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:
lda #0
sta COUNT
sta VALID
sta Z0
sta Z1
sta Z2
sta Z3
sta Z4
sta Z5
sta Z6
sta Z7
sta I0
sta I1
sta I2
sta I3
sta I4
sta I5
sta I6
sta I7
sta T0
sta T1
sta T2
sta T3
sta T4
sta T5
sta T6
sta EXPR_SAVE
rts
stable_depth_order_step:
; VALID = 0
lda #0
sta VALID
; if COUNT > 8:
lda COUNT
cmp #8
beq stable_depth_order_L5
bcs stable_depth_order_L4
stable_depth_order_L5:
jmp stable_depth_order_L2
stable_depth_order_L4:
jmp stable_depth_order_L1
stable_depth_order_L1:
; return
rts
jmp stable_depth_order_L3
stable_depth_order_L2:
stable_depth_order_L3:
; T0 = 0
lda #0
sta T0
; while T0 < 8:
stable_depth_order_L6:
lda T0
cmp #8
bcc stable_depth_order_L9
stable_depth_order_L10:
jmp stable_depth_order_L8
stable_depth_order_L9:
jmp stable_depth_order_L7
stable_depth_order_L7:
; I[T0] = T0
lda T0
sta EXPR_SAVE
ldx T0
lda EXPR_SAVE
sta I0,x
; T0 = T0 + 1
lda T0
clc
adc #1
sta T0
jmp stable_depth_order_L6
stable_depth_order_L8:
; T0 = 1
lda #1
sta T0
; while T0 < COUNT:
stable_depth_order_L11:
lda T0
cmp COUNT
bcc stable_depth_order_L14
stable_depth_order_L15:
jmp stable_depth_order_L13
stable_depth_order_L14:
jmp stable_depth_order_L12
stable_depth_order_L12:
; T1 = I[T0]
ldx T0
lda I0,x
sta T1
; T2 = Z[T1]
ldx T1
lda Z0,x
sta T2
; T3 = T0
lda T0
sta T3
; while T3 != 0:
stable_depth_order_L16:
lda T3
cmp #0
bne stable_depth_order_L19
stable_depth_order_L20:
jmp stable_depth_order_L18
stable_depth_order_L19:
jmp stable_depth_order_L17
stable_depth_order_L17:
; T4 = T3 - 1
lda T3
sec
sbc #1
sta T4
; T5 = I[T4]
ldx T4
lda I0,x
sta T5
; T6 = Z[T5]
ldx T5
lda Z0,x
sta T6
; if T6 <= T2:
lda T6
cmp T2
bcc stable_depth_order_L24
beq stable_depth_order_L24
stable_depth_order_L25:
jmp stable_depth_order_L22
stable_depth_order_L24:
jmp stable_depth_order_L21
stable_depth_order_L21:
; break
jmp stable_depth_order_L18
jmp stable_depth_order_L23
stable_depth_order_L22:
stable_depth_order_L23:
; I[T3] = T5
lda T5
sta EXPR_SAVE
ldx T3
lda EXPR_SAVE
sta I0,x
; T3 = T3 - 1
lda T3
sec
sbc #1
sta T3
jmp stable_depth_order_L16
stable_depth_order_L18:
; I[T3] = T1
lda T1
sta EXPR_SAVE
ldx T3
lda EXPR_SAVE
sta I0,x
; T0 = T0 + 1
lda T0
clc
adc #1
sta T0
jmp stable_depth_order_L11
stable_depth_order_L13:
; 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. Scope or rename routine and field labels and allocate a separate block for each independent instance. 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
COUNT=$80
VALID=$81
Z0=$82
Z1=$83
Z2=$84
Z3=$85
Z4=$86
Z5=$87
Z6=$88
Z7=$89
I0=$8a
I1=$8b
I2=$8c
I3=$8d
I4=$8e
I5=$8f
I6=$90
I7=$91
T0=$92
T1=$93
T2=$94
T3=$95
T4=$96
T5=$97
T6=$98
EXPR_SAVE=$99
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 {
; COUNT = 5
lda #5
sta COUNT
; Z0 = 1
lda #1
sta Z0
; Z1 = 8
lda #8
sta Z1
; Z2 = 1
lda #1
sta Z2
; Z3 = 8
lda #8
sta Z3
; Z4 = 2
lda #2
sta Z4
!if BROKEN {
; COUNT = 0
lda #0
sta COUNT
}
jsr checked_step
jsr emit_state
rts
} else {
; COUNT = 5
lda #5
sta COUNT
; Z0 = 8
lda #8
sta Z0
; Z1 = 2
lda #2
sta Z1
; Z2 = 8
lda #8
sta Z2
; Z3 = 1
lda #1
sta Z3
; Z4 = 2
lda #2
sta Z4
!if BROKEN {
; COUNT = 0
lda #0
sta COUNT
}
jsr checked_step
jsr emit_state
}
rtsThe 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
COUNT=$80
VALID=$81
Z0=$82
Z1=$83
Z2=$84
Z3=$85
Z4=$86
Z5=$87
Z6=$88
Z7=$89
I0=$8a
I1=$8b
I2=$8c
I3=$8d
I4=$8e
I5=$8f
I6=$90
I7=$91
T0=$92
T1=$93
T2=$94
T3=$95
T4=$96
T5=$97
T6=$98
EXPR_SAVE=$99
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 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
COUNT=$80
VALID=$81
Z0=$82
Z1=$83
Z2=$84
Z3=$85
Z4=$86
Z5=$87
Z6=$88
Z7=$89
I0=$8a
I1=$8b
I2=$8c
I3=$8d
I4=$8e
I5=$8f
I6=$90
I7=$91
T0=$92
T1=$93
T2=$94
T3=$95
T4=$96
T5=$97
T6=$98
EXPR_SAVE=$99
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 241 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 PAL stock-ROM PRG, 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.