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HP Forum Archive 16

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x^y and y^x
Message #1 Posted by Walter B on 7 June 2006, 2:23 a.m.

Does anyone know why 40gs has x^y ? 50g has y^x again.

Cannot name any of both exponentiation keys "traditional", because hp35 had x^y d:)

      
Re: x^y and y^x
Message #2 Posted by Han on 7 June 2006, 2:31 a.m.,
in response to message #1 by Walter B

The HP40GS is an algebraic-entry calculator whereas the HP50G is an RPN-entry calculator.

            
Re: x^y and y^x
Message #3 Posted by Walter B on 7 June 2006, 4:25 p.m.,
in response to message #2 by Han

Quote:
The HP40GS is an algebraic-entry calculator whereas the HP50G is an RPN-entry calculator.

You are right for sure. But I don't comprehend why this shall be a reason. Please explain for me dummy.

Edited: 7 June 2006, 4:37 p.m.

                  
Re: x^y and y^x
Message #4 Posted by Han on 7 June 2006, 5:51 p.m.,
in response to message #3 by Walter B

The x and y refer to the order of input. That is, the x is the first argument, and the y is the second argument (using a natural lexicographic ordering).

For the algebraic x^y:

Since algebraic notation is essentially the same as what you see, x^y means just that. That is, if you see 2^3, you enter in 2 [x^y] 3. With algebraic notation, it's first-in-first-out. So if your inputs are 2 and 3, the first argument is the 2.

For the RPN y^x:

Since RPN uses a last-in-first-out (i.e. the last input is the first argument) model, it is natural to use (for a 2-level stack) "y" for the second level and "x" for the first level (this is just a lexicographical ordering). We still enter the arguments the same way. That is, if we want to compute 2^3, we would still enter in 2 followed by 3. But this puts 2 on level two (y) and 3 on level one (x). So the ^ command, in order for its label to properly reflect the correct input paring, is called y^x and not x^y due to the input method of last-in-first-out (hence the R in RPN -- it stands for reverse).

I hope I did not muddy up the waters even more with that poor attempt at an explanation.

Edited: 7 June 2006, 5:58 p.m.

                        
Thanks, Han! d:-) (NT)
Message #5 Posted by Walter B on 8 June 2006, 3:30 p.m.,
in response to message #4 by Han

NT!

      
Re: x^y and y^x
Message #6 Posted by Eric Smith on 7 June 2006, 3:16 a.m.,
in response to message #1 by Walter B

Quote:
Cannot name any of both exponentiation keys "traditional", because hp35 had x^y

For RPN, y^x is definitely traditional. The 35 was one of the first RPN calculators, and the details of RPN hadn't yet completely solidified. So the 35 predates the tradition.

            
Re: x^y and y^x
Message #7 Posted by Thomas Radtke on 7 June 2006, 4:04 a.m.,
in response to message #6 by Eric Smith

I thought the variable names were chosen according to the stack convention. On a 35, you really have to enter the exponent first and the base second (which is then located in the x register). AFAIK it was designed this way to compensate for the missing 10^x function or is this a legend?

                  
Re: x^y and y^x
Message #8 Posted by Eric Smith on 7 June 2006, 4:28 a.m.,
in response to message #7 by Thomas Radtke

Quote:
I thought the variable names were chosen according to the stack convention.

Yes; that doesn't contradict what I said. The 35 predates the "traditional" RPN y^x function. The tradition was established with the 45, 65, etc.

                  
Re: x^y and y^x & function-key placement
Message #9 Posted by Karl Schneider on 7 June 2006, 10:45 p.m.,
in response to message #7 by Thomas Radtke

Quote:
On a 35, you really have to enter the exponent first and the base second (which is then located in the x register). AFAIK it was designed this way to compensate for the missing 10^x function or is this a legend?

I would say that this is the most plausible explanation -- i.e., to raise an entered x-value to a power of 10, just do 10 xy.

