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233
mandel.s
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@ -1,42 +1,43 @@
; Our zero-page vars ; Our zero-page vars
ox = $80 ; fixed8.24: center point x sx = $80 ; i16: screen pixel x
oy = $84 ; fixed8.24: center point y sy = $82 ; i16: screen pixel y
cx = $88 ; fixed8.24: c_x ox = $84 ; fixed4.12: center point x
cy = $8c ; fixed8.24: c_y oy = $86 ; fixed4.12: center point y
cx = $88 ; fixed4.12: c_x
cy = $8a ; fixed4.12: c_y
zx = $8c ; fixed4.12: z_x
zy = $8e ; fixed4.12: z_y
zx = $90 ; fixed8.24: z_x zx_2 = $90 ; fixed4.12: z_x^2
zy = $94 ; fixed8.24: z_y zy_2 = $92 ; fixed4.12: z_y^2
zx_2 = $98 ; fixed8.24: z_x^2 zx_zy = $94 ; fixed4.12: z_x * z_y
zy_2 = $9c ; fixed8.24: z_y^2 dist = $96 ; fixed4.12: z_x^2 + z_y^2
zx_zy = $a0 ; fixed8.24: z_x * z_y iter = $a0 ; u8: iteration count
dist = $a4 ; fixed8.24: z_x^2 + z_y^2
sx = $a8 ; i16: screen pixel x
sy = $aa ; i16: screen pixel y
z_buffer_active = $ac ; boolean: 1 if we triggered the lake, 0 if not
z_buffer_start = $ad ; u8: index into z_buffer
z_buffer_end = $ae ; u8: index into z_buffer
iter = $af ; u8: iteration count
ptr = $b0 ; u16 zoom = $a1 ; u8: zoom shift level
pixel_ptr = $b2 ; u16 count_frames = $a2 ; u8
zoom = $b4 ; u8: zoom shift level count_pixels = $a3 ; u8
fill_level = $b5 ; u8 total_ms = $a4 ; float48
pixel_color = $b6 ; u8 total_pixels = $aa ; float48
pixel_mask = $b7 ; u8
pixel_shift = $b8 ; u8
pixel_offset = $b9 ; u8
palette_offset = $ba ; u8
chroma_offset = $bb ; u8
palette_ticks = $bc ; u8
chroma_ticks = $bd ; u8
count_frames = $be ; u8
count_pixels = $bf ; u8
total_pixels = $c0 ; float48 z_buffer_active = $b0 ; boolean: 1 if we triggered the lake, 0 if not
total_ms = $c6 ; float48 z_buffer_start = $b1 ; u8: index into z_buffer
temp = $cc ; u16 z_buffer_end = $b2 ; u8: index into z_buffer
temp2 = $ce ; u16 temp = $b4 ; u16
temp2 = $b6 ; u16
pixel_ptr = $b8 ; u16
pixel_color = $ba ; u8
pixel_mask = $bb ; u8
pixel_shift = $bc ; u8
pixel_offset = $bd ; u8
fill_level = $be ; u8
palette_offset = $bf ; u8
palette_ticks = $c0 ; u8
chroma_ticks = $c1 ; u8
chroma_offset = $c2 ; u8
ptr = $c4 ; u16
palette_delay = 23 palette_delay = 23
chroma_delay = 137 chroma_delay = 137
@ -292,16 +293,16 @@ viewport_zoom:
.byte 6 .byte 6
viewport_ox: viewport_ox:
.dword $00000000 .word $0000
.dword $ff110000 .word $f110
.dword $ff110000 .word $f110
.dword $fe400000 .word $e400
viewport_oy: viewport_oy:
.dword $00000000 .word $0000
.dword $ffb60000 .word $fb60
.dword $ffbe0000 .word $fbe0
.dword $00000000 .word $0000
; 2 + 9 * byte cycles ; 2 + 9 * byte cycles
.macro add bytes, dest, arg1, arg2 .macro add bytes, dest, arg1, arg2
@ -320,7 +321,7 @@ viewport_oy:
; 38 cycles ; 38 cycles
.macro add32 dest, arg1, arg2 .macro add32 dest, arg1, arg2
add 4, dest, arg1, arg2 add 4, dest, arg2, dest
.endmacro .endmacro
; 8 cycles ; 8 cycles
@ -425,25 +426,22 @@ viewport_oy:
round16 arg ; 11-27 cycles round16 arg ; 11-27 cycles
.endmacro .endmacro
; input: arg1, arg2 as fixed4.12 .macro imul16_round dest, arg1, arg2, shift
; output: dest as fixed8.24
.macro imul16 dest, arg1, arg2
copy16 FR0, arg1 ; 12 cyc copy16 FR0, arg1 ; 12 cyc
copy16 FR1, arg2 ; 12 cyc copy16 FR1, arg2 ; 12 cyc
jsr imul16_func ; ? cyc jsr imul16_func ; ? cyc
copy32 dest, FR2 ; 24 cyc shift_round_16 FR2, shift ; 103-119 cycles for shift=4
copy16 dest, FR2 + 2 ; 12 cyc
.endmacro .endmacro
; input: arg as fixed4.12 .macro sqr16_round dest, arg, shift
; output: dest as fixed8.24 ;imul16_round dest, arg, arg, shift
.macro sqr16 dest, arg
copy16 FR0, arg ; 12 cyc copy16 FR0, arg ; 12 cyc
jsr sqr16_func ; ? cyc jsr sqr16_func ; ? cyc
