Atan2 in assembler for "integer" / screen-ish coordinates

PaulF · Today, 12:25

Hi all , I'm needing an atan2 function in assembler. I have a 2D delta between objects , and want to determine the angle between then to rotate one towards the other. So far the best I can do is to decide on a which quadrant (aka delta signs) the line lines in; take the abs of both dx and dy whilst clamping each to a max value. Then scaling the dx and dy down and combining to form an index into a lookup table , modifying the result based on the original quadrant. So I have 2 main compromises , (1) the clamp will distort the line and (2) the scale down (to reduce the overall table size) will "pixelate" the results.
Any thoughts on how to do this better , thanks for any help.
Paul.

AtanTable:
dc.w 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
dc.w 256,128,75,52,39,32,26,23,20,18,16,14,13,12,11,10
dc.w 256,180,128,95,75,62,52,45,39,35,32,29,26,24,23,21
dc.w 256,203,160,128,104,88,75,65,58,52,47,43,39,36,34,32
dc.w 256,216,180,151,128,109,95,84,75,68,62,56,52,48,45,42
dc.w 256,223,193,167,146,128,113,101,91,82,75,69,64,59,55,52
dc.w 256,229,203,180,160,142,128,115,104,95,88,81,75,70,65,62
dc.w 256,232,210,190,171,154,140,128,117,107,99,92,86,80,75,71
dc.w 256,235,216,197,180,164,151,138,128,118,109,102,95,89,84,79
dc.w 256,237,220,203,187,173,160,148,137,128,119,111,104,98,93,88
dc.w 256,239,223,208,193,180,167,156,146,136,128,120,113,106,101,95
dc.w 256,241,226,212,199,186,174,163,153,144,135,128,120,114,108,103
dc.w 256,242,229,216,203,191,180,169,160,151,142,135,128,121,115,109
dc.w 256,243,231,219,207,196,185,175,166,157,149,141,134,128,121,116
dc.w 256,244,232,221,210,200,190,180,171,162,154,147,140,134,128,122
dc.w 256,245,234,223,213,203,193,184,176,167,160,152,146,139,133,128

GetATan2:
;of d0= dy
; d1= dx
; returns in d2 , 0..$3FF << 1

clr.w d2
tst.w d0
bpl.s .notnegY
bset #0,d2
neg.w d0
.notnegY
tst.w d1
bpl.s .notnegX
bset #1,d2
neg.w d1
.notnegX
.clamp
cmp.w #256,d0
blt.s .noyclamp
move.w #255,d0
.noyclamp
cmp.w #256,d1
blt.s .noxclamp
move.w #255,d1
.noxclamp
;16 entries to span 0..255
lsr.w #4,d1
add.w d1,d1
and.w #$F0,d0
add.w d0,d0
add.w d1,d0
lea.l AtanTable(pc),a4
move.w 0(a4,d0),d3
btst #0,d2
beq .noybias
neg.w d3
add.w #1024,d3
.noybias
btst #1,d2
beq .noxbias
neg.w d3
add.w #512,d3
.noxbias
move.w d3,d2
add.w d2,d2
and.w #$3FF<<1,d2
rts

PaulF · Today, 14:17

So , tried this (forgive the first pass code) , but its got a juicy divide in there.
Atan table is now spans a 1/8th of a circle . Do quadrant stuff, now consider dy/dx , if > 1 , flip to dx/dy , look up angle and correct for >1 (45 degress) and quadrant. No clmaping or loss or resolution.

AtanTable:
dc.w 0,0,1,1,2,3,3,4,5,5,6,6,7,8,8,9
dc.w 10,10,11,12,12,13,13,14,15,15,16,17,17,18,19,19
dc.w 20,20,21,22,22,23,24,24,25,25,26,27,27,28,28,29
dc.w 30,30,31,32,32,33,33,34,35,35,36,36,37,38,38,39
dc.w 39,40,41,41,42,42,43,44,44,45,45,46,47,47,48,48
dc.w 49,49,50,51,51,52,52,53,53,54,55,55,56,56,57,57
dc.w 58,59,59,60,60,61,61,62,62,63,63,64,65,65,66,66
dc.w 67,67,68,68,69,69,70,70,71,71,72,72,73,74,74,75
dc.w 75,76,76,77,77,78,78,79,79,80,80,81,81,82,82,83
dc.w 83,83,84,84,85,85,86,86,87,87,88,88,89,89,90,90
dc.w 91,91,91,92,92,93,93,94,94,95,95,95,96,96,97,97
dc.w 98,98,99,99,99,100,100,101,101,101,102,102,103,103,104,104
dc.w 104,105,105,106,106,106,107,107,108,108,108,109,109,110,110,110
dc.w 111,111,111,112,112,113,113,113,114,114,114,115,115,116,116,116
dc.w 117,117,117,118,118,118,119,119,119,120,120,121,121,121,122,122
dc.w 122,123,123,123,124,124,124,125,125,125,126,126,126,127,127,127
dc.w 128

