A world can be larger than the screen even when the drawing routine expects byte-sized screen coordinates.
Use it in a project
World and camera positions are unsigned little-endian words. WIDTH/HEIGHT are 1–255 logical units. A point is visible only when world−camera is nonnegative on each axis and strictly below the corresponding extent. Return byte SCREEN_X/Y and VISIBLE=1; hidden points return zero coordinates. Zero extents return VALID=0. Preserve inputs.
Include component.inc once (MOS callers include the shared 6502 implementation through it). Reserve the public fields in this exact order: SCREEN_X, SCREEN_Y, VISIBLE, VALID, WORLD_X_LO, WORLD_X_HI, WORLD_Y_LO, WORLD_Y_HI, CAMERA_X_LO, CAMERA_X_HI, CAMERA_Y_LO, CAMERA_Y_HI, WIDTH, HEIGHT. They occupy 14 contiguous bytes. Also reserve the private workspace: T0, T1, T2, T3 (4 bytes). Array names in the explanation refer to the numbered consecutive bindings, such as C0, C1 and so on.
Call viewport_world_transform_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 viewport_world_transform_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 | world/camera words and WIDTH/HEIGHT |
| Read after service | SCREEN_X/Y, VISIBLE and VALID |
First reject negative differences with full-word comparisons. Subtract each low byte and borrow into its high byte, then accept only a zero high difference and a low difference inside the viewport.
Reusable initialisation and service
; SPDX-License-Identifier: MIT
; Project World Points into a Viewport. See README.md for the byte interface and ownership.
; init clears the public fields and private workspace; set inputs afterwards.
viewport_world_transform_init:
ld a,0
ld (SCREEN_X),a
ld (SCREEN_Y),a
ld (VISIBLE),a
ld (VALID),a
ld (WORLD_X_LO),a
ld (WORLD_X_HI),a
ld (WORLD_Y_LO),a
ld (WORLD_Y_HI),a
ld (CAMERA_X_LO),a
ld (CAMERA_X_HI),a
ld (CAMERA_Y_LO),a
ld (CAMERA_Y_HI),a
ld (WIDTH),a
ld (HEIGHT),a
ld (T0),a
ld (T1),a
ld (T2),a
ld (T3),a
ret
viewport_world_transform_step:
; SCREEN_X = 0
ld a,0
ld (SCREEN_X),a
; SCREEN_Y = 0
ld a,0
ld (SCREEN_Y),a
; VISIBLE = 0
ld a,0
ld (VISIBLE),a
; VALID = 0
ld a,0
ld (VALID),a
; if WIDTH == 0:
ld a,(WIDTH)
cp 0
jp z,viewport_world_transform_L1
jp viewport_world_transform_L2
viewport_world_transform_L1:
; return
ret
jp viewport_world_transform_L3
viewport_world_transform_L2:
viewport_world_transform_L3:
; if HEIGHT == 0:
ld a,(HEIGHT)
cp 0
jp z,viewport_world_transform_L4
jp viewport_world_transform_L5
viewport_world_transform_L4:
; return
ret
jp viewport_world_transform_L6
viewport_world_transform_L5:
viewport_world_transform_L6:
; VALID = 1
ld a,1
ld (VALID),a
; if WORLD_X_HI < CAMERA_X_HI:
ld a,(WORLD_X_HI)
ld b,a
ld a,(CAMERA_X_HI)
ld c,a
ld a,b
cp c
jp c,viewport_world_transform_L7
jp viewport_world_transform_L8
viewport_world_transform_L7:
; return
ret
jp viewport_world_transform_L9
viewport_world_transform_L8:
viewport_world_transform_L9:
; if WORLD_X_HI == CAMERA_X_HI:
ld a,(WORLD_X_HI)
ld b,a
ld a,(CAMERA_X_HI)
ld c,a
ld a,b
cp c
jp z,viewport_world_transform_L10
jp viewport_world_transform_L11
viewport_world_transform_L10:
; if WORLD_X_LO < CAMERA_X_LO:
ld a,(WORLD_X_LO)
ld b,a
ld a,(CAMERA_X_LO)
ld c,a
ld a,b
cp c
jp c,viewport_world_transform_L13
jp viewport_world_transform_L14
viewport_world_transform_L13:
; return
ret
jp viewport_world_transform_L15
