An enemy can walk around a wall without pretending that moving towards the player is already pathfinding.
Use it in a project
A 4×4 row-major grid uses zero for traversable and nonzero for blocked cells. FROM and TO must be 0–15. Return FOUND=1, shortest four-connected DISTANCE and the first MOVE (1 left, 2 right, 3 up, 4 down). Already at a clear destination returns distance zero and move zero. Blocked or unreachable endpoints return FOUND=0, DISTANCE=255 and MOVE=0 with VALID=1. Bad indices return VALID=0.
Include component.inc once (MOS callers include the shared 6502 implementation through it). Reserve the public fields in this exact order: MOVE, DISTANCE, FOUND, VALID, FROM, TO, C0, C1, C2, C3, C4, C5, C6, C7, C8, C9, C10, C11, C12, C13, C14, C15. They occupy 22 contiguous bytes. Also reserve the private workspace: T0, T1, T2, T3, T4, T5, T6, T7, EXPR_SAVE, V0, V1, V2, V3, V4, V5, V6, V7, V8, V9, V10, V11, V12, V13, V14, V15 (25 bytes). Array names in the explanation refer to the numbered consecutive bindings, such as C0, C1 and so on.
Call bounded_grid_path_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 bounded_grid_path_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 | MOVE, DISTANCE, FOUND and VALID |
Build distance layers outwards from the destination. A cell can join only the next layer, so scanning order cannot turn a long route into a falsely short one. A neighbour one layer closer supplies a valid first move.
Reusable initialisation and service
; SPDX-License-Identifier: MIT
; Find the First Step Along a Shortest Grid Path. See README.md for the byte interface and ownership.
; init clears the public fields and private workspace; set inputs afterwards.
bounded_grid_path_init:
ld a,0
ld (MOVE),a
ld (DISTANCE),a
ld (FOUND),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 (EXPR_SAVE),a
ld (V0),a
ld (V1),a
ld (V2),a
ld (V3),a
ld (V4),a
ld (V5),a
ld (V6),a
ld (V7),a
ld (V8),a
ld (V9),a
ld (V10),a
ld (V11),a
ld (V12),a
ld (V13),a
ld (V14),a
ld (V15),a
ret
bounded_grid_path_step:
; MOVE = 0
ld a,0
ld (MOVE),a
; DISTANCE = 255
ld a,255
ld (DISTANCE),a
; FOUND = 0
ld a,0
ld (FOUND),a
; VALID = 0
ld a,0
ld (VALID),a
; if FROM >= 16:
ld a,(FROM)
cp 16
jp nc,bounded_grid_path_L1
jp bounded_grid_path_L2
bounded_grid_path_L1:
; return
ret
jp bounded_grid_path_L3
bounded_grid_path_L2:
bounded_grid_path_L3:
; if TO >= 16:
ld a,(TO)
cp 16
jp nc,bounded_grid_path_L4
jp bounded_grid_path_L5
bounded_grid_path_L4:
; return
ret
jp bounded_grid_path_L6
bounded_grid_path_L5:
bounded_grid_path_L6:
; VALID = 1
ld a,1
ld (VALID),a
; T0 = C[FROM]
ld a,(FROM)
ld e,a
ld d,0
ld hl,C0
add hl,de
ld a,(hl)
ld (T0),a
; if T0 != 0:
ld a,(T0)
cp 0
jp nz,bounded_grid_path_L7
jp bounded_grid_path_L8
bounded_grid_path_L7:
; return
ret
jp bounded_grid_path_L9
bounded_grid_path_L8:
bounded_grid_path_L9:
; T0 = C[TO]
ld a,(TO)
ld e,a
ld d,0
ld hl,C0
add hl,de
ld a,(hl)
ld (T0),a
; if T0 != 0:
ld a,(T0)
cp 0
jp nz,bounded_grid_path_L10
jp bounded_grid_path_L11
bounded_grid_path_L10:
; return
ret
jp bounded_grid_path_L12
bounded_grid_path_L11:
bounded_grid_path_L12:
; T0 = 0
ld a,0
