mandel.s

@@ -1,16 +1,16 @@
 ; Our zero-page vars
-ox              = $80 ; fixed6.26: center point x
+ox              = $80 ; fixed8.24: center point x
-oy              = $84 ; fixed6.26: center point y
+oy              = $84 ; fixed8.24: center point y
-cx              = $88 ; fixed6.26: c_x
+cx              = $88 ; fixed8.24: c_x
-cy              = $8c ; fixed6.26: c_y
+cy              = $8c ; fixed8.24: c_y
 
-zx              = $90 ; fixed6.26: z_x
+zx              = $90 ; fixed8.24: z_x
-zy              = $94 ; fixed6.26: z_y
+zy              = $94 ; fixed8.24: z_y
-zx_2            = $98 ; fixed6.26: z_x^2
+zx_2            = $98 ; fixed8.24: z_x^2
-zy_2            = $9c ; fixed6.26: z_y^2
+zy_2            = $9c ; fixed8.24: z_y^2
 
-zx_zy           = $a0 ; fixed6.26: z_x * z_y
+zx_zy           = $a0 ; fixed8.24: z_x * z_y
-dist            = $a4 ; fixed6.26: z_x^2 + z_y^2
+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
@@ -31,10 +31,10 @@ chroma_offset   = $bb ; u8
 palette_ticks   = $bc ; u8
 chroma_ticks    = $bd ; u8
 count_frames    = $be ; u8
-; free space $bf
+count_pixels    = $bf ; u8
 
-count_iters     = $c0 ; u16
+total_pixels    = $c0 ; float48
-; free space c2-cb
+total_ms        = $c6 ; float48
 temp            = $cc ; u16
 temp2           = $ce ; u16
 
@@ -59,12 +59,10 @@ LBUFF  = $0580 ; result buffer for FASC routine
 ; FP ROM routine vectors
 FASC   = $D8E6 ; FLOATING POINT TO ASCII (output in INBUFF, last char has high bit set)
 IFP    = $D9AA ; INTEGER TO FLOATING POINT CONVERSION (FR0:u16 -> FR0:float48)
-FPI    = $D9D2 ; floating point to integer
 FADD   = $DA66 ; ADDITION       (FR0 += FR1)
 FSUB   = $DA60 ; SUBTRACTION    (FR0 -= FR1)
 FMUL   = $DADB ; MULTIPLICATION (FR0 *= FR1)
 FDIV   = $DB28 ; DIVISION       (FR0 /= FR1)
-ZFR0   = $DA44 ; clear FR0
 ZF1    = $DA46 ; CLEAR ZERO PAGE FLOATING POINT NUMBER (XX)
 FLD0R  = $DD89 ; LOAD FR0 WITH FLOATING POINT NUMBER (YYXX)
 FLD1R  = $DD98 ; LOAD FR1 WITH FLOATING POINT NUMBER (YYXX)
@@ -143,7 +141,7 @@ str_self:
     .byte "MANDEL-6502"
 str_self_end:
 str_speed:
-    .byte "us/iter: "
+    .byte " ms/px"
 str_speed_end:
 str_run:
     .byte " RUN"
@@ -191,38 +189,20 @@ aspect:
     ;
     ; 184h is the equiv of 220.8h at square pixels
     ; 320 / 220.8 = 1.45 display aspect ratio
-aspect_x: ; fixed3.13 5/4
+aspect_x: ; fixed4.16 5/4
-    .word 5 << (13 - 2)
+    .word 5 << (12 - 2)
 
-aspect_y: ; fixed3.13 3/4
+aspect_y: ; fixed4.16 3/4
-    .word 3 << (13 - 2)
+    .word 3 << (12 - 2)
 
-sec_per_frame: ; float48 00 . 01 66 66 66 67
+ms_per_frame: ; float48 16.66666667
-    .byte 63  ; exponent/sign - -1 bytes
+    .byte 64  ; exponent/sign
-    .byte $01 ; BCD digits
+    .byte $16 ; BCD digits
     .byte $66
     .byte $66
     .byte $66
     .byte $67
 
