shave some cycles off 16-bit squaring with shift instead of add

also fix the comments about how many cycles shift takes

mandel.s

@@ -1,42 +1,43 @@
 ; Our zero-page vars
-ox              = $80 ; fixed6.26: center point x
+sx    = $80     ; i16: screen pixel x
-oy              = $84 ; fixed6.26: center point y
+sy    = $82     ; i16: screen pixel y
-cx              = $88 ; fixed6.26: c_x
+ox    = $84     ; fixed4.12: center point x
-cy              = $8c ; fixed6.26: 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 ; fixed6.26: z_x
+zx_2  = $90     ; fixed4.12: z_x^2
-zy              = $94 ; fixed6.26: z_y
+zy_2  = $92     ; fixed4.12: z_y^2
-zx_2            = $98 ; fixed6.26: z_x^2
+zx_zy = $94     ; fixed4.12: z_x * z_y
-zy_2            = $9c ; fixed6.26: z_y^2
+dist  = $96     ; fixed4.12: z_x^2 + z_y^2
 
-zx_zy           = $a0 ; fixed6.26: z_x * z_y
+iter          = $a0 ; u8: iteration count
-dist            = $a4 ; fixed6.26: 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
-; free space $bf
 
-count_iters     = $c0 ; u16
+z_buffer_active = $b0 ; boolean: 1 if we triggered the lake, 0 if not
-; free space c2-cb
+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
 chroma_delay = 137
@@ -59,12 +60,10 @@ 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)
@@ -130,11 +129,8 @@ KEY_0     = 50
     mantissa .byte 5
 .endstruct
 
-.import mul_lobyte256
+.import mul_lobyte
-.import mul_hibyte256
+.import mul_hibyte
-.import mul_hibyte512
-.import sqr_lobyte
-.import sqr_hibyte
 
 .data
 
@@ -143,7 +139,7 @@ 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 +187,20 @@ 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 +232,9 @@ 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 +283,23 @@ 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
+    .word $0000
-    .dword ($ff110000 & $3fffffff) << 2
+    .word $f110
-    .dword ($ff110000 & $3fffffff) << 2
+    .word $f110
-    .dword ($fe400000 & $3fffffff) << 2
+    .word $e400
-    .dword ($fe3b0000 & $3fffffff) << 2
-    .dword $fd220000
 
 viewport_oy:
-    .dword ($00000000 & $3fffffff) << 2
+    .word $0000
-    .dword ($ffb60000 & $3fffffff) << 2
+    .word $fb60
-    .dword ($ffbe0000 & $3fffffff) << 2
+    .word $fbe0
-    .dword ($00000000 & $3fffffff) << 2
+    .word $0000
-    .dword ($fffe0000 & $3fffffff) << 2
-    .dword $ff000000
 
 ; 2 + 9 * byte cycles
 .macro add bytes, dest, arg1, arg2
@@ -351,7 +318,7 @@ viewport_oy:
 
 ; 38 cycles
 .macro add32 dest, arg1, arg2
-    add 4, dest, arg1, arg2
+    add 4, dest, arg2, dest
 .endmacro
 
 ; 8 cycles
@@ -381,7 +348,7 @@ viewport_oy:
     sub 4, dest, arg1, arg2
 .endmacro
 
-; 3 + 5 * bytes cycles
+; 3 + 5 * (bytes - 1) cycles
 .macro shl bytes, arg
     asl arg              ; 3 cyc
     .repeat bytes-1, i
@@ -389,17 +356,17 @@ viewport_oy:
     .endrepeat
 .endmacro
 
-; 13 cycles
+; 8 cycles
 .macro shl16 arg
     shl 2, arg
 .endmacro
 
-; 18 cycles
+; 13 cycles
 .macro shl24 arg
     shl 3, arg
 .endmacro
 
-; 23 cycles
+; 18 cycles
 .macro shl32 arg
     shl 4, arg
 .endmacro
@@ -456,31 +423,32 @@ viewport_oy:
     round16 arg ; 11-27 cycles
 .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 FR1, arg2  ; 12 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
 
-; 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
     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
 
-; input: arg as u8
-; output: dest as u16
 ; clobbers a, x
 .macro sqr8 dest, arg
     ldx arg
-    lda sqr_lobyte,x
+    txa
+    lsr
+    lda mul_lobyte,x
+    rol
     sta dest
-    lda sqr_hibyte,x
+    lda mul_hibyte,x
+    rol
     sta dest + 1
 .endmacro
 
@@ -569,22 +537,25 @@ bank_switch_table:
             clc                   ; 2 cyc         
             adc mul_factor_x      ; 3 cyc
             tax                   ; 2 cyc
-            bcc under256          ; 2 cyc
+            lda mul_hibyte,x      ; 4 cyc
-            lda mul_hibyte512,x   ; 4 cyc
+            bcc next              ; 2 cyc
-            bcs next              ; 2 cyc
+            ; carry is set so we get to add 1 for free, but need to add 0x80
-        under256:
+            adc #$7f              ; 2 cyc
-            lda mul_hibyte256,x   ; 4 cyc
+            clc                   ; 2 cyc
-            sec                   ; 2 cyc
+            ; stash the sum temporarily so we can use it as an operand to add
+            stx mul_product_lo    ; 3 cyc
+            adc mul_product_lo    ; 3 cyc
         next:
+            sec                   ; 2 cyc
             sta mul_product_hi    ; 3 cyc
-            lda mul_lobyte256,x   ; 4 cyc
+            lda mul_lobyte,x      ; 4 cyc
 
