Interpolate Between Byte Endpoints on Amiga | Pattern Library

A menu panel or camera can move towards an endpoint without a different hand-written position for every frame.

Amiga shows the working diagnostic row 6E 0A D2 80 00 00 00 00. — A completed native caller displays 6E 0A D2 80 00 00 00 00. The public field order below identifies these bytes; the capture is a state diagnostic, not a recording of a finished game.

Use it in a project

FRACTION is 0–255, mapping exactly to START and END at its two endpoints. Return START+floor((END−START)×FRACTION/255) when ascending; when descending, subtract floor((START−END)×FRACTION/255). This rounds the travel towards START. All inputs are preserved.

Include component.inc once (MOS callers include the shared 6502 implementation through it). Reserve the public fields in this exact order: VALUE, START, END, FRACTION. They occupy 4 contiguous bytes. Also reserve the private workspace: T0, T1, T2, T4, T5, T6, T7, T8, T9, T10, T11 (11 bytes). Array names in the explanation refer to the numbered consecutive bindings, such as C0, C1 and so on.

Call byte_interpolation_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 byte_interpolation_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	START, END and FRACTION
Read after service	VALUE

First measure unsigned travel, scale it by the fraction, then apply that travel in the chosen direction. Dividing by 255 rather than 256 makes both endpoint values exact.

Reusable initialisation and service

component.inc

; SPDX-License-Identifier: MIT
; Interpolate Between Byte Endpoints. See README.md for the byte interface and ownership.
; init clears the public fields and private workspace; set inputs afterwards.
byte_interpolation_init:
    move.b #0,d0
    move.b d0,VALUE
    move.b d0,START
    move.b d0,END
    move.b d0,FRACTION
    move.b d0,T0
    move.b d0,T1
    move.b d0,T2
    move.b d0,T4
    move.b d0,T5
    move.b d0,T6
    move.b d0,T7
    move.b d0,T8
    move.b d0,T9
    move.b d0,T10
    move.b d0,T11
    rts
byte_interpolation_step:
; T10 = 0
    move.b #0,d0
    move.b d0,T10
; if END >= START:
    move.b END,d0
    move.b START,d1
    cmp.b d1,d0
    bcc byte_interpolation_L1
    jmp byte_interpolation_L2
byte_interpolation_L1:
; T11 = END - START
    move.b END,d0
    move.b START,d1
    sub.b d1,d0
    move.b d0,T11
    jmp byte_interpolation_L3
byte_interpolation_L2:
; T11 = START - END
    move.b START,d0
    move.b END,d1
    sub.b d1,d0
    move.b d0,T11
; T10 = 1
    move.b #1,d0
    move.b d0,T10
byte_interpolation_L3:
; T4 = T11
    move.b T11,d0
    move.b d0,T4
; T5 = 0
    move.b #0,d0
    move.b d0,T5
; T1 = FRACTION
    move.b FRACTION,d0
    move.b d0,T1
; T6 = 0
    move.b #0,d0
    move.b d0,T6
; T7 = 0
    move.b #0,d0
    move.b d0,T7
; T0 = 8
    move.b #8,d0
    move.b d0,T0
; while T0 != 0:
byte_interpolation_L4:
    move.b T0,d0
    cmp.b #0,d0
    bne byte_interpolation_L5
    jmp byte_interpolation_L6
byte_interpolation_L5:
; T9 = T1 & 1
    move.b T1,d0
    and.b #1,d0
    move.b d0,T9
; if T9 != 0:
    move.b T9,d0
    cmp.b #0,d0
    bne byte_interpolation_L7
    jmp byte_interpolation_L8
byte_interpolation_L7:
; T8 = T6
    move.b T6,d0
    move.b d0,T8
; T6 = T6 + T4
    move.b T6,d0
    move.b T4,d1
    add.b d1,d0
    move.b d0,T6
; T9 = 0
    move.b #0,d0
    move.b d0,T9
; if T6 < T8:
    move.b T6,d0
    move.b T8,d1
    cmp.b d1,d0
    bcs byte_interpolation_L10
    jmp byte_interpolation_L11
byte_interpolation_L10:
; T9 = 1
    move.b #1,d0
    move.b d0,T9
    jmp byte_interpolation_L12
byte_interpolation_L11:
byte_interpolation_L12:
; T7 = T7 + T5
    move.b T7,d0
    move.b T5,d1
    add.b d1,d0
    move.b d0,T7
; T7 = T7 + T9
    move.b T7,d0
    move.b T9,d1
    add.b d1,d0
    move.b d0,T7
    jmp byte_interpolation_L9
byte_interpolation_L8:
byte_interpolation_L9:
; T9 = T4 >> 7
    move.b T4,d0
    lsr.b #7,d0
    move.b d0,T9
; T4 = T4 << 1
    move.b T4,d0
    lsl.b #1,d0
    move.b d0,T4
; T5 = T5 << 1
    move.b T5,d0
    lsl.b #1,d0
    move.b d0,T5
; T5 = T5 | T9
    move.b T5,d0
    move.b T9,d1
    or.b d1,d0
    move.b d0,T5
; T1 = T1 >> 1
    move.b T1,d0
    lsr.b #1,d0
    move.b d0,T1
; T0 = T0 - 1
    move.b T0,d0
    sub.b #1,d0
    move.b d0,T0
    jmp byte_interpolation_L4
byte_interpolation_L6:
; T2 = 0
    move.b #0,d0
    move.b d0,T2
; while T7 != 0:
byte_interpolation_L13:
    move.b T7,d0
    cmp.b #0,d0
    bne byte_interpolation_L14
    jmp byte_interpolation_L15
byte_interpolation_L14:
; T8 = 0
    move.b #0,d0
    move.b d0,T8
; if T6 < 255:
    move.b T6,d0
    cmp.b #255,d0
    bcs byte_interpolation_L16
    jmp byte_interpolation_L17
byte_interpolation_L16:
; T8 = 1
    move.b #1,d0
    move.b d0,T8
    jmp byte_interpolation_L18
byte_interpolation_L17:
byte_interpolation_L18:
; T6 = T6 - 255
    move.b T6,d0
    sub.b #255,d0
    move.b d0,T6
; T7 = T7 - T8
    move.b T7,d0
    move.b T8,d1
    sub.b d1,d0
    move.b d0,T7
; T2 = T2 + 1
    move.b T2,d0
    add.b #1,d0
    move.b d0,T2
    jmp byte_interpolation_L13
byte_interpolation_L15:
; if T6 == 255:
    move.b T6,d0
    cmp.b #255,d0
    beq byte_interpolation_L19
    jmp byte_interpolation_L20
byte_interpolation_L19:
; T2 = T2 + 1
    move.b T2,d0
    add.b #1,d0
    move.b d0,T2
    jmp byte_interpolation_L21
byte_interpolation_L20:
byte_interpolation_L21:
; VALUE = START
    move.b START,d0
    move.b d0,VALUE
; if T10 == 0:
    move.b T10,d0
    cmp.b #0,d0
    beq byte_interpolation_L22
    jmp byte_interpolation_L23
byte_interpolation_L22:
; VALUE = VALUE + T2
    move.b VALUE,d0
    move.b T2,d1
    add.b d1,d0
    move.b d0,VALUE
    jmp byte_interpolation_L24
byte_interpolation_L23:
; VALUE = VALUE - T2
    move.b VALUE,d0
    move.b T2,d1
    sub.b d1,d0
    move.b d0,VALUE
byte_interpolation_L24:
    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