Another possible explanation is that "xy" was thought to be more intuitive, since y is above x in the stack. Unfortunately, that convention differs from the subtraction and division operators, which perform "y minus x" and "y divided by x", respectively. "y raised to power of x" is certainly more consistent.

Speaking of 10x, it was thoughtful of HP to make LN and ex unshifted keys on the Pioneers, with LOG and 10x both shifted. The "base-e" functions are used much more frequently than the "base 10" functions.

On the previous models -- HP-41 and Voyager-series HP-10C, HP-11C, and HP-15C -- these functions were placed differently, most likely by deliberate intent:

  • On the Voyagers, having LN shifted on ex and LOG shifted on 10x established a consistent pattern of "shifted inverse functions" -- along with x2 shifted on SQRT(x) -- that was naturally used for the trigonometric functions on the second row. Also, ex, 10x, and yx side-by-side provided a pleasing visual symmetry.

  • On the HP-41, the same "shifted inverse functions" pattern was present, but yx was shifted, since Sigma+ occupied a spot on the top row. Lacking the pattern of three exponentials, LOG and LN were unshifted, instead.

One more thing: yx and 1/x are side-by-side on the Voyagers, and on the same key (with yx shifted) on the HP-41. Why? This facilitates using the two functions together to execute the root function y1/x.

That's thoughtful attention to detail! You won't find it on the mass-market calculators of today -- their designers don't have a clue...

-- KS

                        
Re: x^y and y^x & function-key placement
Message #10 Posted by Antonio Maschio (Italy) on 8 June 2006, 5:31 a.m.,
in response to message #9 by Karl Schneider

Quote:
One more thing: yx and 1/x are side-by-side on the Voyagers, and on the same key (with yx shifted) on the HP-41. Why? This facilitates using the two functions together to execute the root function y1/x.

That's thoughtful attention to detail! You won't find it on the mass-market calculators of today -- their designers don't have a clue...

Wow! I didn't pay so much attention to this kind of details!

-- Antonio

                        
Re: function-key placement
Message #11 Posted by Walter B on 8 June 2006, 7:18 p.m.,
in response to message #9 by Karl Schneider

Karl, thanks for pointing to the design details reflecting the thoughtful and careful work of the engineers who layed out the vintage models. There's quite some hidden beauty in those items. One more reason for using and collecting them - and only them.

In an humble attempt to transfer and extrapolate this into our time, where display technology has reached a far higher level and memory is readily available, here are 2 proposals I ask for your votes, please. I did these layouts more as a mental exercise than believing in an immediate application. Perhaps somebody cares - maybe even HP is listening or somebody else interested in this topic. After all, the density of such folks is at least elevated in this forum. And it is frequented by many more nerds than other sites (if those are up at all ;) ).

Both proposals are based on the Voyagers and will keep their size. Contrasting colors are used for different classes of operations (white, blue, gold, orange, and green on a dark background - better to read than any "platinum"-scheme I know). As many functions as possible can be accessed directly using 3 prefix keys (because I find it hard to remember where an invisible function is hidden), the rest is stored in menus. You will find consistent patterns of direct and inverse functions. Related operations, functions or menus, are placed next to each other. Both layouts feature a QWERTY keyboard, too. Menu names often start with the letter becoming effective in alpha mode at the same key. And SPACE and TIME will be treated with one key ;)

Both proposals combine the full set of features of the 42S and the 16C with minor contributions from other newer and older models as well. Keys are labeled in a way they can be used in different modes, e.g. x^-1 will calculate 1/x for real numbers, invert a matrix or flip the bits of an integer. Another example is ^, acting as y^x for real numbers and "up arrow" in alpha mode. Or |x| returns the absolute value of a real or complex number, eliminates the sign of an integer, calculates the length of a vector or the norm of a matrix.

The main difference between both layouts is one has the traditional vertical ENTER

while the other one features an horizontal ENTER key, innovative for Voyager-like models:

So which one is your favourite? May I ask for your votes, please?

