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:
move.b #0,d0
move.b d0,NORMAL_OUT
move.b d0,DIRECTION_OUT
move.b d0,TANGENT_OUT
move.b d0,VALID
move.b d0,NORMAL_IN
move.b d0,DIRECTION_IN
move.b d0,TANGENT_IN
move.b d0,RESTITUTION
move.b d0,T0
move.b d0,T1
move.b d0,T2
move.b d0,T3
rts
surface_response_step:
; NORMAL_OUT = 0
move.b #0,d0
move.b d0,NORMAL_OUT
; DIRECTION_OUT = 0
move.b #0,d0
move.b d0,DIRECTION_OUT
; TANGENT_OUT = 0
move.b #0,d0
move.b d0,TANGENT_OUT
; VALID = 0
move.b #0,d0
move.b d0,VALID
; if DIRECTION_IN > 1:
move.b DIRECTION_IN,d0
cmp.b #1,d0
bhi surface_response_L1
jmp surface_response_L2
surface_response_L1:
; return
rts
jmp surface_response_L3
surface_response_L2:
surface_response_L3:
; if RESTITUTION > 4:
move.b RESTITUTION,d0
cmp.b #4,d0
bhi surface_response_L4
jmp surface_response_L5
surface_response_L4:
; return
rts
jmp surface_response_L6
surface_response_L5:
surface_response_L6:
; VALID = 1
move.b #1,d0
move.b d0,VALID
; DIRECTION_OUT = DIRECTION_IN ^ 1
move.b DIRECTION_IN,d0
eor.b #1,d0
move.b d0,DIRECTION_OUT
; TANGENT_OUT = TANGENT_IN
move.b TANGENT_IN,d0
move.b d0,TANGENT_OUT
; T0 = NORMAL_IN >> 2
move.b NORMAL_IN,d0
lsr.b #2,d0
move.b d0,T0
; T1 = NORMAL_IN & 3
move.b NORMAL_IN,d0
and.b #3,d0
move.b d0,T1
; T2 = 0
move.b #0,d0
move.b d0,T2
; T3 = RESTITUTION
move.b RESTITUTION,d0
move.b d0,T3
; while T3 != 0:
surface_response_L7:
move.b T3,d0
cmp.b #0,d0
bne surface_response_L8
jmp surface_response_L9
surface_response_L8:
; NORMAL_OUT = NORMAL_OUT + T0
move.b NORMAL_OUT,d0
move.b T0,d1
add.b d1,d0
move.b d0,NORMAL_OUT
; T2 = T2 + T1
move.b T2,d0
move.b T1,d1
add.b d1,d0
move.b d0,T2
; T3 = T3 - 1
move.b T3,d0
sub.b #1,d0
move.b d0,T3
jmp surface_response_L7
surface_response_L9:
; T2 = T2 >> 2
move.b T2,d0
lsr.b #2,d0
move.b d0,T2
; NORMAL_OUT = NORMAL_OUT + T2
move.b NORMAL_OUT,d0
move.b T2,d1
add.b d1,d0
move.b d0,NORMAL_OUT
rts
component_end:Machine contract
D0–D3/A0–A1/CCR may change; D4–D7/A2–A6 are preserved. A direct BSR/JSR needs four 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 A500 OCS diagnostic cold-boots an OFS disk, owns the Copper and bitplane and disables interrupt/DMA sources. The helper does not take over hardware or allocate Chip RAM.
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 and BUILD198X=/path/to/build198x. The Makefile produces normal, custom, deliberately wrong and repaired programs. Tools must already be installed; the sample downloads nothing.
