Multiply Two Bytes into a Word on Spectrum

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

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.

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

; 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:
    ld a,0
    ld (PRODUCT_LO),a
    ld (PRODUCT_HI),a
    ld (LEFT),a
    ld (RIGHT),a
    ld (T0),a
    ld (T1),a
    ld (T4),a
    ld (T5),a
    ld (T6),a
    ld (T7),a
    ld (T8),a
    ld (T9),a
    ret
byte_product_step:
; T4 = LEFT
    ld a,(LEFT)
    ld (T4),a
; T5 = 0
    ld a,0
    ld (T5),a
; T1 = RIGHT
    ld a,(RIGHT)
    ld (T1),a
; T6 = 0
    ld a,0
    ld (T6),a
; T7 = 0
    ld a,0
    ld (T7),a
; T0 = 8
    ld a,8
    ld (T0),a
; while T0 != 0:
byte_product_L1:
    ld a,(T0)
    cp 0
    jp nz,byte_product_L2
    jp byte_product_L3
byte_product_L2:
; T9 = T1 & 1
    ld a,(T1)
    and 1
    ld (T9),a
; if T9 != 0:
    ld a,(T9)
    cp 0
    jp nz,byte_product_L4
    jp byte_product_L5
byte_product_L4:
; T8 = T6
    ld a,(T6)
    ld (T8),a
; T6 = T6 + T4
    ld a,(T6)
    ld b,a
    ld a,(T4)
    ld c,a
    ld a,b
    add a,c
    ld (T6),a
; T9 = 0
    ld a,0
    ld (T9),a
; if T6 < T8:
    ld a,(T6)
    ld b,a
    ld a,(T8)
    ld c,a
    ld a,b
    cp c
    jp c,byte_product_L7
    jp byte_product_L8
byte_product_L7:
; T9 = 1
    ld a,1
    ld (T9),a
    jp byte_product_L9
byte_product_L8:
byte_product_L9:
; T7 = T7 + T5
    ld a,(T7)
    ld b,a
    ld a,(T5)
    ld c,a
    ld a,b
    add a,c
    ld (T7),a
; T7 = T7 + T9
    ld a,(T7)
    ld b,a
    ld a,(T9)
    ld c,a
    ld a,b
    add a,c
    ld (T7),a
    jp byte_product_L6
byte_product_L5:
byte_product_L6:
; T9 = T4 >> 7
    ld a,(T4)
    srl a
    srl a
    srl a
    srl a
    srl a
    srl a
    srl a
    ld (T9),a
; T4 = T4 << 1
    ld a,(T4)
    sla a
    ld (T4),a
; T5 = T5 << 1
    ld a,(T5)
    sla a
    ld (T5),a
; T5 = T5 | T9
    ld a,(T5)
    ld b,a
    ld a,(T9)
    ld c,a
    ld a,b
    or c
    ld (T5),a
; T1 = T1 >> 1
    ld a,(T1)
    srl a
    ld (T1),a
; T0 = T0 - 1
    ld a,(T0)
    sub 1
    ld (T0),a
    jp byte_product_L1
byte_product_L3:
; PRODUCT_LO = T6
    ld a,(T6)
    ld (PRODUCT_LO),a
; PRODUCT_HI = T7
    ld a,(T7)
    ld (PRODUCT_HI),a
    ret
component_end:

Machine contract

AF/BC/DE/HL may change; IX/IY are preserved. A direct CALL 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 48K diagnostic boots through ROM tape loading and USR, disables interrupts and owns the screen. The helper performs no port or screen writes.

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

    org $8000
CUSTOM equ 0
BROKEN equ 0
COYOTE_STEPS equ 4
BUFFER_STEPS equ 4
TEXT_CAP equ 8
PROPERTY_COUNT equ 16
STREAM_BYTES equ 13
CRC_POLY equ 7
    include "caller.inc"
    include "exercise.inc"
component_start:
    include "component.inc"
    include "data.inc"
    include "cases.inc"
    include "../../physics/rectangle-overlap/display.inc"
code_end:
STATE:
PRODUCT_LO: defb 0
PRODUCT_HI: defb 0
LEFT: defb 0
RIGHT: defb 0
T0: defb 0
T1: defb 0
T4: defb 0
T5: defb 0
T6: defb 0
T7: defb 0
T8: defb 0
T9: defb 0
input_ptr: defw 0
output_ptr: defw 0
cases_left: defb 0
ready: defb 0
preview: defs 8,0
OUTPUT: defs 1300,0
    end start

A client retaining state between calls

preview_rules:
    if CUSTOM
; LEFT = 255
    ld a,255
    ld (LEFT),a
; RIGHT = 255
    ld a,255
    ld (RIGHT),a
    if BROKEN
; RIGHT = 1
    ld a,1
    ld (RIGHT),a
    endif
    call checked_step
    call emit_state
    ret
    else
; LEFT = 200
    ld a,200
    ld (LEFT),a
; RIGHT = 3
    ld a,3
    ld (RIGHT),a
    if BROKEN
; RIGHT = 1
    ld a,1
    ld (RIGHT),a
    endif
    call checked_step
    call emit_state
    endif
    ret

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

    org $8000
CUSTOM equ 1
BROKEN equ 0
COYOTE_STEPS equ 2
BUFFER_STEPS equ 2
TEXT_CAP equ 4
PROPERTY_COUNT equ 16
STREAM_BYTES equ 13
CRC_POLY equ 49
    include "caller.inc"
    include "exercise.inc"
component_start:
    include "component.inc"
    include "data.inc"
    include "cases.inc"
    include "../../physics/rectangle-overlap/display.inc"
code_end:
STATE:
PRODUCT_LO: defb 0
PRODUCT_HI: defb 0
LEFT: defb 0
RIGHT: defb 0
T0: defb 0
T1: defb 0
T4: defb 0
T5: defb 0
T6: defb 0
T7: defb 0
T8: defb 0
T9: defb 0
input_ptr: defw 0
output_ptr: defw 0
cases_left: defb 0
ready: defb 0
preview: defs 8,0
OUTPUT: defs 1300,0
    end start

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

    org $8000
CUSTOM equ 0
BROKEN equ 1
COYOTE_STEPS equ 4
BUFFER_STEPS equ 4
TEXT_CAP equ 8
PROPERTY_COUNT equ 16
STREAM_BYTES equ 13
CRC_POLY equ 7
    include "caller.inc"
    include "exercise.inc"
component_start:
    include "component.inc"
    include "data.inc"
    include "cases.inc"
    include "../../physics/rectangle-overlap/display.inc"
code_end:
STATE:
PRODUCT_LO: defb 0
PRODUCT_HI: defb 0
LEFT: defb 0
RIGHT: defb 0
T0: defb 0
T1: defb 0
T4: defb 0
T5: defb 0
T6: defb 0
T7: defb 0
T8: defb 0
T9: defb 0
input_ptr: defw 0
output_ptr: defw 0
cases_left: defb 0
ready: defb 0
preview: defs 8,0
OUTPUT: defs 1300,0
    end start

Cost and alternatives

The measured helper extent is 259 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 48K PAL ROM tape load and USR, 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

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.