Omnimaga
Calculator Community => TI Calculators => TI-BASIC => Topic started by: AngelFish on February 16, 2011, 03:03:09 am
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(http://img.removedfromgame.com/imgs/Add_it.gif)
I made this little utility in response to a topic on TI-BASIC Developer. It's an addition utility that can get around the OS imposed arithmetic limit of 14 digits of precision. Nothing special and not worth releasing on Ticalc.org, but I hope someone finds it useful.
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What exactly is it doing? I'm having a hard time following the code.
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I'm a bit confused as well... isn't 123456789+1 perfectly within the realms of what the calc can do?
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Are you saying it rounds to a certain precision? I'm a bit confused as to how it works, though.
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I'm a bit confused as well... isn't 123456789+1 perfectly within the realms of what the calc can do?
(methinks he just used it as a quick example)
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but how could the program have calculated 123456789+1 if he typed that into the homescreen and not into the program? What is this doing exactly?
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I used 123456789+1 as an example to prove that the program gets the correct results. If I had used 1E23+1, you would have a more difficult time confirming it. The program basically works by entering digits of the number into the list entries (notice L1(1)=123, L1(2)=456, etc...) and then running the program. It returns the answer in L1.
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Oooooh I get it now :D I didn't connect that what was on the homescreen was just a demonstration and not actual program XD Nice! How high have you tested it with?
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Oh, I see. I didn't notice L1 changed after running prgmADD :D
EDIT: 3001: Final Odyssey
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Ah ok. I gotcha. Didn't make the connection that what was in L1 was the number separated. I have no idea what this would be used for really though.
Just curious, but once you reassemble a number that is greater than fourteen digits won't it just round it anyways when it is displayed?
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Oooooh I get it now :D I didn't connect that what was on the homescreen was just a demonstration and not actual program XD Nice! How high have you tested it with?
Um, 123456789 :P
The principle is sound as long as the values in each cell don't exceed 14 digits. In theory, it can handle numbers up to 10^13986, which is 10^13786 times larger than a Googleplex. In short, feel free to enumerate all of the atoms in the universe in your calculator ;D
@Meishe, the number displayed is not the number stored. You can still recall L1(A) and get the proper answer, even if the display is truncated.
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Then, isn't the max 10^2997 because of the limit of the dimensions of a list?
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Nope. It's 10^(Precision of list elements*999)
Either way, it's insanely high. 10^2997 is still larger than all of the atoms in the universe.
EDIT: My respect is the answer to Life, the Universe, and Everything.
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Nope. It's 10^(Precision of list elements*999)
Either way, it's insanely high. 10^2997 is still larger than all of the atoms in the universe.
EDIT: My respect is the answer to Life, the Universe, and Everything.
Nah, it's a bit more.
But back to the topic, there's still a practical limit based on how much free RAM you have ;)
Still, this is a lot more accurate than the calculator usually holds, great for calculating large operations. Mind if I look in your code? :D
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Nope. Be prepared to cringe at my abuse of the DSC<( command, though.
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As long as it's not with labels I think I'd be fine :)
EDIT: Oh ... oh God...
EDIT2: Still pretty fast, so great job :D
EDIT3: Those are some awesome optimizations...
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Er...
>_>
<_<
EDIT: Optimizations? ???
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Er...
>_>
<_<
EDIT: Optimizations? ???
I mean the way you set it up. Coulda used some For(s, though ;)
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For( loops would have required that I update more variables than were necessary and I didn't want to destroy to many global variables when there are only 37 available. DSC<( loops were better in my opinion.
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Hmm, for
:Lbl 01
:L1(D)+L2(D→L1(D
:DS<(D,1
:Goto 01
why not just L1+L2→L1?
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No idea. It was like 1 AM when I wrote that :P
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Oh, and another huge optimization:
Instead of
:DelVar Bdim(L1→D
:dim(L2→E
:If D>E:Then
:L2→L3
:L1→L2
:0L2→L2
:dim(L3→B
:D→C
:Lbl 00
:L3(B→L2(C
:C-1→C
:DS<(B,1
:Goto 00
:End
just
:DelVar L3D-E→dim(L3
:augment(L3,L2→L2
Smaller and faster? :)
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/me facepalms
Thanks DThought
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Actually...
