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cc83c76706
...
61eb1aaf21
3 changed files with 92 additions and 153 deletions
237
mandel.s
237
mandel.s
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@ -1,42 +1,43 @@
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; Our zero-page vars
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ox = $80 ; fixed8.24: center point x
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oy = $84 ; fixed8.24: center point y
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cx = $88 ; fixed8.24: c_x
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cy = $8c ; fixed8.24: c_y
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sx = $80 ; i16: screen pixel x
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sy = $82 ; i16: screen pixel y
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ox = $84 ; fixed4.12: center point x
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oy = $86 ; fixed4.12: center point y
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cx = $88 ; fixed4.12: c_x
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cy = $8a ; fixed4.12: c_y
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zx = $8c ; fixed4.12: z_x
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zy = $8e ; fixed4.12: z_y
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zx = $90 ; fixed8.24: z_x
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zy = $94 ; fixed8.24: z_y
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zx_2 = $98 ; fixed8.24: z_x^2
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zy_2 = $9c ; fixed8.24: z_y^2
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zx_2 = $90 ; fixed4.12: z_x^2
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zy_2 = $92 ; fixed4.12: z_y^2
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zx_zy = $94 ; fixed4.12: z_x * z_y
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dist = $96 ; fixed4.12: z_x^2 + z_y^2
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zx_zy = $a0 ; fixed8.24: z_x * z_y
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dist = $a4 ; fixed8.24: z_x^2 + z_y^2
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sx = $a8 ; i16: screen pixel x
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sy = $aa ; i16: screen pixel y
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z_buffer_active = $ac ; boolean: 1 if we triggered the lake, 0 if not
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z_buffer_start = $ad ; u8: index into z_buffer
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z_buffer_end = $ae ; u8: index into z_buffer
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iter = $af ; u8: iteration count
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iter = $a0 ; u8: iteration count
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ptr = $b0 ; u16
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pixel_ptr = $b2 ; u16
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zoom = $b4 ; u8: zoom shift level
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fill_level = $b5 ; u8
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pixel_color = $b6 ; u8
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pixel_mask = $b7 ; u8
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pixel_shift = $b8 ; u8
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pixel_offset = $b9 ; u8
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palette_offset = $ba ; u8
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chroma_offset = $bb ; u8
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palette_ticks = $bc ; u8
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chroma_ticks = $bd ; u8
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count_frames = $be ; u8
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count_pixels = $bf ; u8
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zoom = $a1 ; u8: zoom shift level
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count_frames = $a2 ; u8
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count_pixels = $a3 ; u8
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total_ms = $a4 ; float48
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total_pixels = $aa ; float48
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total_pixels = $c0 ; float48
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total_ms = $c6 ; float48
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temp = $cc ; u16
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temp2 = $ce ; u16
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z_buffer_active = $b0 ; boolean: 1 if we triggered the lake, 0 if not
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z_buffer_start = $b1 ; u8: index into z_buffer
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z_buffer_end = $b2 ; u8: index into z_buffer
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temp = $b4 ; u16
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temp2 = $b6 ; u16
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pixel_ptr = $b8 ; u16
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pixel_color = $ba ; u8
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pixel_mask = $bb ; u8
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pixel_shift = $bc ; u8
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pixel_offset = $bd ; u8
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fill_level = $be ; u8
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palette_offset = $bf ; u8
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palette_ticks = $c0 ; u8
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chroma_ticks = $c1 ; u8
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chroma_offset = $c2 ; u8
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ptr = $c4 ; u16
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palette_delay = 23
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chroma_delay = 137
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@ -292,16 +293,16 @@ viewport_zoom:
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.byte 6
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viewport_ox:
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.dword $00000000
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.dword $ff110000
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.dword $ff110000
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.dword $fe400000
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.word $0000
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.word $f110
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.word $f110
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.word $e400
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viewport_oy:
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.dword $00000000
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.dword $ffb60000
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.dword $ffbe0000
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.dword $00000000
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.word $0000
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.word $fb60
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.word $fbe0
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.word $0000
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; 2 + 9 * byte cycles
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.macro add bytes, dest, arg1, arg2
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@ -320,7 +321,7 @@ viewport_oy:
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; 38 cycles
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.macro add32 dest, arg1, arg2
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add 4, dest, arg1, arg2
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add 4, dest, arg2, dest
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.endmacro
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; 8 cycles
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@ -425,25 +426,22 @@ viewport_oy:
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round16 arg ; 11-27 cycles
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.endmacro
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; input: arg1, arg2 as fixed4.12
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; output: dest as fixed8.24
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.macro imul16 dest, arg1, arg2
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.macro imul16_round dest, arg1, arg2, shift
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copy16 FR0, arg1 ; 12 cyc
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copy16 FR1, arg2 ; 12 cyc
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jsr imul16_func ; ? cyc
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copy32 dest, FR2 ; 24 cyc
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shift_round_16 FR2, shift ; 103-119 cycles for shift=4
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copy16 dest, FR2 + 2 ; 12 cyc
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.endmacro
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; input: arg as fixed4.12
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; output: dest as fixed8.24
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.macro sqr16 dest, arg
