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


Wow, it has been over a year since I last updated this thread. I followed up on that todo list a while ago, but I'm posting to announce a new addition to the library: 24-bit floats! I basically wrote all of these in the last 48 hours and I'm pretty burned-out:
https://github.com/Zeda/z80float/tree/master/f24

These floats are a fantastic balance of speed and usefulness on the Z80, and I think all of the routines fit into about 2500 bytes, so they are compact, too.