bubble: add optimized versions

512 bytes fast, 256 bytes slow
This commit is contained in:
Vince Weaver 2024-03-03 22:15:03 -05:00
parent f58040b071
commit f07bb3d42a
4 changed files with 846 additions and 3 deletions

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@ -9,7 +9,7 @@ all: bubble.dsk make_table make_table2 make_table3 compact_sine
bubble.dsk: HELLO BUBBLE.BAS BUBBLE BUBBLE_C64 \
BUBBLE_ORIG BUBBLE_ROLLED DIAMOND FAST_DOTS \
BUBBLE_TINY
BUBBLE_TINY BUBBLE_ROM BUBBLE_XOR
cp $(EMPTY_DISK)/empty.dsk bubble.dsk
$(DOS33) -y bubble.dsk SAVE A HELLO
$(DOS33) -y bubble.dsk SAVE A BUBBLE.BAS
@ -20,6 +20,8 @@ bubble.dsk: HELLO BUBBLE.BAS BUBBLE BUBBLE_C64 \
$(DOS33) -y bubble.dsk BSAVE -a 0x0C00 FAST_DOTS
$(DOS33) -y bubble.dsk BSAVE -a 0x0C00 BUBBLE_C64
$(DOS33) -y bubble.dsk BSAVE -a 0x0C00 BUBBLE_TINY
$(DOS33) -y bubble.dsk BSAVE -a 0x0C00 BUBBLE_ROM
$(DOS33) -y bubble.dsk BSAVE -a 0x0C00 BUBBLE_XOR
###
@ -36,6 +38,22 @@ bubble.o: bubble.s hgr_clear_part.s sin_unrolled.s
###
BUBBLE_XOR: bubble_xor.o
ld65 -o BUBBLE_XOR bubble_xor.o -C $(LINKER_SCRIPTS)/apple2_c00.inc
bubble_xor.o: bubble_xor.s hgr_clear_codegen.s
ca65 -o bubble_xor.o bubble_xor.s -l bubble_xor.lst
###
BUBBLE_ROM: bubble_rom.o
ld65 -o BUBBLE_ROM bubble_rom.o -C $(LINKER_SCRIPTS)/apple2_c00.inc
bubble_rom.o: bubble_rom.s hgr_clear_codegen.s
ca65 -o bubble_rom.o bubble_rom.s -l bubble_rom.lst
###
BUBBLE_TINY: bubble_tiny.o
ld65 -o BUBBLE_TINY bubble_tiny.o -C $(LINKER_SCRIPTS)/apple2_c00.inc
@ -132,4 +150,5 @@ compact_sine.o: compact_sine.c
clean:
rm -f *~ *.o *.lst BUBBLE.BAS HELLO BUBBLE BUBBLE_C64 \
DIAMOND BUBBLE_ORIG BUBBLE_ROLLED FAST_DOTS \
make_table make_table2 make_table3 compact_sine
make_table make_table2 make_table3 compact_sine \
BUBBLE_ROM BUBBLE_XOR

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@ -0,0 +1,304 @@
; bubble universe -- Apple II Hires
; size optimized version, using ROM (slower)
; by Vince `deater` Weaver
; this version based on fast c64 code by serato_fig
; as posted to the sizecoding discord
; based on his TIC-80 variant
; originally was working off the BASIC code posted on the pouet forum
; original effect by yuruyrau on twitter
; 534 bytes -- tiny version
; 250 bytes -- strip out fast clear and hplot code and use ROM
; 76d03 cycles = 486659 cycles = 2fps
; soft-switches
KEYPRESS = $C000
KEYRESET = $C010
PAGE1 = $C054
PAGE2 = $C055
; ROM routines
BKGND0 = $F3F4 ; clear current page to A
HGR2 = $F3D8 ; set hires page2 and clear $4000-$5fff
HGR = $F3E2 ; set hires page1 and clear $2000-$3fff
