Multiply Two Bytes into a Word on Amiga | Pattern Library

A small machine still needs products larger than one byte: an area, a score multiplier or a scaled distance.

Amiga shows the working diagnostic row 58 02 C8 03 00 00 00 00. — A completed native caller displays 58 02 C8 03 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

LEFT and RIGHT are unsigned 0–255. Return their exact product in PRODUCT_LO/PRODUCT_HI, low byte first. Both inputs are preserved. There is no overflow for this input domain: 255×255 is 65,025.

Include component.inc once (MOS callers include the shared 6502 implementation through it). Reserve the public fields in this exact order: PRODUCT_LO, PRODUCT_HI, LEFT, RIGHT. They occupy 4 contiguous bytes. Also reserve the private workspace: T0, T1, T4, T5, T6, T7, T8, T9 (8 bytes). Array names in the explanation refer to the numbered consecutive bindings, such as C0, C1 and so on.

Call byte_product_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_product_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	LEFT and RIGHT
Read after service	PRODUCT_LO and PRODUCT_HI

The multiplier is inspected one bit at a time. Each set bit adds a shifted multiplicand into a two-byte result. Carry is handled explicitly, so the same byte interface works on the three CPU families.

Reusable initialisation and service

component.inc

; SPDX-License-Identifier: MIT
; Multiply Two Bytes into a Word. See README.md for the byte interface and ownership.
; init clears the public fields and private workspace; set inputs afterwards.
byte_product_init:
    move.b #0,d0
    move.b d0,PRODUCT_LO
    move.b d0,PRODUCT_HI
    move.b d0,LEFT
    move.b d0,RIGHT
    move.b d0,T0
    move.b d0,T1
    move.b d0,T4
    move.b d0,T5
    move.b d0,T6
    move.b d0,T7
    move.b d0,T8
    move.b d0,T9
    rts
byte_product_step:
; T4 = LEFT
    move.b LEFT,d0
    move.b d0,T4
; T5 = 0
    move.b #0,d0
    move.b d0,T5
; T1 = RIGHT
    move.b RIGHT,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_product_L1:
    move.b T0,d0
    cmp.b #0,d0
    bne byte_product_L2
    jmp byte_product_L3
byte_product_L2:
; 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_product_L4
    jmp byte_product_L5
byte_product_L4:
; 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_product_L7
    jmp byte_product_L8
byte_product_L7:
; T9 = 1
    move.b #1,d0
    move.b d0,T9
    jmp byte_product_L9
byte_product_L8:
byte_product_L9:
; 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_product_L6
byte_product_L5:
byte_product_L6:
; 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_product_L1
byte_product_L3:
; PRODUCT_LO = T6
    move.b T6,d0
    move.b d0,PRODUCT_LO
; PRODUCT_HI = T7
    move.b T7,d0
    move.b d0,PRODUCT_HI
    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:
PRODUCT_LO: dc.b 0
PRODUCT_HI: dc.b 0
LEFT: dc.b 0
RIGHT: dc.b 0
T0: dc.b 0
T1: 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
    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
; LEFT = 255
    move.b #255,d0
    move.b d0,LEFT
; RIGHT = 255
    move.b #255,d0
    move.b d0,RIGHT
    ifne BROKEN
; RIGHT = 1
    move.b #1,d0
    move.b d0,RIGHT
    endif
    bsr checked_step
    bsr emit_state
    rts
    else
; LEFT = 200
    move.b #200,d0
    move.b d0,LEFT
; RIGHT = 3
    move.b #3,d0
    move.b d0,RIGHT
    ifne BROKEN
; RIGHT = 1
    move.b #1,d0
    move.b d0,RIGHT
    endif
    bsr checked_step
    bsr emit_state
    endif
    rts

Customise it

Use the maximum two-byte result instead of a small factor. 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:
PRODUCT_LO: dc.b 0
PRODUCT_HI: dc.b 0
LEFT: dc.b 0
RIGHT: dc.b 0
T0: dc.b 0
T1: 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
    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 01 FE FF FF 00 00 00 00. The full client trace in the source explains how it gets there.

Mistake and repair

The wrong caller substitutes a factor of one, often mistaken for a default scale. The result is the original value rather than the requested product. Pass both actual factors; keep the high result byte.

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:
PRODUCT_LO: dc.b 0
PRODUCT_HI: dc.b 0
LEFT: dc.b 0
RIGHT: dc.b 0
T0: dc.b 0
T1: 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
    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 C8 00 C8 01 00 00 00 00. — The wrong client completes with C8 00 C8 01 00 00 00 00; its changed inputs and state explain the result.

Cost and alternatives

The measured helper extent is 380 code bytes; public state is 4 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.

Eight bit stages, with additions only for set multiplier bits. The 68000 has hardware multiplication; a word-oriented MULU implementation is a useful faster alternative. This common byte routine makes the representation visible rather than claiming to be the fastest native implementation.

This is unsigned integer multiplication. Signed values, fixed-point scaling and saturation require explicit conversions; discarding PRODUCT_HI changes the result to multiplication modulo 256.

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

Fractional positions: A fixed-point product needs an explicit decision about which result bits represent the chosen unit.

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