                              
Re: function-key placement
Message #12 Posted by Wayne Brown on 9 June 2006, 10:53 a.m.,
in response to message #11 by Walter B

I vote for the first one (with the vertical [ENTER]. I think that looks much nicer on a Voyager-style layout (which is my favorite HP style, BTW).

                              
Re: function-key placement
Message #13 Posted by Massimo Gnerucci (Italy) on 9 June 2006, 11:33 a.m.,
in response to message #11 by Walter B

The second layout is better in my opinion: much more consistent with the horizontal large ENTER key in every HP calc apart from the Voyagers, and since it serves as a SPACE key too... central and horizontal is nice!

Greetings,
Massimo

                              
Your two Voyager-platform concepts
Message #14 Posted by Karl Schneider on 9 June 2006, 10:29 p.m.,
in response to message #11 by Walter B

Walter --

I congratulate your efforts in development of advanced calculator models on the Voyager-series platform. Utilizing a longer display with a sharp dot-matrix LCD for equations, complex numbers, and more menu options is an idea I had, as well.

My basic assessment, though, is that your concepts are overambitious -- there's too much diverse functionality crammed into a limited package. Thus, the crisp, organized and cohesive layout of the Voyagers is not replicated.

My main comments:

  1. Why graphing capabilities (3d even!), with a long, squat display like that of the HP-28C/S? The graphs wouldn't look very good.
  2. Why a QWERTY keyboard? One wouldn't be able to type fast enough to exploit it, and it's not the same as a conventional one, anyway. If not sequential A, B, C, D... why not Dvorak?
  3. Why are |x| and n! unshifted functions -- they aren't used very often.
  4. Why is R/S shifted?
  5. I wouldn't advocate a return to the HP-34C, with SIN, COS, TAN, LN, ex and R_dn all shifted -- too inconvenient.
  6. I wouldn't denote 10x and ex as LOG-1 and LN-1, or ->HMS as H-1, or ->RAD as H-1, or ->R as P-1 -- too unintuitive.
  7. Placing backspace ("<-X") right next to number keys might lead to some unnoticed data-entry errors.
  8. Why is the n!/PERM/COMB key so far away from the PROB menu? Why is STAT so far away from PROB?
  9. Mean and standard deviation (x-bar, s), estimators (x-hat, y-hat), and the STAT menu are not adjacent. If some commands in a functional set are directly-accessible, but others are in a menu, the menu and the commnds should be on the same key if at all possible.
  10. Couldn't Sigma+ and Sigma- be on the STAT menu? They aren't used very much.
  11. Would there be enough battery power and space for the I/O?
  12. Some legends on the keyboard are not very recognizable.

Well, I could go on, but I think you see the point. Cramming an HP-42S, HP-15C, HP-16C, HP-12C (TVM) and HP-32SII (equations and fractions) coherently into a Voyager-series package is a daunting task, indeed. I've thought about how to meld the HP-15C and HP-32SII into a compact, non-graphing unit, and haven't yet been able to crystallize the concept...

I've posted a discussion extolling the HP-15C layout (derived from the HP-11C), which is as close to perfection as has ever been achieved. Readers should keep it in mind when designing conceptual calculators -- I've yet to see one that meets the high standard.

Cheers,

-- KS

Edited: 10 June 2006, 2:11 a.m.

                                    
Re: Your two Voyager-platform concepts
Message #15 Posted by Walter B on 11 June 2006, 12:54 a.m.,
in response to message #14 by Karl Schneider

@All,

thanks! Now it's Horizontal 1, Vertical 1. Which team will score next?

@Karl,

thanks for your elaborate response. It deserves a detailed answer you'll get later. For now:

I must admit I rated the value of a QWERTY alpha keyboard rather high. Whenever you want to type more than just one English word, it's the fastest entry method, because everybody knows it. So, many of your points can be attributed to this decision, since I wanted a menu to appear at the position of the corresponding letter. I may drop this requirement for a more cohesive *calculator* layout and give the QWERTY as a separate bonus.

