A guard looking across a room needs more than a same-row check.
Use it in a project
FROM and TO are row-major indices 0–15 in a 4×4 grid. Zero cells are transparent and nonzero cells block. Trace a thin Bresenham line, excluding the observer and including the destination; a cell sees itself. Invalid coordinates return VALID=0 and VISIBLE=0 without indexing the grid.
Include component.inc once (MOS callers include the shared 6502 implementation through it). Reserve the public fields in this exact order: VISIBLE, VALID, FROM, TO, C0, C1, C2, C3, C4, C5, C6, C7, C8, C9, C10, C11, C12, C13, C14, C15. They occupy 20 contiguous bytes. Also reserve the private workspace: T0, T1, T2, T3, T4, T5, T6, T7, T8, T9, T10, T11 (12 bytes). Array names in the explanation refer to the numbered consecutive bindings, such as C0, C1 and so on.
Call grid_line_sight_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 grid_line_sight_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, TO and C0–C15 |
| Read after service | VISIBLE and VALID |
The error accumulator decides when to advance each axis. A bias of 128 represents the small signed error using byte comparisons; doubled error stays within range on this fixed 4×4 domain.
Reusable initialisation and service
; SPDX-License-Identifier: MIT
; Trace a Thin Grid Line of Sight. See README.md for the byte interface and ownership.
; init clears the public fields and private workspace; set inputs afterwards.
grid_line_sight_init:
move.b #0,d0
move.b d0,VISIBLE
move.b d0,VALID
move.b d0,FROM
move.b d0,TO
move.b d0,C0
move.b d0,C1
move.b d0,C2
move.b d0,C3
move.b d0,C4
move.b d0,C5
move.b d0,C6
move.b d0,C7
move.b d0,C8
move.b d0,C9
move.b d0,C10
move.b d0,C11
move.b d0,C12
move.b d0,C13
move.b d0,C14
move.b d0,C15
move.b d0,T0
move.b d0,T1
move.b d0,T2
move.b d0,T3
move.b d0,T4
move.b d0,T5
move.b d0,T6
move.b d0,T7
move.b d0,T8
move.b d0,T9
move.b d0,T10
move.b d0,T11
rts
grid_line_sight_step:
; VISIBLE = 0
move.b #0,d0
move.b d0,VISIBLE
; VALID = 0
move.b #0,d0
move.b d0,VALID
; if FROM >= 16:
move.b FROM,d0
cmp.b #16,d0
bcc grid_line_sight_L1
jmp grid_line_sight_L2
grid_line_sight_L1:
; return
rts
jmp grid_line_sight_L3
grid_line_sight_L2:
grid_line_sight_L3:
; if TO >= 16:
move.b TO,d0
cmp.b #16,d0
bcc grid_line_sight_L4
jmp grid_line_sight_L5
grid_line_sight_L4:
; return
rts
jmp grid_line_sight_L6
grid_line_sight_L5:
grid_line_sight_L6:
; VALID = 1
move.b #1,d0
move.b d0,VALID
; T0 = FROM & 3
move.b FROM,d0
and.b #3,d0
move.b d0,T0
; T1 = FROM >> 2
move.b FROM,d0
lsr.b #2,d0
move.b d0,T1
; T2 = TO & 3
move.b TO,d0
and.b #3,d0
move.b d0,T2
; T3 = TO >> 2
move.b TO,d0
lsr.b #2,d0
move.b d0,T3
; T6 = 1
move.b #1,d0
move.b d0,T6
; if T2 >= T0:
move.b T2,d0
move.b T0,d1
cmp.b d1,d0
bcc grid_line_sight_L7
jmp grid_line_sight_L8
grid_line_sight_L7:
; T4 = T2 - T0
move.b T2,d0
move.b T0,d1
sub.b d1,d0
move.b d0,T4
jmp grid_line_sight_L9
grid_line_sight_L8:
; T4 = T0 - T2
move.b T0,d0
move.b T2,d1
sub.b d1,d0
move.b d0,T4
; T6 = 255
move.b #255,d0
move.b d0,T6
grid_line_sight_L9:
; T7 = 1
move.b #1,d0
move.b d0,T7
; if T3 >= T1:
move.b T3,d0
move.b T1,d1
cmp.b d1,d0
bcc grid_line_sight_L10
jmp grid_line_sight_L11
grid_line_sight_L10:
; T5 = T3 - T1
move.b T3,d0
move.b T1,d1
sub.b d1,d0
move.b d0,T5
jmp grid_line_sight_L12
grid_line_sight_L11:
; T5 = T1 - T3
move.b T1,d0
move.b T3,d1
sub.b d1,d0
move.b d0,T5
; T7 = 255
move.b #255,d0
move.b d0,T7
grid_line_sight_L12:
; T8 = 128 + T4
move.b #128,d0
move.b T4,d1
add.b d1,d0
move.b d0,T8
; T8 = T8 - T5
move.b T8,d0
move.b T5,d1
sub.b d1,d0
move.b d0,T8
; T9 = FROM
move.b FROM,d0
move.b d0,T9
; while T9 != TO:
grid_line_sight_L13:
move.b T9,d0
move.b TO,d1
cmp.b d1,d0
bne grid_line_sight_L14
jmp grid_line_sight_L15
grid_line_sight_L14:
; T10 = T8 - 128
move.b T8,d0
sub.b #128,d0
move.b d0,T10
; T10 = T10 << 1
move.b T10,d0
lsl.b #1,d0
move.b d0,T10
; T10 = T10 + 128
move.b T10,d0
add.b #128,d0
move.b d0,T10
; T11 = 128 - T5
move.b #128,d0
move.b T5,d1
sub.b d1,d0
move.b d0,T11
; if T10 > T11:
move.b T10,d0
move.b T11,d1
cmp.b d1,d0
bhi grid_line_sight_L16
jmp grid_line_sight_L17
grid_line_sight_L16:
; T8 = T8 - T5
move.b T8,d0
move.b T5,d1
sub.b d1,d0
move.b d0,T8
; T0 = T0 + T6
move.b T0,d0
move.b T6,d1
add.b d1,d0
move.b d0,T0
jmp grid_line_sight_L18
grid_line_sight_L17:
grid_line_sight_L18:
; T11 = 128 + T4
move.b #128,d0
move.b T4,d1
add.b d1,d0
move.b d0,T11
; if T10 < T11:
move.b T10,d0
move.b T11,d1
cmp.b d1,d0
bcs grid_line_sight_L19
jmp grid_line_sight_L20
grid_line_sight_L19:
; T8 = T8 + T4
move.b T8,d0
move.b T4,d1
add.b d1,d0
move.b d0,T8
; T1 = T1 + T7
move.b T1,d0
move.b T7,d1
add.b d1,d0
move.b d0,T1
jmp grid_line_sight_L21
grid_line_sight_L20:
grid_line_sight_L21:
; T9 = T1 << 2
move.b T1,d0
lsl.b #2,d0
move.b d0,T9
; T9 = T9 + T0
move.b T9,d0
move.b T0,d1
add.b d1,d0
move.b d0,T9
; T11 = C[T9]
moveq #0,d1
move.b T9,d1
lea C0,a0
move.b 0(a0,d1.w),d0
move.b d0,T11
; if T11 != 0:
move.b T11,d0
cmp.b #0,d0
bne grid_line_sight_L22
jmp grid_line_sight_L23
grid_line_sight_L22:
; return
rts
jmp grid_line_sight_L24
grid_line_sight_L23:
grid_line_sight_L24:
jmp grid_line_sight_L13
grid_line_sight_L15:
; VISIBLE = 1
move.b #1,d0
move.b d0,VISIBLE
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:
VISIBLE: dc.b 0
VALID: dc.b 0
FROM: dc.b 0
TO: dc.b 0
C0: dc.b 0
C1: dc.b 0
C2: dc.b 0
C3: dc.b 0
C4: dc.b 0
C5: dc.b 0
C6: dc.b 0
C7: dc.b 0
C8: dc.b 0
C9: dc.b 0
C10: dc.b 0
C11: dc.b 0
C12: dc.b 0
C13: dc.b 0
C14: dc.b 0
C15: dc.b 0
T0: dc.b 0
T1: dc.b 0
T2: dc.b 0
T3: dc.b 0
T4: dc.b 0
T5: dc.b 0
T6: dc.b 0
T7: dc.b 0
T8: dc.b 0
T9: dc.b 0
T10: dc.b 0
T11: dc.b 0
even
ready: dc.w 0
