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.
| Ownership | Fields |
|---|---|
| Retain between calls | none |
| Supply before service | LEFT_LO/HI and RIGHT_LO/HI |
| Read after service | SUM_LO/HI and CLAMPED |
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:
lda #0
sta SUM_LO
sta SUM_HI
sta CLAMPED
sta LEFT_LO
sta LEFT_HI
sta RIGHT_LO
sta RIGHT_HI
sta T0
sta T1
rts
saturating_word_add_step:
; SUM_LO = LEFT_LO + RIGHT_LO
lda LEFT_LO
clc
adc RIGHT_LO
sta SUM_LO
; T0 = 0
lda #0
sta T0
; if SUM_LO < LEFT_LO:
lda SUM_LO
cmp LEFT_LO
bcc saturating_word_add_L4
saturating_word_add_L5:
jmp saturating_word_add_L2
saturating_word_add_L4:
jmp saturating_word_add_L1
saturating_word_add_L1:
; T0 = 1
lda #1
sta T0
jmp saturating_word_add_L3
saturating_word_add_L2:
saturating_word_add_L3:
; SUM_HI = LEFT_HI + RIGHT_HI
lda LEFT_HI
clc
adc RIGHT_HI
sta SUM_HI
; CLAMPED = 0
lda #0
sta CLAMPED
; if SUM_HI < LEFT_HI:
lda SUM_HI
cmp LEFT_HI
bcc saturating_word_add_L9
saturating_word_add_L10:
jmp saturating_word_add_L7
saturating_word_add_L9:
jmp saturating_word_add_L6
saturating_word_add_L6:
; CLAMPED = 1
lda #1
sta CLAMPED
jmp saturating_word_add_L8
saturating_word_add_L7:
saturating_word_add_L8:
; T1 = SUM_HI
lda SUM_HI
sta T1
; SUM_HI = SUM_HI + T0
lda SUM_HI
clc
adc T0
sta SUM_HI
; if SUM_HI < T1:
lda SUM_HI
cmp T1
bcc saturating_word_add_L14
saturating_word_add_L15:
jmp saturating_word_add_L12
saturating_word_add_L14:
jmp saturating_word_add_L11
saturating_word_add_L11:
; CLAMPED = 1
lda #1
sta CLAMPED
jmp saturating_word_add_L13
saturating_word_add_L12:
saturating_word_add_L13:
; if CLAMPED != 0:
lda CLAMPED
cmp #0
bne saturating_word_add_L19
saturating_word_add_L20:
jmp saturating_word_add_L17
saturating_word_add_L19:
jmp saturating_word_add_L16
saturating_word_add_L16:
; SUM_LO = 255
lda #255
sta SUM_LO
; SUM_HI = 255
lda #255
sta SUM_HI
jmp saturating_word_add_L18
saturating_word_add_L17:
saturating_word_add_L18:
rts
component_end:Machine contract
A/X/status may change; Y and decimal mode are preserved. Use CLD for binary arithmetic. A direct JSR 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 diagnostic PRG owns screen, font and colour RAM and disables interrupts; it does not return to BASIC. The reusable helper does none of those things.
