Katie: Questions Re. your "99 digits of Pi" article



#11

Katie (or whoever may provide some answers):

Could you please elucidate on a few points for me?

In your "99 digits of Pi" article, there are a few points in the program that I don't follow. I have not invested a lot of time trying to figure it out, so please excuse me if the questions are dumb.

First, I don't understand your series expansion for ArcTan. What is the "y" in the formula; where did it come from?

Second, how are the "starting values" of 280,000,000 and 30,336,000 computed (I think I understand the method of numeric storage). Are these first-term values for the ArcTan(1/7) and ArcTan(3/79)?

Third, where does the "divide by 50" come from in Subroutine 'X'?

Fourth, where does the "multiply by 9 and divide by 125" come from in Subroutine 'R'?

I have not carefully re-enacted the register manipulations in the routines, but I think that your documentation will be quite sufficient for me to understand all the data manipulation. But after my cursory examination, I was confused on the four points listed above. Thanks in advance for any help!

Bruce.


#12

Hi Bruce,

All good questions because I left out some of crucial mathematics on this. I've corrected the article and reposted it -- it should answer all your questions.

-Katie


#13

Katie:

Thanks! I'm glad to know that the answer wasn't obvious to the ENTIRE world outside me!

 ;-)

Bruce.


p.s. Are the math manipulation routines and numerical storage method of your invention? It appears to be a very efficient use of the 32sII's space! Personally, I can't stand programming the 32sII. I think it is the WORST programming experience HP EVER offered! I still can't believe that there is no editing capability... "Oh, I made a mistake...I guess I get to reenter the whole program again..."

 >:-p

Gee...I get to name my program anything I want---as long as it is ONE SINGLE LETTER!
 >:-p

Programming any HP classic is a breath of fresh air after looking at the 32sII! And what about that memory limitation?!? Sheesh... The one thing the 32sII does have going for it is that it is a real RPN machine; HP sure fixed that, though, didn't they?!

All my HP calculator ranting is a moot point now anyway, considering that it appears that HP is dropping calculators faster than Carly dropped Walter Hewlett! (No more of those pesky founders around to muck-up Carly's $50 million payday for the merger! Gee, I wonder if that money was a conflict of interest? I'm sure it had NO influence whatsoever---she was ALWAYS acting in the best interest of the share holders...Right?...Right?...Anyone? [a cricket chirps])

#14

Relatively scathing article about Carly in this month's (or maybe last month's) Vanity Fair. Basically billed her as a prima donna and made pretty detailed references to HP's culture pre and post the new regime. Also very sympathetic to Walter Hewlett. Recommended read.


#15

I though I could delete and insert individual lines within a program on my 32sii. SO I'm not sure what you mean-


As for Carly. A fried of mine up in OR retired recently (last year). he had managed to collect a few tens of thousands of shares of hp stock over the course of his 20+ years at HP. Even if you ignore the "bubble" of the late 90's, Carly has plan managed to single handedly devastate his reitement plan faster than he could sell stock.

Sad.

#16

You can insert and delete steps on the HP32SII in edit mode. Actually, I like programming on this machine, it's got a few nice features: memory used since the last LBL, store/recall indirect math functions and 1.5 byte functions instead of using up 2 bytes. It's a simple language to learn and pretty easy to enter, it's not meant to be a full blown programmable calculator in the sense of the 41C, 42S, 48, 49. And I like programming in highly constrained memory spaces.

The arctan expansion and term_1/term_2 composition are well known, and very old ways of calculating Pi. Modern ways to compute it converge much, much faster but are much, much more involved to implement -- not at all appropriate for a programmable calculator. [Just an aside here -- did you know that there's an algorithm to compute the n'th digit of Pi directly, without computing the n-1 preceding digits?] Anyway, take a look in "A History of Pi" for more methods of how to calculate it.

Aside form the arctan formula and 2-term decomposition idea all the rest of the stuff is my own.


#17

Katie wrote:

"Just an aside here -- did you know that there's an algorithm to compute the n'th digit of Pi directly, without computing the n-1 preceding digits?"

Corret me if I'm wrong, but I think it can only compute
the n-th *hexadecimal* digit, not *decimal* digit, i.e.:
you can compute the 1,000,000,000th digit of Pi assuming
Pi is expressed in base 16, (digit from 0 to F). There
seems to be no equivalent algorithm for directly finding
the n-th digit in the usual, common base 10 ...

#18

Regarding editing in the 32sII: it appears that I have misled myself. I admit that I have only performed the most cursory programming on the 32sII, but I remember---vividly---that I could NOT see how to move around the code and insert/delete lines. I guess I'll have to look in the manual again. For some reason, though, I seem to remember that I explicitly LOOKED for this feature in the manual, and never found any information about editing code in any way... Maybe I dreamt the whole thing! ;-)

Thanks for the correction. I'll have to give (one of) my 32sII(s) another chance! (Especially now that they're worth >$120 each on eBay! ;-) )

Bruce.


#19

I have only my 32s, (not sII) with me, but it lets you walk up & down in the code with the up & down arrows, and to delete individual lines with the delete (left arrow) key. New lines insert "after" the line you're on.

I assume the sII is the same.

The memory size is the most frustrating aspect, and one-character names are a real problem. The 32s/sII is (I think) a pretty cool device, but one with unnecessarily severe limitations.


#20

Yep- the 32sii is the same method.

even just a 2 char namespace (676 unique vars and unique labels) woul dmake a big difference- But realistically, I can't see that it would matter much without at least 1KB of memory.

For my most recent uses of the 32sii, I'd want 2k. I have reason to want to store an awful lot more formulas than I can right now and still have any useful programming space.

Of course, I'll be using a 32k 42s soon enough. but I like the 32sii for some things.


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