GetATan2:
;of d0= dy
; d1= dx
; returns in d2 , 0..$3FF << 1

clr.w d2
tst.w d0
bpl.s .notnegY
bset #0,d2
neg.w d0
.notnegY
tst.w d1
bpl.s .notnegX
bset #1,d2
neg.w d1
.notnegX
cmp.w d1,d0
blt.s .noswap
exg d0,d1
bset #2,d2
.noswap
ext.l d0
lsl.w #8,d0
tst.w d1
beq.s .div0
divu d1,d0
add.w d0,d0
lea.l AtanTable(pc),a4
move.w 0(a4,d0),d3
btst #2,d2
beq .wasntsteep
neg.w d3
add.w #256,d3
.wasntsteep
btst #0,d2
beq .noybias
neg.w d3
add.w #1024,d3
.noybias
btst #1,d2
beq .noxbias
neg.w d3
add.w #512,d3
.noxbias
move.w d3,d2
add.w d2,d2
and.w #$3FF<<1,d2
rts
.div0
move.w #256<<1,d2
rts

PaulF · Today, 15:25

tidy of post fixes...

CorrectionTable:
;8 zones , b2 = steep , b1 = neg x , b0 = neg y
dc.w 0 ;0 , 0..128 (shallow) base case 0..45 deg , 0...128 in my "angles"
dc.w -1024 ;1, 896..1024 (neg y , shallow)
dc.w -512 ;2, 384..512
dc.w 512 ;3, 512..640
dc.W -256 ;4, 128..256
dc.w 768 ;5, 768..896
dc.w 256 ;6, 256..384
dc.w -768 ;7, 640..768

AtanTable:
dc.w 0,0,1,1,2,3,3,4,5,5,6,6,7,8,8,9
dc.w 10,10,11,12,12,13,13,14,15,15,16,17,17,18,19,19
dc.w 20,20,21,22,22,23,24,24,25,25,26,27,27,28,28,29
dc.w 30,30,31,32,32,33,33,34,35,35,36,36,37,38,38,39
dc.w 39,40,41,41,42,42,43,44,44,45,45,46,47,47,48,48
dc.w 49,49,50,51,51,52,52,53,53,54,55,55,56,56,57,57
dc.w 58,59,59,60,60,61,61,62,62,63,63,64,65,65,66,66
dc.w 67,67,68,68,69,69,70,70,71,71,72,72,73,74,74,75
dc.w 75,76,76,77,77,78,78,79,79,80,80,81,81,82,82,83
dc.w 83,83,84,84,85,85,86,86,87,87,88,88,89,89,90,90
dc.w 91,91,91,92,92,93,93,94,94,95,95,95,96,96,97,97
dc.w 98,98,99,99,99,100,100,101,101,101,102,102,103,103,104,104
dc.w 104,105,105,106,106,106,107,107,108,108,108,109,109,110,110,110
dc.w 111,111,111,112,112,113,113,113,114,114,114,115,115,116,116,116
dc.w 117,117,117,118,118,118,119,119,119,120,120,121,121,121,122,122
dc.w 122,123,123,123,124,124,124,125,125,125,126,126,126,127,127,127
dc.w 128

GetATan2:
;of d0= dy
; d1= dx
; returns in d2 , 0..$3FF << 1

clr.w d2 ;zone code
tst.w d0 ;dy negative ?
bpl.s .notnegY
or.w #2,d2 ;b0<<1
neg.w d0
.notnegY
tst.w d1
bpl.s .notnegX ;dx negative
or.w #4,d2 ;b1<<1
neg.w d1
.notnegX
cmp.w d1,d0 ;dy > dx
blt.s .noswap
exg d0,d1 ;swap so using dx/dy
or.w #8,d2 ;b2<<1
.noswap
ext.l d0 ;dont know what in high word of dx/dy
lsl.w #8,d0 ;table is 256 deep
tst.w d1 ;quick div by 0 check
beq.s .div0
divu d1,d0 ;quotient is table index
add.w d0,d0 ;which is words sized , so *2
lea.l AtanTable(pc),a4
move.w 0(a4,d0),d3 ;look up angle
move.w (CorrectionTable-AtanTable)(a4,d2),d2 ;zone to correction values
bpl.s .nocorrection
neg.w d3 ;if neg , then negate retrieved angle , becomes -45...0
neg.w d2 ;remove neg-ness of correction basis
.nocorrection
add.w d3,d2 ;add correction
add.w d2,d2 ;double result for word access
and.w #$3FF<<1,d2 ;redundant...?
rts
.div0
move.w #256<<1,d2
rts

grond · Today, 16:36

Do you absolutely need to know the angle or just the left/right information? And what processor/hardware configuration are you aiming at?

