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:
lda #0
sta MOVE
sta DISTANCE
sta FOUND
sta VALID
sta FROM
sta TO
sta C0
sta C1
sta C2
sta C3
sta C4
sta C5
sta C6
sta C7
sta C8
sta C9
sta C10
sta C11
sta C12
sta C13
sta C14
sta C15
sta T0
sta T1
sta T2
sta T3
sta T4
sta T5
sta T6
sta T7
sta EXPR_SAVE
sta V0
sta V1
sta V2
sta V3
sta V4
sta V5
sta V6
sta V7
sta V8
sta V9
sta V10
sta V11
sta V12
sta V13
sta V14
sta V15
rts
bounded_grid_path_step:
; MOVE = 0
lda #0
sta MOVE
; DISTANCE = 255
lda #255
sta DISTANCE
; FOUND = 0
lda #0
sta FOUND
; VALID = 0
lda #0
sta VALID
; if FROM >= 16:
lda FROM
cmp #16
bcs bounded_grid_path_L4
bounded_grid_path_L5:
jmp bounded_grid_path_L2
bounded_grid_path_L4:
jmp bounded_grid_path_L1
bounded_grid_path_L1:
; return
rts
jmp bounded_grid_path_L3
bounded_grid_path_L2:
bounded_grid_path_L3:
; if TO >= 16:
lda TO
cmp #16
bcs bounded_grid_path_L9
bounded_grid_path_L10:
jmp bounded_grid_path_L7
bounded_grid_path_L9:
jmp bounded_grid_path_L6
bounded_grid_path_L6:
; return
rts
jmp bounded_grid_path_L8
bounded_grid_path_L7:
bounded_grid_path_L8:
; VALID = 1
lda #1
sta VALID
; T0 = C[FROM]
ldx FROM
lda C0,x
sta T0
; if T0 != 0:
lda T0
cmp #0
bne bounded_grid_path_L14
bounded_grid_path_L15:
jmp bounded_grid_path_L12
bounded_grid_path_L14:
jmp bounded_grid_path_L11
bounded_grid_path_L11:
; return
rts
jmp bounded_grid_path_L13
bounded_grid_path_L12:
bounded_grid_path_L13:
; T0 = C[TO]
ldx TO
lda C0,x
sta T0
; if T0 != 0:
lda T0
cmp #0
bne bounded_grid_path_L19
bounded_grid_path_L20:
jmp bounded_grid_path_L17
bounded_grid_path_L19:
jmp bounded_grid_path_L16
bounded_grid_path_L16:
; return
rts
jmp bounded_grid_path_L18
bounded_grid_path_L17:
bounded_grid_path_L18:
; T0 = 0
lda #0
sta T0
; while T0 < 16:
bounded_grid_path_L21:
lda T0
cmp #16
bcc bounded_grid_path_L24
bounded_grid_path_L25:
jmp bounded_grid_path_L23
bounded_grid_path_L24:
jmp bounded_grid_path_L22
bounded_grid_path_L22:
; V[T0] = 255
lda #255
sta EXPR_SAVE
ldx T0
lda EXPR_SAVE
sta V0,x
; T0 = T0 + 1
lda T0
clc
adc #1
sta T0
jmp bounded_grid_path_L21
bounded_grid_path_L23:
; V[TO] = 0
lda #0
sta EXPR_SAVE
ldx TO
lda EXPR_SAVE
sta V0,x
; T0 = 1
lda #1
sta T0
; while T0 < 16:
bounded_grid_path_L26:
lda T0
cmp #16
bcc bounded_grid_path_L29
bounded_grid_path_L30:
jmp bounded_grid_path_L28
bounded_grid_path_L29:
jmp bounded_grid_path_L27
bounded_grid_path_L27:
; T1 = 0