viewport_world_transform_L14:
viewport_world_transform_L15:
jp viewport_world_transform_L12
viewport_world_transform_L11:
viewport_world_transform_L12:
; if WORLD_Y_HI < CAMERA_Y_HI:
ld a,(WORLD_Y_HI)
ld b,a
ld a,(CAMERA_Y_HI)
ld c,a
ld a,b
cp c
jp c,viewport_world_transform_L16
jp viewport_world_transform_L17
viewport_world_transform_L16:
; return
ret
jp viewport_world_transform_L18
viewport_world_transform_L17:
viewport_world_transform_L18:
; if WORLD_Y_HI == CAMERA_Y_HI:
ld a,(WORLD_Y_HI)
ld b,a
ld a,(CAMERA_Y_HI)
ld c,a
ld a,b
cp c
jp z,viewport_world_transform_L19
jp viewport_world_transform_L20
viewport_world_transform_L19:
; if WORLD_Y_LO < CAMERA_Y_LO:
ld a,(WORLD_Y_LO)
ld b,a
ld a,(CAMERA_Y_LO)
ld c,a
ld a,b
cp c
jp c,viewport_world_transform_L22
jp viewport_world_transform_L23
viewport_world_transform_L22:
; return
ret
jp viewport_world_transform_L24
viewport_world_transform_L23:
viewport_world_transform_L24:
jp viewport_world_transform_L21
viewport_world_transform_L20:
viewport_world_transform_L21:
; T0 = WORLD_X_LO - CAMERA_X_LO
ld a,(WORLD_X_LO)
ld b,a
ld a,(CAMERA_X_LO)
ld c,a
ld a,b
sub c
ld (T0),a
; T1 = WORLD_X_HI - CAMERA_X_HI
ld a,(WORLD_X_HI)
ld b,a
ld a,(CAMERA_X_HI)
ld c,a
ld a,b
sub c
ld (T1),a
; if WORLD_X_LO < CAMERA_X_LO:
ld a,(WORLD_X_LO)
ld b,a
ld a,(CAMERA_X_LO)
ld c,a
ld a,b
cp c
jp c,viewport_world_transform_L25
jp viewport_world_transform_L26
viewport_world_transform_L25:
; T1 = T1 - 1
ld a,(T1)
sub 1
ld (T1),a
jp viewport_world_transform_L27
viewport_world_transform_L26:
viewport_world_transform_L27:
; if T1 != 0:
ld a,(T1)
cp 0
jp nz,viewport_world_transform_L28
jp viewport_world_transform_L29
viewport_world_transform_L28:
; return
ret
jp viewport_world_transform_L30
viewport_world_transform_L29:
viewport_world_transform_L30:
; if T0 >= WIDTH:
ld a,(T0)
ld b,a
ld a,(WIDTH)
ld c,a
ld a,b
cp c
jp nc,viewport_world_transform_L31
jp viewport_world_transform_L32
viewport_world_transform_L31:
; return
ret
jp viewport_world_transform_L33
viewport_world_transform_L32:
viewport_world_transform_L33:
; T2 = WORLD_Y_LO - CAMERA_Y_LO
ld a,(WORLD_Y_LO)
ld b,a
ld a,(CAMERA_Y_LO)
ld c,a
ld a,b
sub c
ld (T2),a
; T3 = WORLD_Y_HI - CAMERA_Y_HI
ld a,(WORLD_Y_HI)
ld b,a
ld a,(CAMERA_Y_HI)
ld c,a
ld a,b
sub c
ld (T3),a
; if WORLD_Y_LO < CAMERA_Y_LO:
ld a,(WORLD_Y_LO)
ld b,a
ld a,(CAMERA_Y_LO)
ld c,a
ld a,b
cp c
jp c,viewport_world_transform_L34
jp viewport_world_transform_L35
viewport_world_transform_L34:
; T3 = T3 - 1
ld a,(T3)
sub 1
ld (T3),a
jp viewport_world_transform_L36
viewport_world_transform_L35:
viewport_world_transform_L36:
; if T3 != 0:
ld a,(T3)
cp 0
jp nz,viewport_world_transform_L37
jp viewport_world_transform_L38
viewport_world_transform_L37:
; return
ret
jp viewport_world_transform_L39
viewport_world_transform_L38:
viewport_world_transform_L39:
; if T2 >= HEIGHT:
ld a,(T2)
ld b,a
ld a,(HEIGHT)
ld c,a
ld a,b
cp c
jp nc,viewport_world_transform_L40
jp viewport_world_transform_L41
viewport_world_transform_L40:
; return
ret
jp viewport_world_transform_L42
viewport_world_transform_L41:
viewport_world_transform_L42:
; SCREEN_X = T0
ld a,(T0)
ld (SCREEN_X),a
; SCREEN_Y = T2
ld a,(T2)
ld (SCREEN_Y),a
; VISIBLE = 1
ld a,1
ld (VISIBLE),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:
SCREEN_X: defb 0
SCREEN_Y: defb 0
VISIBLE: defb 0
VALID: defb 0