ld (T0),a
; while T0 < 16:
bounded_grid_path_L13:
ld a,(T0)
cp 16
jp c,bounded_grid_path_L14
jp bounded_grid_path_L15
bounded_grid_path_L14:
; V[T0] = 255
ld a,255
ld c,a
ld a,(T0)
ld e,a
ld d,0
ld hl,V0
add hl,de
ld (hl),c
; T0 = T0 + 1
ld a,(T0)
add a,1
ld (T0),a
jp bounded_grid_path_L13
bounded_grid_path_L15:
; V[TO] = 0
ld a,0
ld c,a
ld a,(TO)
ld e,a
ld d,0
ld hl,V0
add hl,de
ld (hl),c
; T0 = 1
ld a,1
ld (T0),a
; while T0 < 16:
bounded_grid_path_L16:
ld a,(T0)
cp 16
jp c,bounded_grid_path_L17
jp bounded_grid_path_L18
bounded_grid_path_L17:
; T1 = 0
ld a,0
ld (T1),a
; while T1 < 16:
bounded_grid_path_L19:
ld a,(T1)
cp 16
jp c,bounded_grid_path_L20
jp bounded_grid_path_L21
bounded_grid_path_L20:
; T2 = C[T1]
ld a,(T1)
ld e,a
ld d,0
ld hl,C0
add hl,de
ld a,(hl)
ld (T2),a
; T3 = V[T1]
ld a,(T1)
ld e,a
ld d,0
ld hl,V0
add hl,de
ld a,(hl)
ld (T3),a
; if T2 == 0:
ld a,(T2)
cp 0
jp z,bounded_grid_path_L22
jp bounded_grid_path_L23
bounded_grid_path_L22:
; if T3 == 255:
ld a,(T3)
cp 255
jp z,bounded_grid_path_L25
jp bounded_grid_path_L26
bounded_grid_path_L25:
; T4 = T0 - 1
ld a,(T0)
sub 1
ld (T4),a
; T5 = T1 & 3
ld a,(T1)
and 3
ld (T5),a
; if T5 != 0:
ld a,(T5)
cp 0
jp nz,bounded_grid_path_L28
jp bounded_grid_path_L29
bounded_grid_path_L28:
; T6 = T1 - 1
ld a,(T1)
sub 1
ld (T6),a
; T7 = V[T6]
ld a,(T6)
ld e,a
ld d,0
ld hl,V0
add hl,de
ld a,(hl)
ld (T7),a
; if T7 == T4:
ld a,(T7)
ld b,a
ld a,(T4)
ld c,a
ld a,b
cp c
jp z,bounded_grid_path_L31
jp bounded_grid_path_L32
bounded_grid_path_L31:
; V[T1] = T0
ld a,(T0)
ld c,a
ld a,(T1)
ld e,a
ld d,0
ld hl,V0
add hl,de
ld (hl),c
jp bounded_grid_path_L33
bounded_grid_path_L32:
bounded_grid_path_L33:
jp bounded_grid_path_L30
bounded_grid_path_L29:
bounded_grid_path_L30:
; if T5 != 3:
ld a,(T5)
cp 3
jp nz,bounded_grid_path_L34
jp bounded_grid_path_L35
bounded_grid_path_L34:
; T6 = T1 + 1
ld a,(T1)
add a,1
ld (T6),a
; T7 = V[T6]
ld a,(T6)
ld e,a
ld d,0
ld hl,V0
add hl,de
ld a,(hl)
ld (T7),a
; if T7 == T4:
ld a,(T7)
ld b,a
ld a,(T4)
ld c,a
ld a,b
cp c
jp z,bounded_grid_path_L37
jp bounded_grid_path_L38
bounded_grid_path_L37:
; V[T1] = T0
ld a,(T0)
ld c,a
ld a,(T1)
ld e,a
ld d,0
ld hl,V0
add hl,de
ld (hl),c
jp bounded_grid_path_L39
bounded_grid_path_L38:
bounded_grid_path_L39:
jp bounded_grid_path_L36
bounded_grid_path_L35:
bounded_grid_path_L36:
; if T1 >= 4:
ld a,(T1)
cp 4
jp nc,bounded_grid_path_L40
jp bounded_grid_path_L41
bounded_grid_path_L40:
; T6 = T1 - 4
ld a,(T1)
sub 4
ld (T6),a
; T7 = V[T6]
ld a,(T6)
ld e,a
ld d,0
ld hl,V0
add hl,de
ld a,(hl)
ld (T7),a
; if T7 == T4:
ld a,(T7)
ld b,a
ld a,(T4)
ld c,a
ld a,b
cp c
jp z,bounded_grid_path_L43
jp bounded_grid_path_L44
bounded_grid_path_L43:
; V[T1] = T0
ld a,(T0)
ld c,a
ld a,(T1)
ld e,a
ld d,0
ld hl,V0
add hl,de
ld (hl),c
jp bounded_grid_path_L45
bounded_grid_path_L44:
bounded_grid_path_L45:
jp bounded_grid_path_L42
bounded_grid_path_L41:
bounded_grid_path_L42:
; if T1 < 12:
ld a,(T1)
cp 12
jp c,bounded_grid_path_L46
jp bounded_grid_path_L47
bounded_grid_path_L46:
; T6 = T1 + 4
ld a,(T1)
add a,4
ld (T6),a
; T7 = V[T6]
ld a,(T6)
ld e,a
ld d,0
ld hl,V0
add hl,de
ld a,(hl)
ld (T7),a