Just to clarify the 3d: This is meant for stats and coordinate transformations, only. Graphs shall be confined to simple 2d function plots. If such graphs can be displayed on a 42S or 28C, they must be possible here, too.

That's all for now. Thanks again.

Walter

Edited: 12 June 2006, 6:42 p.m.

                                    
Re: Your two Voyager-platform concepts
Message #16 Posted by Walter B on 13 June 2006, 8:14 a.m.,
in response to message #14 by Karl Schneider

Karl,

My remaining answers to your comments:

Quote:
Placing backspace ("<-X") right next to number keys might lead to some unnoticed data-entry errors.
Thanks for your advise. Will be changed.

Quote:
Why a QWERTY keyboard? One wouldn't be able to type fast enough to exploit it, and it's not the same as a conventional one, anyway. If not sequential A, B, C, D... why not Dvorak?
Please look at Blackberry, Nokia, etc. – they all use QWERTY. For size reasons, these keyboards are never conventional, but most people still find the letters intuitively. ABCD is not suited to write words or sentences. Dvorak may be intuitive, but only a minute fraction of the population of the world work with it. If you require need for a scientific calc and knowledge of Dvorak keyboards, you’ll end up with less than ppm (will be different for the Czech composer ;-) )

Quote:
Couldn't Sigma+ and Sigma- be on the STAT menu? They aren't used very much.
Here I definitively disagree. Sigma+ is used frequently, and Sigma- is the inverse also needed for error recovery. You find them on every keyboard of a scientific since the HP45.

Quote:
I wouldn't advocate a return to the HP-34C, with SIN, COS, TAN, LN, ex and R_dn all shifted -- too inconvenient.
HP15C had a panel of 111 operations (39 keys + 36 shifted operations with 2 prefix keys) and contained >130 built in functions. HP42S had a panel of 73 operations (37 keys + 36 shifted operations and contained >350 functions, so functions like hyperbolics were placed in menus you had to remember. I agree with you to have them visible on the panel is better than to bury them in a menu. The limit of 39 keys may require trigonometry shifted, however, because other functions may be more important to appear on the key tops.

In your remaining comments, you criticize consequences of my intention to have e.g. STAT at the position of the letter S and PROB at P. As admitted already, this was less than optimum. I will change it.

Quote:
Cramming an HP-42S, HP-15C, HP-16C, HP-12C (TVM) and HP-32SII (equations and fractions) coherently into a Voyager-series package is a daunting task, indeed.
That exactly is the challenge.

Regards,

Walter

                        
The perfect functional layout of the HP-15C
Message #17 Posted by Karl Schneider on 10 June 2006, 1:41 a.m.,
in response to message #9 by Karl Schneider

All --

Recently, a few contributors have developed images of faceplates for conceptual scientific calculators, based on the Voyager and Pioneer platforms. Anyone who undertakes such an effort ought first to fully appreciate the careful thought and attention to detail encomapassed in the organization of its functionality on the HP-15C keyboard, and try to match that in his own concept.

While the cohesiveness and completeness of that functionality alone is impressive (as documented by Valentin Albillo in "Long Live the HP-15C" and short essays in the MoHPC Forum), I will describe how meticulously crafted the keyboard arrangement really was. Its impeccable organization adds value by making any function easy to find, thus saving time and effort. Thoughtful layout was very important, because the lack of an alphanumeric capability to allow softkey menus and named commands dictated a direct placement of every function on the keyboard.

The HP-15C was developed from the fine HP-11C, augmented by extensive amounts of advanced functionality in the same compact package. HP even managed to slightly improve the layout while "shoe-horning" the new functions. An article in the May 1983 Hewlett-Packard Journal, "Scientific Pocket Calculator Extends Range of Built-in Functions", describes the engineering effort. (A scan of this article is available for purchase on CD #3 or DVD from the MoHPC.)