HPLOT0 = $F457 ; plot at (Y,X), (A)
HCOLOR1 = $F6F0 ; set HGR_COLOR to value in X
;COLORTBL = $F6F6
;WAIT = $FCA8 ; delay 1/2(26+27A+5A^2) us
; zero page
GBASL = $26
GBASH = $27
HPLOTYL = $92
I = $D0
J = $D1
T = $D7
U = $D8
V = $D9
HGR_PAGE = $E6
INL = $FC
INH = $FD
OUTL = $FE
OUTH = $FF
; const
;NUM = 32
;NUM = 24
bubble:
;========================
; setup lookup tables
; jsr hgr_make_tables
; jsr hgr_clear_codegen
jsr setup_sine_table
;=======================
; init graphics
jsr HGR
jsr HGR2
;=======================
; init variables
; HGR leaves A at 0
; lda #0
sta U
sta V
sta T
ldx #7
jsr HCOLOR1
;=========================
;=========================
; main loop
;=========================
;=========================
next_frame:
; reset I*T
lda T
sta it1_smc+1
sta it2_smc+1
; reset I*S
lda #0
sta is1_smc+1
sta is2_smc+1
num1_smc:
lda #24 ; 40
sta I
i_loop:
num2_smc:
lda #24 ; 200
sta J
j_loop:
ldx U
ldy V
; where S=41 (approximately 1/6.28)
clc ; 2
; calc: b=i+t+u;
; u=cosines[a]+cosines[b];
is2_smc:
lda cosines,Y ; 4+
it2_smc:
adc cosines,X ; 4+
sta V
; calc: a=i*s+v;
; u=sines[a]+sines[b];
is1_smc:
lda sines,Y ; 4+
it1_smc:
adc sines,X ; 4+
sta U ; 3
;===========================================================
; HPLOT U+44,V+96
; U is centered at 96, to get to center of 280 screen add 44
; U already in A
adc #44 ; 2
tax ; 2
; calculate Ypos
lda V
;HPLOT0 = $F457 ; plot at (Y,X), (A)
ldy #0
jsr HPLOT0
dec J
bne j_loop
done_j:
lda is1_smc+1
clc
adc #41 ; 1/6.28 = 0.16 = 0 0 1 0 1 0 0 0 = 0x28
sta is1_smc+1
sta is2_smc+1
dec I
bne i_loop
done_i:
; sty V
inc T
end:
.if 0
lda KEYPRESS
bpl flip_pages
bit KEYRESET
; 0110 -> 0100
and #$5f ; to handle lowercase too...
cmp #'A'
bne check_z
inc num1_smc+1
jmp done_keys
check_z:
cmp #'Z'
bne check_j
dec num1_smc+1
jmp done_keys
check_j:
cmp #'J'
bne check_m
inc num2_smc+1
jmp done_keys
check_m:
cmp #'M'
bne done_keys
dec num2_smc+1
.endif
done_keys:
flip_pages:
; flip pages
; if $20 (draw PAGE1) draw PAGE2, SHOW page1
; if $40 (draw PAGE2) draw PAGE1, SHOW page2
lda HGR_PAGE
eor #$60
sta HGR_PAGE
cmp #$40
bne flip2
flip1:
bit PAGE1
lda #0
jsr BKGND0
; jsr hgr_page2_clearscreen
jmp next_frame
flip2:
bit PAGE2
lda #0
jsr BKGND0
; jsr hgr_page1_clearscreen
jmp next_frame
; floor(s*sin((x-96)*PI*2/256.0)+48.5);
; note: min=7, around 32
; max=89 ($59), around 160
; subtract 7, so 0...82? halfway = 41 = $29 + 7 = $30
; halfway= 6*16 = 96
sines = $6c00
sines2 = $6d00
cosines = $6e00
cosines2= $6f00
;===================================
;