             ; - a^2/2
             ldx mul_factor_a      ; 3 cyc
-            sbc mul_lobyte256,x   ; 4 cyc
+            sbc mul_lobyte,x      ; 4 cyc
             sta mul_product_lo    ; 3 cyc
             lda mul_product_hi    ; 3 cyc
-            sbc mul_hibyte256,x   ; 4 cyc
+            sbc mul_hibyte,x      ; 4 cyc
             sta mul_product_hi    ; 3 cyc
 
             ; + x & a & 1:
@@ -603,10 +574,10 @@ bank_switch_table:
             ; - x^2/2
         small_product:
             sec                   ; 2 cyc
-            sbc mul_lobyte256,x   ; 4 cyc
+            sbc mul_lobyte,x      ; 4 cyc
             sta mul_product_lo    ; 3 cyc
             lda mul_product_hi    ; 3 cyc
-            sbc mul_hibyte256,x   ; 4 cyc
+            sbc mul_hibyte,x      ; 4 cyc
             sta mul_product_hi    ; 3 cyc
         .endscope
     .endif
@@ -766,8 +737,9 @@ 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 +749,9 @@ 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
@@ -809,11 +784,10 @@ arg2_pos:
         ; h*h*256*256 + h*l*256 + h*l*256 + l*l
 
         sqr8 result, arg
-
         sqr8 result + 2, arg + 1
 
         imul8 inter, arg + 1, arg, xe
-        add16 result + 1, result + 1, inter
+        shl16 inter
         add_carry result + 3
         add16 result + 1, result + 1, inter
         add_carry result + 3
@@ -885,8 +859,8 @@ next:
 
 .proc mandelbrot
     ; input:
-    ; cx: position scaled to 6.26 fixed point - -32..+31.9
+    ; cx: position scaled to 4.12 fixed point - -8..+7.9
-    ; cy: position scaled to 6.26
+    ; cy: position scaled to 4.12
     ;
     ; output:
     ; iter: iteration count at escape or 0
@@ -898,50 +872,16 @@ next:
     ; zx_zy = 0
     ; dist = 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
-    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_end
 
 loop:
-    inc count_iters
-    bne low_iters
-    inc count_iters + 1
-low_iters:
-
     ; iter++ & max-iters break
     inc iter
     bne keep_going
@@ -949,8 +889,6 @@ low_iters:
 keep_going:
 
     .macro quick_exit arg, max
-        ; arg: fixed6.26
-        ; max: integer
         .local positive
         .local negative
         .local nope_out
@@ -958,16 +896,16 @@ keep_going:
         .local all_done
 
         ; check sign bit
-        lda arg + 3
+        lda arg + 1
         bmi negative
 
     positive:
-        cmp #(max << 2)
+        cmp #((max) << 4)
         bmi all_done ; 'less than'
         jmp exit_path
 
     negative:
-        cmp #(256 - (max << 2))
+        cmp #(256 - ((max) << 4))
         beq first_equal ; 'equal' on first byte
         bpl all_done    ; 'greater than'
 
@@ -975,44 +913,34 @@ keep_going:
         jmp exit_path
     
     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
-        bne all_done
+        beq nope_out  ; 2nd byte 0 shows it's really 'equal'
-        jmp exit_path
 
     all_done:
     .endmacro
 
-    ; 6.26: (-32 .. 31.9)
+    ; 4.12: (-8 .. +7.9)
     ; 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
 
     ; 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
 
-    ; convert 6.26 -> 3.13: (-4 .. +3.9)
-    shift_round_16 zx, 3
-    shift_round_16 zy, 3
-
     ; zx_2 = zx * zx
-    sqr16 zx_2, zx + 2
+    sqr16_round zx_2, zx, 4
 
     ; zy_2 = zy * zy
-    sqr16 zy_2, zy + 2
+    sqr16_round zy_2, zy, 4
 
     ; zx_zy = zx * zy
-    imul16 zx_zy, zx + 2, zy + 2
+    imul16_round zx_zy, zx, zy, 4
 
     ; dist = zx_2 + zy_2
-    add32 dist, zx_2, zy_2
+    add16 dist, zx_2, zy_2
     quick_exit dist, 4
 
     ; if may be in the lake, look for looping output with a small buffer
@@ -1049,10 +977,10 @@ z_buffer_loop:
 
     ; Compare the previously stored z values
     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
     bne z_no_matches
@@ -1067,10 +995,10 @@ z_no_matches:
 z_nothing_to_read:
 
