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:
ld a,0
ld (VISIBLE),a
ld (VALID),a
ld (FROM),a
ld (TO),a
ld (C0),a
ld (C1),a
ld (C2),a
ld (C3),a
ld (C4),a
ld (C5),a
ld (C6),a
ld (C7),a
ld (C8),a
ld (C9),a
ld (C10),a
ld (C11),a
ld (C12),a
ld (C13),a
ld (C14),a
ld (C15),a
ld (T0),a
ld (T1),a
ld (T2),a
ld (T3),a
ld (T4),a
ld (T5),a
ld (T6),a
ld (T7),a
ld (T8),a
ld (T9),a
ld (T10),a
ld (T11),a
ret
grid_line_sight_step:
; VISIBLE = 0
ld a,0
ld (VISIBLE),a
; VALID = 0
ld a,0
ld (VALID),a
; if FROM >= 16:
ld a,(FROM)
cp 16
jp nc,grid_line_sight_L1
jp grid_line_sight_L2
grid_line_sight_L1:
; return
ret
jp grid_line_sight_L3
grid_line_sight_L2:
grid_line_sight_L3:
; if TO >= 16:
ld a,(TO)
cp 16
jp nc,grid_line_sight_L4
jp grid_line_sight_L5
grid_line_sight_L4:
; return
ret
jp grid_line_sight_L6
grid_line_sight_L5:
grid_line_sight_L6:
; VALID = 1
ld a,1
ld (VALID),a
; T0 = FROM & 3
ld a,(FROM)
and 3
ld (T0),a
; T1 = FROM >> 2
ld a,(FROM)
srl a
srl a
ld (T1),a
; T2 = TO & 3
ld a,(TO)
and 3
ld (T2),a
; T3 = TO >> 2
ld a,(TO)
srl a
srl a
ld (T3),a
; T6 = 1
ld a,1
ld (T6),a
; if T2 >= T0:
ld a,(T2)
ld b,a
ld a,(T0)
ld c,a
ld a,b
cp c
jp nc,grid_line_sight_L7
jp grid_line_sight_L8
grid_line_sight_L7:
; T4 = T2 - T0
ld a,(T2)
ld b,a
ld a,(T0)
ld c,a
ld a,b
sub c
ld (T4),a
jp grid_line_sight_L9
grid_line_sight_L8:
; T4 = T0 - T2
ld a,(T0)
ld b,a
ld a,(T2)
ld c,a
ld a,b
sub c
ld (T4),a
; T6 = 255
ld a,255
ld (T6),a
grid_line_sight_L9:
; T7 = 1
ld a,1
ld (T7),a
; if T3 >= T1:
ld a,(T3)
ld b,a
ld a,(T1)
ld c,a
ld a,b
cp c
jp nc,grid_line_sight_L10
jp grid_line_sight_L11
grid_line_sight_L10:
; T5 = T3 - T1
ld a,(T3)
ld b,a
ld a,(T1)
ld c,a
ld a,b
sub c
ld (T5),a
jp grid_line_sight_L12
grid_line_sight_L11:
; T5 = T1 - T3
ld a,(T1)
ld b,a
ld a,(T3)
ld c,a
ld a,b
sub c
ld (T5),a
; T7 = 255
ld a,255
ld (T7),a
grid_line_sight_L12:
; T8 = 128 + T4
ld a,128
ld b,a
ld a,(T4)
ld c,a
ld a,b
add a,c
ld (T8),a
; T8 = T8 - T5
ld a,(T8)
ld b,a
ld a,(T5)
ld c,a
ld a,b
sub c
ld (T8),a
; T9 = FROM
ld a,(FROM)
ld (T9),a
; while T9 != TO:
grid_line_sight_L13:
ld a,(T9)