lda #0
sta T1
; while T1 < 16:
bounded_grid_path_L31:
lda T1
cmp #16
bcc bounded_grid_path_L34
bounded_grid_path_L35:
jmp bounded_grid_path_L33
bounded_grid_path_L34:
jmp bounded_grid_path_L32
bounded_grid_path_L32:
; T2 = C[T1]
ldx T1
lda C0,x
sta T2
; T3 = V[T1]
ldx T1
lda V0,x
sta T3
; if T2 == 0:
lda T2
cmp #0
beq bounded_grid_path_L39
bounded_grid_path_L40:
jmp bounded_grid_path_L37
bounded_grid_path_L39:
jmp bounded_grid_path_L36
bounded_grid_path_L36:
; if T3 == 255:
lda T3
cmp #255
beq bounded_grid_path_L44
bounded_grid_path_L45:
jmp bounded_grid_path_L42
bounded_grid_path_L44:
jmp bounded_grid_path_L41
bounded_grid_path_L41:
; T4 = T0 - 1
lda T0
sec
sbc #1
sta T4
; T5 = T1 & 3
lda T1
and #3
sta T5
; if T5 != 0:
lda T5
cmp #0
bne bounded_grid_path_L49
bounded_grid_path_L50:
jmp bounded_grid_path_L47
bounded_grid_path_L49:
jmp bounded_grid_path_L46
bounded_grid_path_L46:
; T6 = T1 - 1
lda T1
sec
sbc #1
sta T6
; T7 = V[T6]
ldx T6
lda V0,x
sta T7
; if T7 == T4:
lda T7
cmp T4
beq bounded_grid_path_L54
bounded_grid_path_L55:
jmp bounded_grid_path_L52
bounded_grid_path_L54:
jmp bounded_grid_path_L51
bounded_grid_path_L51:
; V[T1] = T0
lda T0
sta EXPR_SAVE
ldx T1
lda EXPR_SAVE
sta V0,x
jmp bounded_grid_path_L53
bounded_grid_path_L52:
bounded_grid_path_L53:
jmp bounded_grid_path_L48
bounded_grid_path_L47:
bounded_grid_path_L48:
; if T5 != 3:
lda T5
cmp #3
bne bounded_grid_path_L59
bounded_grid_path_L60:
jmp bounded_grid_path_L57
bounded_grid_path_L59:
jmp bounded_grid_path_L56
bounded_grid_path_L56:
; T6 = T1 + 1
lda T1
clc
adc #1
sta T6
; T7 = V[T6]
ldx T6
lda V0,x
sta T7
; if T7 == T4:
lda T7
cmp T4
beq bounded_grid_path_L64
bounded_grid_path_L65:
jmp bounded_grid_path_L62
bounded_grid_path_L64:
jmp bounded_grid_path_L61
bounded_grid_path_L61:
; V[T1] = T0
lda T0
sta EXPR_SAVE
ldx T1
lda EXPR_SAVE
sta V0,x
jmp bounded_grid_path_L63
bounded_grid_path_L62:
bounded_grid_path_L63:
jmp bounded_grid_path_L58
bounded_grid_path_L57:
bounded_grid_path_L58:
; if T1 >= 4:
lda T1
cmp #4
bcs bounded_grid_path_L69
bounded_grid_path_L70:
jmp bounded_grid_path_L67
bounded_grid_path_L69:
jmp bounded_grid_path_L66
bounded_grid_path_L66:
; T6 = T1 - 4
lda T1
sec
sbc #4
sta T6
; T7 = V[T6]
ldx T6
lda V0,x
sta T7
; if T7 == T4:
lda T7
cmp T4
beq bounded_grid_path_L74
bounded_grid_path_L75:
jmp bounded_grid_path_L72
bounded_grid_path_L74:
jmp bounded_grid_path_L71
