Larger stack size

12292020, 06:18 PM
Post: #21




RE: Larger stack size
In conventional math notation, serial exponentiation is rightassociative: https://en.wikipedia.org/wiki/Order_of_o...nentiation
Best! Mike 

12292020, 06:20 PM
Post: #22




RE: Larger stack size
(12292020 05:56 PM)Allen Wrote: Symbolically it does. This is exactly the reason exponentiation is evaluated from right to left. (had it been from left to right, we could have rewritten as products of exponents) lua> pow(2, pow(1.8, pow(1.6, pow(1.4, 1.2)))) 9.72086810644022 lua> 2 ^ 1.8 ^ 1.6 ^ 1.4 ^ 1.2 9.72086810644022 

12292020, 06:23 PM
(This post was last modified: 12292020 06:25 PM by Massimo Gnerucci.)
Post: #23




RE: Larger stack size
Greetings, Massimo +×÷ ↔ left is right and right is wrong 

12292020, 06:26 PM
Post: #24




RE: Larger stack size
(12292020 05:56 PM)Allen Wrote:(12292020 04:59 PM)Valentin Albillo Wrote: Wrong. Yout code above does not compute correctly that tower of exponentials. I think there's some disagreement over the associativity of exponentiation. The 65 Notes article suggests it's right associative  i.e. 2^1.8^1.6^1.4^1.2 = 2^(1.8^(1.6^(1.4^1.2)))  which the 35's x^y is particularly well suited to handle. That is, of course, most definitely not equal to 2^(1.8*1.6*1.4*1.2). If we assume the exponents are leftassociative, then you are correct. It seems like TI treats it as leftassociative (28.6) according to my 58C, 85, and 84 Plus, and Casio changed from leftassociative to rightassociative (9.72) at some point: my fx7000G is leftassociative, and the fx5800P and fx991EX both display the operator as ^( in line I/O mode, clearly showing the right associativity. 

12292020, 06:29 PM
Post: #25




RE: Larger stack size
(12292020 06:26 PM)Dave Britten Wrote: I think there's some disagreement over the associativity of exponentiation. Mathematically none that I know of. Greetings, Massimo +×÷ ↔ left is right and right is wrong 

12292020, 06:31 PM
Post: #26




RE: Larger stack size
(12292020 06:29 PM)Massimo Gnerucci Wrote:(12292020 06:26 PM)Dave Britten Wrote: I think there's some disagreement over the associativity of exponentiation. Between calculator models, there certainly seems to be. The TI 84 Plus is worse than I thought: it's leftassociative in classic mode, and rightassociative in Math Print mode. The exact same key sequence will give you a different result depending on which of the two display modes you're in! I think Casio has the right idea of making it clearly rightassociative, with a forced ( in lineI/O mode. 

12292020, 09:07 PM
Post: #27




RE: Larger stack size
(12292020 05:56 PM)Allen Wrote:(12292020 04:59 PM)Valentin Albillo Wrote: \( 2^{1.8^{1.6^{1.4^{1.2}}}} \) Nope. Written as you posted, it's evaluated from right to left, i.e.: you first evaluate 1.4^1.2, then 1.6 raised to the last result, then 1.8 raised to the last result, then 2 raised to the last result. That final result is 9.720868106440216192155483936635... V. All My Articles & other Materials here: Valentin Albillo's HP Collection 

12292020, 10:10 PM
(This post was last modified: 12292020 10:11 PM by robve.)
Post: #28




RE: Larger stack size
(12292020 09:07 PM)Valentin Albillo Wrote:(12292020 05:56 PM)Allen Wrote: Symbolically it does. Since the dawn of computing it's been "top down" or right associative. Otherwise it is a bug. However, mathematicians like Neil Sloane take a much more creative look at this problem with "Dungeon Numbers  Numberphile" giving "top down" an entirely different meaning https://www.youtube.com/watch?v=xNx3JxRhnZE One of my favorite videos. "I count on old friends to remain rational" 

12302020, 01:49 PM
Post: #29




RE: Larger stack size
(12292020 06:31 PM)Dave Britten Wrote:(12292020 06:29 PM)Massimo Gnerucci Wrote: Mathematically none that I know of. The Casio solution is a good technique. For the TI, you can understand why they would have made it leftassociative in classic mode for consistency with other binary operators, and perhaps for consistency with earlier AOS models. Back to HP Land, the HP27S also has a leftassociative exponentiation operator, but it displays partially evaluated results as it goes, so that [3] [x^y] [3] [x^y] [3] is finally displayed as 27^3. — Ian Abbott 

12302020, 02:11 PM
Post: #30




RE: Larger stack size
(12302020 01:49 PM)ijabbott Wrote:(12292020 06:31 PM)Dave Britten Wrote: Between calculator models, there certainly seems to be. Interestingly, the fxCG500 (the calculator formerly known as ClassPad) will display the entry as 3^3^3 without any parentheses, but still evaluates it as rightassociative (i.e. 7.63E12 rather than 19683). The fx991MS 2nd Edition also does not include parentheses, but evaluates this as leftassociative. The TI Voyage 200  and presumably 92 and 89  are rightassociative, and will even automatically change your input to 3^(3^3) after entry if pretty print mode is turned off (if it's on you get a tower of superscripts). Very strange to see so much inconsistency on this, even between calculators from a single manufacturer. 

12302020, 02:19 PM
(This post was last modified: 12302020 10:35 PM by robve.)
Post: #31




RE: Larger stack size
(12292020 06:31 PM)Dave Britten Wrote:(12292020 06:29 PM)Massimo Gnerucci Wrote: Mathematically none that I know of. No, no, no! The Ti 84 Plus is not that bad. Let's take a look at Ti BA II Plus Professional. Quoting from the manual: Choosing Calculation Methods When you choose chain (Chn) calculation method, the calculator solves problems in the order that you enter them. (Most financial calculators use Chn.) For example, when you enter 3[+]2[x]4[=], the Chn answer is 20 (3+2=5, 5*4=20). The worst part is that Chn is the default method on all of these calculator models. Their AOS^tm (algebraic operation system) is only optional, and "solves problems according to the standard rules of algebraic hierarchy." Apparently financial calculators only offer one register to calculate with, i.e. a stack of one register (an accumulator). Why bother calculating with a stack of four registers? PS. Funny that they introduce fancy names for standard stuff, like AOS^tm and also APD^tm (automatic power down). I'm sure their marketing department had some say in this crap.  Rob "I count on old friends to remain rational" 

01042021, 12:21 PM
Post: #32




RE: Larger stack size
Hi,
on the HP28S if I type '3^3^3 [EVAL] I get 19683 Fail :( JSB 

01042021, 03:58 PM
Post: #33




RE: Larger stack size
This appears to have changed at some point, the 50g returns 7625597484987, which is 3^(3^3) as opposed to (3^3)^3.


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