When two sprites have the same depth, their order should not flicker from frame to frame.
Use it in a project
COUNT 0–8 selects a prefix of eight depth bytes. Return indices I0–I7, initialised to identity, with the active prefix sorted by ascending Z. Insertion sort moves only strictly greater depths, preserving original index order for ties. Depth inputs remain unchanged. Invalid COUNT leaves order bytes unchanged and returns VALID=0.
Include component.inc once (MOS callers include the shared 6502 implementation through it). Reserve the public fields in this exact order: COUNT, VALID, Z0, Z1, Z2, Z3, Z4, Z5, Z6, Z7, I0, I1, I2, I3, I4, I5, I6, I7. They occupy 18 contiguous bytes. Also reserve the private workspace: T0, T1, T2, T3, T4, T5, T6, EXPR_SAVE (8 bytes). Array names in the explanation refer to the numbered consecutive bindings, such as C0, C1 and so on.
Call stable_depth_order_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 stable_depth_order_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 between complete sorts |
| Supply before service | COUNT and Z0–Z7 |
| Read after service | I0–I7 and VALID |
Insertion sort keeps a sorted prefix and inserts the next index into it. Equal depths never move past each other. Sorting indices also keeps the actual object records in place.
Reusable initialisation and service
; SPDX-License-Identifier: MIT
; Sort a Small Draw Order Stably. See README.md for the byte interface and ownership.
; init clears the public fields and private workspace; set inputs afterwards.
stable_depth_order_init:
ld a,0
ld (COUNT),a
ld (VALID),a
ld (Z0),a
ld (Z1),a
ld (Z2),a
ld (Z3),a
ld (Z4),a
ld (Z5),a
ld (Z6),a
ld (Z7),a
ld (I0),a
ld (I1),a
ld (I2),a
ld (I3),a
ld (I4),a
ld (I5),a
ld (I6),a
ld (I7),a
ld (T0),a
ld (T1),a
ld (T2),a
ld (T3),a
ld (T4),a
ld (T5),a
ld (T6),a
ld (EXPR_SAVE),a
ret
stable_depth_order_step:
; VALID = 0
ld a,0
ld (VALID),a
; if COUNT > 8:
ld a,(COUNT)
cp 8
jp z,stable_depth_order_L2
jp nc,stable_depth_order_L1
jp stable_depth_order_L2
stable_depth_order_L1:
; return
ret
jp stable_depth_order_L3
stable_depth_order_L2:
stable_depth_order_L3:
; T0 = 0
ld a,0
ld (T0),a
; while T0 < 8:
stable_depth_order_L4:
ld a,(T0)
cp 8
jp c,stable_depth_order_L5
jp stable_depth_order_L6
stable_depth_order_L5:
; I[T0] = T0
ld a,(T0)
ld c,a
ld a,(T0)
ld e,a
ld d,0
ld hl,I0
add hl,de
ld (hl),c
; T0 = T0 + 1
ld a,(T0)
add a,1
ld (T0),a
jp stable_depth_order_L4
stable_depth_order_L6:
; T0 = 1
ld a,1
ld (T0),a
; while T0 < COUNT:
stable_depth_order_L7:
ld a,(T0)
ld b,a
ld a,(COUNT)
ld c,a
ld a,b
cp c
jp c,stable_depth_order_L8
jp stable_depth_order_L9
stable_depth_order_L8:
; T1 = I[T0]
ld a,(T0)
ld e,a
ld d,0
ld hl,I0
add hl,de
ld a,(hl)
ld (T1),a
; T2 = Z[T1]
ld a,(T1)
ld e,a
ld d,0
ld hl,Z0
add hl,de
ld a,(hl)
ld (T2),a
; T3 = T0
ld a,(T0)
ld (T3),a
; while T3 != 0:
stable_depth_order_L10:
ld a,(T3)
cp 0
jp nz,stable_depth_order_L11
jp stable_depth_order_L12
stable_depth_order_L11:
; T4 = T3 - 1
ld a,(T3)
sub 1
ld (T4),a
; T5 = I[T4]
ld a,(T4)
ld e,a
ld d,0
ld hl,I0
add hl,de
ld a,(hl)
ld (T5),a
; T6 = Z[T5]
ld a,(T5)
ld e,a
ld d,0
ld hl,Z0
add hl,de
ld a,(hl)
ld (T6),a
; if T6 <= T2:
ld a,(T6)
ld b,a
ld a,(T2)
ld c,a
ld a,b
cp c
jp c,stable_depth_order_L13
jp z,stable_depth_order_L13
jp stable_depth_order_L14
stable_depth_order_L13:
; break
jp stable_depth_order_L12
jp stable_depth_order_L15
stable_depth_order_L14:
stable_depth_order_L15:
; I[T3] = T5
ld a,(T5)
ld c,a
ld a,(T3)
ld e,a
ld d,0
ld hl,I0
add hl,de
ld (hl),c
; T3 = T3 - 1
ld a,(T3)
sub 1
ld (T3),a
jp stable_depth_order_L10
stable_depth_order_L12:
; I[T3] = T1
ld a,(T1)
ld c,a
ld a,(T3)
ld e,a
ld d,0
ld hl,I0
add hl,de
ld (hl),c
; T0 = T0 + 1
ld a,(T0)
add a,1
ld (T0),a
jp stable_depth_order_L7
stable_depth_order_L9:
; 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. Scope or rename routine and field labels and allocate a separate block for each independent instance. 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:
COUNT: defb 0
VALID: defb 0
Z0: defb 0
Z1: defb 0
Z2: defb 0
Z3: defb 0
Z4: defb 0
Z5: defb 0
Z6: defb 0
Z7: defb 0
I0: defb 0
I1: defb 0
I2: defb 0
I3: defb 0
I4: defb 0
I5: defb 0
I6: defb 0
I7: defb 0
T0: defb 0
T1: defb 0
T2: defb 0
T3: defb 0
T4: defb 0
T5: defb 0
T6: 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
; COUNT = 5
ld a,5
ld (COUNT),a
; Z0 = 1
ld a,1
ld (Z0),a
; Z1 = 8
ld a,8
ld (Z1),a
; Z2 = 1
ld a,1
ld (Z2),a
; Z3 = 8
ld a,8
ld (Z3),a
; Z4 = 2
ld a,2
ld (Z4),a
if BROKEN
; COUNT = 0
ld a,0
ld (COUNT),a
endif
call checked_step
call emit_state
ret
else
; COUNT = 5
ld a,5
ld (COUNT),a
; Z0 = 8
ld a,8
ld (Z0),a
; Z1 = 2
ld a,2
ld (Z1),a
; Z2 = 8
ld a,8
ld (Z2),a
; Z3 = 1
ld a,1
ld (Z3),a
; Z4 = 2
ld a,2
ld (Z4),a
if BROKEN
; COUNT = 0
ld a,0
ld (COUNT),a
endif
call checked_step
call emit_state
endif
retThe normal caller returns the active draw indices 3, 1, 4, 0, 2. Their depths are 1, 2, 2, 8, 8. Notice that items 1 and 4 keep their original order at depth 2, as do items 0 and 2 at depth 8. The wrong caller returns the identity order instead. The screenshot displays COUNT, VALID and the first depth bytes; the returned indices are retained in the full native packet.
Customise it
Reverse the depth values while preserving stable ties. 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:
COUNT: defb 0
VALID: defb 0
Z0: defb 0
Z1: defb 0
Z2: defb 0
Z3: defb 0
Z4: defb 0
Z5: defb 0
Z6: defb 0
Z7: defb 0
I0: defb 0
I1: defb 0
I2: defb 0
I3: defb 0
I4: defb 0
I5: defb 0
I6: defb 0
I7: defb 0
T0: defb 0
T1: defb 0
T2: defb 0
T3: defb 0
T4: defb 0
T5: defb 0
T6: 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 05 01 01 08 01 08 02 00. The full client trace in the source explains how it gets there.
Mistake and repair
The wrong caller passes COUNT=0 for a populated scene. The identity order remains instead of the requested depth order. Pass the actual active prefix, not the capacity or an uninitialised object count.
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:
COUNT: defb 0
VALID: defb 0
Z0: defb 0
Z1: defb 0
Z2: defb 0
Z3: defb 0
Z4: defb 0
Z5: defb 0
Z6: defb 0
Z7: defb 0
I0: defb 0
I1: defb 0
I2: defb 0
I3: defb 0
I4: defb 0
I5: defb 0
I6: defb 0
I7: defb 0
T0: defb 0
T1: defb 0
T2: defb 0
T3: defb 0
T4: defb 0
T5: defb 0
T6: 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 331 code bytes; public state is 18 bytes and private scratch is 8 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.
Worst-case comparisons grow quadratically: eight reverse-ordered objects require 28. Nearly sorted lists need fewer moves. Measure before choosing it for many objects.
At eight objects insertion sort has a bounded 28 comparisons in the reverse-order case. This returns an order; it does not overcome hardware sprite limits or move attributes. Larger scenes need a measured choice of bucket sorting, partial ordering or another algorithm.
Execution evidence
Four variants run on 48K PAL ROM tape load and USR, using Asm198x 0.0.72, Emu198x 0.44.2. Each executes 55 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
Object pools: Keep object records in their pool and sort a separate active draw list; do not accidentally sort inactive slots.