     ; 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
     stx z_buffer_end
 
@@ -1121,17 +1049,14 @@ cont:
 enough:
 .endmacro
 
-.macro zoom_factor dest, src, aspect
+.macro zoom_factor dest, src, zoom, aspect
-    ; output: dest: fixed6.26
-    ; input: src: fixed3.13
-    ; aspect: fixed3.13
     ; clobbers A, X, flags, etc
     copy16 dest, src
     scale_zoom dest
 
     ; cy = cy * (3 / 4)
     ; cx = cx * (5 / 4)
-    imul16 dest, dest, aspect
+    imul16_round dest, dest, aspect, 4
 .endmacro
 
 .proc pset
@@ -1142,11 +1067,8 @@ 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 +1117,22 @@ 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 +1140,12 @@ 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 +1153,6 @@ done:
     ; clobbers A, X
     .local loop
     .local done
-    .local padding
     ldx #0
 loop:
     cpx #len
@@ -1253,27 +1160,11 @@ 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
 
@@ -1390,15 +1281,12 @@ skip_luma:
     cpy #KEY_MINUS
     beq minus
 
-    ; temp+temp2 = $00010000 << (8 - zoom)
+    ; temp = $0010 << (8 - zoom)
-    lda #$00
+    lda #$10
     sta temp
-    sta temp + 1
-    lda #$01
-    sta temp + 2
     lda #$00
-    sta temp + 3
+    sta temp + 1
-    scale_zoom temp + 2
+    scale_zoom temp
 
     cpy #KEY_UP
     beq up
@@ -1408,7 +1296,14 @@ skip_luma:
     beq left
     cpy #KEY_RIGHT
     beq right
-    jmp number_keys
+    cpy #KEY_1
+    beq one
+    cpy #KEY_2
+    beq two
+    cpy #KEY_3
+    beq three
+    cpy #KEY_4
+    beq four
  
 skip_char:
     lda #0
@@ -1416,7 +1311,7 @@ skip_char:
 
 plus:
     lda zoom
-    cmp #7
+    cmp #8
     bpl skip_char
     inc zoom
     jmp done
@@ -1427,33 +1322,17 @@ minus:
     dec zoom
     jmp done
 up:
-    sub32 oy, oy, temp
+    sub16 oy, oy, temp 
     jmp done
 down:
-    add32 oy, oy, temp
+    add16 oy, oy, temp
     jmp done
 left:
-    sub32 ox, ox, temp
+    sub16 ox, ox, temp
     jmp done
 right:
-    add32 ox, ox, temp
+    add16 ox, ox, temp
     jmp done
-
-number_keys:
-    cpy #KEY_1
-    beq one
-    cpy #KEY_2
-    beq two
-    cpy #KEY_3
-    beq three
-    cpy #KEY_4
-    beq four
-    cpy #KEY_5
-    beq five
-    cpy #KEY_6
-    beq six
-    jmp skip_char
-
 one:
     ldx #0
     jmp load_key_viewport
@@ -1465,12 +1344,6 @@ 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
@@ -1521,32 +1394,17 @@ zero_byte_loop:
 
     txa
     asl a
-    asl a
-
     tax
     lda viewport_ox,x
     sta ox
     lda viewport_oy,x
     sta oy
-
     inx
     lda viewport_ox,x
     sta ox + 1
     lda viewport_oy,x
     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
 .endproc
 
@@ -1601,20 +1459,16 @@ 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
@@ -1672,10 +1526,10 @@ skipped_mask:
 not_skipped_mask:
 
     ; 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 pset
 
@@ -1686,32 +1540,38 @@ 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 +1584,44 @@ 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 +1631,12 @@ 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. It may be possible to squish this down to 3.13.
 
 Iterations are capped at 255.
 

tables.js

@@ -11,40 +11,19 @@ function db(func) {
     return lines.join('\n');
 }
 
-let squares = [];
-for (let i = 0; i < 512; i++) {
-    squares.push(Math.trunc((i * i + 1) / 2));
-}
-
 console.log(
 `.segment "TABLES"
 
-.export mul_lobyte256
+.export mul_lobyte
-.export mul_hibyte256
+.export mul_hibyte
-.export mul_hibyte512
-.export sqr_lobyte
-.export sqr_hibyte
 
-; (i * i + 1) / 2 for the multiplier
+; (i * i) / 2 for the multiplier
 .align 256
-mul_lobyte256:
+mul_lobyte:
-${db((i) => squares[i] & 0xff)}
+${db((i) => ((i * i) >> 1) & 0xff)}
 
 .align 256
-mul_hibyte256:
+mul_hibyte:
-${db((i) => (squares[i] >> 8) & 0xff)}
+${db((i) => ((i * i) >> 9) & 0xff)}
-
-.align 256
-mul_hibyte512:
-${db((i) => (squares[i + 256] >> 8) & 0xff)}
-
-; (i * i) for the plain squares
-.align 256
-sqr_lobyte:
-${db((i) => (i * i) & 0xff)}
-
-.align 256
-sqr_hibyte:
-${db((i) => ((i * i) >> 8) & 0xff)}
 
 `);

todo.md

@@ -1,17 +1,15 @@
 things to try:
 
-* fix status bar to show elapsed time, per-iter time, per-pixel iter count
-
-* '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
 
 * 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