to ask, but did not dare to ask so far. Continued questions lead to continuous improvement. Else, the knowledge about such matters will be extincted in some years.
                        
HP-15C: HYP, ARC and the rest
Message #16 Posted by Karl Schneider on 6 June 2007, 12:53 a.m.,
in response to message #13 by GE

Hi, all --

I agree with GE's summary of HYP and HYP-1, and note Antonio's mention of the HP-15C's thoughtful abbreviated keystroke sequences.

It should also be noted that the context-specific abbreviations and the HYP-1 prefix were necessary in order to avoid four-keystroke sequences that don't include a ".", as the numeric keycodes for such sequences would not fit in the PRGM display.

As such, 

[f][HYP][g][SIN-1]
and 
[RCL][f][MATRIX][f][A]
would not have been not only cumbersome, but also unworkable.

-- KS

                  
I loved OP codes
Message #17 Posted by Palmer O. Hanson, Jr. on 5 June 2007, 10:38 a.m.,
in response to message #12 by Gene

Gene:

As you well know I did a lot of work on the so-called "dark side" so I can't let your comments go by without a response.

Quote:
HP adopted a more direct "key for each function" approach when compared to TI. In general, on most HP scientifics until recently, if you wanted a function, there was a place on a keyboard to press it.

That led to three second function keys, yellow, blue and black, on the HP-67 and a horribly cluttered keyboard.

Quote:
The TI 58/59 series took this to an extreme with 40 OP Codes enterable using the OP function.

I loved most of the OP codes! Eight of them provided alphanumeric printing -- not to be available in RPN-land until the HP-41 arrived. Twenty of them (OP-20 through OP-39) provided the capability to increment or decrement data registers 0 through 9 without messing with the Dsz register or with bringing a one into the stack. That feature was invaluable when doing matrix manipulation. Four of them (OP-12 through OP-15) provided linear regression using sums in the statistics registers. With the HP-67 you had to implement those functions in user memory.

                        
Re: I loved OP codes
Message #18 Posted by Gene on 5 June 2007, 11:53 a.m.,
in response to message #17 by Palmer O. Hanson, Jr.

Hi Palmer! the Dark Side was meant as a good natured jab. After all, in the TI-58/59 days, I was a member OF the Dark Side. I bought a TI-58c when it came out long before I ever owned an HP.

The OP Codes did allow for functionality, but they are a horrible user interface issue. A calculator ought to be a key-per-function approach. Having a list of 40 op codes that are only useful if the user remembers them or has them written down is not very friendly.

The never released TI-88 took this to another extreme. How many Op Codes was that supposed to have? Hundreds? Why not have a machine then with only 20 keys and an Op key. Need to do addition? That's OP 01. Need to do a SIN calculation? OP 29. Need to convert from base 2 to Base 16, Op 221, etc.

The TI 58/59 really did have some bad user interface decisions, IMO. The INV 2nd x-bar for standard deviation really did set a low point. The standard deviation is in now way an inverse function of the mean, but that's the key sequence you had to press.

Ah, the good old days. :-)

Hope you're feeling well. Thanks for the card! It was great!

                              
Re: I loved OP codes
Message #19 Posted by GE on 5 June 2007, 12:03 p.m.,
in response to message #18 by Gene

Funny that it all started with a TI58C back "a few" years ago for me too... I still have that machine sitting mint in box at the best viewing point in my storage area.
Actually my first machine was a Radofin 2200, a wonderful 4-banger which was dismantled to bits by young me (I still keep the pieces).
TI was the only affordable choice at the time (for me), plain and simple, and these machines were really good - **too** !!!

                        
Re: I loved OP codes
Message #20 Posted by Wayne Brown on 5 June 2007, 1:05 p.m.,
in response to message #17 by Palmer O. Hanson, Jr.

Quote:
I loved most of the OP codes!

I can understand that. The HP-41 provides something similar (via synthetic programming) with the eG0BEEP codes. I love those; in fact, if lower-case letters were available on license plates, I'd have put an "eG0BEEP" plate on my car by now!

                              
Re: I loved OP codes
Message #21 Posted by Valentin Albillo on 6 June 2007, 5:57 a.m.,
in response to message #20 by Wayne Brown

Hi, Wayne:

Wayne posted:

    "I can understand that. The HP-41 provides something similar (via synthetic programming) with the eG0BEEP codes."

