This function calculates the angle, in a 256-degree circle. The trick is to use logarithmic division to get the y/x ratio and integrate the power function into the atan table. The idea comes from a 6502 routine.
It seems (to me) the fastest solution ever seen on z80 to compute angles. It should be perfect for bullet hell shooters.
Maybe someone has a faster solution, any proposal for improvements ?
; 8-bit atan2
; Calculate the angle, in a 256-degree circle.
; The trick is to use logarithmic division to get the y/x ratio and
; integrate the power function into the atan table.
; input
; B = x, C = y in -128,127
;
; output
; A = angle in 0-255
; |
; q1 | q0
;------+-------
; q3 | q2
; |
atan2:
ld de,0x8000
ld a,c
add a,d
rl e ; y-
ld a,b
add a,d
rl e ; x-
dec e
jp z,q1
dec e
jp z,q2
dec e
jp z,q3
q0:
ld h,log2_tab / 256
ld l,b
ld a,(hl) ; 32*log2(x)
ld l,c
sub a,(hl) ; 32*log2(x/y)
jr nc,1f ; |x|>|y|
neg ; |x|<|y| A = 32*log2(y/x)
1: ld l,a
ld h,atan_tab / 256
ld a,(hl)
ret c ; |x|<|y|
neg
and 0x3F ; |x|>|y|
ret
q1: ld a,b
neg
ld b,a
call q0
neg
and 0x7F
ret
q2: ld a,c
neg
ld c,a
call q0
neg
ret
q3: ld a,b
neg
ld b,a
ld a,c
neg
ld c,a
call q0
add a,128
ret
; align to byte
align 0x100
; z=0:255; sprintf('%d,',fix(atan(2.^(z/32))*128/pi))
;;;;;;;; atan(2^(x/32))*128/pi ;;;;;;;;
atan_tab:
db 020h,020h,020h,021h,021h,022h,022h,023h,023h,023h,024h,024h,025h,025h,026h,026h
db 026h,027h,027h,028h,028h,028h,029h,029h,02Ah,02Ah,02Ah,02Bh,02Bh,02Ch,02Ch,02Ch
db 02Dh,02Dh,02Dh,02Eh,02Eh,02Eh,02Fh,02Fh,02Fh,030h,030h,030h,031h,031h,031h,031h
db 032h,032h,032h,032h,033h,033h,033h,033h,034h,034h,034h,034h,035h,035h,035h,035h
db 036h,036h,036h,036h,036h,037h,037h,037h,037h,037h,037h,038h,038h,038h,038h,038h
db 038h,039h,039h,039h,039h,039h,039h,039h,039h,03Ah,03Ah,03Ah,03Ah,03Ah,03Ah,03Ah
db 03Ah,03Bh,03Bh,03Bh,03Bh,03Bh,03Bh,03Bh,03Bh,03Bh,03Bh,03Bh,03Ch,03Ch,03Ch,03Ch
db 03Ch,03Ch,03Ch,03Ch,03Ch,03Ch,03Ch,03Ch,03Ch,03Dh,03Dh,03Dh,03Dh,03Dh,03Dh,03Dh
db 03Dh,03Dh,03Dh,03Dh,03Dh,03Dh,03Dh,03Dh,03Dh,03Dh,03Dh,03Dh,03Eh,03Eh,03Eh,03Eh