Don_Adan · Today, 16:47

Test for div by 0 check can be at begining of code.
AtanTable can be byte table.
And you can use
move.w AtanTable(PC,D0),D3
After moving both tables at end of code.

BTW. Still dont know why some coders prefers to use "lea.l" when exist only "lea", 2 bytes shortest.

PaulF · Today, 16:51

Quote:

Originally Posted by Don_Adan

Test for div by 0 check can be at begining of code.
AtanTable can be byte table.
And you can use
move.w AtanTable(PC,D0),D3
After moving both tables at end of code.

BTW. Still dont know why some coders prefers to use "lea.l" when exist only "lea", 2 bytes shortest.

I cant check for div 0 at the beginning as what is being used to divide by could change form the dx to the dy. I will take the other suggestions on board , thankyou.

PaulF · Today, 16:54

Quote:

Originally Posted by grond

Do you absolutely need to know the angle or just the left/right information? And what processor/hardware configuration are you aiming at?

I would like to use the func for various things , so would prefer the actual angle. What would "just left/right" look like ?
Targeting an A500 / OCS.

PaulF · Today, 17:20

GetATan2:
;of d0= dy
; d1= dx
; returns in d2 , 0..$3FF << 1

clr.w d2 ;zone code
tst.w d0 ;dy negative ?
bpl.s .notnegY
or.w #2,d2 ;b0<<1
neg.w d0
.notnegY
tst.w d1
bpl.s .notnegX ;dx negative
or.w #4,d2 ;b1<<1
neg.w d1
.notnegX
cmp.w d1,d0 ;dy > dx
blt.s .noswap
exg d0,d1 ;swap so using dx/dy
or.w #8,d2 ;b2<<1
.noswap
ext.l d0 ;dont know what in high word of dx/dy
lsl.w #8,d0 ;table is 256 deep
tst.w d1 ;quick div by 0 check
beq.s .div0
divu d1,d0 ;quotient is table index
moveq #0,d3
move.b AtanTable(pc,d0),d3 ;look up angle
move.w CorrectionTable(pc,d2),d2 ;zone to correction values
bpl.s .nocorrection
neg.w d3 ;if neg , then negate retrieved angle , becomes -45...0
neg.w d2 ;remove neg-ness of correction basis
.nocorrection
add.w d3,d2 ;add correction
add.w d2,d2 ;double result for word access
and.w #$3FF<<1,d2 ;redundant...?
rts
.div0
move.w #256<<1,d2
rts

CorrectionTable:
;8 zones , b2 = steep , b1 = neg x , b0 = neg y
dc.w 0 ;0 , 0..128 (shallow) base case 0..45 deg , 0...128 in my "angles"
dc.w -1024 ;1, 896..1024 (neg y , shallow)
dc.w -512 ;2, 384..512
dc.w 512 ;3, 512..640
dc.W -256 ;4, 128..256
dc.w 768 ;5, 768..896
dc.w 256 ;6, 256..384
dc.w -768 ;7, 640..768

AtanTable:
dc.b 0,0,1,1,2,3,3,4,5,5,6,6,7,8,8,9

hooverphonique · Today, 17:21

your or's can be exchanged to addq's - not that it matters much in the shadow of that divu.

PaulF · Today, 17:25

Quote:

Originally Posted by hooverphonique

your or's can be exchanged to addq's - not that it matters much in the shadow of that divu.

Indeed! Evil it is. Open to some math trickery.

