A character can face a target in eight directions without angles, trigonometry or a lookup table.
Use it in a project
Return DIRECTION=0 when points coincide, otherwise 1 north, 2 north-east, 3 east, 4 south-east, 5 south, 6 south-west, 7 west, 8 north-west. Screen Y increases downwards. Choose a cardinal direction when its absolute displacement is at least twice the other; remaining vectors are diagonal. DX/DY return unsigned magnitudes.
Include component.inc once (MOS callers include the shared 6502 implementation through it). Reserve the public fields in this exact order: DIRECTION, DX, DY, FROM_X, FROM_Y, TO_X, TO_Y. They occupy 7 contiguous bytes. Also reserve the private workspace: T0, T1, T2 (3 bytes). Array names in the explanation refer to the numbered consecutive bindings, such as C0, C1 and so on.
Call eight_way_direction_init once at the intended reset boundary. It clears inputs as well as outputs and workspace. Set your starting state and configuration afterwards, then call eight_way_direction_step whenever the described event occurs. The helper reads no device, waits for no frame and installs no interrupt handler.
| Ownership | Fields |
|---|---|
| Retain between calls | none |
| Supply before service | FROM_X/Y and TO_X/Y |
| Read after service | DIRECTION and DX/DY |
Compare a magnitude with half the other to avoid overflow from doubling a byte. Two sign flags select the quadrant after choosing horizontal, vertical or diagonal.
Reusable initialisation and service
; SPDX-License-Identifier: MIT
; Choose an Eight-way Direction. See README.md for the byte interface and ownership.
; init clears the public fields and private workspace; set inputs afterwards.
eight_way_direction_init:
move.b #0,d0
move.b d0,DIRECTION
move.b d0,DX
move.b d0,DY
move.b d0,FROM_X
move.b d0,FROM_Y
move.b d0,TO_X
move.b d0,TO_Y
move.b d0,T0
move.b d0,T1
move.b d0,T2
rts
eight_way_direction_step:
; T0 = 0
move.b #0,d0
move.b d0,T0
; T1 = 0
move.b #0,d0
move.b d0,T1
; if TO_X >= FROM_X:
move.b TO_X,d0
move.b FROM_X,d1
cmp.b d1,d0
bcc eight_way_direction_L1
jmp eight_way_direction_L2
eight_way_direction_L1:
; DX = TO_X - FROM_X
move.b TO_X,d0
move.b FROM_X,d1
sub.b d1,d0
move.b d0,DX
jmp eight_way_direction_L3
eight_way_direction_L2:
; DX = FROM_X - TO_X
move.b FROM_X,d0
move.b TO_X,d1
sub.b d1,d0
move.b d0,DX
; T0 = 1
move.b #1,d0
move.b d0,T0
eight_way_direction_L3:
; if TO_Y >= FROM_Y:
move.b TO_Y,d0
move.b FROM_Y,d1
cmp.b d1,d0
bcc eight_way_direction_L4
jmp eight_way_direction_L5
eight_way_direction_L4:
; DY = TO_Y - FROM_Y
move.b TO_Y,d0
move.b FROM_Y,d1
sub.b d1,d0
move.b d0,DY
jmp eight_way_direction_L6
eight_way_direction_L5:
; DY = FROM_Y - TO_Y
move.b FROM_Y,d0
move.b TO_Y,d1
sub.b d1,d0
move.b d0,DY
; T1 = 1
move.b #1,d0
move.b d0,T1
eight_way_direction_L6:
; DIRECTION = 0
move.b #0,d0
move.b d0,DIRECTION
; if DX == 0:
move.b DX,d0
cmp.b #0,d0
beq eight_way_direction_L7
jmp eight_way_direction_L8
eight_way_direction_L7:
; if DY == 0:
move.b DY,d0
cmp.b #0,d0
beq eight_way_direction_L10
jmp eight_way_direction_L11
eight_way_direction_L10:
; return
rts
jmp eight_way_direction_L12
eight_way_direction_L11:
eight_way_direction_L12:
jmp eight_way_direction_L9
eight_way_direction_L8:
eight_way_direction_L9:
; T2 = DY >> 1
move.b DY,d0
lsr.b #1,d0
move.b d0,T2
; if DX <= T2:
move.b DX,d0
move.b T2,d1
cmp.b d1,d0
bls eight_way_direction_L13
jmp eight_way_direction_L14
eight_way_direction_L13:
; DIRECTION = 5
move.b #5,d0
move.b d0,DIRECTION
; if T1 != 0:
move.b T1,d0
cmp.b #0,d0
bne eight_way_direction_L16
jmp eight_way_direction_L17
eight_way_direction_L16:
; DIRECTION = 1
move.b #1,d0
move.b d0,DIRECTION
jmp eight_way_direction_L18
eight_way_direction_L17:
eight_way_direction_L18:
; return
rts
jmp eight_way_direction_L15
eight_way_direction_L14:
eight_way_direction_L15:
; T2 = DX >> 1
move.b DX,d0
lsr.b #1,d0
move.b d0,T2
; if DY <= T2:
move.b DY,d0
move.b T2,d1
cmp.b d1,d0
bls eight_way_direction_L19
jmp eight_way_direction_L20
eight_way_direction_L19:
; DIRECTION = 3
move.b #3,d0
move.b d0,DIRECTION
; if T0 != 0:
move.b T0,d0
cmp.b #0,d0
