A trailing companion needs where the leader was, not another guess at where it might be going.
Use it in a project
An eight-entry ring stores byte X/Y pairs. HEAD is the next write index 0–7; COUNT is 0–8. PUSH nonzero appends the supplied position, advances HEAD modulo eight and saturates COUNT at eight. Then query LAG entries back from newest: zero means newest. A lag outside COUNT returns VALID=0 and zero outputs but does not undo a valid append. Invalid HEAD/COUNT rejects before writing.
Include component.inc once (MOS callers include the shared 6502 implementation through it). Reserve the public fields in this exact order: OUT_X, OUT_Y, VALID, HEAD, COUNT, INPUT_X, INPUT_Y, LAG, PUSH, HX0, HX1, HX2, HX3, HX4, HX5, HX6, HX7, HY0, HY1, HY2, HY3, HY4, HY5, HY6, HY7. They occupy 25 contiguous bytes. Also reserve the private workspace: T0, EXPR_SAVE (2 bytes). Array names in the explanation refer to the numbered consecutive bindings, such as C0, C1 and so on.
Call motion_history_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 motion_history_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 | HEAD, COUNT and HX0–HX7/HY0–HY7 |
| Supply before service | INPUT_X, INPUT_Y, LAG and PUSH |
| Read after service | OUT_X, OUT_Y and VALID |
The write cursor wraps cheaply because capacity is a power of two. A lag query subtracts from the next-write cursor rather than treating physical array order as chronological order.
Reusable initialisation and service
; SPDX-License-Identifier: MIT
; Keep a Small Position History. See README.md for the byte interface and ownership.
; init clears the public fields and private workspace; set inputs afterwards.
motion_history_init:
lda #0
sta OUT_X
sta OUT_Y
sta VALID
sta HEAD
sta COUNT
sta INPUT_X
sta INPUT_Y
sta LAG
sta PUSH
sta HX0
sta HX1
sta HX2
sta HX3
sta HX4
sta HX5
sta HX6
sta HX7
sta HY0
sta HY1
sta HY2
sta HY3
sta HY4
sta HY5
sta HY6
sta HY7
sta T0
sta EXPR_SAVE
rts
motion_history_step:
; OUT_X = 0
lda #0
sta OUT_X
; OUT_Y = 0
lda #0
sta OUT_Y
; VALID = 0
lda #0
sta VALID
; if HEAD >= 8:
lda HEAD
cmp #8
bcs motion_history_L4
motion_history_L5:
jmp motion_history_L2
motion_history_L4:
jmp motion_history_L1
motion_history_L1:
; return
rts
jmp motion_history_L3
motion_history_L2:
motion_history_L3:
; if COUNT > 8:
lda COUNT
cmp #8
beq motion_history_L10
bcs motion_history_L9
motion_history_L10:
jmp motion_history_L7
motion_history_L9:
jmp motion_history_L6
motion_history_L6:
; return
rts
jmp motion_history_L8
motion_history_L7:
motion_history_L8:
; if PUSH != 0:
lda PUSH
cmp #0
bne motion_history_L14
motion_history_L15:
jmp motion_history_L12
motion_history_L14:
jmp motion_history_L11
motion_history_L11:
; HX[HEAD] = INPUT_X
lda INPUT_X
sta EXPR_SAVE
ldx HEAD
lda EXPR_SAVE
sta HX0,x
; HY[HEAD] = INPUT_Y
lda INPUT_Y
sta EXPR_SAVE
ldx HEAD
lda EXPR_SAVE
sta HY0,x
; HEAD = HEAD + 1
lda HEAD
clc
adc #1
sta HEAD
; HEAD = HEAD & 7
lda HEAD
and #7
sta HEAD
; if COUNT < 8:
lda COUNT
cmp #8
bcc motion_history_L19
motion_history_L20:
jmp motion_history_L17
motion_history_L19:
jmp motion_history_L16
motion_history_L16:
; COUNT = COUNT + 1
lda COUNT
clc
adc #1
sta COUNT
jmp motion_history_L18
motion_history_L17:
motion_history_L18:
jmp motion_history_L13
motion_history_L12:
motion_history_L13:
; if LAG >= COUNT:
lda LAG
cmp COUNT
bcs motion_history_L24
motion_history_L25:
jmp motion_history_L22
motion_history_L24:
jmp motion_history_L21
motion_history_L21:
; return
rts
jmp motion_history_L23
motion_history_L22:
motion_history_L23:
; T0 = HEAD - 1
lda HEAD
sec
sbc #1
sta T0
; T0 = T0 - LAG
lda T0
sec
sbc LAG
sta T0
; T0 = T0 & 7
lda T0
and #7
sta T0
; OUT_X = HX[T0]
ldx T0
lda HX0,x
sta OUT_X
; OUT_Y = HY[T0]
ldx T0
lda HY0,x
sta OUT_Y
; VALID = 1
lda #1
sta VALID
rts
component_end:Machine contract
A/X/status may change; Y and decimal mode are preserved. Use CLD for binary arithmetic. 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 diagnostic PRG owns screen, font and colour RAM and disables interrupts; it does not return to BASIC. The reusable helper does none of those things.