ld b,a
ld a,(TO)
ld c,a
ld a,b
cp c
jp nz,grid_line_sight_L14
jp grid_line_sight_L15
grid_line_sight_L14:
; T10 = T8 - 128
ld a,(T8)
sub 128
ld (T10),a
; T10 = T10 << 1
ld a,(T10)
sla a
ld (T10),a
; T10 = T10 + 128
ld a,(T10)
add a,128
ld (T10),a
; T11 = 128 - T5
ld a,128
ld b,a
ld a,(T5)
ld c,a
ld a,b
sub c
ld (T11),a
; if T10 > T11:
ld a,(T10)
ld b,a
ld a,(T11)
ld c,a
ld a,b
cp c
jp z,grid_line_sight_L17
jp nc,grid_line_sight_L16
jp grid_line_sight_L17
grid_line_sight_L16:
; T8 = T8 - T5
ld a,(T8)
ld b,a
ld a,(T5)
ld c,a
ld a,b
sub c
ld (T8),a
; T0 = T0 + T6
ld a,(T0)
ld b,a
ld a,(T6)
ld c,a
ld a,b
add a,c
ld (T0),a
jp grid_line_sight_L18
grid_line_sight_L17:
grid_line_sight_L18:
; T11 = 128 + T4
ld a,128
ld b,a
ld a,(T4)
ld c,a
ld a,b
add a,c
ld (T11),a
; if T10 < T11:
ld a,(T10)
ld b,a
ld a,(T11)
ld c,a
ld a,b
cp c
jp c,grid_line_sight_L19
jp grid_line_sight_L20
grid_line_sight_L19:
; T8 = T8 + T4
ld a,(T8)
ld b,a
ld a,(T4)
ld c,a
ld a,b
add a,c
ld (T8),a
; T1 = T1 + T7
ld a,(T1)
ld b,a
ld a,(T7)
ld c,a
ld a,b
add a,c
ld (T1),a
jp grid_line_sight_L21
grid_line_sight_L20:
grid_line_sight_L21:
; T9 = T1 << 2
ld a,(T1)
sla a
sla a
ld (T9),a
; T9 = T9 + T0
ld a,(T9)
ld b,a
ld a,(T0)
ld c,a
ld a,b
add a,c
ld (T9),a
; T11 = C[T9]
ld a,(T9)
ld e,a
ld d,0
ld hl,C0
add hl,de
ld a,(hl)
ld (T11),a
; if T11 != 0:
ld a,(T11)
cp 0
jp nz,grid_line_sight_L22
jp grid_line_sight_L23
grid_line_sight_L22:
; return
ret
jp grid_line_sight_L24
grid_line_sight_L23:
grid_line_sight_L24:
jp grid_line_sight_L13
grid_line_sight_L15:
; VISIBLE = 1
ld a,1
ld (VISIBLE),a
ret
component_end:Machine contract
AF/BC/DE/HL may change; IX/IY are preserved. A direct CALL needs two 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 48K diagnostic boots through ROM tape loading and USR, disables interrupts and owns the screen. The helper performs no port or screen writes.
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. The Makefile produces normal, custom, deliberately wrong and repaired programs. Tools must already be installed; the sample downloads nothing.