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.macro sqr16_round dest, arg, shift
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;imul16_round dest, arg, arg, shift
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copy16 FR0, arg ; 12 cyc
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jsr sqr16_func ; ? cyc
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copy32 dest, FR2 ; 24 cyc
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jsr sqr16_func ; ? cyc
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shift_round_16 FR2, shift ; 103-119 cycles for shift=4
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copy16 dest, FR2 + 2 ; 12 cyc
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.endmacro
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; input: arg as u8
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; output: dest as u16
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; clobbers a, x
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.macro sqr8 dest, arg
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ldx arg
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@ -453,8 +451,6 @@ viewport_oy:
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sta dest + 1
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.endmacro
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; input: arg as u8
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; input/output: dest as u16
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; clobbers a, x
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.macro sqr8_add16 dest, arg
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ldx arg
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@ -875,8 +871,8 @@ next:
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.proc mandelbrot
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; input:
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; cx: position scaled to 8.24 fixed point - -128..+127.9
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; cy: position scaled to 8.24
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; cx: position scaled to 4.12 fixed point - -8..+7.9
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; cy: position scaled to 4.12
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;
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; output:
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; iter: iteration count at escape or 0
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@ -888,41 +884,12 @@ next:
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; zx_zy = 0
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; dist = 0
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; iter = 0
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; lda #00
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; ldx #(iter - zx + 1)
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;initloop:
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; sta zx - 1,x
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; dex
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; bne initloop
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; sta z_buffer_start
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; sta z_buffer_end
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lda #00
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sta zx
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sta zx + 1
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sta zx + 2
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sta zx + 3
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sta zy
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sta zy + 1
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sta zy + 2
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sta zy + 3
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sta zx_2
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sta zx_2 + 1
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sta zx_2 + 2
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sta zx_2 + 3
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sta zy_2
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sta zy_2 + 1
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sta zy_2 + 2
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sta zy_2 + 3
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sta zx_zy
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sta zx_zy + 1
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sta zx_zy + 2
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sta zx_zy + 3
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sta dist
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sta dist + 1
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sta dist + 2
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sta dist + 3
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sta iter
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ldx #(iter - zx + 1)
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initloop:
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sta zx - 1,x
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dex
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bne initloop
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sta z_buffer_start
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sta z_buffer_end
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@ -934,8 +901,6 @@ loop:
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keep_going:
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.macro quick_exit arg, max
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; arg: fixed8.24
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; max: integer
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.local positive
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.local negative
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.local nope_out
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@ -943,61 +908,51 @@ keep_going:
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.local all_done
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; check sign bit
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lda arg + 3
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lda arg + 1
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bmi negative
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positive:
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cmp #max
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cmp #((max) << 4)
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bmi all_done ; 'less than'
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jmp exit_path
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negative:
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cmp #(256 - max)
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cmp #(256 - ((max) << 4))
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beq first_equal ; 'equal' on first byte
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bpl all_done ; 'greater than'
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nope_out:
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jmp exit_path
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first_equal:
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; following bytes all 0 shows it's really 'equal'
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lda arg + 2
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bne all_done
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lda arg + 1
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bne all_done
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lda arg
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bne all_done
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jmp exit_path
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beq nope_out ; 2nd byte 0 shows it's really 'equal'
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all_done:
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.endmacro
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; 8.24: (-128 .. 127.9)
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; 4.12: (-8 .. +7.9)
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; zx = zx_2 - zy_2 + cx
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sub32 zx, zx_2, zy_2
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add32 zx, zx, cx
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sub16 zx, zx_2, zy_2
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add16 zx, zx, cx
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quick_exit zx, 2
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; zy = zx_zy + zx_zy + cy
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add32 zy, zx_zy, zx_zy
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add32 zy, zy, cy
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add16 zy, zx_zy, zx_zy
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add16 zy, zy, cy
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quick_exit zy, 2
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; convert 8.24 -> 4.12: (-8 .. +7.9)
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shift_round_16 zx, 4
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shift_round_16 zy, 4