-us_per_sec: ; float48 1e9 01 00 0,0 00 . 00
-    .byte 67  ; exponent/sign +3 bytes
-    .byte $01 ; BCD digits
-    .byte $00
-    .byte $00
-    .byte $00
-    .byte $00
-
-total_iters: ; float48
-    .repeat 6
-        .byte 0
-    .endrepeat
-
-total_sec: ; float48
-    .repeat 6
-        .byte 0
-    .endrepeat
-
 display_list_start:
     ; 24 lines overscan
     .repeat 3
@@ -254,9 +234,9 @@ display_list_len = display_list_end - display_list_start
 color_map:
     .byte 0
     .repeat 85
-        .byte %01010101
+        .byte 1
-        .byte %10101010
+        .byte 2
-        .byte %11111111
+        .byte 3
     .endrepeat
 
 
@@ -305,34 +285,23 @@ fill_masks:
     .byte %00000001
     .byte %00000000
 
-pixel_masks:
-    .byte %11111111
-    .byte %11110000
-    .byte %11000000
-
 viewport_zoom:
-    .byte 0
+    .byte 1
-    .byte 5
+    .byte 6
-    .byte 7
+    .byte 8
-    .byte 5
+    .byte 6
-    .byte 7
-    .byte 7
 
 viewport_ox:
-    .dword ($00000000 & $3fffffff) << 2
+    .dword $00000000
-    .dword ($ff110000 & $3fffffff) << 2
+    .dword $ff110000
-    .dword ($ff110000 & $3fffffff) << 2
+    .dword $ff110000
-    .dword ($fe400000 & $3fffffff) << 2
+    .dword $fe400000
-    .dword ($fe3b0000 & $3fffffff) << 2
-    .dword $fd220000
 
 viewport_oy:
-    .dword ($00000000 & $3fffffff) << 2
+    .dword $00000000
-    .dword ($ffb60000 & $3fffffff) << 2
+    .dword $ffb60000
-    .dword ($ffbe0000 & $3fffffff) << 2
+    .dword $ffbe0000
-    .dword ($00000000 & $3fffffff) << 2
+    .dword $00000000
-    .dword ($fffe0000 & $3fffffff) << 2
-    .dword $ff000000
 
 ; 2 + 9 * byte cycles
 .macro add bytes, dest, arg1, arg2
@@ -484,6 +453,20 @@ viewport_oy:
     sta dest + 1
 .endmacro
 
+; input: arg as u8
+; input/output: dest as u16
+; clobbers a, x
+.macro sqr8_add16 dest, arg
+    ldx arg
+    clc
+    lda sqr_lobyte,x
+    adc dest
+    sta dest
+    lda sqr_hibyte,x
+    adc dest + 1
+    sta dest + 1
+.endmacro
+
 .segment "TABLES"
 ; lookup table for top byte -> PORTB value for bank-switch
 .align 256
@@ -766,8 +749,9 @@ inner_loop:
     ; h1*h2*256*256 + h1*l2*256 + h2*l1*256 + l1*l2
 
     imul8 result, arg1, arg2, xe
-
+    lda #0
-    imul8 result + 2, arg1 + 1, arg2 + 1, xe
+    sta result + 2
+    sta result + 3
 
     imul8 inter, arg1 + 1, arg2, xe
     add16 result + 1, result + 1, inter
@@ -777,6 +761,9 @@ inner_loop:
     add16 result + 1, result + 1, inter
     add_carry result + 3
 
+    imul8 inter, arg1 + 1, arg2 + 1, xe
+    add16 result + 2, result + 2, inter
+
     ; In case of negative inputs, adjust high word
     ; https://stackoverflow.com/a/28827013
     lda arg1 + 1
@@ -809,8 +796,9 @@ arg2_pos:
         ; h*h*256*256 + h*l*256 + h*l*256 + l*l
 
         sqr8 result, arg
-
+        lda #0
-        sqr8 result + 2, arg + 1
+        sta result + 2
+        sta result + 3
 
         imul8 inter, arg + 1, arg, xe
         add16 result + 1, result + 1, inter
@@ -818,6 +806,8 @@ arg2_pos:
         add16 result + 1, result + 1, inter
         add_carry result + 3
 