Bindings and include order
section code,code_c
CUSTOM = 0
BROKEN = 0
COYOTE_STEPS = 4
BUFFER_STEPS = 4
TEXT_CAP = 8
PROPERTY_COUNT = 16
STREAM_BYTES = 13
CRC_POLY = 7
include "caller.inc"
include "exercise.inc"
component_start:
include "component.inc"
even
include "data.inc"
include "cases.inc"
even
include "display.inc"
include "../../framework/turn-deadline/font.inc"
code_end:
STATE:
NORMAL_OUT: dc.b 0
DIRECTION_OUT: dc.b 0
TANGENT_OUT: dc.b 0
VALID: dc.b 0
NORMAL_IN: dc.b 0
DIRECTION_IN: dc.b 0
TANGENT_IN: dc.b 0
RESTITUTION: dc.b 0
T0: dc.b 0
T1: dc.b 0
T2: dc.b 0
T3: dc.b 0
even
ready: dc.w 0
preview: dcb.b 8,0
OUTPUT: dcb.b 1300,0
even
signature: dc.b "198XNIGHTONE000",0
even
copperlist:
dc.w $08e,$2c81,$090,$2cc1,$092,$0038,$094,$00d0
dc.w $100,$1200,$102,0,$104,0,$108,0,$10a,0
dc.w $180,$012,$182,$fff
copbpl:
dc.w $0e0,0,$0e2,0
dc.w $ffff,$fffe
plane: dcb.b 10240,0A client retaining state between calls
preview_rules:
ifne CUSTOM
; NORMAL_IN = 255
move.b #255,d0
move.b d0,NORMAL_IN
; DIRECTION_IN = 0
move.b #0,d0
move.b d0,DIRECTION_IN
; TANGENT_IN = 128
move.b #128,d0
move.b d0,TANGENT_IN
; RESTITUTION = 4
move.b #4,d0
move.b d0,RESTITUTION
ifne BROKEN
; RESTITUTION = 4
move.b #4,d0
move.b d0,RESTITUTION
endif
bsr checked_step
bsr emit_state
rts
else
; NORMAL_IN = 11
move.b #11,d0
move.b d0,NORMAL_IN
; DIRECTION_IN = 1
move.b #1,d0
move.b d0,DIRECTION_IN
; TANGENT_IN = 254
move.b #254,d0
move.b d0,TANGENT_IN
; RESTITUTION = 3
move.b #3,d0
move.b d0,RESTITUTION
ifne BROKEN
; RESTITUTION = 4
move.b #4,d0
move.b d0,RESTITUTION
endif
bsr checked_step
bsr emit_state
endif
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
section code,code_c
CUSTOM = 1
BROKEN = 0
COYOTE_STEPS = 2
BUFFER_STEPS = 2
TEXT_CAP = 4
PROPERTY_COUNT = 16
STREAM_BYTES = 13
CRC_POLY = 49
include "caller.inc"
include "exercise.inc"
component_start:
include "component.inc"
even
include "data.inc"
include "cases.inc"
even
include "display.inc"
include "../../framework/turn-deadline/font.inc"
code_end:
STATE:
NORMAL_OUT: dc.b 0
DIRECTION_OUT: dc.b 0
TANGENT_OUT: dc.b 0
VALID: dc.b 0
NORMAL_IN: dc.b 0
DIRECTION_IN: dc.b 0
TANGENT_IN: dc.b 0
RESTITUTION: dc.b 0
T0: dc.b 0
T1: dc.b 0
T2: dc.b 0
T3: dc.b 0
even
ready: dc.w 0
preview: dcb.b 8,0
OUTPUT: dcb.b 1300,0
even
signature: dc.b "198XNIGHTONE000",0
even
copperlist:
dc.w $08e,$2c81,$090,$2cc1,$092,$0038,$094,$00d0
dc.w $100,$1200,$102,0,$104,0,$108,0,$10a,0
dc.w $180,$012,$182,$fff
copbpl:
dc.w $0e0,0,$0e2,0
dc.w $ffff,$fffe
plane: dcb.b 10240,0The 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
section code,code_c
CUSTOM = 0
BROKEN = 1
COYOTE_STEPS = 4
BUFFER_STEPS = 4
TEXT_CAP = 8
PROPERTY_COUNT = 16
STREAM_BYTES = 13
CRC_POLY = 7
include "caller.inc"
include "exercise.inc"
component_start:
include "component.inc"
even
include "data.inc"
include "cases.inc"
even
include "display.inc"
include "../../framework/turn-deadline/font.inc"
code_end:
STATE:
NORMAL_OUT: dc.b 0
DIRECTION_OUT: dc.b 0
TANGENT_OUT: dc.b 0
VALID: dc.b 0
NORMAL_IN: dc.b 0
DIRECTION_IN: dc.b 0
TANGENT_IN: dc.b 0
RESTITUTION: dc.b 0
T0: dc.b 0
T1: dc.b 0
T2: dc.b 0
T3: dc.b 0
even
ready: dc.w 0
preview: dcb.b 8,0
OUTPUT: dcb.b 1300,0
even
signature: dc.b "198XNIGHTONE000",0
even
copperlist:
dc.w $08e,$2c81,$090,$2cc1,$092,$0038,$094,$00d0
dc.w $100,$1200,$102,0,$104,0,$108,0,$10a,0
dc.w $180,$012,$182,$fff
copbpl:
dc.w $0e0,0,$0e2,0
dc.w $ffff,$fffe
plane: dcb.b 10240,0
Cost and alternatives
The measured helper extent is 328 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 A500 OCS PAL, Kickstart1.3 OFS cold boot, using Asm198x 0.0.72, Emu198x 0.44.2 and Build198x 0.2.9. 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.