On a four-way grid, distance is the horizontal gap plus the vertical gap. That makes a useful cheap measure for a guard choosing a nearby target, or a turn-based game showing a movement budget. Two byte coordinates can produce a result larger than a byte.
Include, initialise and call
Bind AX, AY, BX, BY, DIST_LO, DIST_HI as 6 contiguous private bytes in that order. Include the helper once. Call manhattan_distance_init at the deliberate reset boundary: it clears all named bytes, including inputs. Set your starting values afterwards. Call manhattan_distance_step when this service is needed.
Fill both coordinate pairs and call step when the decision needs the distance. Compare both result bytes when selecting a threshold or nearest target. Ties need a separate stable rule. Reusing one scratch block for successive independent queries is safe under a single owner.
AX/AY and BX/BY are unsigned coordinates from 0–255. Step preserves all four inputs and writes DIST_LO/DIST_HI as a little-endian result |AX − BX| + |AY − BY|, from 0–510. A wider result is needed even though each coordinate fits in one byte.
Reusable initialisation and service
; SPDX-License-Identifier: MIT
; Manhattan Distance. Bind these contiguous private bytes: AX, AY, BX, BY, DIST_LO, DIST_HI.
; init clears the whole block; step uses current inputs. No I/O, waits or IRQ owner.
; AF/BC/DE/HL may change; IX/IY survive.
manhattan_distance_init:
xor a
ld (AX),a
ld (AY),a
ld (BX),a
ld (BY),a
ld (DIST_LO),a
ld (DIST_HI),a
ret
manhattan_distance_step:
xor a
ld (DIST_HI),a
ld a,(BX)
ld b,a
ld a,(AX)
sub b
jr nc,distance_save
neg
distance_save:
ld c,a
ld a,(BY)
ld b,a
ld a,(AY)
sub b
jr nc,distance_add
neg
distance_add:
add a,c
ld (DIST_LO),a
ret nc
ld a,1
ld (DIST_HI),a
ret
component_end:State and ownership
Four input bytes and a two-byte output. There is no map, actor state or movement inside this helper. Byte order is explicit on every target, including 68000.
AF/BC/DE/HL may change; IX/IY survive. A direct CALL uses two return-address stack bytes.
This implementation has fixed symbol bindings and one mutation owner. Independent users need distinct state blocks and scoped/renamed bindings; including another copy with the same global labels is not sufficient. Sequential queries may reuse a scratch block only after the previous result has been consumed. Do not let an interrupt and the main loop mutate the same block without a separately designed ownership policy.
The standalone tape program starts at $8000, disables interrupts and owns bitmap/attribute RAM. It does not return to BASIC. The helper itself never disables interrupts or touches the display.
A small caller you can adapt
The standalone program includes the helper and a separate client. Its read-only table exercises 96 valid inputs, then this client initialises once and retains state between calls. Replace the supplied input changes with your own game values; the display and packet machinery are diagnostics rather than dependencies of the component.
Buildable caller, bindings and include order
org $8000
CUSTOM equ 0
BROKEN equ 0
SCORE_CAP equ 65535
QUEUE_CAP equ 4
REPEAT_DELAY equ 4
REPEAT_RATE equ 2
include "caller.inc"
include "exercise.inc"
component_start:
include "component.inc"
include "cases.inc"
include "../../physics/rectangle-overlap/display.inc"
code_end:
STATE:
AX: defb 0
AY: defb 0
BX: defb 0
BY: defb 0
DIST_LO: defb 0
DIST_HI: 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 separate client retaining state between calls
preview_rules:
if CUSTOM
ld a,0
ld (AX),a
ld a,0
ld (AY),a
ld a,200
ld (BX),a
ld a,255
ld (BY),a
if BROKEN
call checked_step
ld a,0
ld (DIST_HI),a
else
call checked_step
endif
call emit_state
else
ld a,0
ld (AX),a
ld a,0
ld (AY),a
ld a,255
ld (BX),a
ld a,255
ld (BY),a
if BROKEN
call checked_step
ld a,0
ld (DIST_HI),a
else
call checked_step
endif
call emit_state
endif
retThe eight display fields follow AX, AY, BX, BY, DIST_LO, DIST_HI; unused display fields are zero. Each field is a hexadecimal byte. The working row is 00 00 FF FF FE 01 00 00. The output is a completed diagnostic state, not a recording of movement, input or sound hardware.
Make it your own
The custom query moves BX from 255 to 200 while BY stays 255 and A remains at the origin. The result is 455, encoded C7 01, rather than 510, encoded FE 01.
Maintained custom configuration or caller
org $8000
CUSTOM equ 1
BROKEN equ 0
SCORE_CAP equ 999
QUEUE_CAP equ 2
REPEAT_DELAY equ 6
REPEAT_RATE equ 3
include "caller.inc"
include "exercise.inc"
component_start:
include "component.inc"
include "cases.inc"
include "../../physics/rectangle-overlap/display.inc"
code_end:
STATE:
AX: defb 0
AY: defb 0
BX: defb 0
BY: defb 0
DIST_LO: defb 0
DIST_HI: 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 observed custom row is 00 00 C8 FF C7 01 00 00. The retained records qualify these named configurations; a new input domain or larger layout needs its own bounds and fresh execution checks.
Common mistake and repair
The wrong client discards DIST_HI after computing the distance. The opposite corners now look 254 units apart rather than 510. Keep the carry byte through both the storage and comparison paths.
Deliberately wrong client selection
org $8000
CUSTOM equ 0
BROKEN equ 1
SCORE_CAP equ 65535
QUEUE_CAP equ 4
REPEAT_DELAY equ 4
REPEAT_RATE equ 2
include "caller.inc"
include "exercise.inc"
component_start:
include "component.inc"
include "cases.inc"
include "../../physics/rectangle-overlap/display.inc"
code_end:
STATE:
AX: defb 0
AY: defb 0
BX: defb 0
BY: defb 0
DIST_LO: defb 0
DIST_HI: 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
The wrong branch is in the displayed client above, selected by BROKEN. repaired.asm selects the original client again. Its executable matches demo exactly; Spectrum tape filenames can differ while loaded CODE is identical. The bad caller is a labelled experiment, not an alternative recommended implementation.
Cost and verification
The measured helper occupies 60 code bytes plus 6 named state bytes in this layout. Return addresses, alignment, tables and display diagnostics are additional. The sizes cover init and step together, not the whole standalone program.
Two absolute differences and one wide sum, with no multiply or square root. That makes the result cheap for grid decisions, but it does not make it an interchangeable estimate for every movement model.
This is the shortest distance on an unobstructed four-way grid. Walls can make the actual route longer or unreachable. Eight-way movement may call for Chebyshev or octile distance; Euclidean movement needs a different metric. Wider or signed coordinates need wider differences before taking absolute values.
Four native runs use Spectrum 48K with stock ROM tape loading and USR entry; Asm198x 0.0.72 and Emu198x 0.44.2. Every run checks 96 table results, dirty initialisation and every state in a separate sequential trace against an independent integer model. This is boundary/varied-input qualification, not exhaustive coverage of every byte combination. Source/tool/firmware hashes, native startup and completion, preserved-register sentinels, immutable loaded code, actual helper extent, capture bytes and pixels, and exact repair are checked. Deliberately changed observations must fail. Firmware is hashed, never distributed.