The Boston Diaries

The ongoing saga of a programmer who doesn't live in Boston, nor does he even like Boston, but yet named his weblog/journal “The Boston Diaries.”

Go figure.

Tuesday, October 01, 2024

“What were the skies like when you were young?” was not asked by LeVar Burton

I always thought that the opening question in the song “Little Fluffy Clouds” by the Orb (music video) was a sample of LeVar Burton, maybe from his show “Reading Rainbow, but apparently, it's not! (link via Jason Kottke) Upon relistening to the song, it's now clear to me that it's not Levar Burton. It's very close though.

And while I like the song, my favorite one from The Orb is “A Huge Ever Growing Pulsating Brain That Rules from the Centre of the Ultraworld,” which is like a fever dream but in a good way [You're insane! —Bunny] [Yes, but in a good way! —Sean].

Sunday, October 13, 2024

A benchmark of three different floating point packages for the 6809

I recently came across another floating point package for the 6809 (written by Lennart Benschop) and I wanted to see how it stacked up against IEEE-754 and BASIC floating point math. To do this, I wanted to add support to my 6809 assembler, but it required some work. There was no support to switch floating point formats—if you picked the rsdos output format, you got the Microsoft floating point, and for the other output formats, you got IEEE-754 support.

The other issue, the format used by the new floating point package I found is ever-so-slightly different from the Microsoft format. It's just a single bit difference—Microsoft uses an exponential bias of 129, whereas this package uses a bias of 128 (and why do floating point packages use an exponential bias? I'm not entirely sure why). But other than this one small difference, they are basially the same.

It turned out not to be that hard to support all three floating point formats. The output formats still select a default format like before, but now, you can use the .OPT directive to select the floating point formats:

	.opt	* real ieee
	.float	3.14159265358979323846
	.opt	* real msfp
	.float	3.14159265358979323846
	.opt	* real lbfp
	.float	3.14159265358979323846

And you get three different formats as output:

                         | FILE p.asm
                       1 |                 .opt    * real ieee
0000: 40490FDB         2 |                 .float  3.14159265358979323846
                       3 |                 .opt    * real msfp
0004: 82490FDAA2       4 |                 .float  3.14159265358979323846
                       5 |                 .opt    * real lbfp
0009: 81490FDAA2       6 |                 .float  3.14159265358979323846

I added some code to my floating point benchmark program, which now uses all three formats to calculate -2π3/3! and times each one. The new code:

        .opt    * real lbfp
        .tron   timing
lb_fp           ldu     #lb_fp.fpstack
                ldx     #.tau
                jsr     fplod   ; t0 = .tau
                ldx     #.tau
                jsr     fplod   ; t1 = .tau
                jsr     fpmul   ; t2 = .t0 * t1
                ldx     #.tau
                jsr     fplod   ; t3 = .tau
                jsr     fpmul   ; t4 = .t2 * t3
                ldx     #.fact3
                jsr     fplod
                jsr     fpdiv
                jsr     fpneg
                ldx     #.answer
                jsr     fpsto
        .troff
		rts

.tau            .float  6.283185307
.fact3          .float  3!
.answer         .float  0
                .float  -(6.283185307 ** 3 / 3!)

.fpstack        rmb     4 * 10

The results are interesting (the IEEE-754 results are from the same package which support both single and double formats):

Benchmark of three floating point packages for the 6809
format cycles instructions
Microsoft 8752 2124
Lennart 7465 1326
IEEE-754 single 14204 2932
IEEE-754 double 31613 6865

The new code is the fastest so far. I think the reason it's faster than Microsoft's is (I think) because Microsoft uses a single codebase for all their various BASIC interpreters, so it's not really “written in 6809 assembler” as much as it is “written in 8080 assembler and semi-automatically converted to 6809 assembly,” which explains why Microsoft BASIC was so ubiquitous for 80s machines.