+        sqr8_add16 result + 2, arg + 1
+
         rts ; 6 cyc
     .endscope
 .endmacro
@@ -885,8 +875,8 @@ next:
 
 .proc mandelbrot
     ; input:
-    ; cx: position scaled to 6.26 fixed point - -32..+31.9
+    ; cx: position scaled to 8.24 fixed point - -128..+127.9
-    ; cy: position scaled to 6.26
+    ; cy: position scaled to 8.24
     ;
     ; output:
     ; iter: iteration count at escape or 0
@@ -937,11 +927,6 @@ next:
     sta z_buffer_end
 
 loop:
-    inc count_iters
-    bne low_iters
-    inc count_iters + 1
-low_iters:
-
     ; iter++ & max-iters break
     inc iter
     bne keep_going
@@ -949,7 +934,7 @@ low_iters:
 keep_going:
 
     .macro quick_exit arg, max
-        ; arg: fixed6.26
+        ; arg: fixed8.24
         ; max: integer
         .local positive
         .local negative
@@ -962,12 +947,12 @@ keep_going:
         bmi negative
 
     positive:
-        cmp #(max << 2)
+        cmp #max
         bmi all_done ; 'less than'
         jmp exit_path
 
     negative:
-        cmp #(256 - (max << 2))
+        cmp #(256 - max)
         beq first_equal ; 'equal' on first byte
         bpl all_done    ; 'greater than'
 
@@ -987,7 +972,7 @@ keep_going:
     all_done:
     .endmacro
 
-    ; 6.26: (-32 .. 31.9)
+    ; 8.24: (-128 .. 127.9)
     ; zx = zx_2  - zy_2  + cx
     sub32 zx, zx_2, zy_2
     add32 zx, zx, cx
@@ -998,9 +983,9 @@ keep_going:
     add32 zy, zy, cy
     quick_exit zy, 2
 
-    ; convert 6.26 -> 3.13: (-4 .. +3.9)
+    ; convert 8.24 -> 4.12: (-8 .. +7.9)
-    shift_round_16 zx, 3
+    shift_round_16 zx, 4
-    shift_round_16 zy, 3
+    shift_round_16 zy, 4
 
     ; zx_2 = zx * zx
     sqr16 zx_2, zx + 2
@@ -1122,9 +1107,9 @@ enough:
 .endmacro
 
 .macro zoom_factor dest, src, aspect
-    ; output: dest: fixed6.26
+    ; output: dest: fixed8.24
-    ; input: src: fixed3.13
+    ; input: src: fixed4.12
-    ; aspect: fixed3.13
+    ; aspect: fixed4.12
     ; clobbers A, X, flags, etc
     copy16 dest, src
     scale_zoom dest
@@ -1142,11 +1127,8 @@ enough:
     ; iter -> color
     ldx iter
     lda color_map,x
-    ldx fill_level
-    and pixel_masks,x
     sta pixel_color
-    lda pixel_masks,x
+    lda #(255 - 3)
-    eor #$ff
     sta pixel_mask
 
     ; sy -> line base address in temp
@@ -1195,23 +1177,22 @@ point:
     ; pixel_mask <<= pixel_shift (shifting in ones)
     and #3
     sta pixel_shift
+    lda #3
+    sec
+    sbc pixel_shift
     tax
 shift_loop:
     beq shift_done
-    lsr pixel_color
+    asl pixel_color
-    lsr pixel_color
+    asl pixel_color
     sec
-    ror pixel_mask
+    rol pixel_mask
     sec
-    ror pixel_mask
+    rol pixel_mask
     dex
     jmp shift_loop
 shift_done:
 
-    ldy fill_level
-    ldx fill_masks,y
-    inx
-
     ; pixel_offset = temp >> 2
     lda temp
     lsr a
@@ -1219,25 +1200,12 @@ shift_done:
     sta pixel_offset
     tay
 
-draw_pixel:
     ; read, mask, or, write
     lda (pixel_ptr),y
     and pixel_mask
     ora pixel_color
     sta (pixel_ptr),y
 
-    dex
-    beq done
-    clc
-    lda #40
-    adc pixel_ptr
-    sta pixel_ptr
-    lda #0
-    adc pixel_ptr + 1
-    sta pixel_ptr + 1
-    jmp draw_pixel
-
-done:
     rts
 .endproc
 