preview: dcb.b 8,0
OUTPUT: dcb.b 1300,0
even
signature: dc.b "198XWORLDKIT000",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 = 0
move.b #0,d0
move.b d0,FROM
; TO = 14
move.b #14,d0
move.b d0,TO
; C5 = 0
move.b #0,d0
move.b d0,C5
ifne BROKEN
; C5 = 0
move.b #0,d0
move.b d0,C5
endif
bsr checked_step
bsr emit_state
rts
else
; FROM = 0
move.b #0,d0
move.b d0,FROM
; TO = 15
move.b #15,d0
move.b d0,TO
; C5 = 1
move.b #1,d0
move.b d0,C5
ifne BROKEN
; C5 = 0
move.b #0,d0
move.b d0,C5
endif
bsr checked_step
bsr emit_state
endif
rtsCustomise it
Trace a different diagonal through a clear grid. 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:
VISIBLE: dc.b 0
VALID: dc.b 0
FROM: dc.b 0
TO: dc.b 0
C0: dc.b 0
C1: dc.b 0
C2: dc.b 0
C3: dc.b 0
C4: dc.b 0
C5: dc.b 0
C6: dc.b 0
C7: dc.b 0
C8: dc.b 0
C9: dc.b 0
C10: dc.b 0
C11: dc.b 0
C12: dc.b 0
C13: dc.b 0
C14: dc.b 0
C15: dc.b 0
T0: dc.b 0
T1: dc.b 0
T2: dc.b 0
T3: dc.b 0
T4: dc.b 0
T5: dc.b 0
T6: dc.b 0
T7: dc.b 0
T8: dc.b 0
T9: dc.b 0
T10: dc.b 0
T11: dc.b 0
even
ready: dc.w 0
preview: dcb.b 8,0
OUTPUT: dcb.b 1300,0
even
signature: dc.b "198XWORLDKIT000",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 01 01 00 0E 00 00 00 00. The full client trace in the source explains how it gets there.
Mistake and repair
The wrong caller clears a blocking cell before the query. The ray becomes clear because the world data was altered, not because the sight algorithm should see through a wall. Keep visibility queries read-only.
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:
VISIBLE: dc.b 0
VALID: dc.b 0
FROM: dc.b 0
TO: dc.b 0
C0: dc.b 0
C1: dc.b 0
C2: dc.b 0
C3: dc.b 0
C4: dc.b 0
C5: dc.b 0
C6: dc.b 0
C7: dc.b 0
C8: dc.b 0
C9: dc.b 0
C10: dc.b 0
C11: dc.b 0
C12: dc.b 0
C13: dc.b 0
C14: dc.b 0
C15: dc.b 0
T0: dc.b 0
T1: dc.b 0
T2: dc.b 0
T3: dc.b 0
T4: dc.b 0
T5: dc.b 0
T6: dc.b 0
T7: dc.b 0
T8: dc.b 0
T9: dc.b 0
T10: dc.b 0
T11: dc.b 0
even
ready: dc.w 0
preview: dcb.b 8,0
OUTPUT: dcb.b 1300,0
even
signature: dc.b "198XWORLDKIT000",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 780 code bytes; public state is 20 bytes and private scratch is 12 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.
At most three visited cells after the observer. A cardinal corridor query is cheaper. Larger grids need wider coordinate/error arithmetic and a freshly checked bound.
This is a thin line with a stated tie rule, not a conservative supercover or a complete field-of-view system. Reversing a half-cell tie can choose a different raster cell. Decide corner visibility deliberately rather than assuming all line algorithms agree.
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 50 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
Cardinal sight: Keep the simpler row/column path when a game’s rules do not need diagonal rays.