bounded_grid_path_L71:
; V[T1] = T0
lda T0
sta EXPR_SAVE
ldx T1
lda EXPR_SAVE
sta V0,x
jmp bounded_grid_path_L73
bounded_grid_path_L72:
bounded_grid_path_L73:
jmp bounded_grid_path_L68
bounded_grid_path_L67:
bounded_grid_path_L68:
; if T1 < 12:
lda T1
cmp #12
bcc bounded_grid_path_L79
bounded_grid_path_L80:
jmp bounded_grid_path_L77
bounded_grid_path_L79:
jmp bounded_grid_path_L76
bounded_grid_path_L76:
; T6 = T1 + 4
lda T1
clc
adc #4
sta T6
; T7 = V[T6]
ldx T6
lda V0,x
sta T7
; if T7 == T4:
lda T7
cmp T4
beq bounded_grid_path_L84
bounded_grid_path_L85:
jmp bounded_grid_path_L82
bounded_grid_path_L84:
jmp bounded_grid_path_L81
bounded_grid_path_L81:
; V[T1] = T0
lda T0
sta EXPR_SAVE
ldx T1
lda EXPR_SAVE
sta V0,x
jmp bounded_grid_path_L83
bounded_grid_path_L82:
bounded_grid_path_L83:
jmp bounded_grid_path_L78
bounded_grid_path_L77:
bounded_grid_path_L78:
jmp bounded_grid_path_L43
bounded_grid_path_L42:
bounded_grid_path_L43:
jmp bounded_grid_path_L38
bounded_grid_path_L37:
bounded_grid_path_L38:
; T1 = T1 + 1
lda T1
clc
adc #1
sta T1
jmp bounded_grid_path_L31
bounded_grid_path_L33:
; T0 = T0 + 1
lda T0
clc
adc #1
sta T0
jmp bounded_grid_path_L26
bounded_grid_path_L28:
; DISTANCE = V[FROM]
ldx FROM
lda V0,x
sta DISTANCE
; if DISTANCE == 255:
lda DISTANCE
cmp #255
beq bounded_grid_path_L89
bounded_grid_path_L90:
jmp bounded_grid_path_L87
bounded_grid_path_L89:
jmp bounded_grid_path_L86
bounded_grid_path_L86:
; return
rts
jmp bounded_grid_path_L88
bounded_grid_path_L87:
bounded_grid_path_L88:
; FOUND = 1
lda #1
sta FOUND
; if DISTANCE == 0:
lda DISTANCE
cmp #0
beq bounded_grid_path_L94
bounded_grid_path_L95:
jmp bounded_grid_path_L92
bounded_grid_path_L94:
jmp bounded_grid_path_L91
bounded_grid_path_L91:
; return
rts
jmp bounded_grid_path_L93
bounded_grid_path_L92:
bounded_grid_path_L93:
; T0 = DISTANCE - 1
lda DISTANCE
sec
sbc #1
sta T0
; T1 = FROM & 3
lda FROM
and #3
sta T1
; if T1 != 0:
lda T1
cmp #0
bne bounded_grid_path_L99
bounded_grid_path_L100:
jmp bounded_grid_path_L97
bounded_grid_path_L99:
jmp bounded_grid_path_L96
bounded_grid_path_L96:
; T2 = FROM - 1
lda FROM
sec
sbc #1
sta T2
; T3 = V[T2]
ldx T2
lda V0,x
sta T3
; if T3 == T0:
lda T3
cmp T0
beq bounded_grid_path_L104
bounded_grid_path_L105:
jmp bounded_grid_path_L102
bounded_grid_path_L104:
jmp bounded_grid_path_L101
bounded_grid_path_L101:
; MOVE = 1
lda #1
sta MOVE
; return
rts
jmp bounded_grid_path_L103
