Necroedit: For a much better routine, please try the routines at the end of this post!

I created this last night for my next project:
PseudoRandWord:
;Outputs:
;     BC was the previous pseudorandom number
;     HL is the pseudorandom number
;f(n+1)=(241f(n)+257) mod 65536   ;65536
;181 cycles, add 17 if called
     ld hl,(randSeed)
     ld c,l
     ld b,h
     add hl,hl
     add hl,bc
     add hl,hl
     add hl,bc
     add hl,hl
     add hl,bc
     add hl,hl
     add hl,hl
     add hl,hl
     add hl,hl
     add hl,bc
     inc h
     inc hl
     ld (randSeed),hl
     ret
There are a few other nice features, too. For example, every 16-bit value is hit if you run this 65536 times. Or, if you only read 1 byte (for example, H from the output), it will hit every 8-bit number once if you run this 256 times. Plus, it can be seeded, which has its own uses. This can be modified to be smaller, too, if you know what you are doing, but I just like the numbers 241 and 257. Anyways, it produces some nice results

P.S.-I used this in a routine called "ShuffleDeck" and it works very well.

Wow, thisis really awesome ! This is a very impressive job!

Hmm, I am going to have to look into that, then Also, I have some more updates and bug fixes. Appparently when I went on an optmising spree, I broke a few things :[

dim(14) and dim(15) now have options for using 2-byte words
dim(124) was added for creating variables
dim(125) was added for executing inline Grammer code
dim(60) now allows you to archive or unarchive a var
dim(29) is fixed (before, it added 1 to the x-coordinate)
dim(29) now has two options for pixel testing rectangle regions

dim(56) and dim(62) have been fixed (pixel test results were broken)
dim(63) was fixed (similar issue)


I found a discrepancy in the compression routine that is now fixed. It sometimes lost data instead of being lossless.


EDIT: Oh! I almost forgot to mention that I made an example program for compressing/decompressing data. It can get great compression ratios depending on the data (I had a tilemap compress down to almost 11%). It is very easy to use, so I hope it can get used in some big projects !

It won't work with zStart because it requires a modification to the app header and zStart already uses that area. But yes, I have already asked Kerm about officially supporting GroupHook with DoorsCS7 and if it gets added, it will be able to work with Omnicalc, Grammer, and BatLib.

I finally got the motivation to rewrite BatLib, so I was working on it all this past week. I have good news and bad news. The good news will hopefully be awesome enough to outweigh the bad

Bad news: I cannot figure out how to make weird names with Brass, so this update uses BatLib with regular letters. Also, I have change the syntax of some ReCode commands and I have yet to document the changes (also, I think I still need to code in 8 more commands).

Awesome news:
I have added in all the other 104 commands as well as 19 more commands. I have updated almost everything, so a bunch of the commands are now more powerful (and still backwards compatible). All the bugs or issues that I could find are now fixed and I have yet to find bugs, now. Here are some changes:

• dim(1) was used to disable Done and turn the run indicator off. Now you can use a digit after the 1 to fine tune that. For example, dim(1.1) does something different from dim(1) or dim(1.2), but all deal with the run indicator and Done message.
• dim(29) now draws rectangles with clipping.
• Which reminds me that negative numbers are now read properly. Before, BatLib just used the absolute value of inputs
• dim(41) now allows the input of all variable types and works just fine with lists and named lists. It also has an otional argument that will let you get the size of a variable as it apears in the memory menu. Before, it just returned the size of the data portion of a var.
• dim(52) and dim(53) now let you draw sprites to pixel coordinates using an otional argument. I finally fixed this all up yesterday and this works with larger srites, too.
• dim(54) now returns the number of lines in the var if you try to read line 0
• dim(59) Now can convert from any base 1 to 36 into any other base 2 to 36. Numbers can even be a few hundred digits long!
• dim(64) (which is Copyprog) now works. The issue was super simple, too, so I wish I had figured it out earlier.
• dim(46) (portedit) now works!
• dim(85) (Getprogname) now works completely and flawlessly

Now for the new commands!

• dim(105) (pxlLine) draws a line with pixel coordinates. There are also draw modes where you supply a list as a draw pattern
• dim(106) draws a circle very quickly using pixel coordinates. There is also a mode for using draw patterns
• dim(107) draws a pxlline to a variable (like a pic var)
• dim(108) draws a pxlcircle to a var
• dim(109) can be used to open up a popup menu. Selecting an otion returns a number.
• dim(110) can be used to convert a number to a string. This does not work with imaginary numbers.
• dim(111) converts a list to a string. This works with imaginary numbers
• dim(112) compresses a string of text. There are two built in codecs.
• dim(113) decompresses a string of compressed text.
• dim(114) will return an optimal codec string for a string of data.
• dim(115) will compress data with a custom codec.
• dim(116) will decompress data with a custom codec.
• dim(117) will perform a search and replace, scanning a variable.
• dim(118) will work like my GetName program. It returns, in alphabetical order, the name of a variable of a given type. For examle, this can be used to get the name of the third program in the program list.
• dim(119) provides lowercase options.
• dim(120) provides text options
• dim(121) and dim(122) are options to draw a sprite to a variable (like a pic var)
• dim(123) will delete a line from a data base

Also, in this release is a beta/test version of BatLib that will be able to use a revolutionary new "GroupHook" that I came up with. Since no other apps have it, I had to perform some modifications to existing apps for demonstration. Basically, I managed to make it so that when I installed BatLibG, I could use the parser hooks in Celtic 3, Omnicalc, and Grammer, too without installing them. Celtic 3 and Omnicalc did conflict with the real( commands, though. I managed to modify DoorsCS7, too, and I could use Celtic 3 and DSC commands, too, but I will not release the modified DCS7 because I haven't talked to Kerm about it.