Thorham · Today, 17:38

Use code tags and formatting:

Code:

GetATan2:
;of d0= dy
; d1= dx
; returns in d2 , 0..$3FF << 1
    clr.w   d2 ;zone code
    tst.w   d0 ;dy negative ?
    bpl.s   .notnegY
    or.w    #2,d2 ;b0<<1
    neg.w   d0
.notnegY
    tst.w   d1
    bpl.s   .notnegX ;dx negative
    or.w    #4,d2 ;b1<<1
    neg.w   d1
.notnegX
    cmp.w   d1,d0 ;dy > dx
    blt.s   .noswap
    exg     d0,d1 ;swap so using dx/dy
    or.w    #8,d2 ;b2<<1
.noswap
    ext.l   d0 ;dont know what in high word of dx/dy
    lsl.w   #8,d0 ;table is 256 deep
    tst.w   d1 ;quick div by 0 check
    beq.s   .div0
    divu    d1,d0 ;quotient is table index
    moveq   #0,d3
    move.b  AtanTable(pc,d0),d3 ;look up angle
    move.w  CorrectionTable(pc,d2),d2 ;zone to correction values
    bpl.s   .nocorrection
    neg.w   d3 ;if neg , then negate retrieved angle , becomes -45...0
    neg.w   d2 ;remove neg-ness of correction basis
.nocorrection
    add.w   d3,d2 ;add correction
    add.w   d2,d2 ;double result for word access
    and.w   #$3FF<<1,d2 ;redundant...?
    rts
.div0
    move.w  #256<<1,d2
    rts

CorrectionTable:
;8 zones , b2 = steep , b1 = neg x , b0 = neg y
dc.w 0 ;0 , 0..128 (shallow) base case 0..45 deg , 0...128 in my "angles"
dc.w -1024 ;1, 896..1024 (neg y , shallow)
dc.w -512 ;2, 384..512
dc.w 512 ;3, 512..640
dc.W -256 ;4, 128..256
dc.w 768 ;5, 768..896
dc.w 256 ;6, 256..384
dc.w -768 ;7, 640..768

AtanTable:
dc.b 0,0,1,1,2,3,3,4,5,5,6,6,7,8,8,9

Thanks

a/b · Today, 17:54

Start with:

Code:

    clr.w   d2	;zone code
    tst.w   d1
    beq.s   .div0
    bpl.s   .notnegX	;dx negative
...

so you can bail out immediately if dx=0, and don't have check d1 again later for division by 0.

Don_Adan · Today, 18:00

Quote:

Originally Posted by PaulF

I cant check for div 0 at the beginning as what is being used to divide by could change form the dx to the dy. I will take the other suggestions on board , thankyou.

Why? I missing something?

Code:

GetATan2
	;of d0= dy
	;   d1= dx
	; returns in d2 , 0..$3FF << 1

	clr.w	d2			;zone code
	tst.w	d0			;dy negative ?	
    beq.b       .div0
	bpl.s	.notnegY
	or.w	#2,d2		;b0<<1
	neg.w	d0
.notnegY	
	tst.w	d1
    beq.b      .div0
	bpl.s	.notnegX	;dx negative
	or.w	#4,d2		;b1<<1
	neg.w	d1
.notnegX	
	cmp.w	d1,d0		;dy > dx
	blt.s	.noswap
	exg		d0,d1		;swap so using dx/dy
	or.w	#8,d2		;b2<<1
.noswap	
	ext.l	d0			;dont know what in high word of dx/dy
	lsl.w	#8,d0		;table is 256 deep
;	tst.w	d1			;quick div by 0 check
;	beq.s	.div0
	divu	d1,d0		;quotient is table index
	moveq	#0,d3
	move.b	AtanTable(pc,d0),d3		;look up angle 
	move.w	CorrectionTable(pc,d2),d2	;zone to correction values
	bpl.s	.nocorrection
	neg.w	d3			;if neg , then negate retrieved angle , becomes -45...0
	neg.w	d2			;remove neg-ness of correction basis
.nocorrection
	add.w	d3,d2		;add correction
	add.w	d2,d2		;double result for word access
	and.w	#$3FF<<1,d2	;redundant...?
	rts
.div0
	move.w	#256<<1,d2	

	rts

CorrectionTable:
			;8 zones , b2 = steep , b1 = neg x , b0 = neg y 
			dc.w	0		;0 , 0..128	(shallow)	base case 0..45 deg , 0...128 in my "angles"
			dc.w	-1024	;1, 896..1024 (neg y , shallow)					
			dc.w	-512	;2, 384..512
			dc.w	512		;3, 512..640
			dc.W	-256	;4, 128..256
			dc.w	768		;5, 768..896
			dc.w	256		;6, 256..384
			dc.w	-768	;7, 640..768

AtanTable:
                dc.b    0,0,1,1,2,3,3,4,5,5,6,6,7,8,8,9

grond · Today, 18:02

Quote:

Originally Posted by PaulF

I would like to use the func for various things , so would prefer the actual angle. What would "just left/right" look like ?
Targeting an A500 / OCS.

