x-post

I have been focusing on the single-precision floats this past week or so. I rewrote or re-worked a lot of routines. I got rid of most of the tables by switching to a polynomial approximation for the 2^x routine (thanks to the Sollya program!) and using the B-G algorithm to compute lnSingle. It turned out to be faster this way, anyways.

I implemented sine, cosine, and tangent, the first  two, again, using minimax polynomial approximation. I optimized the square-root routine (much faster but a few bytes bigger). I re-implemented the B-G algorithm using math optimizations I came up with a few months ago. I opted for two B-G implementations-- one for lnSingle which requires only 1 iteration for single precision, and one for the inverse trig and hyperbolic functions which needs 2 iterations. For anybody looking to save on size, you can just use the second B-G routine for natural logarithm. It will be a little slower, but it'll work just fine (maybe even give you an extra half-bit of precision ).

I included the Python program that I use for converting numbers to my single precision format. You can use it to convert a single float or a bunch of them. I also included a Python tool I made for computing more efficient coefficients in the B-G algorithm, but that'll only be useful to me and maybe a handful of other people. It's there on the off chance somebody stumbles across my project looking for a B-G implementation.


The single precision floats are largely complete in that I can't think of any other functions that I want to add. There is still work to be done on range reduction and verification, as well as bug fixes and more extensive testing.

Here is a current screenshot of some of the routines and their outputs:


The current list of single-precision routines:
Basic arithmetic:
  absSingle     |x| -> z       Computes the absolute value
  addSingle     x+y -> z
  ameanSingle   (x+y)/2 -> z.  Arithmetic mean of two numbers.
  cmpSingle     cmp(x,y)       Compare two numbers. Output is in the flags register!
  rsubSingle    y-x -> z
  subSingle     x-y -> z
  divSingle     x/y -> z
  invSingle     1/x -> z
  mulSingle     x*y -> z
  negSingle     -x  -> z
  sqrtSingle    sqrt(x*y) -> z
  geomeanSingle sqrt(x*y) -> z

Logs, Exponentials, Powers
  expSingle    e^x -> z
  pow2Single   2^x -> z
  pow10Single  10^x-> z
  powSingle    y^x -> z
  lgSingle     log2(x)  -> z
  lnSingle     ln(x)    -> z
  log10Single  log10(x) -> z
  logSingle    log_y(x) -> z

Trig, Hyperbolic, and their Inverses
  acoshSingle   acosh(x) -> z
  acosSingle    acos(x)  -> z
  asinhSingle   asinh(x) -> z
  asinSingle    asin(x)  -> z
  atanhSingle   atanh(x) -> z
  atanSingle    atan(x)  -> z
  coshSingle    cosh(x)  -> z
  cosSingle     cos(x)   -> z
  sinhSingle    sinh(x)  -> z
  sinSingle     sin(x)   -> z
  tanhSingle    tanh(x)  -> z
  tanSingle     tan(x)   -> z

Special-Purpose    Used by various internal functions, or optimized for special cases
  bg2iSingle     1/BG(x,y) -> z   Fewer iterations, but enough to be suitable for ln(x). Kind of a special-purpose routine
  bgiSingle      1/BG(x,y) -> z   More iterations, general-purpose, needed for the inverse trig and hyperbolics
  div255Single   x/255 -> z
  div85Single    x/85  -> z
  div51Single    x/51  -> z
  div17Single    x/17  -> z
  div15Single    x/15  -> z
  div5Single     x/5   -> z
  div3Single     x/3   -> z
  mul10Single    x*10  -> z
  mulSingle_p375         x*0.375  -> z      Used in bg2iSingle.  x*(3/8)
  mulSingle_p34375       x*0.34375-> z      Used in bgiSingle.   x*(11/32)
  mulSingle_p041015625   x*0.041015625-> z  Used in bgiSingle.   x*(21/512)

Miscellaneous and Utility
  randSingle    rand   -> z
  single2str    str(x) -> z           Convert a single to a null-terminated string, with formatting
  single2TI     tifloat(x) -> z       Converts a single to a TI-float. Useful for interacting with the TI-OS
  ti2single     single(tifloat x)->z  Converts a TI-float to a single. Useful for interacting with the TI-OS
  single2char   Honestly, I forgot what it does, but I use it in some string routines. probably converts to a uint8
  pushpop       pushes the main registers to the stack and sets up a routine so that when your code exits, it restores registers. Replaces manually surrounding code with push...pop


So I added in addition/subtraction and float->str. I haven't calculated timing for the add/sub, or float->str, but I would guess about 1500cc and 90000cc are reasonable guesses. The conversion introduces error in the last digits, so I should only return about 16 digits. At the moment, the only formatting that truncates to 16 digits max is when the exponent is too high in magnitude (ex. 1.234567890123456e-9).

Anyways, you can git the source on GitHub, but here are some ugly screenshots attached with evident rounding issues


EDIT: It turns out I computed the 10^-(2^k) table with lower precision. Now that it is fixed, numbers are being displayed with a bit better precision. I am currently working on implementing the B-G algorithm.

One quick thing I notice is that in the APD routine, you halt, but interrupts aren't enabled. As well, it looks like registers will get clobbered.
I'm too lazy to check at the moment, but try this modification:
APD:
 ld hl, (APDCounter)
 dec hl
 ld a, h
 or l
 ld (APDCounter), hl
 ret nz
 ld hl, 1800
 ld (APDCounter), hl
 xor a
 out (30h), a
 ld a, 1
 out (03h), a
 exx
 ex af,af'
 ei
 halt
 exx
 ex af,af'
 xor a
 out (03h), a
 jq initialize


Cool, I'm glad you figured it out!

Okay, added screenshots, thanks!

If you are a masochist, then technically no, as you can type in the hexadecimal opcodes directly on your calc. For everyone else, you can use a program that compiles a text file to a binary. The calculators have two main compilers -- Mimas and asmdream (I'm on mobile, otherwise I would look for the links). On a computer, I prefer spasm-ng, but there is Brass as well.
Personally, I jusy use a text editor, save my file with the .asm or .z80 extension (not really important) and then compile that to a .8xp

I'm too tired for a full report, but I'll use this as a backup.
I fixed a few bugs introduced in the last version, optimized and cleaned up some more code, and most importantly, I totally overhauled the module system. I renamed the token to just '$'. By storing to it, you can basically register a module to be searched after the default one is searched. At the moment, up to 5 additional modules can be used, which could greatly extend the functionality of Grammer. They can be archived now, and I moved the Menu routine to an external module (appv Grampkg). I still need to do a lot of documentation, but not tonight. Attached is a screenshot of what the code looks like (with the token hook). Good night y'all.

Oh, nice work! I wish I knew the HP Prime better so that I could offer some real input