WORLD_X_LO: defb 0
WORLD_X_HI: defb 0
WORLD_Y_LO: defb 0
WORLD_Y_HI: defb 0
CAMERA_X_LO: defb 0
CAMERA_X_HI: defb 0
CAMERA_Y_LO: defb 0
CAMERA_Y_HI: defb 0
WIDTH: defb 0
HEIGHT: defb 0
T0: defb 0
T1: defb 0
T2: defb 0
T3: 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 startA client retaining state between calls
preview_rules:
if CUSTOM
; WORLD_X_LO = 255
ld a,255
ld (WORLD_X_LO),a
; WORLD_X_HI = 255
ld a,255
ld (WORLD_X_HI),a
; WORLD_Y_LO = 255
ld a,255
ld (WORLD_Y_LO),a
; WORLD_Y_HI = 255
ld a,255
ld (WORLD_Y_HI),a
; CAMERA_X_LO = 254
ld a,254
ld (CAMERA_X_LO),a
; CAMERA_X_HI = 255
ld a,255
ld (CAMERA_X_HI),a
; CAMERA_Y_LO = 254
ld a,254
ld (CAMERA_Y_LO),a
; CAMERA_Y_HI = 255
ld a,255
ld (CAMERA_Y_HI),a
; WIDTH = 2
ld a,2
ld (WIDTH),a
; HEIGHT = 2
ld a,2
ld (HEIGHT),a
if BROKEN
; WORLD_X_HI = 0
ld a,0
ld (WORLD_X_HI),a
endif
call checked_step
call emit_state
ret
else
; WORLD_X_LO = 5
ld a,5
ld (WORLD_X_LO),a
; WORLD_X_HI = 1
ld a,1
ld (WORLD_X_HI),a
; WORLD_Y_LO = 10
ld a,10
ld (WORLD_Y_LO),a
; WORLD_Y_HI = 1
ld a,1
ld (WORLD_Y_HI),a
; CAMERA_X_LO = 250
ld a,250
ld (CAMERA_X_LO),a
; CAMERA_X_HI = 0
ld a,0
ld (CAMERA_X_HI),a
; CAMERA_Y_LO = 0
ld a,0
ld (CAMERA_Y_LO),a
; CAMERA_Y_HI = 1
ld a,1
ld (CAMERA_Y_HI),a
; WIDTH = 32
ld a,32
ld (WIDTH),a
; HEIGHT = 24
ld a,24
ld (HEIGHT),a
if BROKEN
; WORLD_X_HI = 0
ld a,0
ld (WORLD_X_HI),a
endif
call checked_step
call emit_state
endif
retCustomise it
Project a point near the maximum word coordinate into a two-unit viewport. 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:
SCREEN_X: defb 0
SCREEN_Y: defb 0
VISIBLE: defb 0
VALID: defb 0
WORLD_X_LO: defb 0
WORLD_X_HI: defb 0
WORLD_Y_LO: defb 0
WORLD_Y_HI: defb 0
CAMERA_X_LO: defb 0
CAMERA_X_HI: defb 0
CAMERA_Y_LO: defb 0
CAMERA_Y_HI: defb 0
WIDTH: defb 0
HEIGHT: defb 0
T0: defb 0
T1: defb 0
T2: defb 0
T3: 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 startThe custom diagnostic row is 01 01 01 01 FF FF FF FF. The full client trace in the source explains how it gets there.
Mistake and repair
The wrong caller drops the world X high byte. A point just beyond 255 appears behind the camera instead of eleven units to its right. Preserve both bytes through the coordinate transform.
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:
SCREEN_X: defb 0
SCREEN_Y: defb 0
VISIBLE: defb 0
VALID: defb 0
WORLD_X_LO: defb 0
WORLD_X_HI: defb 0
WORLD_Y_LO: defb 0
WORLD_Y_HI: defb 0
CAMERA_X_LO: defb 0
CAMERA_X_HI: defb 0
CAMERA_Y_LO: defb 0
CAMERA_Y_HI: defb 0
WIDTH: defb 0
HEIGHT: defb 0
T0: defb 0
T1: defb 0
T2: defb 0
T3: 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 424 code bytes; public state is 14 bytes and private scratch is 4 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 with no division. Subtracting in the world representation before narrowing avoids byte wrap; fixed-point world coordinates additionally need an explicit fractional-bit conversion.
This projects points, not partly visible sprites or rectangles. Extents are at most 255, so a 256-unit viewport needs a wider extent representation. Camera coordinates do not wrap and the routine does not write display registers.
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
Rectangle clipping: After projecting an object’s origin, clip its visible shape with the appropriate signed or wider rectangle representation.