bne eight_way_direction_L22
jmp eight_way_direction_L23
eight_way_direction_L22:
; DIRECTION = 7
move.b #7,d0
move.b d0,DIRECTION
jmp eight_way_direction_L24
eight_way_direction_L23:
eight_way_direction_L24:
; return
rts
jmp eight_way_direction_L21
eight_way_direction_L20:
eight_way_direction_L21:
; DIRECTION = 4
move.b #4,d0
move.b d0,DIRECTION
; if T0 != 0:
move.b T0,d0
cmp.b #0,d0
bne eight_way_direction_L25
jmp eight_way_direction_L26
eight_way_direction_L25:
; DIRECTION = 6
move.b #6,d0
move.b d0,DIRECTION
jmp eight_way_direction_L27
eight_way_direction_L26:
eight_way_direction_L27:
; if T1 != 0:
move.b T1,d0
cmp.b #0,d0
bne eight_way_direction_L28
jmp eight_way_direction_L29
eight_way_direction_L28:
; DIRECTION = 2
move.b #2,d0
move.b d0,DIRECTION
; if T0 != 0:
move.b T0,d0
cmp.b #0,d0
bne eight_way_direction_L31
jmp eight_way_direction_L32
eight_way_direction_L31:
; DIRECTION = 8
move.b #8,d0
move.b d0,DIRECTION
jmp eight_way_direction_L33
eight_way_direction_L32:
eight_way_direction_L33:
jmp eight_way_direction_L30
eight_way_direction_L29:
eight_way_direction_L30:
rts
component_end:Machine contract
D0–D3/A0–A1/CCR may change; D4–D7/A2–A6 are preserved. A direct BSR/JSR needs four return-address stack bytes. The helper makes no nested calls and adds no other stack use. Its named scratch is private workspace, not a pointer, a ROM variable or shared zero-page space that the game may borrow concurrently. The samples use fixed symbol bindings. Scope or rename every label and binding, including the component_end measurement marker, and allocate a separate block for each independent instance. Different helpers can also use common field names, so combining them needs separate namespaces or explicitly renamed bindings. Give each block one mutation owner.
The A500 OCS diagnostic cold-boots an OFS disk, owns the Copper and bitplane and disables interrupt/DMA sources. The helper does not take over hardware or allocate Chip RAM.
Adapt the caller
demo.asm supplies the bindings and include order. exercise.inc first runs table cases, then a separate client retaining state between calls. A game can call the public step entry directly and remove the diagnostic packet and display. Do not copy the diagnostic’s hardware takeover into an existing game loop.
Build with make ASM198X=/path/to/asm198x and BUILD198X=/path/to/build198x. The Makefile produces normal, custom, deliberately wrong and repaired programs. Tools must already be installed; the sample downloads nothing.
Bindings and include order
section code,code_c
CUSTOM = 0
BROKEN = 0
COYOTE_STEPS = 4
BUFFER_STEPS = 4
TEXT_CAP = 8
PROPERTY_COUNT = 16
STREAM_BYTES = 13
CRC_POLY = 7
include "caller.inc"
include "exercise.inc"
component_start:
include "component.inc"
even
include "data.inc"
include "cases.inc"
even
include "display.inc"
include "../../framework/turn-deadline/font.inc"
code_end:
STATE:
DIRECTION: dc.b 0
DX: dc.b 0
DY: dc.b 0
FROM_X: dc.b 0
FROM_Y: dc.b 0
TO_X: dc.b 0
TO_Y: dc.b 0
T0: dc.b 0
T1: dc.b 0
T2: dc.b 0
even
ready: dc.w 0
preview: dcb.b 8,0
OUTPUT: dcb.b 1300,0
even
signature: dc.b "198XTOOLKIT0000",0
even
copperlist:
dc.w $08e,$2c81,$090,$2cc1,$092,$0038,$094,$00d0
dc.w $100,$1200,$102,0,$104,0,$108,0,$10a,0
dc.w $180,$012,$182,$fff
copbpl:
dc.w $0e0,0,$0e2,0
dc.w $ffff,$fffe
plane: dcb.b 10240,0A client retaining state between calls
preview_rules:
ifne CUSTOM
; FROM_X = 100
move.b #100,d0
move.b d0,FROM_X
; FROM_Y = 100
move.b #100,d0
move.b d0,FROM_Y
; TO_X = 90
move.b #90,d0
move.b d0,TO_X
; TO_Y = 90
move.b #90,d0
move.b d0,TO_Y
ifne BROKEN
; TO_Y = FROM_Y
move.b FROM_Y,d0
move.b d0,TO_Y
endif
bsr checked_step
bsr emit_state
rts
else
; TO_X = 10
move.b #10,d0
move.b d0,TO_X
; TO_Y = 3
move.b #3,d0
move.b d0,TO_Y
ifne BROKEN
; TO_Y = FROM_Y
move.b FROM_Y,d0
move.b d0,TO_Y
endif
bsr checked_step
bsr emit_state
endif
rtsCustomise it
Face a target north-west of the origin. The maintained custom caller changes its inputs or client sequence rather than hiding a different implementation behind the same label. Compare every state of the two clients, not only their final display.