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
OUT_X=$80
OUT_Y=$81
VALID=$82
HEAD=$83
COUNT=$84
INPUT_X=$85
INPUT_Y=$86
LAG=$87
PUSH=$88
HX0=$89
HX1=$8a
HX2=$8b
HX3=$8c
HX4=$8d
HX5=$8e
HX6=$8f
HX7=$90
HY0=$91
HY1=$92
HY2=$93
HY3=$94
HY4=$95
HY5=$96
HY6=$97
HY7=$98
T0=$99
EXPR_SAVE=$9a
STATE=$80
input_ptr=$70
cases_left=$72
ptr=$74
saved_y=$76
OUTPUT=$c000
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
!source "caller.inc"
!source "exercise.inc"
component_start:
!source "component.inc"
!source "data.inc"
!source "cases.inc"
hex_font:
!byte 0,0,0,0,0,0,0,0,0,56,40,40,40,56,0,0,0,16,48,16,16,56,0,0,0,56,8,56,32,56,0,0,0,56,8,56,8,56,0,0,0,40,40,56,8,8,0,0,0,56,32,56,8,56,0,0,0,56,32,56,40,56,0,0,0,56,8,8,8,8,0,0,0,56,40,56,40,56,0,0,0,56,40,56,8,56,0,0,0,16,40,56,40,40,0,0,0,48,40,48,40,48,0,0,0,56,32,32,32,56,0,0,0,48,40,40,40,48,0,0,0,56,32,48,32,56,0,0,0,56,32,48,32,32,0,0
code_end:A client retaining state between calls
preview_rules:
!if CUSTOM {
; INPUT_X = 0
lda #0
sta INPUT_X
; INPUT_Y = 1
lda #1
sta INPUT_Y
; PUSH = 1
lda #1
sta PUSH
!if BROKEN {
; HEAD = 0
lda #0
sta HEAD
}
jsr checked_step
jsr emit_state
; INPUT_X = 1
lda #1
sta INPUT_X
; INPUT_Y = 2
lda #2
sta INPUT_Y
; PUSH = 1
lda #1
sta PUSH
!if BROKEN {
; HEAD = 0
lda #0
sta HEAD
}
jsr checked_step
jsr emit_state
; INPUT_X = 2
lda #2
sta INPUT_X
; INPUT_Y = 3
lda #3
sta INPUT_Y
; PUSH = 1
lda #1
sta PUSH
!if BROKEN {
; HEAD = 0
lda #0
sta HEAD
}
jsr checked_step
jsr emit_state
; INPUT_X = 3
lda #3
sta INPUT_X
; INPUT_Y = 4
lda #4
sta INPUT_Y
; PUSH = 1
lda #1
sta PUSH
!if BROKEN {
; HEAD = 0
lda #0
sta HEAD
}
jsr checked_step
jsr emit_state
; INPUT_X = 4
lda #4
sta INPUT_X
; INPUT_Y = 5
lda #5
sta INPUT_Y
; PUSH = 1
lda #1
sta PUSH
!if BROKEN {
; HEAD = 0
lda #0
sta HEAD
}
jsr checked_step
jsr emit_state
; INPUT_X = 5
lda #5
sta INPUT_X
; INPUT_Y = 6
lda #6
sta INPUT_Y
; PUSH = 1
lda #1
sta PUSH
!if BROKEN {
; HEAD = 0
lda #0
sta HEAD
}
jsr checked_step
jsr emit_state
; INPUT_X = 6
lda #6
sta INPUT_X
; INPUT_Y = 7
lda #7
sta INPUT_Y
; PUSH = 1
lda #1
sta PUSH
!if BROKEN {
; HEAD = 0
lda #0
sta HEAD
}
jsr checked_step
jsr emit_state
; INPUT_X = 7
lda #7
sta INPUT_X
; INPUT_Y = 8
lda #8
sta INPUT_Y
; PUSH = 1
lda #1
sta PUSH
!if BROKEN {
; HEAD = 0
lda #0
sta HEAD
}
jsr checked_step
jsr emit_state
; INPUT_X = 8
lda #8
sta INPUT_X
; INPUT_Y = 9
lda #9
sta INPUT_Y
; PUSH = 1
lda #1
sta PUSH
!if BROKEN {
; HEAD = 0
lda #0
sta HEAD
}
jsr checked_step
jsr emit_state
; PUSH = 0
lda #0
sta PUSH
; LAG = 7
lda #7
sta LAG
!if BROKEN {
; HEAD = 0
lda #0
sta HEAD
}
jsr checked_step
jsr emit_state
rts
} else {
; INPUT_X = 10
lda #10
sta INPUT_X
; INPUT_Y = 20
lda #20
sta INPUT_Y
; PUSH = 1
lda #1
sta PUSH
!if BROKEN {
; HEAD = 0
lda #0
sta HEAD
}
jsr checked_step
jsr emit_state
; INPUT_X = 30
lda #30
sta INPUT_X
; INPUT_Y = 40
lda #40
sta INPUT_Y
!if BROKEN {
; HEAD = 0
lda #0
sta HEAD
}
jsr checked_step
jsr emit_state
; INPUT_X = 50
lda #50
sta INPUT_X
; INPUT_Y = 60
lda #60
sta INPUT_Y
!if BROKEN {
; HEAD = 0
lda #0
sta HEAD
}
jsr checked_step
jsr emit_state
; PUSH = 0
lda #0
sta PUSH
; LAG = 2
lda #2
sta LAG
!if BROKEN {
