A variant of the fast signed multiply by Steve Judd & George Taylor from the c=hacking9.txt fanzine
> Ah, now here is something we can fix. Consider the following function:
>
> f(x) = x*x/4
>
> Now notice that
>
> f(a+b) - f(a-b) = a*b
>
> So here is the code to multiply two numbers together:
>
> * A*Y -> A Signed, 8-bit result
>
> STA ZP1 ;ZP1 -- zero page pointer to table of g(x)
> EOR #$FF
> CLC
> ADC #$01
> STA ZP2 ;ZP2 also points to g(x)
> LDA (ZP1),Y ;g(Y+A)
> SEC
> SBC (ZP2),Y ;g(Y-A)
Here is the computation we will perform on the Commodore 64 (well, should actually work on any 6502 processor):
Given A in [0..255] and B in [1..255]
mul(A, B) = int(A*B/16) % 256
Note that the results seem more stable when computing int(A*B)
rather tan round(A*B). Both should be usable though.
We can't use B=0; Results are incorrect (see multiply_tables.py)
Results are accurate +/-1 % 256 with the following distribution:
- err=0 38656
- err=1 26624
Compile / Assemble code for C64
$ make -r
Run binaries in VICE
$ x64sc -autostartprgmode 1 test_fast_multiply
or
$ x64sc -autostartprgmode 1 verify_multiply_tables
Run the Python reference
$ ./multiply_tables.py
Clean everything
$ make clean