Well, assuming you have two vectors, one vector is the orientation of one object and the other is the difference of positions between the two objects, all you need to compute is the cross product of the two vectors. Because both vectors are in the plane of the screen and thus have their z-coordinates as 0, all you need to compute is the z-coordinate of the cross product. The sign of the z-coordinate will then give you the left-of/right-of information. To compute the z-coordinate, you need two MULs and one subtraction, the sign is then in the N-flag. No need to do any trigonometry at all.

https://en.wikipedia.org/wiki/Cross_product

Edited to add: this animation shows why the cross product is useful for what you are trying to do:

https://de.wikipedia.org/wiki/Kreuzp...allelogram.gif

PaulF · Today, 18:11

Quote:

Originally Posted by grond

Well, assuming you have two vectors, one vector is the orientation of one object and the other is the difference of positions between the two objects, all you need to compute is the cross product of the two vectors. Because both vectors are in the plane of the screen and thus have their z-coordinates as 0, all you need to compute is the z-coordinate of the cross product. The sign of the z-coordinate will then give you the left-of/right-of information. To compute the z-coordinate, you need two MULs and one subtraction, the sign is then in the N-flag. No need to do any trigonometry at all.

https://en.wikipedia.org/wiki/Cross_product

Edited to add: this animation shows why the cross product is useful for what you are trying to do:

https://de.wikipedia.org/wiki/Kreuzp...allelogram.gif

I can see how that would be a cheap turn left or left right, thanks.

PaulF · Today, 18:14

Quote:

Originally Posted by Don_Adan

Why? I missing something?

Code:

GetATan2
	;of d0= dy
	;   d1= dx
	; returns in d2 , 0..$3FF << 1

	clr.w	d2			;zone code
	tst.w	d0			;dy negative ?	
    beq.b       .div0
	bpl.s	.notnegY
	or.w	#2,d2		;b0<<1
	neg.w	d0
.notnegY	
	tst.w	d1
    beq.b      .div0
	bpl.s	.notnegX	;dx negative
	or.w	#4,d2		;b1<<1
	neg.w	d1
.notnegX	
	cmp.w	d1,d0		;dy > dx
	blt.s	.noswap
	exg		d0,d1		;swap so using dx/dy
	or.w	#8,d2		;b2<<1
.noswap	
	ext.l	d0			;dont know what in high word of dx/dy
	lsl.w	#8,d0		;table is 256 deep
;	tst.w	d1			;quick div by 0 check
;	beq.s	.div0
	divu	d1,d0		;quotient is table index
	moveq	#0,d3
	move.b	AtanTable(pc,d0),d3		;look up angle 
	move.w	CorrectionTable(pc,d2),d2	;zone to correction values
	bpl.s	.nocorrection
	neg.w	d3			;if neg , then negate retrieved angle , becomes -45...0
	neg.w	d2			;remove neg-ness of correction basis
.nocorrection
	add.w	d3,d2		;add correction
	add.w	d2,d2		;double result for word access
	and.w	#$3FF<<1,d2	;redundant...?
	rts
.div0
	move.w	#256<<1,d2	

	rts

CorrectionTable:
			;8 zones , b2 = steep , b1 = neg x , b0 = neg y 
			dc.w	0		;0 , 0..128	(shallow)	base case 0..45 deg , 0...128 in my "angles"
			dc.w	-1024	;1, 896..1024 (neg y , shallow)					
			dc.w	-512	;2, 384..512
			dc.w	512		;3, 512..640
			dc.W	-256	;4, 128..256
			dc.w	768		;5, 768..896
			dc.w	256		;6, 256..384
			dc.w	-768	;7, 640..768

AtanTable:
                dc.b    0,0,1,1,2,3,3,4,5,5,6,6,7,8,8,9

Ah , I thought you meant just a single "is zero" test , not testing both as a by product of the sign test , hence my "I can't".
Added...

Code:

GetATan2:
	;of d0= dy
	;   d1= dx
	; returns in d2 , 0..$3FF << 1

	clr.w	d2			;zone code
	tst.w	d0			;dy negative ?	
	beq.s	.div0
	bpl.s	.notnegY
	addq.w	#2,d2		;b0<<1
	neg.w	d0
.notnegY	
	tst.w	d1
	beq.s	.div0
	bpl.s	.notnegX	;dx negative
	addq.w	#4,d2		;b1<<1
	neg.w	d1
.notnegX	
	cmp.w	d1,d0		;dy > dx
	blt.s	.noswap
	exg		d0,d1		;swap so using dx/dy
	addq.w	#8,d2		;b2<<1
.noswap	
	ext.l	d0			;dont know what in high word of dx/dy
	lsl.w	#8,d0		;table is 256 deep
	divu	d1,d0		;quotient is table index
	moveq	#0,d3
	move.b	AtanTable(pc,d0),d3		;look up angle 
	move.w	CorrectionTable(pc,d2),d2	;zone to correction values
	bpl.s	.nocorrection
	neg.w	d3			;if neg , then negate retrieved angle , becomes -45...0
	neg.w	d2			;remove neg-ness of correction basis
.nocorrection
	add.w	d3,d2		;add correction
	add.w	d2,d2		;double result for word access
	and.w	#$3FF<<1,d2	;redundant...?
	rts
.div0
	move.w	#256<<1,d2	
	rts

CorrectionTable:

Today, 17:54	#12
a/b Registered User Join Date: Jun 2016 Location: europe Posts: 1,095	Start with: Code: clr.w d2 ;zone code tst.w d1 beq.s .div0 bpl.s .notnegX ;dx negative ... so you can bail out immediately if dx=0, and don't have check d1 again later for division by 0.

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Today, 12:25	#1
PaulF Registered User Join Date: Jan 2021 Location: Frodsham Posts: 10	Atan2 in assembler for "integer" / screen-ish coordinates Hi all , I'm needing an atan2 function in assembler. I have a 2D delta between objects , and want to determine the angle between then to rotate one towards the other. So far the best I can do is to decide on a which quadrant (aka delta signs) the line lines in; take the abs of both dx and dy whilst clamping each to a max value. Then scaling the dx and dy down and combining to form an index into a lookup table , modifying the result based on the original quadrant. So I have 2 main compromises , (1) the clamp will distort the line and (2) the scale down (to reduce the overall table size) will "pixelate" the results. Any thoughts on how to do this better , thanks for any help. Paul. AtanTable: dc.w 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 dc.w 256,128,75,52,39,32,26,23,20,18,16,14,13,12,11,10 dc.w 256,180,128,95,75,62,52,45,39,35,32,29,26,24,23,21 dc.w 256,203,160,128,104,88,75,65,58,52,47,43,39,36,34,32 dc.w 256,216,180,151,128,109,95,84,75,68,62,56,52,48,45,42 dc.w 256,223,193,167,146,128,113,101,91,82,75,69,64,59,55,52 dc.w 256,229,203,180,160,142,128,115,104,95,88,81,75,70,65,62 dc.w 256,232,210,190,171,154,140,128,117,107,99,92,86,80,75,71 dc.w 256,235,216,197,180,164,151,138,128,118,109,102,95,89,84,79 dc.w 256,237,220,203,187,173,160,148,137,128,119,111,104,98,93,88 dc.w 256,239,223,208,193,180,167,156,146,136,128,120,113,106,101,95 dc.w 256,241,226,212,199,186,174,163,153,144,135,128,120,114,108,103 dc.w 256,242,229,216,203,191,180,169,160,151,142,135,128,121,115,109 dc.w 256,243,231,219,207,196,185,175,166,157,149,141,134,128,121,116 dc.w 256,244,232,221,210,200,190,180,171,162,154,147,140,134,128,122 dc.w 256,245,234,223,213,203,193,184,176,167,160,152,146,139,133,128 GetATan2: ;of d0= dy ; d1= dx ; returns in d2 , 0..$3FF << 1 clr.w d2 tst.w d0 bpl.s .notnegY bset #0,d2 neg.w d0 .notnegY tst.w d1 bpl.s .notnegX bset #1,d2 neg.w d1 .notnegX .clamp cmp.w #256,d0 blt.s .noyclamp move.w #255,d0 .noyclamp cmp.w #256,d1 blt.s .noxclamp move.w #255,d1 .noxclamp ;16 entries to span 0..255 lsr.w #4,d1 add.w d1,d1 and.w #$F0,d0 add.w d0,d0 add.w d1,d0 lea.l AtanTable(pc),a4 move.w 0(a4,d0),d3 btst #0,d2 beq .noybias neg.w d3 add.w #1024,d3 .noybias btst #1,d2 beq .noxbias neg.w d3 add.w #512,d3 .noxbias move.w d3,d2 add.w d2,d2 and.w #$3FF<<1,d2 rts Last edited by PaulF; Today at 12:49. Reason: added (first pass!) code & table