@@ -1245,7 +1213,6 @@ done:
     ; clobbers A, X
     .local loop
     .local done
-    .local padding
     ldx #0
 loop:
     cpx #len
@@ -1253,27 +1220,11 @@ loop:
     txa
     tay
     lda (strptr),y
-    pha ; save the char for terminator check
-    and #$7f ; strip the high bit (terminator)
     tay
     lda char_map,y
     sta textbuffer + col,x
     inx
-
-    pla
-    bmi padding
     jmp loop
-
-padding:
-    ldy #32 ; space
-    lda char_map,y
-
-    cpx #len
-    beq done
-    sta textbuffer + col,x
-    inx
-    jmp padding
-
 done:
 .endmacro
 
@@ -1416,7 +1367,7 @@ skip_char:
 
 plus:
     lda zoom
-    cmp #7
+    cmp #8
     bpl skip_char
     inc zoom
     jmp done
@@ -1448,10 +1399,6 @@ number_keys:
     beq three
     cpy #KEY_4
     beq four
-    cpy #KEY_5
-    beq five
-    cpy #KEY_6
-    beq six
     jmp skip_char
 
 one:
@@ -1465,12 +1412,6 @@ three:
     jmp load_key_viewport
 four:
     ldx #3
-    jmp load_key_viewport
-five:
-    ldx #4
-    jmp load_key_viewport
-six:
-    ldx #5
     ; fall through
 load_key_viewport:
     jsr load_viewport
@@ -1601,20 +1542,16 @@ copy_byte_loop:
     jsr SETVBV
 
 main_loop:
-    ; count_frames = 0; count_iters = 0
+    ; count_frames = 0; count_pixels = 0
     lda #0
     sta count_frames
-    sta count_iters
+    sta count_pixels
-    sta count_iters + 1
 
-    ; total_sec = 0.0; total_iters = 0.0
+    ; total_ms = 0.0; total_pixels = 0.0
-    jsr ZFR0
+    ldx #total_ms
-    ldx #.lobyte(total_sec)
+    jsr ZF1
-    ldy #.hibyte(total_sec)
+    ldx #total_pixels
-    jsr FST0R
+    jsr ZF1
-    ldx #.lobyte(total_iters)
-    ldy #.hibyte(total_iters)
-    jsr FST0R
 
     jsr clear_screen
     jsr status_bar
@@ -1686,32 +1623,38 @@ not_skipped_mask:
 
 no_key:
     ; check if we should update the counters
+    ;
+    ; count_pixels >= width? update!
+    inc count_pixels
+    lda count_pixels
+    cmp #width
+    bmi update_status
 
     ; count_frames >= 120? update!
     lda count_frames
     cmp #120 ; >= 2 seconds
-    bpl update_status
+    bmi skipped
-    jmp skipped
 
 update_status:
-    ; FR0 = (float)count_iters & clear count_iters
+    ; FR0 = (float)count_pixels & clear count_pixels
-    copy16 FR0, count_iters
+    lda count_pixels
-    jsr IFP
+    sta FR0
     lda #0
-    sta count_iters
+    sta FR0 + 1
-    sta count_iters + 1
+    sta count_pixels
+    jsr IFP
 
-    ; FR1 = total_iters
+    ; FR1 = total_pixels
-    ldx #.lobyte(total_iters)
+    ldx #.lobyte(total_pixels)
-    ldy #.hibyte(total_iters)
+    ldy #.hibyte(total_pixels)
     jsr FLD1R
 
     ; FR0 += FR1
     jsr FADD
 
-    ; total_iters = FR0
+    ; total_pixels = FR0
-    ldx #.lobyte(total_iters)
+    ldx #.lobyte(total_pixels)
-    ldy #.hibyte(total_iters)
+    ldy #.hibyte(total_pixels)
     jsr FST0R
 
 
@@ -1724,58 +1667,44 @@ update_status:
     sta count_frames
     jsr IFP
 
-    ; FR0 *= sec_per_frame
+    ; FR0 *= ms_per_frame
-    ldx #.lobyte(sec_per_frame)
+    ldx #.lobyte(ms_per_frame)
-    ldy #.hibyte(sec_per_frame)
+    ldy #.hibyte(ms_per_frame)
     jsr FLD1R
     jsr FMUL
 