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; zx_2 = zx * zx
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sqr16 zx_2, zx + 2
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sqr16_round zx_2, zx, 4
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; zy_2 = zy * zy
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sqr16 zy_2, zy + 2
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sqr16_round zy_2, zy, 4
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; zx_zy = zx * zy
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imul16 zx_zy, zx + 2, zy + 2
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imul16_round zx_zy, zx, zy, 4
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; dist = zx_2 + zy_2
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add32 dist, zx_2, zy_2
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add16 dist, zx_2, zy_2
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quick_exit dist, 4
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; if may be in the lake, look for looping output with a small buffer
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@ -1034,10 +989,10 @@ z_buffer_loop:
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; Compare the previously stored z values
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ldy #0
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z_compare zx + 2
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z_compare zx + 3
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z_compare zy + 2
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z_compare zy + 3
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z_compare zx
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z_compare zx + 1
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z_compare zy
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z_compare zy + 1
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cpy #4
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bne z_no_matches
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@ -1052,10 +1007,10 @@ z_no_matches:
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z_nothing_to_read:
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; Store and expand
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z_store zx + 2
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z_store zx + 3
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z_store zy + 2
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z_store zy + 3
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z_store zx
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z_store zx + 1
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z_store zy
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z_store zy + 1
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z_advance
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stx z_buffer_end
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@ -1106,17 +1061,14 @@ cont:
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enough:
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.endmacro
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.macro zoom_factor dest, src, aspect
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; output: dest: fixed8.24
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; input: src: fixed4.12
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; aspect: fixed4.12
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.macro zoom_factor dest, src, zoom, aspect
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; clobbers A, X, flags, etc
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copy16 dest, src
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scale_zoom dest
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; cy = cy * (3 / 4)
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; cx = cx * (5 / 4)
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imul16 dest, dest, aspect
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imul16_round dest, dest, aspect, 4
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.endmacro
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.proc pset
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@ -1454,32 +1406,17 @@ zero_byte_loop:
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txa
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asl a
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asl a
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tax
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lda viewport_ox,x
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sta ox
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lda viewport_oy,x
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sta oy
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inx
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lda viewport_ox,x
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sta ox + 1
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lda viewport_oy,x
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sta oy + 1
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inx
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lda viewport_ox,x
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sta ox + 2
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lda viewport_oy,x
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sta oy + 2
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inx
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lda viewport_ox,x
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sta ox + 3
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lda viewport_oy,x
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sta oy + 3
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rts
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.endproc
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@ -1601,10 +1538,10 @@ skipped_mask:
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not_skipped_mask:
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; run the fractal!
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zoom_factor cx, sx, aspect_x
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add32 cx, cx, ox
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zoom_factor cy, sy, aspect_y
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add32 cy, cy, oy
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zoom_factor cx, sx, zoom, aspect_x
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add16 cx, cx, ox
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zoom_factor cy, sy, zoom, aspect_y
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add16 cy, cy, oy
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jsr mandelbrot
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jsr pset
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@ -27,7 +27,7 @@ The 16-bit signed integer multiplication takes two 16-bit inputs and emits one 3
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* when expanded RAM is available as on 130XE, a 64KB 8-bit multiplication table accelerates the remaining multiplications
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* without expanded RAM, a table of half-squares is used to implement the algorithm from https://everything2.com/title/Fast+6502+multiplication
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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.
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The mandelbrot calculations are done using 4.12-precision fixed point numbers. It may be possible to squish this down to 3.13.
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Iterations are capped at 255.
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@ -47,4 +47,4 @@ Currently produces a `.xex` executable, which can be booted up in common Atari e
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## Todo
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See ideas in `todo.md`.
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See ideas in `todo.md`.
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4
todo.md
4
todo.md
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@ -3,11 +3,13 @@ things to try:
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* skip add on the top-byte multiply in sqr8/mul8
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* should save a few cycles, suggestion by jamey
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* perform the zx += zx^s + cx in 32-bit space, before rounding
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* should improve precision on max zoom, might cost a few cycles
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* patch the entire expanded-ram imul8xe on top of imul8 to avoid the 3-cycle thunk penalty :D
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* try 3.13 fixed point instead of 4.12 for more precision
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* can we get away without the extra bit?
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* since exit compare space would be 6.26 i think so
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* y-axis mirror optimization
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Loading…
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Reference in a new issue