Add Words with Saturation on Spectrum

A large score or resource total should stop at its ceiling rather than wrap back to a small number.

Use it in a project

Add two unsigned little-endian words. Return their sum capped at 65,535 and CLAMPED=1 exactly when the mathematical sum exceeds that limit. Preserve both inputs.

Include component.inc once (MOS callers include the shared 6502 implementation through it). Reserve the public fields in this exact order: SUM_LO, SUM_HI, CLAMPED, LEFT_LO, LEFT_HI, RIGHT_LO, RIGHT_HI. They occupy 7 contiguous bytes. Also reserve the private workspace: T0, T1 (2 bytes). Array names in the explanation refer to the numbered consecutive bindings, such as C0, C1 and so on.

Call saturating_word_add_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 saturating_word_add_step whenever the described event occurs. The helper reads no device, waits for no frame and installs no interrupt handler.

The low addition yields a carry into the high byte. Either overflow in the high addition or overflow when adding that carry saturates both result bytes.

Reusable initialisation and service

; SPDX-License-Identifier: MIT
; Add Words with Saturation. See README.md for the byte interface and ownership.
; init clears the public fields and private workspace; set inputs afterwards.
saturating_word_add_init:
    ld a,0
    ld (SUM_LO),a
    ld (SUM_HI),a
    ld (CLAMPED),a
    ld (LEFT_LO),a
    ld (LEFT_HI),a
    ld (RIGHT_LO),a
    ld (RIGHT_HI),a
    ld (T0),a
    ld (T1),a
    ret
saturating_word_add_step:
; SUM_LO = LEFT_LO + RIGHT_LO
    ld a,(LEFT_LO)
    ld b,a
    ld a,(RIGHT_LO)
    ld c,a
    ld a,b
    add a,c
    ld (SUM_LO),a
; T0 = 0
    ld a,0
    ld (T0),a
; if SUM_LO < LEFT_LO:
    ld a,(SUM_LO)
    ld b,a
    ld a,(LEFT_LO)
    ld c,a
    ld a,b
    cp c
    jp c,saturating_word_add_L1
    jp saturating_word_add_L2
saturating_word_add_L1:
; T0 = 1
    ld a,1
    ld (T0),a
    jp saturating_word_add_L3
saturating_word_add_L2:
saturating_word_add_L3:
; SUM_HI = LEFT_HI + RIGHT_HI
    ld a,(LEFT_HI)
    ld b,a
    ld a,(RIGHT_HI)
    ld c,a
    ld a,b
    add a,c
    ld (SUM_HI),a
; CLAMPED = 0
    ld a,0
    ld (CLAMPED),a
; if SUM_HI < LEFT_HI:
    ld a,(SUM_HI)
    ld b,a
    ld a,(LEFT_HI)
    ld c,a
    ld a,b
    cp c
    jp c,saturating_word_add_L4
    jp saturating_word_add_L5
saturating_word_add_L4:
; CLAMPED = 1
    ld a,1
    ld (CLAMPED),a
    jp saturating_word_add_L6
saturating_word_add_L5:
saturating_word_add_L6:
; T1 = SUM_HI
    ld a,(SUM_HI)
    ld (T1),a
; SUM_HI = SUM_HI + T0
    ld a,(SUM_HI)
    ld b,a
    ld a,(T0)
    ld c,a
    ld a,b
    add a,c
    ld (SUM_HI),a
; if SUM_HI < T1:
    ld a,(SUM_HI)
    ld b,a
    ld a,(T1)
    ld c,a
    ld a,b
    cp c
    jp c,saturating_word_add_L7
    jp saturating_word_add_L8
saturating_word_add_L7:
; CLAMPED = 1
    ld a,1
    ld (CLAMPED),a
    jp saturating_word_add_L9
saturating_word_add_L8:
saturating_word_add_L9:
; if CLAMPED != 0:
    ld a,(CLAMPED)
    cp 0
    jp nz,saturating_word_add_L10
    jp saturating_word_add_L11
saturating_word_add_L10:
; SUM_LO = 255
    ld a,255
    ld (SUM_LO),a
; SUM_HI = 255
    ld a,255
    ld (SUM_HI),a
    jp saturating_word_add_L12
saturating_word_add_L11:
saturating_word_add_L12:
    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:
SUM_LO: defb 0
SUM_HI: defb 0
CLAMPED: defb 0
LEFT_LO: defb 0
LEFT_HI: defb 0
RIGHT_LO: defb 0
RIGHT_HI: defb 0
T0: defb 0
T1: 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_LO = 255
    ld a,255
    ld (LEFT_LO),a
; LEFT_HI = 0
    ld a,0
    ld (LEFT_HI),a
; RIGHT_LO = 1
    ld a,1
    ld (RIGHT_LO),a
; RIGHT_HI = 0
    ld a,0
    ld (RIGHT_HI),a
    if BROKEN
; RIGHT_HI = 0
    ld a,0
    ld (RIGHT_HI),a
    endif
    call checked_step
    call emit_state
    ret
    else
; LEFT_LO = 250
    ld a,250
    ld (LEFT_LO),a
; LEFT_HI = 254
    ld a,254
    ld (LEFT_HI),a
; RIGHT_LO = 10
    ld a,10
    ld (RIGHT_LO),a
; RIGHT_HI = 1
    ld a,1
    ld (RIGHT_HI),a
    if BROKEN
; RIGHT_HI = 0
    ld a,0
    ld (RIGHT_HI),a
    endif
    call checked_step
    call emit_state
    endif
    ret

Customise it

Exercise a low-byte carry without saturating the full word. 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:
SUM_LO: defb 0
SUM_HI: defb 0
CLAMPED: defb 0
LEFT_LO: defb 0
LEFT_HI: defb 0
RIGHT_LO: defb 0
RIGHT_HI: defb 0
T0: defb 0
T1: 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 00 01 00 FF 00 01 00 00. The full client trace in the source explains how it gets there.

Mistake and repair

The wrong caller loses the high byte of the amount being added. Small rewards can hide the mistake; a word-sized reward exposes it. Pass both bytes.

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:
SUM_LO: defb 0
SUM_HI: defb 0
CLAMPED: defb 0
LEFT_LO: defb 0
LEFT_HI: defb 0
RIGHT_LO: defb 0
RIGHT_HI: defb 0
T0: defb 0
T1: 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 182 code bytes; public state is 7 bytes and private scratch is 2 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.

Constant work. Native 16-bit addition is simpler on the 68000; explicit byte carries keep the MOS and Z80 representations clear.

The fixed ceiling is 65,535. Signed saturation and a game-specific maximum need different comparisons.

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

Score counters: Saturating arithmetic is a policy choice distinct from decimal display.

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