Finally, I could not send the as to my actual calc (I need to get new batteries), so I could not check if there were any issues on calc that didn't occur in WabbitEmu.

Hehe, thanks It isn't done yet, though I have been working on this on and off for over a year and it will probably still take a while to finish it. I have too many other projects and IRL things (like school and work), unfortunately Still, I hope it turns out to be as awesome as I plan I am basing most of the work on an older game that was called "Battle 3.2.3.5" that I wrote in TI-BASIC. I lost the program years ago, but it had cool features like a blacksmith, creatures, different maps, over 70 items, a lottery and other such things. When I ported it to Omnicalc and xLIB/Celtic III, I never really finished the port.

EDIT: Also, as a note, this program currently use 8312 bytes which is cool

prgmITEMS    1567 bytes   ;all the item data inlcuding names, description, and code for what it does.
prgmWALK     3642 bytes   ;the main program that will eventually be renamed
appvMapA     2513 bytes   ;the first 50x50 map
appvSamoSave  316 bytes   ;the quick-save file. In the future, there will be an appvar containg several save files. This will be in archive.
appvTiles     274 bytes   ;the tile data

First, let me clarify that I am working solely with positive integers (natural numbers).
These proofs are not very formal, sorry. Typing them is a bit more tedious than writing them on paper

Theorem: All integers except those of the form 4n+2 are the difference of two squares.
Proof:
Here, I will simply show by cases.
Let A be odd, B be even. That is, A=2n+1, B=2m. Then:

• A²-B²=
  
• (2n+1)²-(2m)²=
  
• 4n²+4n+1-4m²=
  
• 4(n²+n-m²)+1=
  
• 4l+1

Now, let A be even, B be odd. That is, A=2n, B=2m+1. Then:

• A²-B²=
  
• (2n)²-(2m+1)²=
  
• 4n²-4m²-4m-1=
  
• 4(n²-m²-m)-1=
  
• 4k-1=
• 4(k-1)+3=
• 4l+3=

If both are even, you have:

• A²-B²=
  
• (2n)²-(2m)²=
  
• 4n²-4m²=
  
• 4(n²-m²)=
  
• 4l

If both are odd, you have:

• A²-B²=
  
• (2n+1)²-(2m+1)²=
  
• 4n²+4n+1-4m²-4m-1=
  
• 4(n²+n-m²-n)+1-1=
  
• 4l

[qed]

These are all the possible case, so you can have 4l,4l+1,and 4l+3 as the difference of two squares.

As a very simple proof that all odd integers can be the difference of two squares, just plug in the trivial solution (c+1)/2 and (c-1)/2 for A and B respectivels. Since c is odd, c+1 and c-1 are even, so you can divide by two. For a process to arrive to this conclusion, forst note that the difference of two consecutive squares is odd. That is:
(n+1)²-n²=n²+2n+1-n²=2n+1

So if you want to find, say, 23 as the difference of squares, 23=2n+1 means n=11. So 12²-11²=23. The powerful result of the math hack I presented says that because 23 is prime, this is the only solution.

Theorem: If c is composite and odd, then there is a non-trivial solution for A²-B²=c.
Proof:
Let c be composite. That is, let c=n*m where n and m are neither 1. Since A²-B²=(A-B)(A+B), let n=(A-B) and m=(A+B). Then:

n+2B=A+B
n+2B=m
2B=n-m
B=(n-m)/2      ;since c is odd, n and m are odd, so n-m is even.
A=(n+m)/2      ;This, too, is an integer.
[qed]

Theorem: If c is an odd prime, then the non-trivial solution for A²-B²=c is the only solution.
Proof:
Assume there is a non trivial solution for A and B, A=D, B=E. This implies that (D-E) and (D+E) are factors of c. Since c is prime, the only factors are 1 and c. Therefore, (D-E)=1, (D+E)=c. This means:

D+E=1+2E, D+E=c
1+2E=c
E=(c-1)/2
D=(c+1)/2

However, this is the trivial solution, so we have met a contradiction. Therefore, the trivial solution is the only solution
[qed]

EDIT: I opened up my notes and followed through some of my work and what I have found so far:
If there is a non-trivial solution for A²-B²=c, then it is of the form (A+2d)²-(B-4e)² where d and e are integers. This will let me speed up my code as I can forget about half or 3/4 of the potential values. I am still working on cutting that down even more :)

Hehe, I still plan to get back to work on this some day. I want to rewrite it to add more commands and add in some more optimisations. I still plan to add in arbitrary precision math commands, too. I have written a multiplication routine that is only limited by the amount of RAM you have. I made it multiply two 100-digit numbers