demo.asm

    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:
VALUE: dc.b 0
START: dc.b 0
END: dc.b 0
FRACTION: dc.b 0
T0: dc.b 0
T1: dc.b 0
T2: dc.b 0
T4: dc.b 0
T5: dc.b 0
T6: dc.b 0
T7: dc.b 0
T8: dc.b 0
T9: dc.b 0
T10: dc.b 0
T11: dc.b 0
    even
ready: dc.w 0
preview: dcb.b 8,0
OUTPUT: dcb.b 1300,0
    even
signature: dc.b "198XWORLDKIT000",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

A client retaining state between calls

exercise.inc, excerpt

preview_rules:
    ifne CUSTOM
; START = 210
    move.b #210,d0
    move.b d0,START
; END = 10
    move.b #10,d0
    move.b d0,END
; FRACTION = 255
    move.b #255,d0
    move.b d0,FRACTION
    ifne BROKEN
; FRACTION = 0
    move.b #0,d0
    move.b d0,FRACTION
    endif
    bsr checked_step
    bsr emit_state
    rts
    else
; START = 10
    move.b #10,d0
    move.b d0,START
; END = 210
    move.b #210,d0
    move.b d0,END
; FRACTION = 128
    move.b #128,d0
    move.b d0,FRACTION
    ifne BROKEN
; FRACTION = 0
    move.b #0,d0
    move.b d0,FRACTION
    endif
    bsr checked_step
    bsr emit_state
    endif
    rts

Customise it

Reverse the endpoints and finish exactly at the destination. 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

custom.asm

    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:
VALUE: dc.b 0
START: dc.b 0
END: dc.b 0
FRACTION: dc.b 0
T0: dc.b 0
T1: dc.b 0
T2: dc.b 0
T4: dc.b 0
T5: dc.b 0
T6: dc.b 0
T7: dc.b 0
T8: dc.b 0
T9: dc.b 0
T10: dc.b 0
T11: dc.b 0
    even
ready: dc.w 0
preview: dcb.b 8,0
OUTPUT: dcb.b 1300,0
    even
signature: dc.b "198XWORLDKIT000",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

The custom diagnostic row is 0A D2 0A FF 00 00 00 00. The full client trace in the source explains how it gets there.

Mistake and repair

The wrong caller sends a fraction of zero on every update. The interpolation stays at its starting point. Advance the fraction separately, and retain the original endpoints while that transition is in progress.

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

wrong.asm

    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:
VALUE: dc.b 0
START: dc.b 0
END: dc.b 0
FRACTION: dc.b 0
T0: dc.b 0
T1: dc.b 0
T2: dc.b 0
T4: dc.b 0
T5: dc.b 0
T6: dc.b 0
T7: dc.b 0
T8: dc.b 0
T9: dc.b 0
T10: dc.b 0
T11: dc.b 0
    even
ready: dc.w 0
preview: dcb.b 8,0
OUTPUT: dcb.b 1300,0
    even
signature: dc.b "198XWORLDKIT000",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

Amiga shows the deliberate error row 0A 0A D2 00 00 00 00 00. — The wrong client completes with 0A 0A D2 00 00 00 00 00; its changed inputs and state explain the result.

Cost and alternatives

The measured helper extent is 644 code bytes; public state is 4 bytes and private scratch is 11 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.

Eight product stages followed by up to 255 subtraction stages. A /256 scale is cheaper but needs an explicit final-endpoint policy. A wider fixed-point interpolation or native 68000 multiply/divide can trade code for faster updates.

This computes a position for a supplied fraction; it does not own a clock or easing curve. Replacing START with the previous output every frame creates a different, asymptotic motion. Descending values deliberately use start-relative rounding rather than floor of the final signed expression.

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

Rational tick division: A scheduling routine can decide when to advance the transition; interpolation decides which position that progress represents.

The Craft · Maths for Games · Source and native evidence.