bounded_grid_path_L102:
bounded_grid_path_L103:
jmp bounded_grid_path_L98
bounded_grid_path_L97:
bounded_grid_path_L98:
; if T1 != 3:
lda T1
cmp #3
bne bounded_grid_path_L109
bounded_grid_path_L110:
jmp bounded_grid_path_L107
bounded_grid_path_L109:
jmp bounded_grid_path_L106
bounded_grid_path_L106:
; T2 = FROM + 1
lda FROM
clc
adc #1
sta T2
; T3 = V[T2]
ldx T2
lda V0,x
sta T3
; if T3 == T0:
lda T3
cmp T0
beq bounded_grid_path_L114
bounded_grid_path_L115:
jmp bounded_grid_path_L112
bounded_grid_path_L114:
jmp bounded_grid_path_L111
bounded_grid_path_L111:
; MOVE = 2
lda #2
sta MOVE
; return
rts
jmp bounded_grid_path_L113
bounded_grid_path_L112:
bounded_grid_path_L113:
jmp bounded_grid_path_L108
bounded_grid_path_L107:
bounded_grid_path_L108:
; if FROM >= 4:
lda FROM
cmp #4
bcs bounded_grid_path_L119
bounded_grid_path_L120:
jmp bounded_grid_path_L117
bounded_grid_path_L119:
jmp bounded_grid_path_L116
bounded_grid_path_L116:
; T2 = FROM - 4
lda FROM
sec
sbc #4
sta T2
; T3 = V[T2]
ldx T2
lda V0,x
sta T3
; if T3 == T0:
lda T3
cmp T0
beq bounded_grid_path_L124
bounded_grid_path_L125:
jmp bounded_grid_path_L122
bounded_grid_path_L124:
jmp bounded_grid_path_L121
bounded_grid_path_L121:
; MOVE = 3
lda #3
sta MOVE
; return
rts
jmp bounded_grid_path_L123
bounded_grid_path_L122:
bounded_grid_path_L123:
jmp bounded_grid_path_L118
bounded_grid_path_L117:
bounded_grid_path_L118:
; if FROM < 12:
lda FROM
cmp #12
bcc bounded_grid_path_L129
bounded_grid_path_L130:
jmp bounded_grid_path_L127
bounded_grid_path_L129:
jmp bounded_grid_path_L126
bounded_grid_path_L126:
; T2 = FROM + 4
lda FROM
clc
adc #4
sta T2
; T3 = V[T2]
ldx T2
lda V0,x
sta T3
; if T3 == T0:
lda T3
cmp T0
beq bounded_grid_path_L134
bounded_grid_path_L135:
jmp bounded_grid_path_L132
bounded_grid_path_L134:
jmp bounded_grid_path_L131
bounded_grid_path_L131:
; MOVE = 4
lda #4
sta MOVE
jmp bounded_grid_path_L133
bounded_grid_path_L132:
bounded_grid_path_L133:
jmp bounded_grid_path_L128
bounded_grid_path_L127:
bounded_grid_path_L128:
rts
component_end:Machine contract
A/X/status may change; Y is preserved. The 2A03 has no decimal arithmetic mode. A direct JSR 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 NROM caller owns PPU setup and background display, with NMI and DMC disabled. Table and packet sizes are bounded to fit the cartridge caller and internal RAM; the helper owns no PPU registers.