copy32 dest, FR2 ; 24 cyc shift_round_16 FR2, shift ; 103-119 cycles for shift=4
copy16 dest, FR2 + 2 ; 12 cyc
.endmacro .endmacro
; input: arg as u8
; output: dest as u16
; clobbers a, x ; clobbers a, x
.macro sqr8 dest, arg .macro sqr8 dest, arg
ldx arg ldx arg
@ -453,8 +451,6 @@ viewport_oy:
sta dest + 1 sta dest + 1
.endmacro .endmacro
; input: arg as u8
; input/output: dest as u16
; clobbers a, x ; clobbers a, x
.macro sqr8_add16 dest, arg .macro sqr8_add16 dest, arg
ldx arg ldx arg
@ -875,8 +871,8 @@ next:
.proc mandelbrot .proc mandelbrot
; input: ; input:
; cx: position scaled to 8.24 fixed point - -128..+127.9 ; cx: position scaled to 4.12 fixed point - -8..+7.9
; cy: position scaled to 8.24 ; cy: position scaled to 4.12
; ;
; output: ; output:
; iter: iteration count at escape or 0 ; iter: iteration count at escape or 0
@ -888,41 +884,12 @@ next:
; zx_zy = 0 ; zx_zy = 0
; dist = 0 ; dist = 0
; iter = 0 ; iter = 0
; lda #00
; ldx #(iter - zx + 1)
;initloop:
; sta zx - 1,x
; dex
; bne initloop
; sta z_buffer_start
; sta z_buffer_end
lda #00 lda #00
sta zx ldx #(iter - zx + 1)
sta zx + 1 initloop:
sta zx + 2 sta zx - 1,x
sta zx + 3 dex
sta zy bne initloop
sta zy + 1
sta zy + 2
sta zy + 3
sta zx_2
sta zx_2 + 1
sta zx_2 + 2
sta zx_2 + 3
sta zy_2
sta zy_2 + 1
sta zy_2 + 2
sta zy_2 + 3
sta zx_zy
sta zx_zy + 1
sta zx_zy + 2
sta zx_zy + 3
sta dist
sta dist + 1
sta dist + 2
sta dist + 3
sta iter
sta z_buffer_start sta z_buffer_start
sta z_buffer_end sta z_buffer_end
@ -934,8 +901,6 @@ loop:
keep_going: keep_going:
.macro quick_exit arg, max .macro quick_exit arg, max
; arg: fixed8.24
; max: integer
.local positive .local positive
.local negative .local negative
.local nope_out .local nope_out
@ -943,16 +908,16 @@ keep_going:
.local all_done .local all_done
; check sign bit ; check sign bit
lda arg + 3 lda arg + 1
bmi negative bmi negative
positive: positive:
cmp #max cmp #((max) << 4)
bmi all_done ; 'less than' bmi all_done ; 'less than'
jmp exit_path jmp exit_path
negative: negative:
cmp #(256 - max) cmp #(256 - ((max) << 4))
beq first_equal ; 'equal' on first byte beq first_equal ; 'equal' on first byte
bpl all_done ; 'greater than' bpl all_done ; 'greater than'
@ -960,44 +925,34 @@ keep_going:
jmp exit_path jmp exit_path
first_equal: first_equal:
; following bytes all 0 shows it's really 'equal'
lda arg + 2
bne all_done
lda arg + 1
bne all_done
lda arg lda arg
bne all_done beq nope_out ; 2nd byte 0 shows it's really 'equal'
jmp exit_path
all_done: all_done:
.endmacro .endmacro
; 8.24: (-128 .. 127.9) ; 4.12: (-8 .. +7.9)
; zx = zx_2 - zy_2 + cx ; zx = zx_2 - zy_2 + cx
sub32 zx, zx_2, zy_2 sub16 zx, zx_2, zy_2
add32 zx, zx, cx add16 zx, zx, cx
quick_exit zx, 2 quick_exit zx, 2
; zy = zx_zy + zx_zy + cy ; zy = zx_zy + zx_zy + cy
add32 zy, zx_zy, zx_zy add16 zy, zx_zy, zx_zy
add32 zy, zy, cy add16 zy, zy, cy
quick_exit zy, 2 quick_exit zy, 2
; convert 8.24 -> 4.12: (-8 .. +7.9)
shift_round_16 zx, 4
shift_round_16 zy, 4
; zx_2 = zx * zx ; zx_2 = zx * zx
sqr16 zx_2, zx + 2 sqr16_round zx_2, zx, 4
; zy_2 = zy * zy ; zy_2 = zy * zy
sqr16 zy_2, zy + 2 sqr16_round zy_2, zy, 4
; zx_zy = zx * zy ; zx_zy = zx * zy
imul16 zx_zy, zx + 2, zy + 2 imul16_round zx_zy, zx, zy, 4
; dist = zx_2 + zy_2 ; dist = zx_2 + zy_2
add32 dist, zx_2, zy_2 add16 dist, zx_2, zy_2
quick_exit dist, 4 quick_exit dist, 4
; if may be in the lake, look for looping output with a small buffer ; if may be in the lake, look for looping output with a small buffer
@ -1034,10 +989,10 @@ z_buffer_loop:
; Compare the previously stored z values ; Compare the previously stored z values
ldy #0 ldy #0