; if T7 == T4:
ld a,(T7)
ld b,a
ld a,(T4)
ld c,a
ld a,b
cp c
jp z,bounded_grid_path_L49
jp bounded_grid_path_L50
bounded_grid_path_L49:
; V[T1] = T0
ld a,(T0)
ld c,a
ld a,(T1)
ld e,a
ld d,0
ld hl,V0
add hl,de
ld (hl),c
jp bounded_grid_path_L51
bounded_grid_path_L50:
bounded_grid_path_L51:
jp bounded_grid_path_L48
bounded_grid_path_L47:
bounded_grid_path_L48:
jp bounded_grid_path_L27
bounded_grid_path_L26:
bounded_grid_path_L27:
jp bounded_grid_path_L24
bounded_grid_path_L23:
bounded_grid_path_L24:
; T1 = T1 + 1
ld a,(T1)
add a,1
ld (T1),a
jp bounded_grid_path_L19
bounded_grid_path_L21:
; T0 = T0 + 1
ld a,(T0)
add a,1
ld (T0),a
jp bounded_grid_path_L16
bounded_grid_path_L18:
; DISTANCE = V[FROM]
ld a,(FROM)
ld e,a
ld d,0
ld hl,V0
add hl,de
ld a,(hl)
ld (DISTANCE),a
; if DISTANCE == 255:
ld a,(DISTANCE)
cp 255
jp z,bounded_grid_path_L52
jp bounded_grid_path_L53
bounded_grid_path_L52:
; return
ret
jp bounded_grid_path_L54
bounded_grid_path_L53:
bounded_grid_path_L54:
; FOUND = 1
ld a,1
ld (FOUND),a
; if DISTANCE == 0:
ld a,(DISTANCE)
cp 0
jp z,bounded_grid_path_L55
jp bounded_grid_path_L56
bounded_grid_path_L55:
; return
ret
jp bounded_grid_path_L57
bounded_grid_path_L56:
bounded_grid_path_L57:
; T0 = DISTANCE - 1
ld a,(DISTANCE)
sub 1
ld (T0),a
; T1 = FROM & 3
ld a,(FROM)
and 3
ld (T1),a
; if T1 != 0:
ld a,(T1)
cp 0
jp nz,bounded_grid_path_L58
jp bounded_grid_path_L59
bounded_grid_path_L58:
; T2 = FROM - 1
ld a,(FROM)
sub 1
ld (T2),a
; T3 = V[T2]
ld a,(T2)
ld e,a
ld d,0
ld hl,V0
add hl,de
ld a,(hl)
ld (T3),a
; if T3 == T0:
ld a,(T3)
ld b,a
ld a,(T0)
ld c,a
ld a,b
cp c
jp z,bounded_grid_path_L61
jp bounded_grid_path_L62
bounded_grid_path_L61:
; MOVE = 1
ld a,1
ld (MOVE),a
; return
ret
jp bounded_grid_path_L63
bounded_grid_path_L62:
bounded_grid_path_L63:
jp bounded_grid_path_L60
bounded_grid_path_L59:
bounded_grid_path_L60:
; if T1 != 3:
ld a,(T1)
cp 3
jp nz,bounded_grid_path_L64
jp bounded_grid_path_L65
bounded_grid_path_L64:
; T2 = FROM + 1
ld a,(FROM)
add a,1
ld (T2),a
; T3 = V[T2]
ld a,(T2)
ld e,a
ld d,0
ld hl,V0
add hl,de
ld a,(hl)
ld (T3),a
; if T3 == T0:
ld a,(T3)
ld b,a
ld a,(T0)
ld c,a
ld a,b
cp c
jp z,bounded_grid_path_L67
jp bounded_grid_path_L68
bounded_grid_path_L67:
; MOVE = 2
ld a,2
ld (MOVE),a
; return
ret
jp bounded_grid_path_L69
bounded_grid_path_L68:
bounded_grid_path_L69:
jp bounded_grid_path_L66
bounded_grid_path_L65:
bounded_grid_path_L66:
; if FROM >= 4:
ld a,(FROM)
cp 4
jp nc,bounded_grid_path_L70
jp bounded_grid_path_L71
bounded_grid_path_L70:
; T2 = FROM - 4
ld a,(FROM)
sub 4
ld (T2),a
; T3 = V[T2]
ld a,(T2)
ld e,a
ld d,0
ld hl,V0
add hl,de
ld a,(hl)
ld (T3),a
; if T3 == T0:
ld a,(T3)
ld b,a
ld a,(T0)
ld c,a
ld a,b
cp c
jp z,bounded_grid_path_L73
jp bounded_grid_path_L74
bounded_grid_path_L73:
; MOVE = 3
ld a,3
ld (MOVE),a
; return
ret
jp bounded_grid_path_L75
bounded_grid_path_L74:
bounded_grid_path_L75:
jp bounded_grid_path_L72
bounded_grid_path_L71:
bounded_grid_path_L72:
; if FROM < 12:
ld a,(FROM)
cp 12
jp c,bounded_grid_path_L76
jp bounded_grid_path_L77
bounded_grid_path_L76:
; T2 = FROM + 4
ld a,(FROM)
add a,4
ld (T2),a
; T3 = V[T2]