It's also smaller than the IEEE-754 package, a bit over 2K vs. the 8K for the IEEE-754 package. It's hard to tell how much bigger it is than Microsoft's, because Microsoft's is buried inside a BASIC interpreter, but it wouldn't surprise me it's smaller given the number of instructions executed.


Discussions about this entry


Unit testing from inside an assembler, part IV

I'm not terribly happy with how running unit tests inside my assembler work. I mean, it works, as in, it tests the code and show problems during the assembly phase, but I don't like how you write the tests in the first place. Here's one of the tests I added to my maze generation program (and the routine it tests):

getpixel        bsr     point_addr      ; get video address
                comb                    ; reverse mask (since we're reading
                stb     ,-s             ; the screen, not writing it)
                ldb     ,x              ; get video data
                andb    ,s+             ; mask off the pixel
                tsta                    ; any shift?
                beq     .done
.rotate         lsrb                    ; shift color bits
                deca
                bne     .rotate
.done           rts                     ; return color in B

        .test
	.opt	test	pokew	ECB.beggrp , $0E00
        .opt    test    poke    $0E00 , %11_11_11_11
                lda     #0
                ldb     #0
                bsr     getpixel
        .assert /d = 3
        .assert /x = @@ECB.beggrp
                lda     #1
                ldb     #0
                bsr     getpixel
        .assert /d = 3
        .assert /x = @@ECB.beggrp
                lda     #2
                ldb     #0
                bsr     getpixel
        .assert /d = 3
        .assert /x = @@ECB.beggrp
                lda     #3
                ldb     #0
                bsr     getpixel
        .assert /d = 3
        .assert /x = @@ECB.beggrp
                rts
        .endtst

The problem is the machine code for the test is included in the final binary output, which is bad because I can't just set an option to run the tests in addition to assembling the code into its final output, which I don't want (and that means when I use the test backend, I tend to generate the output to /dev/null). I've also found that I prefer table-style tests to writing code (for reasons way beyond the scope of this entry). For example, for a C function like this:

int max_monthday(int year,int month)
{
  static int const days[] = { 31,0,31,30,31,30,31,31,30,31,30,31 } ;
  
  assert(year  > 1969);
  assert(month >    0);
  assert(month <   13);
  
  if (month == 2)
  {
    /*----------------------------------------------------------------------
    ; in case you didn't know, leap years are those years that are divisible
    ; by 4, except if it's divisible by 100, then it's not, unless it's
    ; divisible by 400, then it is.  1800 and 1900 were NOT leap years, but
    ; 2000 is.
    ;----------------------------------------------------------------------*/
    
    if ((year % 400) == 0) return 29;
    if ((year % 100) == 0) return 28;
    if ((year %   4) == 0) return 29;
    return 28;
  }
  else
    return days[month - 1];
}

I would prefer to write test code like:

Test code for max_monthday()
output year month
28 1900 2
29 2000 2
28 2100 2
29 1904 2
29 2104 2
28 2001 2

Just specify the inputs and outputs for some corner cases, and let the computer do what is necessary to call the function in question.

But it's not so easy with assembly language, given the large number of ways to pass data into a function, and the number of output results one can have. How would I specify that the inputs come in registers A and B, and the outputs come in A, B and X? The above could be done in a table format, I guess. It might not be pretty, but it's doable.

Then there's these subroutines and their associated tests:

;***********************************************************************
;       RND4            Generate a random number 0 .. 3
;Entry: none
;Exit:  B - random number
;***********************************************************************

rnd4            dec     rnd4.cnt        ; any more cached random #s?
                bpl     .cached         ; yes, get next cached number
                ldb     #3              ; else reset count
                stb     rnd4.cnt
                bsr     random          ; get random number
                stb     rnd4.cache      ; save in the cache
                bra     .ret            ; and return the first number
.cached         ldb     rnd4.cache      ; get cached value
                lsrb                    ; get next 2-bit random number
                lsrb
                stb     rnd4.cache      ; save ermaining bits
.ret            andb    #3              ; mask off our result
                rts