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
.segment "HEADER"
.byte "NES",$1a,2,1,0,0,0,0,0,0,0,0,0,0
MOVE=$80
DISTANCE=$81
FOUND=$82
VALID=$83
FROM=$84
TO=$85
C0=$86
C1=$87
C2=$88
C3=$89
C4=$8a
C5=$8b
C6=$8c
C7=$8d
C8=$8e
C9=$8f
C10=$90
C11=$91
C12=$92
C13=$93
C14=$94
C15=$95
T0=$96
T1=$97
T2=$98
T3=$99
T4=$9a
T5=$9b
T6=$9c
T7=$9d
EXPR_SAVE=$9e
V0=$9f
V1=$a0
V2=$a1
V3=$a2
V4=$a3
V5=$a4
V6=$a5
V7=$a6
V8=$a7
V9=$a8
V10=$a9
V11=$aa
V12=$ab
V13=$ac
V14=$ad
V15=$ae
STATE=$80
input_ptr=$70
cases_left=$72
ptr=$74
saved_y=$76
OUTPUT=$0200
preview=OUTPUT+1400
ready=OUTPUT+1408
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"
.include "data.inc"
.include "cases.inc"
code_end:
.segment "VECTORS"
.word nmi,reset,irq
.segment "CHARS"
.include "../../input/controller-reading/edges-font.inc"
.res 8192-272,0A client retaining state between calls
preview_rules:
.if CUSTOM
; FROM = 0
lda #0
sta FROM
; TO = 15
lda #15
sta TO
.if BROKEN
; C1 = 0
lda #0
sta C1
.endif
jsr checked_step
jsr emit_state
rts
.else
; FROM = 0
lda #0
sta FROM
; TO = 3
lda #3
sta TO
; C1 = 1
lda #1
sta C1
.if BROKEN
; C1 = 0
lda #0
sta C1
.endif
jsr checked_step
jsr emit_state
.endif
rtsCustomise 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
.segment "HEADER"
.byte "NES",$1a,2,1,0,0,0,0,0,0,0,0,0,0
MOVE=$80
DISTANCE=$81
FOUND=$82
VALID=$83
FROM=$84
TO=$85
C0=$86
C1=$87
C2=$88
C3=$89
C4=$8a
C5=$8b
C6=$8c
C7=$8d
C8=$8e
C9=$8f
C10=$90
C11=$91
C12=$92
C13=$93
C14=$94
C15=$95
T0=$96
T1=$97
T2=$98
T3=$99
T4=$9a
T5=$9b
T6=$9c
T7=$9d
EXPR_SAVE=$9e
V0=$9f
V1=$a0
V2=$a1
V3=$a2
V4=$a3
V5=$a4
V6=$a5
V7=$a6
V8=$a7
V9=$a8
V10=$a9
V11=$aa
V12=$ab
V13=$ac
V14=$ad
V15=$ae
STATE=$80
input_ptr=$70
cases_left=$72
ptr=$74
saved_y=$76
OUTPUT=$0200
preview=OUTPUT+1400
ready=OUTPUT+1408
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"
.include "data.inc"
.include "cases.inc"
code_end:
.segment "VECTORS"
.word nmi,reset,irq
.segment "CHARS"
.include "../../input/controller-reading/edges-font.inc"
.res 8192-272,0The 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
.segment "HEADER"
.byte "NES",$1a,2,1,0,0,0,0,0,0,0,0,0,0
MOVE=$80
DISTANCE=$81
FOUND=$82
VALID=$83
FROM=$84
TO=$85
C0=$86
C1=$87
C2=$88
C3=$89
C4=$8a
C5=$8b
C6=$8c
C7=$8d
C8=$8e
C9=$8f
C10=$90
C11=$91
C12=$92
C13=$93
C14=$94
C15=$95
T0=$96
T1=$97
T2=$98
T3=$99
T4=$9a
T5=$9b
T6=$9c
T7=$9d
EXPR_SAVE=$9e
V0=$9f
V1=$a0
V2=$a1
V3=$a2
V4=$a3
V5=$a4
V6=$a5
V7=$a6
V8=$a7
V9=$a8
V10=$a9
V11=$aa
V12=$ab
V13=$ac
V14=$ad
V15=$ae
STATE=$80
input_ptr=$70
cases_left=$72
ptr=$74
saved_y=$76
OUTPUT=$0200
preview=OUTPUT+1400
ready=OUTPUT+1408
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"
.include "data.inc"
.include "cases.inc"
code_end:
.segment "VECTORS"
.word nmi,reset,irq
.segment "CHARS"
.include "../../input/controller-reading/edges-font.inc"
.res 8192-272,0
Cost and alternatives
The measured helper extent is 805 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 NTSC NROM, background only, DMC/NMI disabled, 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.