      Yes, you're right. I did study eG0BEEP decades ago and submitted a detailed report which was published in the Australian "PPC Technical Notes". Months later, the PPC Journal proper featured a whole issue dedicated to the Australian Chapter of PPC, in which my report was again included.

      Talking from memory, as I don't have the relevant issues at hand right now, I remember that filling up the prompt with various combinations of numeric addresses plus indirect addresses and other variants would execute (in RUN mode) or enter into a program (in PRGM mode) a certain XROM mm,nn instruction, with mm and nn both depending on the values entered at the prompt.

      This was intrinsically useful, as you could enter that XROM instruction as a program line even if you hadn't the required ROM plugged in at the moment, but further, some of the XROM instructions belonged to very useful ranges, so that you could then execute a number of common instructions with a single key assigned to eG0BEEP plus filling in the prompt. This would save you a great number of assignments or having to spell out the alpha name, and it's extremely similar to the OP codes operation.

      You can check either PPC Technical Notes or PPC Journal ("From Australia with love" issue) for the exact details, including all supported ranges for any given prompt and comments.

Best regards from V.

                                    
Re: I loved OP codes
Message #22 Posted by Wayne Brown on 6 June 2007, 10:26 a.m.,
in response to message #21 by Valentin Albillo

Quote:
This was intrinsically useful, as you could enter that XROM instruction as a program line even if you hadn't the required ROM plugged in at the moment, but further, some of the XROM instructions belonged to very useful ranges, so that you could then execute a number of common instructions with a single key assigned to eG0BEEP plus filling in the prompt. This would save you a great number of assignments or having to spell out the alpha name, and it's extremely similar to the OP codes operation.

Yes, that's the way I use it. I have eG0BEEP assigned to [SHIFT][CHS] on my HP-41CX and I keep a list of the relevant codes in the case (along with a plastic synthetic programming quick reference card from SYNTHETIX). So I can enter READSUB (XROM 28,11) by pressing eG0BEEP and entering 11 at the prompt, VERIFY (XROM 28,16) with eG0BEEP 16, PRFLAGS (XROM 29,11) with eG0BEEP 76, etc. It saves a lot of typing for HP-IL and printer functions, and I can use one key assignment to do the work of 89 others.

                                          
Re: I loved OP codes
Message #23 Posted by Valentin Albillo on 6 June 2007, 11:09 a.m.,
in response to message #22 by Wayne Brown

Hi again, Wayne:

Wayne posted:

    "It saves a lot of typing for HP-IL and printer functions, and I can use one key assignment to do the work of 89 others."

      Come to think of it, it would have been a *great* feature for power users if the HP42S had included an "OP"-like function as a primary key (in addition to the existing catalog, menu, and assignment functionalities, not as a replacement).

      Pressing this [OP] key and filling up a 3-digit (say) prompt would execute *any* available instruction, from ABS to %CHG, say, very quickly and conveniently, without having to navigate menus, use the catalog, spell out the alpha name, or assign anything.

      Newbies would tend to ignore it at first, but once they became more proficient with the machine's instruction set they could and no doubt would derive a large benefit from this feature, in terms or enhanced useability. I for once would have loved it.

Best regards from V.
      
Re: HYP, ARC and the rest
Message #24 Posted by Tony Duell on 4 June 2007, 1:16 p.m.,
in response to message #1 by Antonio Maschio (Italy)

If I understand you correctly, then this is exactly how the HP9100B's keyboard was laid out.

            
Re: HYP, ARC and the rest
Message #25 Posted by Woody Larkin on 4 June 2007, 7:49 p.m.,
in response to message #24 by Tony Duell

I believe the TI SR-50 had those five keys. See this link:http://www.datamath.org/

                  
Re: HYP, ARC and the rest
Message #26 Posted by Woody Larkin on 4 June 2007, 8:52 p.m.,
in response to message #25 by Woody Larkin

Sorry, here is a more direct link: http://www.datamath.org/Sci/WEDGE/sr-50.htm

                        
Re: HYP, ARC and the rest
Message #27 Posted by Gene on 4 June 2007, 9:00 p.m.,
in response to message #26 by Woody Larkin

Hey, what about my pic? :-)

http://www.rskey.org/gene/hpgene/sr50.GIF

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