z_compare zx + 2 z_compare zx
z_compare zx + 3 z_compare zx + 1
z_compare zy + 2 z_compare zy
z_compare zy + 3 z_compare zy + 1
cpy #4 cpy #4
bne z_no_matches bne z_no_matches
@ -1052,10 +1007,10 @@ z_no_matches:
z_nothing_to_read: z_nothing_to_read:
; Store and expand ; Store and expand
z_store zx + 2 z_store zx
z_store zx + 3 z_store zx + 1
z_store zy + 2 z_store zy
z_store zy + 3 z_store zy + 1
z_advance z_advance
stx z_buffer_end stx z_buffer_end
@ -1106,17 +1061,14 @@ cont:
enough: enough:
.endmacro .endmacro
.macro zoom_factor dest, src, aspect .macro zoom_factor dest, src, zoom, aspect
; output: dest: fixed8.24
; input: src: fixed4.12
; aspect: fixed4.12
; clobbers A, X, flags, etc ; clobbers A, X, flags, etc
copy16 dest, src copy16 dest, src
scale_zoom dest scale_zoom dest
; cy = cy * (3 / 4) ; cy = cy * (3 / 4)
; cx = cx * (5 / 4) ; cx = cx * (5 / 4)
imul16 dest, dest, aspect imul16_round dest, dest, aspect, 4
.endmacro .endmacro
.proc pset .proc pset
@ -1454,32 +1406,17 @@ zero_byte_loop:
txa txa
asl a asl a
asl a
tax tax
lda viewport_ox,x lda viewport_ox,x
sta ox sta ox
lda viewport_oy,x lda viewport_oy,x
sta oy sta oy
inx inx
lda viewport_ox,x lda viewport_ox,x
sta ox + 1 sta ox + 1
lda viewport_oy,x lda viewport_oy,x
sta oy + 1 sta oy + 1
inx
lda viewport_ox,x
sta ox + 2
lda viewport_oy,x
sta oy + 2
inx
lda viewport_ox,x
sta ox + 3
lda viewport_oy,x
sta oy + 3
rts rts
.endproc .endproc
@ -1601,10 +1538,10 @@ skipped_mask:
not_skipped_mask: not_skipped_mask:
; run the fractal! ; run the fractal!
zoom_factor cx, sx, aspect_x zoom_factor cx, sx, zoom, aspect_x
add32 cx, cx, ox add16 cx, cx, ox
zoom_factor cy, sy, aspect_y zoom_factor cy, sy, zoom, aspect_y
add32 cy, cy, oy add16 cy, cy, oy
jsr mandelbrot jsr mandelbrot
jsr pset jsr pset

2
readme.md
View file

@ -27,7 +27,7 @@ The 16-bit signed integer multiplication takes two 16-bit inputs and emits one 3
* when expanded RAM is available as on 130XE, a 64KB 8-bit multiplication table accelerates the remaining multiplications * when expanded RAM is available as on 130XE, a 64KB 8-bit multiplication table accelerates the remaining multiplications
* without expanded RAM, a table of half-squares is used to implement the algorithm from https://everything2.com/title/Fast+6502+multiplication * without expanded RAM, a table of half-squares is used to implement the algorithm from https://everything2.com/title/Fast+6502+multiplication
The mandelbrot calculations are done using 4.12-precision fixed point numbers with 8.24-precision intermediates. It may be possible to squish this down to 3.13/6.26. The mandelbrot calculations are done using 4.12-precision fixed point numbers. It may be possible to squish this down to 3.13.
Iterations are capped at 255. Iterations are capped at 255.

4
todo.md
View file

@ -3,11 +3,13 @@ things to try:
* skip add on the top-byte multiply in sqr8/mul8 * skip add on the top-byte multiply in sqr8/mul8
* should save a few cycles, suggestion by jamey * should save a few cycles, suggestion by jamey
* perform the zx += zx^s + cx in 32-bit space, before rounding
* should improve precision on max zoom, might cost a few cycles
* patch the entire expanded-ram imul8xe on top of imul8 to avoid the 3-cycle thunk penalty :D * patch the entire expanded-ram imul8xe on top of imul8 to avoid the 3-cycle thunk penalty :D
* try 3.13 fixed point instead of 4.12 for more precision * try 3.13 fixed point instead of 4.12 for more precision
* can we get away without the extra bit? * can we get away without the extra bit?
* since exit compare space would be 6.26 i think so
* y-axis mirror optimization * y-axis mirror optimization