;
; final_sine[i]=quarter_sine[i]; // 0..64
; final_sine[128-i]=quarter_sine[i]; // 64..128
; final_sine[128+i]=0x60-quarter_sine[i]; // 128..192
; final_sine[256-i]=0x60-quarter_sine[i]; // 192..256
setup_sine_table:
ldy #64
ldx #64
setup_sine_loop:
lda sines_base,Y
sta sines,Y
sta sines2,Y
sta sines,X
sta sines2,X
lda #$60
sec
sbc sines_base,Y
sta sines+128,Y
sta sines2+128,Y
sta sines+128,X
sta sines2+128,X
inx
dey
bpl setup_sine_loop
ldy #0
cosine_loop:
lda sines+192,Y
sta cosines,Y
sta cosines2,Y
iny
bne cosine_loop
rts
sines_base:
.byte $30,$31,$32,$33,$34,$35,$36,$37,$38,$39,$3A,$3B,$3C,$3D,$3E,$3F
.byte $40,$41,$42,$42,$43,$44,$45,$46,$47,$48,$48,$49,$4A,$4B,$4C,$4C
.byte $4D,$4E,$4E,$4F,$50,$50,$51,$52,$52,$53,$53,$54,$54,$55,$55,$55
.byte $56,$56,$57,$57,$57,$58,$58,$58,$58,$58,$59,$59,$59,$59,$59,$59
.byte $59
; floor(s*cos((x-96)*PI*2/256.0)+48.5);

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@ -21,6 +21,7 @@
; 1434 bytes -- optimize HPLOT
; 1131 bytes -- generate SINE table from 65 entry lookup
; 633 bytes -- generate COSINE table from SINE table
; 534 bytes -- alignment was left on for some reason
; soft-switches
@ -195,6 +196,7 @@ it1_smc:
lda (GBASL),Y ; 5
ora log_lookup,X ; 4
; eor log_lookup,X ; 4
sta (GBASL),Y ; 6
; 46
@ -360,7 +362,6 @@ log_lookup:
.include "hgr_clear_codegen.s"
.align $100
; note: min=7, around 32
; max=89 ($59), around 160

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@ -0,0 +1,519 @@
; bubble universe -- Apple II Hires
; xor?
; size optimized version
; by Vince `deater` Weaver
; this version based on fast c64 code by serato_fig
; as posted to the sizecoding discord
; based on his TIC-80 variant
; originally was working off the BASIC code posted on the pouet forum
; original effect by yuruyrau on twitter
; 2304 bytes -- first working version
; 2560 bytes -- full version with keypress to adjust
; 2326 bytes -- alignment turned off
; 2311 bytes -- optimize mod table generation
; 1447 bytes -- first attempt at hgr_clear codegen
; 1443 bytes -- tail call optimization
; 1436 bytes -- call clear screen from page flip code
; 1434 bytes -- optimize HPLOT
; 1131 bytes -- generate SINE table from 65 entry lookup
; 633 bytes -- generate COSINE table from SINE table
; 534 bytes -- alignment was left on for some reason
; soft-switches
KEYPRESS = $C000
KEYRESET = $C010
PAGE1 = $C054
PAGE2 = $C055
; ROM routines
BKGND0 = $F3F4 ; clear current page to A
HGR2 = $F3D8 ; set hires page2 and clear $4000-$5fff
HGR = $F3E2 ; set hires page1 and clear $2000-$3fff