-    ; FR0 += total_sec
+    ; FR0 += total_ms
-    ldx #.lobyte(total_sec)
+    ldx #total_ms
-    ldy #.hibyte(total_sec)
+    ldy #0
     jsr FLD1R
     jsr FADD
 
-    ; total_sec = FR0
+    ; total_ms = FR0
-    ldx #.lobyte(total_sec)
+    ldx #total_ms
-    ldy #.hibyte(total_sec)
+    ldy #0
     jsr FST0R
 
-    ; FR0 /= total_iters
+    ; FR0 /= total_pixels
-    ldx #.lobyte(total_iters)
+    ldx #total_pixels
-    ldy #.hibyte(total_iters)
+    ldy #0
     jsr FLD1R
     jsr FDIV
 
-    ; FR0 *= us_per_sec
-    ldx #.lobyte(us_per_sec)
-    ldy #.hibyte(us_per_sec)
-    jsr FLD1R
-    jsr FMUL
-
-    ; round (down) to integer
-    jsr FPI
-    clc
-    jsr IFP
-
     ; convert to ASCII in INBUFF
     jsr FASC
 
     ; print the first 6 digits
-    draw_text speed_start, str_speed_len, str_speed
+    draw_text_indirect speed_start, speed_precision, INBUFF
-    draw_text_indirect speed_start + str_speed_len, speed_precision, INBUFF
+    draw_text speed_start + speed_precision, str_speed_len, str_speed
 
 skipped:
 
-    ; sx += fill_level[fill_masks] + 1
-    ldx fill_level
-    lda fill_masks,x
     clc
-    adc #1 ; will never carry
+    lda sx
-    adc sx
+    adc #1
     sta sx
-    lda #0
+    lda sx + 1
-    adc sx + 1
+    adc #0
     sta sx + 1
 
     lda sx
@@ -1785,15 +1714,12 @@ skipped:
 
 loop_sx_done:
 
-    ; sy += fill_level[fill_masks] + 1
-    ldx fill_level
-    lda fill_masks,x
     clc
-    adc #1 ; will never carry
+    lda sy
-    adc sy
+    adc #1
     sta sy
-    lda #0
+    lda sy + 1
-    adc sy + 1
+    adc #0
     sta sy + 1
 
     lda sy

readme.md

@@ -18,7 +18,7 @@ Enjoy! I'll probably work on this off and on for the next few weeks until I've g
 
 ## Current state
 
-Basic rendering is functional, with interactive zoom/pan (+/-/arrows) and 6 preset viewports via the number keys.
+Basic rendering is functional, with interactive zoom/pan (+/-/arrows) and 4 preset viewports via the number keys.
 
 The 16-bit signed integer multiplication takes two 16-bit inputs and emits one 32-bit output in the zero page, using the Atari OS ROM's floating point registers as workspaces. Inputs are clobbered.
 
@@ -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
 * 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 3.13-precision fixed point numbers with 6.26-precision intermediates.
+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.
 
 Iterations are capped at 255.
 

todo.md

@@ -1,17 +1,19 @@
 things to try:
 
-* fix status bar to show elapsed time, per-iter time, per-pixel iter count
+* skip add on the top-byte multiply in sqr8/mul8
-
+  * should save a few cycles, suggestion by jamey
-* 'turbo' mode disabling graphics in full or part
 
 * patch the entire expanded-ram imul8xe on top of imul8 to avoid the 3-cycle thunk penalty :D
 
-* maybe clean up the load/layout of the big mul table
+* try 3.13 fixed point instead of 4.12 for more precision
-
+  * can we get away without the extra bit?
-* consider alternate lookup tables in the top 16KB under ROM
+  * since exit compare space would be 6.26 i think so
 
 * y-axis mirror optimization
 
+* 'wide pixels' 2x and 4x for a fuller initial image in the tiered rendering
+  * maybe redo tiering to just 4x4, 2x2, 1x1?
+
 * extract viewport for display & re-input via keyboard
 
 * fujinet screenshot/viewport uploader