:dim(L1)-dim(L2
:If Ans
:not(binomcdf(Ans,0→L2
:L1+L2→L1
Destroys no variables. At all. And only 36 bytes :D
EDIT: I really miss programming BASIC now...
EDIT2: Edited to fix a bug. Now at 40 bytes.
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Can you show a screenshot of 15-digit precision?
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Sure. I'll post something later tonight when I build up an interface around this.
EDIT: DThought, Neither of our routines propagates the carry correctly. I'll fix it in the update.
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Hmm, you have something figured out already?
And yeah, forgot about the carry...
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(http://img.removedfromgame.com/imgs/ADD.gif)
The operation 31,415,926,535,897,932,384+115.
Both my program and wolfram alpha return 31,415,926,535,897,932,499 which is an odd number. TI-OS returns that the number is even.
I'm working on converting the answer back to a more easily readable string format, but that's not yet finished.
BTW: For the curious, yes, that is indeed pi*10^20.
EDIT: Also, to demonstrate carrying:
(http://img.removedfromgame.com/imgs/ADD2.gif)
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Once you get the string format done, this is going to rock! It does already, but still
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Thanks :)
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No offence but I'm still incredibly confused on what this does exactly ??? Could someone please explain?
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You have a number in L1, and a number in L2, the program merely does arithmetic on them. The difference is that since you are storing them in a List, you have an arbitrary amount of digits to work with. (123456789 would be stored as {123,456,789})
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Ah ok, that's what I thought but it sounded like Qwerty said that isn't what happened. What is the number in L2 for?
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That's the second operand. The program basically does this:
<Number in L1> + <Number in L2> ->L1
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Ah ok. Just curious, but why does there need to be an operation preformed? Couldn't you just take the number and store it?
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Um, the point of the program is to do arbitrary precision arithmetic. If it didn't perform arbitrary precision operations (+,-,*,/), it wouldn't need to exist.
EDIT: Finished the List-> String converter. It's slow, but I kind of had to abuse the math commands to get it to work at all because of the 7 digits per cell formatting.
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Ohhhh ok. Sorry, been quite tired. I got it now. I thought the point was just to be able to store arbitrarily large numbers.
And cool, do you mind posting the list to string converter?
Edit:
Is it something like:
{0,1→L3
"_→Str1
For(A,1,dim(L1
{0,L1(A→L4
LinReg(ax+b) L3,L4,Y1
Equ►String(Y1,Str2
Str1+sub(Str2,1,length(Str2)-3→Str1
End
sub(Ans,2,length(Ans)-1→Str1
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That's the general idea, although there's obviously some extra code to account for zero extensions.
EDIT: I accidentally my sentence.
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Ah ok. Ya, I would have incorporated that but I don't know how you are storing just zeros into one list element so wasn't sure what to do.
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Wait so it is always 7 digits or is it just uniform digits?
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It's always 7 digits per list element, although the user can enter as many or as few digits as they'd like (up to 6,993 digits per operand). The program itself handles all of the aligning. You just need to tell it what to operate on.
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Okay, so that program >_> It might be easier now... I thought it had to look for the longest string of numbers and make each element use that many digits :D
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It's always 7 digits per list element, although the user can enter as many or as few digits as they'd like (up to 6,993 digits per operand). The program itself handles all of the aligning. You just need to tell it what to operate on.
Hmm, why not 6? That shows up the best in the list editor.
But then since you're converting it to a string anyway, I guess it doesn't matter. You could use 12 for more data in fewer bytes :D
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You could use up to 13 if you really wanted to conserve space. ;)
I like the output as a String idea. :)
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Okay,
torture test demo time.
(http://img.removedfromgame.com/imgs/ADDdemo.gif)
Here's a pre-alpha version, using horrible coding techniques that I'll improve by the final version.
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Nice. :D
What are its current speeds? (Especially for multiplication and division)
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Added support for signed numbers and I'm working on decimals. It also eliminates the need for a a separate subtraction routine from the addition routine, as all I have to do for subtraction is set a flag variable in the addition routine.
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So, now can I haz RSA cracker on my calc? :P
Hey, it can handle numbers that large :P Nice work.
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So, now can I haz RSA cracker on my calc? :P
Hey, it can handle numbers that large :P Nice work.
Sure, if you don't mind 10 minutes a number <_<
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Only 10 minutes to factor the Nspire key? :P
More seriously, can't wait to see further features and speed increases. :D