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I'm still learning how to work with GitHub/git, but you can help or access the code for this project here.

The library of "single precision" floats (they don't conform to IEEE standards Sad ) needs a lot of work using my newer knowledge. However, it does have abs, add, sub, rsub, negate, arithmetic mean, square root, geometric mean, Borschardt-Gauss, compare, 1/x, division, multiplication, e^x, 2^x, 10^x, x^y, ln(x), log2(x), log10(x), log_y(x), atanh, acosh, asinh, atan, asin, acos, rand, float→TI float, float→str, str→float.

The extended precision floats (15-bit exponent, 64-bit mantissa) are not as compete yet, but I have implemented: add, sub, rsub, arithmetic mean, multiplication, division, square roots, geometric mean, Borschardt-Gauss, acos, asin, atan, acosh, asinh, atanh, ln(x), and float→str.

I am particularly proud of the fact that square roots average under 6600cc, about 13 times faster than TI's (and to about 5 digits more precision).

Later when I am home I'll come up with screen shots. I hope these are useful ! There is a lot more work to be done. Maybe even make eZ80 versions ! This has been kind of exhausting, honestly.
EDIT: Screenshot:

For 64-bit floats, results are only good to about 19 digits, though 20 digits are displayed. With that in mind, the biggest error is less than half a digit so I'm calling it rounding error, both of the inputs (constants are only stored to 64 bits precision) and during intermediate calculations. Razz

EDIT: 14 Jan 2019
Here is a screenshot of some of the single-precision routines!
Fantastic work as always Xeda!

Will you be incorporating this library into KnightOS?
As awesome as that would be, I don't think I'm up to that task. If somebody else wants to, I encourage it!
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 Razz).

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
For the extended-precision floats, I added:


xcmp     for comparing two numbers
xneg     -x -> z
xabs     |x|-> z
xinv     1/x -> z   Observed a bug in 1/pi !
xpow     x^y -> z
xpow2    2^x
xpow10   10^x
xlog     log_y(x)   It's failing miserably
xlg      log2(x)
xlog10   log10(x)   Observed a bug in log10(pi)

I made the str->single routine better (it had been quickly thrown together and failed on many/most cases due to lost precision). Now it appears that digits get swapped in some cases! Sad I have to look into this.

To Do:
Look into the string->single routine and figure out what is wrong
I still have to look into the bugs observed in the single-precision Mandelbrot set program
Look into the errors in xinv, xlog, and xlog10 (these might all be related, or maybe I accidentally a byte in the built-in constants).
Have to make xsin, xcos, xtan, xsinh, xcosh, xtanh, xtoTI (x-float to TI float), TItox (TI float to x-float), and strtox (string --> x-float).
For all of the trig routines, I still need to apply range-reduction Neutral

Once these are done, it's just finding and fixing bugs and optimizing, and the project is as complete as what I wanted to do. BCD floats were a cute idea, but I'm a bit more realistic now Razz Maybe I'll be motivated to add in stuff like gamma / log-gamma ?
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