HPLOT0 = $F457 ; plot at (Y,X), (A)
;HCOLOR1 = $F6F0 ; set HGR_COLOR to value in X
;COLORTBL = $F6F6
;WAIT = $FCA8 ; delay 1/2(26+27A+5A^2) us
; zero page
GBASL = $26
GBASH = $27
HPLOTYL = $92
I = $D0
J = $D1
T = $D7
U = $D8
V = $D9
HGR_PAGE = $E6
INL = $FC
INH = $FD
OUTL = $FE
OUTH = $FF
; const
;NUM = 32
;NUM = 24
bubble:
;========================
; setup lookup tables
jsr hgr_make_tables
; jsr hgr_clear_codegen
jsr setup_sine_table
;=======================
; init graphics
jsr HGR
jsr HGR2
;=======================
; init variables
; HGR leaves A at 0
; lda #0
sta U
sta V
sta T
;=========================
;=========================
; main loop
;=========================
;=========================
next_frame:
; reset I*T
lda T
sta it1_smc+1
sta it2_smc+1
; reset I*S
lda #0
sta is1_smc+1
sta is2_smc+1
num1_smc:
lda #24 ; 40
sta I
i_loop:
num2_smc:
lda #24 ; 200
sta J
j_loop:
ldx U
ldy V
; where S=41 (approximately 1/6.28)
clc ; 2
; calc: b=i+t+u;
; u=cosines[a]+cosines[b];
is2_smc:
lda cosines,Y ; 4+
it2_smc:
adc cosines,X ; 4+
sta V
; calc: a=i*s+v;
; u=sines[a]+sines[b];
is1_smc:
lda sines,Y ; 4+
it1_smc:
adc sines,X ; 4+
sta U ; 3
;===========================================================
; HPLOT U+44,V+96
; U is centered at 96, to get to center of 280 screen add 44
; U already in A
adc #44 ; 2
tax ; 2
; calculate Ypos
ldy V
; "fast" hplot, Xpos in X, Ypos in A
; Apple II hi-res is more-or-less 280x192
; two consecutive pixels on are white
; single pixels are colored based on palette
; we treat things as a monochrome display, on a color
; display odd/even pixels will have different colors
; The Y memory offset is a horrible interleaved mess, so we use
; a lookup table we generated at start. We also add in
; the proper value for page-flipping
; Apple II hi-res is 7 pixels/byte, so we also pre-generate
; div and mod by 7 tables at start and use those
; instead of dividing by 7
; We cheat and don't worry about the X positions larger
; than 256 because our algorithm only goes up to 208
lda hposn_low,Y ; 4
sta GBASL ; 3
lda hposn_high,Y ; 4
ora HGR_PAGE ; 3
sta GBASH ; 3
; 21
ldy div7_table,X ; 4
lda mod7_table,X ; 4
tax ; 2
; 31
; get current 7-bit pixel range, OR in to set new pixel
lda (GBASL),Y ; 5
; ora log_lookup,X ; 4
eor log_lookup,X ; 4
sta (GBASL),Y ; 6
; 46
dec J
bne j_loop
done_j:
lda is1_smc+1
clc
adc #41 ; 1/6.28 = 0.16 = 0 0 1 0 1 0 0 0 = 0x28
sta is1_smc+1
sta is2_smc+1
dec I
bne i_loop
done_i:
; sty V
inc T
end:
lda KEYPRESS
bpl flip_pages
bit KEYRESET
