====== 8bit_atan2_using_the_cordic_algorithm ======
By Oswald

64tass source below, it will calculate the angles for the default char screen and display them on it. it is possible to get more than 8 precise bit by increasing the angleslo/hi tables and running the loop as many times as many entries in the tables. 16 is too much, at that stage all bits are 0 in the angleslo/hi tables.

explanation of the algorithm: [[https://www.eit.lth.se/fileadmin/eit/courses/eitf35/2017/CORDIC_For_Dummies.pdf]]

this routine was used in this prod: [[https://www.pouet.net/prod.php?which=91340]] (a more size optimised version ofcourse)


<code>
loopcount	= $0f

x	= $10

y	= $12

xxl	= $14
xxh	= $15

yyl	= $16
yyh	= $17

xxshiftl	= $18
xxshifth	= $19

yyshiftl	= $1a
yyshifth	= $1b

anglelo	= $1c
anglehi	= $1d

sanglelo	= $1e
sanglehi	= $1f


	*= $1000
	
	sei
	
	lda #20
	sta 53272
	lda #200
	sta xxl
	lda #100
	sta yyl
	lda #0
	sta xxh
	sta yyh
	jsr cordic
	inc $d020
	;jmp *-3
	
	lda #0
	sta x
	sta y
-	
	lda x
	sec
	sbc #20
	sta xxh
	lda #0
	sbc #$01
	sta xxl

	
	lda y
	sec
	sbc #12
	sta yyh
	lda #0
	sbc #$80
	sta yyl

	
	lda y
	asl
	tay
	lda mul40+0,y
	clc
	adc x
	sta dst+1
	lda mul40+1,y
	adc #0
	sta dst+2
	
	jsr cordic
dst	sta $0400
	
	inc x
	lda x
	cmp #40
	bne -
	
	lda #0
	sta x
	
	inc y
	lda y
	cmp #25
	bne -
	
	
	jmp *
	
neg
	lda xxh
	bpl +
	lda xxshiftl
	eor #$ff
	clc
	adc #$01
	sta xxshiftl
	lda xxshifth
	eor #$ff
	adc #$00
	sta xxshifth
+

	lda yyh
	bpl +
	lda yyshiftl
	eor #$ff
	clc
	adc #$01
	sta yyshiftl
	lda yyshifth
	eor #$ff
	adc #$00
	sta yyshifth
+	rts	

cordic	lda #0
	sta loopcount
	sta sanglelo
	sta sanglehi

	lda xxh
	bpl notneg
	
	lda xxl
	eor #$ff
	clc
	adc #$01
	sta xxl
	lda xxh
	eor #$ff
	adc #$00
	sta xxh

	lda yyl
	eor #$ff
	clc
	adc #$01
	sta yyl
	lda yyh
	eor #$ff
	adc #$00
	sta yyh
	
	lda #$80
	sta sanglehi
notneg	
cordicloop		
	lda xxl
	sta xxshiftl
	lda xxh
	sta xxshifth

	lda yyl
	sta yyshiftl
	lda yyh
	sta yyshifth



	
	ldx loopcount	
	beq noshift
	

	jsr neg	;if xxshifth (xxh) neg make pos
-	
	lda xxshifth
	cmp #$80
	ror xxshifth
	ror xxshiftl
	
	lda yyshifth
	cmp #$80
	ror yyshifth
	ror yyshiftl
	dex
	bne -

	jsr neg	;iff xxshifth was neg make neg again
	

noshift	

	lda yyh
	bmi yisneg

yispos	

	;Xnew = X + (Y >> LoopNum) 
	lda xxl
	clc
	adc yyshiftl
	sta xxl

	lda xxh
	adc yyshifth
	sta xxh
	
	; Ynew = Y - (X >> LoopNum) 
	lda yyl
	sec
	sbc xxshiftl
	sta yyl

	lda yyh
	sbc xxshifth
	sta yyh


	ldx loopcount
	lda sanglelo
	clc
	adc angleslo,x
	sta sanglelo
	
	lda sanglehi
	adc angleshi,x
	sta sanglehi
	
	jmp cordicloopend
yisneg


	; Xnew = X - (Y >> LoopNum) 
	lda xxl
	sec
	sbc yyshiftl
	sta xxl

	lda xxh
	sbc yyshifth
	sta xxh
	
	; Ynew = Y + (X >> LoopNum) 

	lda yyl
	clc
	adc xxshiftl
	sta yyl

	lda yyh
	adc xxshifth
	sta yyh

	ldx loopcount
	lda sanglelo
	sec
	sbc angleslo,x
	sta sanglelo
	lda sanglehi
	sbc angleshi,x
	sta sanglehi
	
	
cordicloopend
	
	
	inc loopcount
	lda loopcount
	cmp #8
	bne cordicloop
	
	lda sanglehi
	rts
	
	;360 = 2 * pi
	;360 = 255
	;(2*pi)/65536 = step
	
angleslo	.for ue=0,ue<8,ue=ue+1
	;.warn tan(atan(1.0/(2**ue)))
	
	.byte <round(atan(1.0/(2**ue))/((2*pi)/65536))
	;.warn ue
	.next	
	
angleshi	.for ue=0,ue<8,ue=ue+1
	;.warn tan(atan(1.0/(2**ue)))
	
	.byte >round(atan(1.0/(2**ue))/((2*pi)/65536))
	;.warn ue
	.next	


mul40	.for ue=0,ue<25,ue=ue+1
	
	.word $0400+ue*40
	.next

</code>