; HEAD = 0
lda #0
sta HEAD
}
jsr checked_step
jsr emit_state
}
rtsCustomise it
Append nine positions, then query the oldest retained entry after wrap. 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
OUT_X=$80
OUT_Y=$81
VALID=$82
HEAD=$83
COUNT=$84
INPUT_X=$85
INPUT_Y=$86
LAG=$87
PUSH=$88
HX0=$89
HX1=$8a
HX2=$8b
HX3=$8c
HX4=$8d
HX5=$8e
HX6=$8f
HX7=$90
HY0=$91
HY1=$92
HY2=$93
HY3=$94
HY4=$95
HY5=$96
HY6=$97
HY7=$98
T0=$99
EXPR_SAVE=$9a
STATE=$80
input_ptr=$70
cases_left=$72
ptr=$74
saved_y=$76
OUTPUT=$c000
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
!source "caller.inc"
!source "exercise.inc"
component_start:
!source "component.inc"
!source "data.inc"
!source "cases.inc"
hex_font:
!byte 0,0,0,0,0,0,0,0,0,56,40,40,40,56,0,0,0,16,48,16,16,56,0,0,0,56,8,56,32,56,0,0,0,56,8,56,8,56,0,0,0,40,40,56,8,8,0,0,0,56,32,56,8,56,0,0,0,56,32,56,40,56,0,0,0,56,8,8,8,8,0,0,0,56,40,56,40,56,0,0,0,56,40,56,8,56,0,0,0,16,40,56,40,40,0,0,0,48,40,48,40,48,0,0,0,56,32,32,32,56,0,0,0,48,40,40,40,48,0,0,0,56,32,48,32,56,0,0,0,56,32,48,32,32,0,0
code_end:The custom diagnostic row is 01 02 01 01 08 08 09 07. The full client trace in the source explains how it gets there.
Mistake and repair
The wrong caller resets HEAD on every service. New positions overwrite one slot and older queries read unrelated entries. Keep the ring cursor alongside the stored history.
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
OUT_X=$80
OUT_Y=$81
VALID=$82
HEAD=$83
COUNT=$84
INPUT_X=$85
INPUT_Y=$86
LAG=$87
PUSH=$88
HX0=$89
HX1=$8a
HX2=$8b
HX3=$8c
HX4=$8d
HX5=$8e
HX6=$8f
HX7=$90
HY0=$91
HY1=$92
HY2=$93
HY3=$94
HY4=$95
HY5=$96
HY6=$97
HY7=$98
T0=$99
EXPR_SAVE=$9a
STATE=$80
input_ptr=$70
cases_left=$72
ptr=$74
saved_y=$76
OUTPUT=$c000
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
!source "caller.inc"
!source "exercise.inc"
component_start:
!source "component.inc"
!source "data.inc"
!source "cases.inc"
hex_font:
!byte 0,0,0,0,0,0,0,0,0,56,40,40,40,56,0,0,0,16,48,16,16,56,0,0,0,56,8,56,32,56,0,0,0,56,8,56,8,56,0,0,0,40,40,56,8,8,0,0,0,56,32,56,8,56,0,0,0,56,32,56,40,56,0,0,0,56,8,8,8,8,0,0,0,56,40,56,40,56,0,0,0,56,40,56,8,56,0,0,0,16,40,56,40,40,0,0,0,48,40,48,40,48,0,0,0,56,32,32,32,56,0,0,0,48,40,40,40,48,0,0,0,56,32,48,32,56,0,0,0,56,32,48,32,32,0,0
code_end:
Cost and alternatives
The measured helper extent is 226 code bytes; public state is 25 bytes and private scratch is 2 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.
Constant work without shifting old positions. Eight pairs cost sixteen data bytes. A timestamped history costs more storage but can answer elapsed-time rather than sample-age queries.
These are serviced samples, not time-stamped seconds. Variable update spacing changes the time represented by a lag. Interpolation, full-state rewind and collision-safe followers require additional state and rules.
Execution evidence
Four variants run on PAL stock-ROM PRG, using Asm198x 0.0.72, Emu198x 0.44.2. Each executes 40 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
Event queues: Both use bounded storage, but a history retains recent samples for age queries rather than consuming queued events.