; 0110 -> 0100
and #$5f ; to handle lowercase too...
cmp #'A'
bne check_z
inc num1_smc+1
jmp done_keys
check_z:
cmp #'Z'
bne check_j
dec num1_smc+1
jmp done_keys
check_j:
cmp #'J'
bne check_m
inc num2_smc+1
jmp done_keys
check_m:
cmp #'M'
bne done_keys
dec num2_smc+1
done_keys:
flip_pages:
; flip pages
; if $20 (draw PAGE1) draw PAGE2, SHOW page1
; if $40 (draw PAGE2) draw PAGE1, SHOW page2
; lda HGR_PAGE
; eor #$60
; sta HGR_PAGE
; cmp #$40
; bne flip2
;flip1:
; bit PAGE1
; lda #0
; jsr hgr_page2_clearscreen
; jmp next_frame
;flip2:
; bit PAGE2
; lda #0
; jsr hgr_page1_clearscreen
jmp next_frame
div7_table = $6800
mod7_table = $6900
hposn_high = $6a00
hposn_low = $6b00
hgr_make_tables:
;=====================
; make /7 %7 tables
;=====================
hgr_make_7_tables:
lda #0
tax
tay
div7_loop:
sta div7_table,Y
mod7_smc:
stx mod7_table
inx
cpx #7
bne div7_not7
clc
adc #1
ldx #0
div7_not7:
inc mod7_smc+1 ; assume on page boundary
iny
bne div7_loop
; Hposn table
; hposn_low, hposn_high will each be filled with $C0 bytes
; based on routine by John Brooks
; posted on comp.sys.apple2 on 2018-07-11
; https://groups.google.com/d/msg/comp.sys.apple2/v2HOfHOmeNQ/zD76fJg_BAAJ
; clobbers A,X
; preserves Y
; vmw note: version I was using based on applesoft HPOSN was ~64 bytes
; this one is 37 bytes
build_hposn_tables:
ldx #0
btmi:
txa
and #$F8
bpl btpl1
ora #5
btpl1:
asl
bpl btpl2
ora #5
btpl2:
asl
asl
sta hposn_low, X
txa
and #7
rol
asl hposn_low, X
rol
; ora #$20
sta hposn_high, X
inx
cpx #$C0
bne btmi
rts
; which of 7 pixels to draw
; note high bit is set to pick blue/orange palette
; clear to get purple/green instead
log_lookup:
.byte $81,$82,$84,$88,$90,$A0,$C0,$80
; the current "fast" code expects to be aligned on boundary
; also have to double things up as the code can go up to 255 off
; end for speed reasons
; floor(s*sin((x-96)*PI*2/256.0)+48.5);
;.include "hgr_clear_codegen.s"
; note: min=7, around 32
; max=89 ($59), around 160
; subtract 7, so 0...82? halfway = 41 = $29 + 7 = $30
; halfway= 6*16 = 96
sines = $6c00
sines2 = $6d00
cosines = $6e00
cosines2= $6f00
;===================================
;
;
; final_sine[i]=quarter_sine[i]; // 0..64
; final_sine[128-i]=quarter_sine[i]; // 64..128
; final_sine[128+i]=0x60-quarter_sine[i]; // 128..192
; final_sine[256-i]=0x60-quarter_sine[i]; // 192..256
setup_sine_table:
ldy #64
ldx #64
setup_sine_loop:
lda sines_base,Y
sta sines,Y
sta sines2,Y
sta sines,X
sta sines2,X
lda #$60
sec
sbc sines_base,Y
sta sines+128,Y
sta sines2+128,Y
sta sines+128,X