Today, 14:17	#2
PaulF Registered User Join Date: Jan 2021 Location: Frodsham Posts: 10	So , tried this (forgive the first pass code) , but its got a juicy divide in there. Atan table is now spans a 1/8th of a circle . Do quadrant stuff, now consider dy/dx , if > 1 , flip to dx/dy , look up angle and correct for >1 (45 degress) and quadrant. No clmaping or loss or resolution. AtanTable: dc.w 0,0,1,1,2,3,3,4,5,5,6,6,7,8,8,9 dc.w 10,10,11,12,12,13,13,14,15,15,16,17,17,18,19,19 dc.w 20,20,21,22,22,23,24,24,25,25,26,27,27,28,28,29 dc.w 30,30,31,32,32,33,33,34,35,35,36,36,37,38,38,39 dc.w 39,40,41,41,42,42,43,44,44,45,45,46,47,47,48,48 dc.w 49,49,50,51,51,52,52,53,53,54,55,55,56,56,57,57 dc.w 58,59,59,60,60,61,61,62,62,63,63,64,65,65,66,66 dc.w 67,67,68,68,69,69,70,70,71,71,72,72,73,74,74,75 dc.w 75,76,76,77,77,78,78,79,79,80,80,81,81,82,82,83 dc.w 83,83,84,84,85,85,86,86,87,87,88,88,89,89,90,90 dc.w 91,91,91,92,92,93,93,94,94,95,95,95,96,96,97,97 dc.w 98,98,99,99,99,100,100,101,101,101,102,102,103,103,104,104 dc.w 104,105,105,106,106,106,107,107,108,108,108,109,109,110,110,110 dc.w 111,111,111,112,112,113,113,113,114,114,114,115,115,116,116,116 dc.w 117,117,117,118,118,118,119,119,119,120,120,121,121,121,122,122 dc.w 122,123,123,123,124,124,124,125,125,125,126,126,126,127,127,127 dc.w 128 GetATan2: ;of d0= dy ; d1= dx ; returns in d2 , 0..$3FF << 1 clr.w d2 tst.w d0 bpl.s .notnegY bset #0,d2 neg.w d0 .notnegY tst.w d1 bpl.s .notnegX bset #1,d2 neg.w d1 .notnegX cmp.w d1,d0 blt.s .noswap exg d0,d1 bset #2,d2 .noswap ext.l d0 lsl.w #8,d0 tst.w d1 beq.s .div0 divu d1,d0 add.w d0,d0 lea.l AtanTable(pc),a4 move.w 0(a4,d0),d3 btst #2,d2 beq .wasntsteep neg.w d3 add.w #256,d3 .wasntsteep btst #0,d2 beq .noybias neg.w d3 add.w #1024,d3 .noybias btst #1,d2 beq .noxbias neg.w d3 add.w #512,d3 .noxbias move.w d3,d2 add.w d2,d2 and.w #$3FF<<1,d2 rts .div0 move.w #256<<1,d2 rts

Today, 15:25	#3
PaulF Registered User Join Date: Jan 2021 Location: Frodsham Posts: 10	tidy of post fixes... CorrectionTable: ;8 zones , b2 = steep , b1 = neg x , b0 = neg y dc.w 0 ;0 , 0..128 (shallow) base case 0..45 deg , 0...128 in my "angles" dc.w -1024 ;1, 896..1024 (neg y , shallow) dc.w -512 ;2, 384..512 dc.w 512 ;3, 512..640 dc.W -256 ;4, 128..256 dc.w 768 ;5, 768..896 dc.w 256 ;6, 256..384 dc.w -768 ;7, 640..768 AtanTable: dc.w 0,0,1,1,2,3,3,4,5,5,6,6,7,8,8,9 dc.w 10,10,11,12,12,13,13,14,15,15,16,17,17,18,19,19 dc.w 20,20,21,22,22,23,24,24,25,25,26,27,27,28,28,29 dc.w 30,30,31,32,32,33,33,34,35,35,36,36,37,38,38,39 dc.w 39,40,41,41,42,42,43,44,44,45,45,46,47,47,48,48 dc.w 49,49,50,51,51,52,52,53,53,54,55,55,56,56,57,57 dc.w 58,59,59,60,60,61,61,62,62,63,63,64,65,65,66,66 dc.w 67,67,68,68,69,69,70,70,71,71,72,72,73,74,74,75 dc.w 75,76,76,77,77,78,78,79,79,80,80,81,81,82,82,83 dc.w 83,83,84,84,85,85,86,86,87,87,88,88,89,89,90,90 dc.w 91,91,91,92,92,93,93,94,94,95,95,95,96,96,97,97 dc.w 98,98,99,99,99,100,100,101,101,101,102,102,103,103,104,104 dc.w 104,105,105,106,106,106,107,107,108,108,108,109,109,110,110,110 dc.w 111,111,111,112,112,113,113,113,114,114,114,115,115,116,116,116 dc.w 117,117,117,118,118,118,119,119,119,120,120,121,121,121,122,122 dc.w 122,123,123,123,124,124,124,125,125,125,126,126,126,127,127,127 dc.w 128 GetATan2: ;of d0= dy ; d1= dx ; returns in d2 , 0..$3FF << 1 clr.w d2 ;zone code tst.w d0 ;dy negative ? bpl.s .notnegY or.w #2,d2 ;b0<<1 neg.w d0 .notnegY tst.w d1 bpl.s .notnegX ;dx negative or.w #4,d2 ;b1<<1 neg.w d1 .notnegX cmp.w d1,d0 ;dy > dx blt.s .noswap exg d0,d1 ;swap so using dx/dy or.w #8,d2 ;b2<<1 .noswap ext.l d0 ;dont know what in high word of dx/dy lsl.w #8,d0 ;table is 256 deep tst.w d1 ;quick div by 0 check beq.s .div0 divu d1,d0 ;quotient is table index add.w d0,d0 ;which is words sized , so *2 lea.l AtanTable(pc),a4 move.w 0(a4,d0),d3 ;look up angle move.w (CorrectionTable-AtanTable)(a4,d2),d2 ;zone to correction values bpl.s .nocorrection neg.w d3 ;if neg , then negate retrieved angle , becomes -45...0 neg.w d2 ;remove neg-ness of correction basis .nocorrection add.w d3,d2 ;add correction add.w d2,d2 ;double result for word access and.w #$3FF<<1,d2 ;redundant...? rts .div0 move.w #256<<1,d2 rts