This is a case where annotated pictures would certainly help to illustrate, but I'll just provide links to two unmodified photographs against which to verify my descriptions:

http://www.hpmuseum.org/15.jpg

http://www.hpmuseum.org/11c.jpg

One thing that stands out in these photos: The keyboard and faceplate do not look cluttered, despite the abundance of functions. This is because the two shift colors (yellow and blue) contrast well with both the faceplate and each other. Also, the beveled keys allow the blue shift functions to be printed directly on the keys, right below the primary key legends. Thus, everything is neatly arranged, with plenty of space between rows. (Compare that with an HP-33S!)

Here are the compact and coherent functional groupings I've identified on the HP-15C keyboard layout, which can readily be seen in the photo:

  1. Data entry: Keyboard rows 1-4, columns 6-9.
    This category includes the numbers 0-9, decimal point, CHS, pi, EEX, ENTER, LASTx, Sigma+, and Sigma-. The handy backarrow for error-correction and deletion is in column 5, near but outside the group of "constructive" data-entry keys.

  2. Arithmetic: Keyboard rows 1-4, column 10.
    This category includes /, *, -, and +. The four functions perform different operations based upon the types of the two input arguments -- real scalar, complex scalar, or matrix.

  3. Probability and Statistics: Keyboard row 4, columns 6-10.
    This category includes Sigma+ and Sigma-, factorial and gamma function (x!), mean, standard deviation, linear regression, y-estimator, correlation coefficient, permutation, combination, and random number.

  4. Transcedental functions: Keyboard rows 1-2, columns 1-5.
    This category includes trigonometrics, hyperbolics, logarithmic and exponential functions, reciprocal, square and square root, percent and delta-percent. All inverse functions are blue-shifted. 1/x is adjacent to yx to calculate general roots.

  5. Stack manipulation: Keyboard row 3, columns 3-5.
    This category includes x<>y, roll down, roll up, and CLx.

  6. Storage-register access: Keyboard row 4, columns 4-5.
    This category includes STO and RCL, which are used with A-E, I, (i), 0-9 and .0-.9, MATRIX, RESULT, and RAN#. Arithmetic operations are permitted in conjunction with virtually all of these identifiers.

  7. Program entry, navigation, and execution: Keyboard rows 2-3, columns 1-2.
    This category includes P/R, GSB, GTO, R/S, LBL, SST, BST, and PSE.

  8. Display and angular mode: Keyboard row 1, columns 7-9.
    This category includes FIX, SCI, ENG, DEG, RAD, and GRD.

  9. Conversions: Keyboard row 3, columns 7-9.
    This category includes ->R, ->H.MS, ->RAD and their respective inverses ->P, ->H, and ->DEG.

  10. Flag and looping control: Keyboard row 2, columns 7-9.
    This category includes DSE, ISG, SF, CF, and F?.

  11. Conditional testing: Keyboard rows 1-3, column 10.
    This category includes x<=y, x=0, and the TEST command.

  12. Scalar parts and values: Keyboard rows 3-4, column 4.
    This category includes FRAC, INT, and RND. (ABS is in row 1 -- a carryover from the HP-11C.)

  13. Matrix operations: Keyboard rows 1-2, column 6.
    This category includes MATRIX and RESULT. Either of these would be used with a matrix identifier A-E, which are nearby. MATRIX can be used with a one-digit code 0-9, which are also nearby.

  14. Advanced functions: Keyboard rows 1-2, column 10.
    This category includes SOLVE and INTEG, which would be used with labels A-E, 0-9, or .0-.9. The numerical labels are nearby.