sta sines2+128,X
inx
dey
bpl setup_sine_loop
ldy #0
cosine_loop:
lda sines+192,Y
sta cosines,Y
sta cosines2,Y
iny
bne cosine_loop
rts
sines_base:
.byte $30,$31,$32,$33,$34,$35,$36,$37,$38,$39,$3A,$3B,$3C,$3D,$3E,$3F
.byte $40,$41,$42,$42,$43,$44,$45,$46,$47,$48,$48,$49,$4A,$4B,$4C,$4C
.byte $4D,$4E,$4E,$4F,$50,$50,$51,$52,$52,$53,$53,$54,$54,$55,$55,$55
.byte $56,$56,$57,$57,$57,$58,$58,$58,$58,$58,$59,$59,$59,$59,$59,$59
.byte $59
.if 0
sines:
.byte $30,$31,$32,$33,$34,$35,$36,$37,$38,$39,$3A,$3B,$3C,$3D,$3E,$3F
.byte $40,$41,$42,$42,$43,$44,$45,$46,$47,$48,$48,$49,$4A,$4B,$4C,$4C
.byte $4D,$4E,$4E,$4F,$50,$50,$51,$52,$52,$53,$53,$54,$54,$55,$55,$55
.byte $56,$56,$57,$57,$57,$58,$58,$58,$58,$58,$59,$59,$59,$59,$59,$59
.byte $59,$59,$59,$59,$59,$59,$59,$58,$58,$58,$58,$58,$57,$57,$57,$56
.byte $56,$55,$55,$55,$54,$54,$53,$53,$52,$52,$51,$50,$50,$4F,$4E,$4E
.byte $4D,$4C,$4C,$4B,$4A,$49,$48,$48,$47,$46,$45,$44,$43,$42,$42,$41
.byte $40,$3F,$3E,$3D,$3C,$3B,$3A,$39,$38,$37,$36,$35,$34,$33,$32,$31
.byte $30,$2F,$2E,$2D,$2C,$2B,$2A,$29,$28,$27,$26,$25,$24,$23,$22,$21
.byte $20,$1F,$1E,$1E,$1D,$1C,$1B,$1A,$19,$18,$18,$17,$16,$15,$14,$14
; original start
.byte $13,$12,$12,$11,$10,$10,$0F,$0E,$0E,$0D,$0D,$0C,$0C,$0B,$0B,$0B
.byte $0A,$0A,$09,$09,$09,$08,$08,$08,$08,$08,$07,$07,$07,$07,$07,$07
.byte $07,$07,$07,$07,$07,$07,$07,$08,$08,$08,$08,$08,$09,$09,$09,$0A
.byte $0A,$0B,$0B,$0B,$0C,$0C,$0D,$0D,$0E,$0E,$0F,$10,$10,$11,$12,$12
.byte $13,$14,$14,$15,$16,$17,$18,$18,$19,$1A,$1B,$1C,$1D,$1E,$1E,$1F
.byte $20,$21,$22,$23,$24,$25,$26,$27,$28,$29,$2A,$2B,$2C,$2D,$2E,$2F
sines2:
.byte $30,$31,$32,$33,$34,$35,$36,$37,$38,$39,$3A,$3B,$3C,$3D,$3E,$3F
.byte $40,$41,$42,$42,$43,$44,$45,$46,$47,$48,$48,$49,$4A,$4B,$4C,$4C
.byte $4D,$4E,$4E,$4F,$50,$50,$51,$52,$52,$53,$53,$54,$54,$55,$55,$55
.byte $56,$56,$57,$57,$57,$58,$58,$58,$58,$58,$59,$59,$59,$59,$59,$59
.byte $59,$59,$59,$59,$59,$59,$59,$58,$58,$58,$58,$58,$57,$57,$57,$56
.byte $56,$55,$55,$55,$54,$54,$53,$53,$52,$52,$51,$50,$50,$4F,$4E,$4E
.byte $4D,$4C,$4C,$4B,$4A,$49,$48,$48,$47,$46,$45,$44,$43,$42,$42,$41
.byte $40,$3F,$3E,$3D,$3C,$3B,$3A,$39,$38,$37,$36,$35,$34,$33,$32,$31
.byte $30,$2F,$2E,$2D,$2C,$2B,$2A,$29,$28,$27,$26,$25,$24,$23,$22,$21
.byte $20,$1F,$1E,$1E,$1D,$1C,$1B,$1A,$19,$18,$18,$17,$16,$15,$14,$14
.byte $13,$12,$12,$11,$10,$10,$0F,$0E,$0E,$0D,$0D,$0C,$0C,$0B,$0B,$0B
.byte $0A,$0A,$09,$09,$09,$08,$08,$08,$08,$08,$07,$07,$07,$07,$07,$07
.byte $07,$07,$07,$07,$07,$07,$07,$08,$08,$08,$08,$08,$09,$09,$09,$0A
