The Museum of HP Calculators

HP Forum Archive 16

 x^y and y^xMessage #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^xMessage #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^xMessage #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^xMessage #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^xMessage #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^xMessage #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^xMessage #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 placementMessage #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 placementMessage #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 placementMessage #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 placementMessage #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

 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.