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
SUM_LO=$80
SUM_HI=$81
CLAMPED=$82
LEFT_LO=$83
LEFT_HI=$84
RIGHT_LO=$85
RIGHT_HI=$86
T0=$87
T1=$88
STATE=$80
input_ptr=$70
cases_left=$72
ptr=$74
saved_y=$76
OUTPUT=$c000
preview=OUTPUT+1400
ready=OUTPUT+1408
CUSTOM=0
BROKEN=0
COYOTE_STEPS=4
BUFFER_STEPS=4
TEXT_CAP=8
PROPERTY_COUNT=16
STREAM_BYTES=13
CRC_POLY=7
!source "caller.inc"
!source "exercise.inc"
component_start:
!source "component.inc"
!source "data.inc"
!source "cases.inc"
hex_font:
!byte 0,0,0,0,0,0,0,0,0,56,40,40,40,56,0,0,0,16,48,16,16,56,0,0,0,56,8,56,32,56,0,0,0,56,8,56,8,56,0,0,0,40,40,56,8,8,0,0,0,56,32,56,8,56,0,0,0,56,32,56,40,56,0,0,0,56,8,8,8,8,0,0,0,56,40,56,40,56,0,0,0,56,40,56,8,56,0,0,0,16,40,56,40,40,0,0,0,48,40,48,40,48,0,0,0,56,32,32,32,56,0,0,0,48,40,40,40,48,0,0,0,56,32,48,32,56,0,0,0,56,32,48,32,32,0,0
code_end:A client retaining state between calls
preview_rules:
!if CUSTOM {
; LEFT_LO = 255
lda #255
sta LEFT_LO
; LEFT_HI = 0
lda #0
sta LEFT_HI
; RIGHT_LO = 1
lda #1
sta RIGHT_LO
; RIGHT_HI = 0
lda #0
sta RIGHT_HI
!if BROKEN {
; RIGHT_HI = 0
lda #0
sta RIGHT_HI
}
jsr checked_step
jsr emit_state
rts
} else {
; LEFT_LO = 250
lda #250
sta LEFT_LO
; LEFT_HI = 254
lda #254
sta LEFT_HI
; RIGHT_LO = 10
lda #10
sta RIGHT_LO
; RIGHT_HI = 1
lda #1
sta RIGHT_HI
!if BROKEN {
; RIGHT_HI = 0
lda #0
sta RIGHT_HI
}
jsr checked_step
jsr emit_state
}
rtsCustomise 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
SUM_LO=$80
SUM_HI=$81
CLAMPED=$82
LEFT_LO=$83
LEFT_HI=$84
RIGHT_LO=$85
RIGHT_HI=$86
T0=$87
T1=$88
STATE=$80
input_ptr=$70
cases_left=$72
ptr=$74
saved_y=$76
OUTPUT=$c000
preview=OUTPUT+1400
ready=OUTPUT+1408
CUSTOM=1
BROKEN=0
COYOTE_STEPS=2
BUFFER_STEPS=2
TEXT_CAP=4
PROPERTY_COUNT=16
STREAM_BYTES=13
CRC_POLY=49
!source "caller.inc"
!source "exercise.inc"
component_start:
!source "component.inc"
!source "data.inc"
!source "cases.inc"
hex_font:
!byte 0,0,0,0,0,0,0,0,0,56,40,40,40,56,0,0,0,16,48,16,16,56,0,0,0,56,8,56,32,56,0,0,0,56,8,56,8,56,0,0,0,40,40,56,8,8,0,0,0,56,32,56,8,56,0,0,0,56,32,56,40,56,0,0,0,56,8,8,8,8,0,0,0,56,40,56,40,56,0,0,0,56,40,56,8,56,0,0,0,16,40,56,40,40,0,0,0,48,40,48,40,48,0,0,0,56,32,32,32,56,0,0,0,48,40,40,40,48,0,0,0,56,32,48,32,56,0,0,0,56,32,48,32,32,0,0
code_end: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
SUM_LO=$80
SUM_HI=$81
CLAMPED=$82
LEFT_LO=$83
LEFT_HI=$84
RIGHT_LO=$85
RIGHT_HI=$86
T0=$87
T1=$88
STATE=$80
input_ptr=$70
cases_left=$72
ptr=$74
saved_y=$76
OUTPUT=$c000
preview=OUTPUT+1400
ready=OUTPUT+1408
CUSTOM=0
BROKEN=1
COYOTE_STEPS=4
BUFFER_STEPS=4
TEXT_CAP=8
PROPERTY_COUNT=16
STREAM_BYTES=13
CRC_POLY=7
!source "caller.inc"
!source "exercise.inc"
component_start:
!source "component.inc"
!source "data.inc"
!source "cases.inc"
hex_font:
!byte 0,0,0,0,0,0,0,0,0,56,40,40,40,56,0,0,0,16,48,16,16,56,0,0,0,56,8,56,32,56,0,0,0,56,8,56,8,56,0,0,0,40,40,56,8,8,0,0,0,56,32,56,8,56,0,0,0,56,32,56,40,56,0,0,0,56,8,8,8,8,0,0,0,56,40,56,40,56,0,0,0,56,40,56,8,56,0,0,0,16,40,56,40,40,0,0,0,48,40,48,40,48,0,0,0,56,32,32,32,56,0,0,0,48,40,40,40,48,0,0,0,56,32,48,32,56,0,0,0,56,32,48,32,32,0,0
code_end:
Cost and alternatives
The measured helper extent is 135 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 PAL stock-ROM PRG, 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.