.byte $0A,$0B,$0B,$0B,$0C,$0C,$0D,$0D,$0E,$0E,$0F,$10,$10,$11,$12,$12
.byte $13,$14,$14,$15,$16,$17,$18,$18,$19,$1A,$1B,$1C,$1D,$1E,$1E,$1F
.byte $20,$21,$22,$23,$24,$25,$26,$27,$28,$29,$2A,$2B,$2C,$2D,$2E,$2F
; floor(s*cos((x-96)*PI*2/256.0)+48.5);
cosines:
; sine[64]
.byte $59,$59,$59,$59,$59,$59,$59,$58,$58,$58,$58,$58,$57,$57,$57,$56
.byte $56,$55,$55,$55,$54,$54,$53,$53,$52,$52,$51,$50,$50,$4F,$4E,$4E
.byte $4D,$4C,$4C,$4B,$4A,$49,$48,$48,$47,$46,$45,$44,$43,$42,$42,$41
.byte $40,$3F,$3E,$3D,$3C,$3B,$3A,$39,$38,$37,$36,$35,$34,$33,$32,$31
; sine[128]
.byte $30,$2F,$2E,$2D,$2C,$2B,$2A,$29,$28,$27,$26,$25,$24,$23,$22,$21
.byte $20,$1F,$1E,$1E,$1D,$1C,$1B,$1A,$19,$18,$18,$17,$16,$15,$14,$14
.byte $13,$12,$12,$11,$10,$10,$0F,$0E,$0E,$0D,$0D,$0C,$0C,$0B,$0B,$0B
.byte $0A,$0A,$09,$09,$09,$08,$08,$08,$08,$08,$07,$07,$07,$07,$07,$07
; sine[192]
.byte $07,$07,$07,$07,$07,$07,$07,$08,$08,$08,$08,$08,$09,$09,$09,$0A
.byte $0A,$0B,$0B,$0B,$0C,$0C,$0D,$0D,$0E,$0E,$0F,$10,$10,$11,$12,$12
.byte $13,$14,$14,$15,$16,$17,$18,$18,$19,$1A,$1B,$1C,$1D,$1E,$1E,$1F
.byte $20,$21,$22,$23,$24,$25,$26,$27,$28,$29,$2A,$2B,$2C,$2D,$2E,$2F
; sine[0]
.byte $30,$31,$32,$33,$34,$35,$36,$37,$38,$39,$3A,$3B,$3C,$3D,$3E,$3F
.byte $40,$41,$42,$42,$43,$44,$45,$46,$47,$48,$48,$49,$4A,$4B,$4C,$4C
.byte $4D,$4E,$4E,$4F,$50,$50,$51,$52,$52,$53,$53,$54,$54,$55,$55,$55
.byte $56,$56,$57,$57,$57,$58,$58,$58,$58,$58,$59,$59,$59,$59,$59,$59
cosines2:
.byte $59,$59,$59,$59,$59,$59,$59,$58,$58,$58,$58,$58,$57,$57,$57,$56
.byte $56,$55,$55,$55,$54,$54,$53,$53,$52,$52,$51,$50,$50,$4F,$4E,$4E
.byte $4D,$4C,$4C,$4B,$4A,$49,$48,$48,$47,$46,$45,$44,$43,$42,$42,$41
.byte $40,$3F,$3E,$3D,$3C,$3B,$3A,$39,$38,$37,$36,$35,$34,$33,$32,$31
.byte $30,$2F,$2E,$2D,$2C,$2B,$2A,$29,$28,$27,$26,$25,$24,$23,$22,$21
.byte $20,$1F,$1E,$1E,$1D,$1C,$1B,$1A,$19,$18,$18,$17,$16,$15,$14,$14
.byte $13,$12,$12,$11,$10,$10,$0F,$0E,$0E,$0D,$0D,$0C,$0C,$0B,$0B,$0B
.byte $0A,$0A,$09,$09,$09,$08,$08,$08,$08,$08,$07,$07,$07,$07,$07,$07
.byte $07,$07,$07,$07,$07,$07,$07,$08,$08,$08,$08,$08,$09,$09,$09,$0A
.byte $0A,$0B,$0B,$0B,$0C,$0C,$0D,$0D,$0E,$0E,$0F,$10,$10,$11,$12,$12
.byte $13,$14,$14,$15,$16,$17,$18,$18,$19,$1A,$1B,$1C,$1D,$1E,$1E,$1F
.byte $20,$21,$22,$23,$24,$25,$26,$27,$28,$29,$2A,$2B,$2C,$2D,$2E,$2F
.byte $30,$31,$32,$33,$34,$35,$36,$37,$38,$39,$3A,$3B,$3C,$3D,$3E,$3F
.byte $40,$41,$42,$42,$43,$44,$45,$46,$47,$48,$48,$49,$4A,$4B,$4C,$4C
.byte $4D,$4E,$4E,$4F,$50,$50,$51,$52,$52,$53,$53,$54,$54,$55,$55,$55
.byte $56,$56,$57,$57,$57,$58,$58,$58,$58,$58,$59,$59,$59,$59,$59,$59
.endif