;***********************************************************************
;       RANDOM          Generate a random number
;Entry: none
;Exit:  B - random number (1 - 255)
;***********************************************************************

random          ldb     lfsr
                andb    #1
                negb
                andb    #$B4
                stb     ,-s             ; lsb = -(lfsr & 1) & taps
                ldb     lfsr
                lsrb                    ; lfsr >>= 1
                eorb    ,s+             ; lfsr ^=  lsb
                stb     lfsr
                rts

        .test
                ldx     #.result_array
                clra
                clrb
.setmem         sta     ,x+
                decb
                bne     .setmem
                ldx     #.result_array + 128
                lda     #1
                sta     lfsr
                lda     #255
.loop           bsr     random
        .assert /b <> 0         , "degenerate LFSR"
        .assert @/b,x = 0       , "non-repeating LFSR"
                inc     b,x
                deca
                bne     .loop

                clr     ,x
                clr     1,x
                clr     2,x
                clr     3,x
                lda     #255
.chk4           bsr     rnd4
        .assert /b >= 0
        .assert /b <= 3
                inc     b,x
                deca
                bne     .chk4
        .tron
                ldb     ,x      ; to check the spread
                ldb     1,x     ; of results, basically
                ldb     2,x     ; these should be roughly
                ldb     3,x     ; 1/4 of 256
        .troff
        .assert @/,x + @/1,x + @/2,x + @/3,x = 255
                rts
.result_array   rmb     256
        .endtst

        .test   "whole program"
        .opt    test    pokew   $A000 , KEYIN
        .opt    test    pokew   $FFFE , END
        .opt    test    prot    r,$A000,$A001

                lbsr    start
KEYIN           lda     #'Q'
END             rts

        .endtst

And … just uhg. I mean, this checks that the 8-bit LFSR I'm using to generate random numbers actually doesn't repeat within it's 255-period cycle, and that the number of 2-bit random numbers I generate from RND4 is more or less evenly spread, and for both of those, I use an array to store the intermediate results. I leary about including an interpreter just for the tests, because I don't think it would be any better. At least the test code is largely written in the target language of 6809 assembly.

Then again, I could embed Lua, and write the tests like:

	.test
		local array = {}
		for i = 0 , 255 do array[i] = 0 end

		mem['lfsr'] = 1
		for i = 0 , 255 do
		  call 'random'
		  assert(cpu.B ~= 0)
		  assert(array[cpu.B] == 0)
		  array[cpu.B] = 1
		end

		array[0] = 0
		array[1] = 0
		array[2] = 0
		array[3] = 0

		for i = 0 , 255 do
		  call 'rnd4'
		  assert(cpu.B >= 0)
		  assert(cpu.B <= 3)
		  array[cpu.B] = array[cpu.B] + 1
		end

		assert(array[0] + array[1] + array[2] + array[3] == 255)
	.endtst

I suppose? I would still need to somehow code the fake KEYIN and END routines required for the test. And the first test at the start of this post would then look like:

	.test
		memw['ECB.beggrp'] = 0x0E00
		mem[0x0E00] = '%11_11_11_11'
		cpu.A = 0
		cpu.B = 0
		call 'getpixel'
		assert(cpu.D == 3)
		assert(cpu.X == memw['ECB.beggrp'])
		cpu.A = 1
		cpu.B = 0
		call 'getpixel'
		assert(cpu.D == 3)
		assert(cpu.X == memw['ECB.beggrp'])
		cpu.A = 2
		cpu.B = 0
		call 'getpixel'
		assert(cpu.D == 3)
		assert(cpu.X == memw['ECB.beggrp'])
		cpu.A = 3
		cpu.B = 0
		call 'getpixel'
		assert(cpu.D == 3)
		assert(cpu.X == memw['ECB.beggrp'])
	.endtst

which isn't any longer than the original test, but still … uhg. But doing this means I won't have 6809 code for testing in the final output, which means I could run tests with any backend.

I'll have to think on this.

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