FORTH for the PC-G850(V)(S)

[robve]

I've written new IEEE 754 floating point routines from scratch in Z80 for Forth850. I wasn't happy with the Z80 floating point libraries I found on GitHub and elsewhere, which appear to have sizable code bases and are heavy on memory access and use. The new Z80 floating point routines I wrote operate with Z80 registers only, including the shadow registers, except for a one push-pop pair to pass a value from a shadow register pair to a register pair. The shadow registers are available for use with the PC-G850 (i.e. not used by interrupts). So let's put them to work.

The new math.asm Z80 library:

• IEEE 754 single precision floating point addition, subtraction, negation, multiplication, division, integer <-> float conversion, string <-> float conversion
• "memoryless" using registers only (+shadow), at most one push+pop per flop
• optimized for speed and reduced code size (no loop unrolling)
• extensively tested
  

But lacks (at this time):

• no INF/NAN values; routines return error condition (cf set)
• truncated 24 bit mantissa instead of IEEE 754 unbiased "banker's rounding" (floating point string parsing and output use rounding)
  

I may extend the library to support INF/NAN and banker's rounding to make it compliant with IEEE 754. Right now, the only observable difference is the rounding (lack thereof). Consistency of the numerical treatment is important.

The Forth code for the Sine plot shown in the picture:

Code:

3.14159265E0 2CONSTANT PI
PI 72E0 F/ 2VALUE SCALE \ free to change e.g.: PI 144E0 F/ TO SCALE
: SINE
  PAGE
  144 0 DO
    I DUP S>D D>F SCALE F*
    FSIN 24E0 F*
    F>D D>S 24 + POINT
  LOOP
  GETKEY DROP ;

Trig functions in Forth:

Code:

: FSIN  ( r1 -- r2 ) \ only valid for -2pi <= r1 <= 2pi
  2DUP 2DUP 2DUP F* FNEGATE
  2ROT 2ROT
  15 2 DO
    5 PICK 5 PICK
    F* I I 1+ *
    S>D D>F F/
    2DUP 2ROT F+ 2SWAP
  2 +LOOP
  2DROP 2SWAP 2DROP ;
: FCOS  ( r1 -- r2 ) 1.5707962E0 2SWAP F- FSIN ;
: FTAN  ( r1 -- r2 ) 2DUP FSIN 2SWAP FCOS F/ ;

I've updated the forth850-full version with the new features. The binary is about 10K, so there is plenty of space left on the machine. I've tested the implementation extensively and will continue to do so in the near future.

- Rob