db 03Eh,03Eh,03Eh,03Eh,03Eh,03Eh,03Eh,03Eh,03Eh,03Eh,03Eh,03Eh,03Eh,03Eh,03Eh,03Eh
db 03Eh,03Eh,03Eh,03Eh,03Eh,03Eh,03Eh,03Eh,03Eh,03Eh,03Eh,03Eh,03Fh,03Fh,03Fh,03Fh
db 03Fh,03Fh,03Fh,03Fh,03Fh,03Fh,03Fh,03Fh,03Fh,03Fh,03Fh,03Fh,03Fh,03Fh,03Fh,03Fh
db 03Fh,03Fh,03Fh,03Fh,03Fh,03Fh,03Fh,03Fh,03Fh,03Fh,03Fh,03Fh,03Fh,03Fh,03Fh,03Fh
db 03Fh,03Fh,03Fh,03Fh,03Fh,03Fh,03Fh,03Fh,03Fh,03Fh,03Fh,03Fh,03Fh,03Fh,03Fh,03Fh
db 03Fh,03Fh,03Fh,03Fh,03Fh,03Fh,03Fh,03Fh,03Fh,03Fh,03Fh,03Fh,03Fh,03Fh,03Fh,03Fh
db 03Fh,03Fh,03Fh,03Fh,03Fh,03Fh,03Fh,03Fh,03Fh,03Fh,03Fh,03Fh,03Fh,03Fh,03Fh,03Fh
; x=0:255;x(1)=1; sprintf('%d,',fix(32*log2(x)))
;;;;;;;; log2(x)*32 ;;;;;;;;
log2_tab:
db 000h,000h,020h,032h,040h,04Ah,052h,059h,060h,065h,06Ah,06Eh,072h,076h,079h,07Dh
db 080h,082h,085h,087h,08Ah,08Ch,08Eh,090h,092h,094h,096h,098h,099h,09Bh,09Dh,09Eh
db 0A0h,0A1h,0A2h,0A4h,0A5h,0A6h,0A7h,0A9h,0AAh,0ABh,0ACh,0ADh,0AEh,0AFh,0B0h,0B1h
db 0B2h,0B3h,0B4h,0B5h,0B6h,0B7h,0B8h,0B9h,0B9h,0BAh,0BBh,0BCh,0BDh,0BDh,0BEh,0BFh
db 0C0h,0C0h,0C1h,0C2h,0C2h,0C3h,0C4h,0C4h,0C5h,0C6h,0C6h,0C7h,0C7h,0C8h,0C9h,0C9h
db 0CAh,0CAh,0CBh,0CCh,0CCh,0CDh,0CDh,0CEh,0CEh,0CFh,0CFh,0D0h,0D0h,0D1h,0D1h,0D2h
db 0D2h,0D3h,0D3h,0D4h,0D4h,0D5h,0D5h,0D5h,0D6h,0D6h,0D7h,0D7h,0D8h,0D8h,0D9h,0D9h
db 0D9h,0DAh,0DAh,0DBh,0DBh,0DBh,0DCh,0DCh,0DDh,0DDh,0DDh,0DEh,0DEh,0DEh,0DFh,0DFh
db 0DFh,0E0h,0E0h,0E1h,0E1h,0E1h,0E2h,0E2h,0E2h,0E3h,0E3h,0E3h,0E4h,0E4h,0E4h,0E5h
db 0E5h,0E5h,0E6h,0E6h,0E6h,0E7h,0E7h,0E7h,0E7h,0E8h,0E8h,0E8h,0E9h,0E9h,0E9h,0EAh
db 0EAh,0EAh,0EAh,0EBh,0EBh,0EBh,0ECh,0ECh,0ECh,0ECh,0EDh,0EDh,0EDh,0EDh,0EEh,0EEh
db 0EEh,0EEh,0EFh,0EFh,0EFh,0EFh,0F0h,0F0h,0F0h,0F1h,0F1h,0F1h,0F1h,0F1h,0F2h,0F2h
db 0F2h,0F2h,0F3h,0F3h,0F3h,0F3h,0F4h,0F4h,0F4h,0F4h,0F5h,0F5h,0F5h,0F5h,0F5h,0F6h
db 0F6h,0F6h,0F6h,0F7h,0F7h,0F7h,0F7h,0F7h,0F8h,0F8h,0F8h,0F8h,0F9h,0F9h,0F9h,0F9h
db 0F9h,0FAh,0FAh,0FAh,0FAh,0FAh,0FBh,0FBh,0FBh,0FBh,0FBh,0FCh,0FCh,0FCh,0FCh,0FCh
db 0FDh,0FDh,0FDh,0FDh,0FDh,0FDh,0FEh,0FEh,0FEh,0FEh,0FEh,0FFh,0FFh,0FFh,0FFh,0FFh
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