Today, 16:36	#4
grond Registered User Join Date: Jun 2015 Location: Germany Posts: 1,961	Do you absolutely need to know the angle or just the left/right information? And what processor/hardware configuration are you aiming at?

Today, 16:47	#5
Don_Adan Registered User Join Date: Jan 2008 Location: Warsaw/Poland Age: 56 Posts: 2,124	Test for div by 0 check can be at begining of code. AtanTable can be byte table. And you can use move.w AtanTable(PC,D0),D3 After moving both tables at end of code. BTW. Still dont know why some coders prefers to use "lea.l" when exist only "lea", 2 bytes shortest.

Today, 17:20	#8
PaulF Registered User Join Date: Jan 2021 Location: Frodsham Posts: 10	GetATan2: ;of d0= dy ; d1= dx ; returns in d2 , 0..$3FF << 1 clr.w d2 ;zone code tst.w d0 ;dy negative ? bpl.s .notnegY or.w #2,d2 ;b0<<1 neg.w d0 .notnegY tst.w d1 bpl.s .notnegX ;dx negative or.w #4,d2 ;b1<<1 neg.w d1 .notnegX cmp.w d1,d0 ;dy > dx blt.s .noswap exg d0,d1 ;swap so using dx/dy or.w #8,d2 ;b2<<1 .noswap ext.l d0 ;dont know what in high word of dx/dy lsl.w #8,d0 ;table is 256 deep tst.w d1 ;quick div by 0 check beq.s .div0 divu d1,d0 ;quotient is table index moveq #0,d3 move.b AtanTable(pc,d0),d3 ;look up angle move.w CorrectionTable(pc,d2),d2 ;zone to correction values bpl.s .nocorrection neg.w d3 ;if neg , then negate retrieved angle , becomes -45...0 neg.w d2 ;remove neg-ness of correction basis .nocorrection add.w d3,d2 ;add correction add.w d2,d2 ;double result for word access and.w #$3FF<<1,d2 ;redundant...? rts .div0 move.w #256<<1,d2 rts CorrectionTable: ;8 zones , b2 = steep , b1 = neg x , b0 = neg y dc.w 0 ;0 , 0..128 (shallow) base case 0..45 deg , 0...128 in my "angles" dc.w -1024 ;1, 896..1024 (neg y , shallow) dc.w -512 ;2, 384..512 dc.w 512 ;3, 512..640 dc.W -256 ;4, 128..256 dc.w 768 ;5, 768..896 dc.w 256 ;6, 256..384 dc.w -768 ;7, 640..768 AtanTable: dc.b 0,0,1,1,2,3,3,4,5,5,6,6,7,8,8,9

Today, 17:21	#9
hooverphonique ex. demoscener "Bigmama" Join Date: Jun 2012 Location: Fyn / Denmark Posts: 1,660	your or's can be exchanged to addq's - not that it matters much in the shadow of that divu.

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