Custom client selection
section code,code_c
CUSTOM = 1
BROKEN = 0
COYOTE_STEPS = 2
BUFFER_STEPS = 2
TEXT_CAP = 4
PROPERTY_COUNT = 16
STREAM_BYTES = 13
CRC_POLY = 49
include "caller.inc"
include "exercise.inc"
component_start:
include "component.inc"
even
include "data.inc"
include "cases.inc"
even
include "display.inc"
include "../../framework/turn-deadline/font.inc"
code_end:
STATE:
DIRECTION: dc.b 0
DX: dc.b 0
DY: dc.b 0
FROM_X: dc.b 0
FROM_Y: dc.b 0
TO_X: dc.b 0
TO_Y: dc.b 0
T0: dc.b 0
T1: dc.b 0
T2: dc.b 0
even
ready: dc.w 0
preview: dcb.b 8,0
OUTPUT: dcb.b 1300,0
even
signature: dc.b "198XTOOLKIT0000",0
even
copperlist:
dc.w $08e,$2c81,$090,$2cc1,$092,$0038,$094,$00d0
dc.w $100,$1200,$102,0,$104,0,$108,0,$10a,0
dc.w $180,$012,$182,$fff
copbpl:
dc.w $0e0,0,$0e2,0
dc.w $ffff,$fffe
plane: dcb.b 10240,0The custom diagnostic row is 08 0A 0A 64 64 5A 5A 00. The full client trace in the source explains how it gets there.
Mistake and repair
The wrong caller flattens the target’s vertical coordinate. DY becomes zero instead of three in the normal client; a steeper vector can also acquire the wrong facing. Preserve both coordinates.
The BROKEN branch lives in the sequential client, not the reusable helper. wrong.asm selects it; repaired.asm restores the normal call sequence. The repaired executable matches the normal program (for Spectrum, compare loaded CODE rather than the tape filename).
Select the deliberately wrong client
section code,code_c
CUSTOM = 0
BROKEN = 1
COYOTE_STEPS = 4
BUFFER_STEPS = 4
TEXT_CAP = 8
PROPERTY_COUNT = 16
STREAM_BYTES = 13
CRC_POLY = 7
include "caller.inc"
include "exercise.inc"
component_start:
include "component.inc"
even
include "data.inc"
include "cases.inc"
even
include "display.inc"
include "../../framework/turn-deadline/font.inc"
code_end:
STATE:
DIRECTION: dc.b 0
DX: dc.b 0
DY: dc.b 0
FROM_X: dc.b 0
FROM_Y: dc.b 0
TO_X: dc.b 0
TO_Y: dc.b 0
T0: dc.b 0
T1: dc.b 0
T2: dc.b 0
even
ready: dc.w 0
preview: dcb.b 8,0
OUTPUT: dcb.b 1300,0
even
signature: dc.b "198XTOOLKIT0000",0
even
copperlist:
dc.w $08e,$2c81,$090,$2cc1,$092,$0038,$094,$00d0
dc.w $100,$1200,$102,0,$104,0,$108,0,$10a,0
dc.w $180,$012,$182,$fff
copbpl:
dc.w $0e0,0,$0e2,0
dc.w $ffff,$fffe
plane: dcb.b 10240,0
Cost and alternatives
The measured helper extent is 484 code bytes; public state is 7 bytes and private scratch is 3 bytes. There are no immutable helper tables. Caller data, the test cases, return-address stack, alignment and display buffers cost additional space. These are assembled sizes, not cycle measurements.
Constant work with no table. A finer angular quantiser can use a ratio table; continuous steering needs a different representation.
These sectors use a 2:1 slope threshold, not exact 22.5-degree boundaries. This selects facing; it does not normalise movement speed.
Execution evidence
Four variants run on A500 OCS PAL, Kickstart1.3 OFS cold boot, using Asm198x 0.0.72, Emu198x 0.44.2 and Build198x 0.2.9. Each executes 64 boundary/varied/error table cases, dirty initialisation and the separate retained-state client. An independent mathematical/container model checks every public byte after every call. This is bounded example coverage, not exhaustive correctness for every possible state.
The records retain loaded immutable code, completion, register sentinels, full packets, source/tool/firmware hashes and captures. The public gate validates these retained observations and rejects altered evidence; it does not run restricted firmware. No firmware is distributed. The eight displayed bytes are the first eight public fields, zero-padded when shorter; the packet includes every field.
Where it fits
Four-way input: Facing selection and movement constraints can use different direction sets.