Bindings and include order
org $8000
CUSTOM equ 0
BROKEN equ 0
COYOTE_STEPS equ 4
BUFFER_STEPS equ 4
TEXT_CAP equ 8
PROPERTY_COUNT equ 16
STREAM_BYTES equ 13
CRC_POLY equ 7
include "caller.inc"
include "exercise.inc"
component_start:
include "component.inc"
include "data.inc"
include "cases.inc"
include "../../physics/rectangle-overlap/display.inc"
code_end:
STATE:
VISIBLE: defb 0
VALID: defb 0
FROM: defb 0
TO: defb 0
C0: defb 0
C1: defb 0
C2: defb 0
C3: defb 0
C4: defb 0
C5: defb 0
C6: defb 0
C7: defb 0
C8: defb 0
C9: defb 0
C10: defb 0
C11: defb 0
C12: defb 0
C13: defb 0
C14: defb 0
C15: defb 0
T0: defb 0
T1: defb 0
T2: defb 0
T3: defb 0
T4: defb 0
T5: defb 0
T6: defb 0
T7: defb 0
T8: defb 0
T9: defb 0
T10: defb 0
T11: defb 0
input_ptr: defw 0
output_ptr: defw 0
cases_left: defb 0
ready: defb 0
preview: defs 8,0
OUTPUT: defs 1300,0
end startA client retaining state between calls
preview_rules:
if CUSTOM
; FROM = 0
ld a,0
ld (FROM),a
; TO = 14
ld a,14
ld (TO),a
; C5 = 0
ld a,0
ld (C5),a
if BROKEN
; C5 = 0
ld a,0
ld (C5),a
endif
call checked_step
call emit_state
ret
else
; FROM = 0
ld a,0
ld (FROM),a
; TO = 15
ld a,15
ld (TO),a
; C5 = 1
ld a,1
ld (C5),a
if BROKEN
; C5 = 0
ld a,0
ld (C5),a
endif
call checked_step
call emit_state
endif
retCustomise 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
org $8000
CUSTOM equ 1
BROKEN equ 0
COYOTE_STEPS equ 2
BUFFER_STEPS equ 2
TEXT_CAP equ 4
PROPERTY_COUNT equ 16
STREAM_BYTES equ 13
CRC_POLY equ 49
include "caller.inc"
include "exercise.inc"
component_start:
include "component.inc"
include "data.inc"
include "cases.inc"
include "../../physics/rectangle-overlap/display.inc"
code_end:
STATE:
VISIBLE: defb 0
VALID: defb 0
FROM: defb 0
TO: defb 0
C0: defb 0
C1: defb 0
C2: defb 0
C3: defb 0
C4: defb 0
C5: defb 0
C6: defb 0
C7: defb 0
C8: defb 0
C9: defb 0
C10: defb 0
C11: defb 0
C12: defb 0
C13: defb 0
C14: defb 0
C15: defb 0
T0: defb 0
T1: defb 0
T2: defb 0
T3: defb 0
T4: defb 0
T5: defb 0
T6: defb 0
T7: defb 0
T8: defb 0
T9: defb 0
T10: defb 0
T11: defb 0
input_ptr: defw 0
output_ptr: defw 0
cases_left: defb 0
ready: defb 0
preview: defs 8,0
OUTPUT: defs 1300,0
end startThe 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
org $8000
CUSTOM equ 0
BROKEN equ 1
COYOTE_STEPS equ 4
BUFFER_STEPS equ 4
TEXT_CAP equ 8
PROPERTY_COUNT equ 16
STREAM_BYTES equ 13
CRC_POLY equ 7
include "caller.inc"
include "exercise.inc"
component_start:
include "component.inc"
include "data.inc"
include "cases.inc"
include "../../physics/rectangle-overlap/display.inc"
code_end:
STATE:
VISIBLE: defb 0
VALID: defb 0
FROM: defb 0
TO: defb 0
C0: defb 0
C1: defb 0
C2: defb 0
C3: defb 0
C4: defb 0
C5: defb 0
C6: defb 0
C7: defb 0
C8: defb 0
C9: defb 0
C10: defb 0
C11: defb 0
C12: defb 0
C13: defb 0
C14: defb 0
C15: defb 0
T0: defb 0
T1: defb 0
T2: defb 0
T3: defb 0
T4: defb 0
T5: defb 0
T6: defb 0
T7: defb 0
T8: defb 0
T9: defb 0
T10: defb 0
T11: defb 0
input_ptr: defw 0
output_ptr: defw 0
cases_left: defb 0
ready: defb 0
preview: defs 8,0
OUTPUT: defs 1300,0
end start
Cost and alternatives
The measured helper extent is 539 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 48K PAL ROM tape load and USR, using Asm198x 0.0.72, Emu198x 0.44.2. 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.