Sixteen tile values do not need sixteen whole bytes when each value fits in four bits.
Use it in a project
Sixteen cells occupy eight caller-owned bytes: an even cell uses the high nibble and the following odd cell the low nibble. CELL must be 0–15. WRITE=0 reads; nonzero writes NEW_VALUE 0–15 and returns that value. Invalid requests return VALUE=0 and VALID=0 without changing packed bytes. An unused NEW_VALUE is ignored on reads.
Include component.inc once (MOS callers include the shared 6502 implementation through it). Reserve the public fields in this exact order: VALUE, VALID, CELL, WRITE, NEW_VALUE, B0, B1, B2, B3, B4, B5, B6, B7. They occupy 13 contiguous bytes. Also reserve the private workspace: T0, T1, T2, T3, EXPR_SAVE (5 bytes). Array names in the explanation refer to the numbered consecutive bindings, such as C0, C1 and so on.
Call packed_nibble_map_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 packed_nibble_map_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 | B0–B7 |
| Supply before service | CELL, WRITE and NEW_VALUE |
| Read after service | VALUE and VALID |
Shift the cell index once to select its byte, then use the low index bit to select a nibble. A write masks only the chosen half and preserves its neighbour.
Reusable initialisation and service
; SPDX-License-Identifier: MIT
; Read and Update Packed Four-bit Cells. See README.md for the byte interface and ownership.
; init clears the public fields and private workspace; set inputs afterwards.
packed_nibble_map_init:
ld a,0
ld (VALUE),a
ld (VALID),a
ld (CELL),a
ld (WRITE),a
ld (NEW_VALUE),a
ld (B0),a
ld (B1),a
ld (B2),a
ld (B3),a
ld (B4),a
ld (B5),a
ld (B6),a
ld (B7),a
ld (T0),a
ld (T1),a
ld (T2),a
ld (T3),a
ld (EXPR_SAVE),a
ret
packed_nibble_map_step:
; VALUE = 0
ld a,0
ld (VALUE),a
; VALID = 0
ld a,0
ld (VALID),a
; if CELL >= 16:
ld a,(CELL)
cp 16
jp nc,packed_nibble_map_L1
jp packed_nibble_map_L2
packed_nibble_map_L1:
; return
ret
jp packed_nibble_map_L3
packed_nibble_map_L2:
packed_nibble_map_L3:
; if WRITE != 0:
ld a,(WRITE)
cp 0
jp nz,packed_nibble_map_L4
jp packed_nibble_map_L5
packed_nibble_map_L4:
; if NEW_VALUE >= 16:
ld a,(NEW_VALUE)
cp 16
jp nc,packed_nibble_map_L7
jp packed_nibble_map_L8
packed_nibble_map_L7:
; return
ret
jp packed_nibble_map_L9
packed_nibble_map_L8:
packed_nibble_map_L9:
jp packed_nibble_map_L6
packed_nibble_map_L5:
packed_nibble_map_L6:
; T0 = CELL >> 1
ld a,(CELL)
srl a
ld (T0),a
; T1 = CELL & 1
ld a,(CELL)
and 1
ld (T1),a
; T2 = B[T0]
ld a,(T0)
ld e,a
ld d,0
ld hl,B0
add hl,de
ld a,(hl)
ld (T2),a
; if WRITE != 0:
ld a,(WRITE)
cp 0
jp nz,packed_nibble_map_L10
jp packed_nibble_map_L11
packed_nibble_map_L10:
; if T1 == 0:
ld a,(T1)
cp 0
jp z,packed_nibble_map_L13
jp packed_nibble_map_L14
packed_nibble_map_L13:
; T2 = T2 & 15
ld a,(T2)
and 15
ld (T2),a
; T3 = NEW_VALUE << 4
ld a,(NEW_VALUE)
sla a
sla a
sla a
sla a
ld (T3),a
; T2 = T2 | T3
ld a,(T2)
ld b,a
ld a,(T3)
ld c,a
ld a,b
or c
ld (T2),a
jp packed_nibble_map_L15
packed_nibble_map_L14:
; T2 = T2 & 240
ld a,(T2)
and 240
ld (T2),a
; T2 = T2 | NEW_VALUE
ld a,(T2)
ld b,a
ld a,(NEW_VALUE)
ld c,a
ld a,b
or c
ld (T2),a
packed_nibble_map_L15:
; B[T0] = T2
ld a,(T2)
ld c,a
ld a,(T0)
ld e,a
ld d,0
ld hl,B0
add hl,de
ld (hl),c
jp packed_nibble_map_L12
packed_nibble_map_L11:
packed_nibble_map_L12:
; if T1 == 0:
ld a,(T1)
cp 0
jp z,packed_nibble_map_L16
jp packed_nibble_map_L17
packed_nibble_map_L16:
; VALUE = T2 >> 4
ld a,(T2)
srl a
srl a
srl a
srl a
ld (VALUE),a
jp packed_nibble_map_L18
packed_nibble_map_L17:
; VALUE = T2 & 15
ld a,(T2)
and 15
ld (VALUE),a
packed_nibble_map_L18:
; VALID = 1
ld a,1
ld (VALID),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:
VALUE: defb 0
VALID: defb 0
CELL: defb 0
WRITE: defb 0
NEW_VALUE: defb 0
B0: defb 0
B1: defb 0
B2: defb 0
B3: defb 0
B4: defb 0
B5: defb 0
B6: defb 0
B7: defb 0
T0: defb 0
T1: defb 0
T2: defb 0
T3: defb 0
EXPR_SAVE: 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
; CELL = 15
ld a,15
ld (CELL),a
; WRITE = 1
ld a,1
ld (WRITE),a
; NEW_VALUE = 15
ld a,15
ld (NEW_VALUE),a
if BROKEN
; CELL = 0
ld a,0
ld (CELL),a
endif
call checked_step
call emit_state
; WRITE = 0
ld a,0
ld (WRITE),a
if BROKEN
; CELL = 0
ld a,0
ld (CELL),a
endif
call checked_step
call emit_state
ret
else
; B1 = 171
ld a,171
ld (B1),a
; CELL = 3
ld a,3
ld (CELL),a
if BROKEN
; CELL = 0
ld a,0
ld (CELL),a
endif
call checked_step
call emit_state
; WRITE = 1
ld a,1
ld (WRITE),a
; NEW_VALUE = 5
ld a,5
ld (NEW_VALUE),a
if BROKEN
; CELL = 0
ld a,0
ld (CELL),a
endif
call checked_step
call emit_state
; WRITE = 0
ld a,0
ld (WRITE),a
; CELL = 2
ld a,2
ld (CELL),a
if BROKEN
; CELL = 0
ld a,0
ld (CELL),a
endif
call checked_step
call emit_state
endif
retCustomise it
Write and read the final low nibble. 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:
VALUE: defb 0
VALID: defb 0
CELL: defb 0
WRITE: defb 0
NEW_VALUE: defb 0
B0: defb 0
B1: defb 0
B2: defb 0
B3: defb 0
B4: defb 0
B5: defb 0
B6: defb 0
B7: defb 0
T0: defb 0
T1: defb 0
T2: defb 0
T3: defb 0
EXPR_SAVE: 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 0F 01 0F 00 0F 00 00 00. The full client trace in the source explains how it gets there.
Mistake and repair
The wrong caller passes cell zero instead of the requested cell. Reads look plausible and writes succeed, but the wrong map location changes. Keep the logical cell index separate from its packed-byte offset.
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:
VALUE: defb 0
VALID: defb 0
CELL: defb 0
WRITE: defb 0
NEW_VALUE: defb 0
B0: defb 0
B1: defb 0
B2: defb 0
B3: defb 0
B4: defb 0
B5: defb 0
B6: defb 0
B7: defb 0
T0: defb 0
T1: defb 0
T2: defb 0
T3: defb 0
EXPR_SAVE: 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 282 code bytes; public state is 13 bytes and private scratch is 5 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, with masks and shifts in place of direct byte indexing. Byte-per-cell maps are easier to edit and can hold more values; packing pays when memory is tighter than update time.
This halves storage only when values fit 0–15. Packed writes are read-modify-write operations; an interrupt must not update the same byte concurrently without an ownership policy. Rendering and collision properties remain separate.
Execution evidence
Four variants run on 48K PAL ROM tape load and USR, using Asm198x 0.0.72, Emu198x 0.44.2. Each executes 64 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
Tile maps: The same logical map queries can sit over different storage representations, provided their value range stays explicit.