  15. Clearing operations: Keyboard row 3, columns 2-5.
    As indicated in yellow on the faceplate.

The HP-15C functions DIM, MATRIX, RESULT, x<>, SOLVE, INTEG, TEST, and Re<->Im replaced six conditional-test operations along with x<>I and x<>(i) from the HP-11C. This provided the following new functionality and improvements:

  • The open-ended x<> replaced both x<>I, and x<>(i), and is also much more flexible: x<> can be used with I, (i), and with any directly-accessible numbered storage register (0-9 and .0-.9) or matrix identifier (A-E).

  • DIM serves double-duty to dimension matrices and to manaully allocate the number of storage registers. This manual allocation -- which replaced the automatic allocation of the HP-11C -- was absolutely essential. It allowed the user to specify the amount of free memory available for matrices, complex number stack, SOLVE, and INTEG -- all of which were lacking on the HP-11C.

  • The I and (i) functions serve double-duty on the HP-15C for complex-number operations, as well for indirect memory access. The I register can also be used for indirect access of matrices and with FIX/SCI/ENG (not supported in the HP-11C).

  • TEST is used in conjunction with a single-digit code 0-9 that provides the remaining ten of the complete set of 12 conditional tests. (The HP-11C had only eight of the 12 tests.)

  • All functions in the categories of "Conversions" and "Probability and Statistics" are adjacent to one another in the same row on the HP-15C. This is not true of the HP-11C.

  • The Pi-entry function is closer to its shift key on the HP-15C than on the HP-11C.

  • ABS is more useful on the HP-15C than on the HP-11C -- it can calculate the magnitude of a complex number, also.

  • As a bonus, the HP-15C offers more flags than the HP-11C, as well as recall arithmetic (lacking on the HP-11C). The HP-15C also offers more than twice as much RAM, in order to make the matrix functions useful.

  • MATRIX and RESULT -- instead of SOLVE and INTEG -- are placed next to the letters A-E, because MATRIX and RESULT would be used repeatedly when needed, whereas SOLVE and INTEG might be invoked only once or twice when used with A-E.

This excellence of design was made possible only by the careful thought and concerted effort that went into the HP-15C and its immediate predecessors, the HP-11C and HP-34C. These attributes are not particularly evident in the calculators and consumer-electronics products of today -- most of which are not intended to be enduring devices for long-term use. But, we should keep them in mind when using Photoshop or other software for our own concepts.

-- KS

Edited: 11 June 2006, 8:00 p.m.

                              
Re: The perfect functional layout of the HP-15C
Message #18 Posted by Antonio Maschio (Italy) on 12 June 2006, 3:28 a.m.,
in response to message #17 by Karl Schneider

This is the most thorough and precise description of a calculator keyboard layout I've ever read, and it pictures exactly what I feel when I see the proposals for new "Voyager" or "Pioneer" style calculators (e.g. OpenRPN): they seem good, yes, but the HP-15C was... mmmh... better.

Now I can say why.

Thanks, Karl.

-- Antonio

No calculator is better for me than the 15C. Hope either HP or someone else will reissue it, identical or improved, but I'd like to feel the same sensations when I hold it in my hands.

                                    
Re: The perfect functional layout of the HP-15C
Message #19 Posted by Karl Schneider on 13 June 2006, 2:14 a.m.,
in response to message #18 by Antonio Maschio (Italy)

Antonio --

Thank you for the compliment. It's a topic that's been rattling around my head for a while -- one which I felt has not been fully appreciated by even today's so-called "professional" designers of calculators. As evidence, consider the HP-33S as well as the incoherent and incohesive low-end "student learning assistants" being sold for US$15 today.

So, the front-panel images being presented gave me a reason to formulate the "short essay". I might turn it into an article by stipping off the contemporary commentary and adding something more of substance.

Best regards,

-- KS

                                          
Re: The perfect functional layout of the HP-15C
Message #20 Posted by Antonio Maschio (Italy) on 13 June 2006, 2:41 a.m.,
in response to message #19 by Karl Schneider

Karl wrote:

Quote:
I might turn it into an article by stipping off the contemporary commentary and adding something more of substance.

I wish!

Ciao!

-- Antonio

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