ld a,(T2)
ld e,a
ld d,0
ld hl,V0
add hl,de
ld a,(hl)
ld (T3),a
; if T3 == T0:
ld a,(T3)
ld b,a
ld a,(T0)
ld c,a
ld a,b
cp c
jp z,bounded_grid_path_L79
jp bounded_grid_path_L80
bounded_grid_path_L79:
; MOVE = 4
ld a,4
ld (MOVE),a
jp bounded_grid_path_L81
bounded_grid_path_L80:
bounded_grid_path_L81:
jp bounded_grid_path_L78
bounded_grid_path_L77:
bounded_grid_path_L78:
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:
MOVE: defb 0
DISTANCE: defb 0
FOUND: 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
EXPR_SAVE: defb 0
V0: defb 0
V1: defb 0
V2: defb 0
V3: defb 0
V4: defb 0
V5: defb 0
V6: defb 0
V7: defb 0
V8: defb 0
V9: defb 0
V10: defb 0
V11: defb 0
V12: defb 0
V13: defb 0
V14: defb 0
V15: 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 = 15
ld a,15
ld (TO),a
if BROKEN
; C1 = 0
ld a,0
ld (C1),a
endif
call checked_step
call emit_state
ret
else
; FROM = 0
ld a,0
ld (FROM),a
; TO = 3
ld a,3
ld (TO),a
; C1 = 1
ld a,1
ld (C1),a
if BROKEN
; C1 = 0
ld a,0
ld (C1),a
endif
call checked_step
call emit_state
endif
retCustomise it
Search across a clear board to the opposite corner. 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:
MOVE: defb 0
DISTANCE: defb 0
FOUND: 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
EXPR_SAVE: defb 0
V0: defb 0
V1: defb 0
V2: defb 0
V3: defb 0
V4: defb 0
V5: defb 0
V6: defb 0
V7: defb 0
V8: defb 0
V9: defb 0
V10: defb 0
V11: defb 0
V12: defb 0
V13: defb 0
V14: defb 0
V15: 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 02 06 01 01 00 0F 00 00. The full client trace in the source explains how it gets there.
Mistake and repair
The wrong caller removes the obstacle before searching. The returned first step goes through the cell that should be blocked. A path query should read the collision map, not clear cells to make a route possible.
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:
MOVE: defb 0
DISTANCE: defb 0
FOUND: 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
EXPR_SAVE: defb 0
V0: defb 0
V1: defb 0
V2: defb 0
V3: defb 0
V4: defb 0
V5: defb 0
V6: defb 0
V7: defb 0
V8: defb 0
V9: defb 0
V10: defb 0
V11: defb 0
V12: defb 0
V13: defb 0
V14: defb 0
V15: 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 1027 code bytes; public state is 22 bytes and private scratch is 25 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.
Fifteen layers scan sixteen cells each, using sixteen private distance bytes. A queue-based breadth-first search avoids many repeated probes on larger boards but needs a bounded queue. Incremental search can spread work across frames.
This unit-cost four-neighbour search chooses the first available downhill neighbour in left/right/up/down order. It returns a first step, not a full persistent path. Diagonals, terrain costs and moving obstacles require different rules or a new query.
Execution evidence
Four variants run on 48K PAL ROM tape load and USR, using Asm198x 0.0.72, Emu198x 0.44.2. Each executes 45 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
Grid sight: Seeing the target and finding a walkable route are different questions; a clear ray does not replace a path search.