A bounce can lose speed along a wall’s normal while keeping its sideways motion.
Use it in a project
NORMAL_IN is an unsigned incoming speed magnitude. DIRECTION_IN is 0 or 1 for its sign along the chosen axis. RESTITUTION is 0–4 quarters. Return NORMAL_OUT=floor(NORMAL_IN*RESTITUTION/4), reverse the direction, and copy the encoded tangent byte unchanged. Invalid direction/restitution returns zero outputs and VALID=0. The caller supplies a surface-aligned basis and establishes a genuine incoming contact.
Include component.inc once (MOS callers include the shared 6502 implementation through it). Reserve the public fields in this exact order: NORMAL_OUT, DIRECTION_OUT, TANGENT_OUT, VALID, NORMAL_IN, DIRECTION_IN, TANGENT_IN, RESTITUTION. They occupy 8 contiguous bytes. Also reserve the private workspace: T0, T1, T2, T3 (4 bytes). Array names in the explanation refer to the numbered consecutive bindings, such as C0, C1 and so on.
Call surface_response_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 surface_response_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 |
| Supply before service | incoming normal magnitude/direction, tangent encoding and restitution |
| Read after service | NORMAL_OUT, DIRECTION_OUT, TANGENT_OUT and VALID |
Split speed into quotient and remainder on division by four. Multiply those small parts by at most four before combining them, retaining the full result without overflowing a byte product.
Reusable initialisation and service
; SPDX-License-Identifier: MIT
; Reflect a Surface-normal Speed with Restitution. See README.md for the byte interface and ownership.
; init clears the public fields and private workspace; set inputs afterwards.
surface_response_init:
lda #0
sta NORMAL_OUT
sta DIRECTION_OUT
sta TANGENT_OUT
sta VALID
sta NORMAL_IN
sta DIRECTION_IN
sta TANGENT_IN
sta RESTITUTION
sta T0
sta T1
sta T2
sta T3
rts
surface_response_step:
; NORMAL_OUT = 0
lda #0
sta NORMAL_OUT
; DIRECTION_OUT = 0
lda #0
sta DIRECTION_OUT
; TANGENT_OUT = 0
lda #0
sta TANGENT_OUT
; VALID = 0
lda #0
sta VALID
; if DIRECTION_IN > 1:
lda DIRECTION_IN
cmp #1
beq surface_response_L5
bcs surface_response_L4
surface_response_L5:
jmp surface_response_L2
surface_response_L4:
jmp surface_response_L1
surface_response_L1:
; return
rts
jmp surface_response_L3
surface_response_L2:
surface_response_L3:
; if RESTITUTION > 4:
lda RESTITUTION
cmp #4
beq surface_response_L10
bcs surface_response_L9
surface_response_L10:
jmp surface_response_L7
surface_response_L9:
jmp surface_response_L6
surface_response_L6:
; return
rts
jmp surface_response_L8
surface_response_L7:
surface_response_L8:
; VALID = 1
lda #1
sta VALID
; DIRECTION_OUT = DIRECTION_IN ^ 1
lda DIRECTION_IN
eor #1
sta DIRECTION_OUT
; TANGENT_OUT = TANGENT_IN
lda TANGENT_IN
sta TANGENT_OUT
; T0 = NORMAL_IN >> 2
lda NORMAL_IN
lsr
lsr
sta T0
; T1 = NORMAL_IN & 3
lda NORMAL_IN
and #3
sta T1
; T2 = 0
lda #0
sta T2
; T3 = RESTITUTION
lda RESTITUTION
sta T3
; while T3 != 0:
surface_response_L11:
lda T3
cmp #0
bne surface_response_L14
surface_response_L15:
jmp surface_response_L13
surface_response_L14:
jmp surface_response_L12
surface_response_L12:
; NORMAL_OUT = NORMAL_OUT + T0
lda NORMAL_OUT
clc
adc T0
sta NORMAL_OUT
; T2 = T2 + T1
lda T2
clc
adc T1
sta T2
; T3 = T3 - 1
lda T3
sec
sbc #1
sta T3
jmp surface_response_L11
surface_response_L13:
; T2 = T2 >> 2
lda T2
lsr
lsr
sta T2
; NORMAL_OUT = NORMAL_OUT + T2
lda NORMAL_OUT
clc
adc T2
sta NORMAL_OUT
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
NORMAL_OUT=$80
DIRECTION_OUT=$81
TANGENT_OUT=$82
VALID=$83
NORMAL_IN=$84
DIRECTION_IN=$85
TANGENT_IN=$86
RESTITUTION=$87
T0=$88
T1=$89
T2=$8a
T3=$8b
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 {
; NORMAL_IN = 255
lda #255
sta NORMAL_IN
; DIRECTION_IN = 0
lda #0
sta DIRECTION_IN
; TANGENT_IN = 128
lda #128
sta TANGENT_IN
; RESTITUTION = 4
lda #4
sta RESTITUTION
!if BROKEN {
; RESTITUTION = 4
lda #4
sta RESTITUTION
}
jsr checked_step
jsr emit_state
rts
} else {
; NORMAL_IN = 11
lda #11
sta NORMAL_IN
; DIRECTION_IN = 1
lda #1
sta DIRECTION_IN
; TANGENT_IN = 254
lda #254
sta TANGENT_IN
; RESTITUTION = 3
lda #3
sta RESTITUTION
!if BROKEN {
; RESTITUTION = 4
lda #4
sta RESTITUTION
}
jsr checked_step
jsr emit_state
}
rtsCustomise it
Use a perfectly elastic bounce at the largest byte speed. 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
NORMAL_OUT=$80
DIRECTION_OUT=$81
TANGENT_OUT=$82
VALID=$83
NORMAL_IN=$84
DIRECTION_IN=$85
TANGENT_IN=$86
RESTITUTION=$87
T0=$88
T1=$89
T2=$8a
T3=$8b
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 FF 01 80 01 FF 00 80 04. The full client trace in the source explains how it gets there.
Mistake and repair
The wrong caller forces perfectly elastic restitution. A speed of eleven returns eleven instead of eight, so the intended energy loss disappears. Preserve the material’s chosen coefficient.
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
NORMAL_OUT=$80
DIRECTION_OUT=$81
TANGENT_OUT=$82
VALID=$83
NORMAL_IN=$84
DIRECTION_IN=$85
TANGENT_IN=$86
RESTITUTION=$87
T0=$88
T1=$89
T2=$8a
T3=$8b
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 163 code bytes; public state is 8 bytes and private scratch is 4 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.
At most four accumulation stages. The 68000 can use word multiplication and a shift; the explicit byte decomposition makes the small-machine representation visible. Repeated bounces lose an extra fraction through integer rounding.
The coefficient is a speed ratio, not an energy ratio. This is an axis/surface-basis response, not arbitrary-angle collision detection, friction, penetration resolution or mass exchange. For zero normal speed, the returned direction bit is immaterial.
Execution evidence
Four variants run on PAL stock-ROM PRG, 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
Reflected axis motion: Boundary reflection and impact restitution are different decisions: one chooses contact, the other chooses returned speed.