A broad phase can discover the same two objects through several cells. Without a shared memory of pairs, one collision might inflict damage twice. This cache answers whether an unordered pair is new to the current traversal.
Include and initialise
DIM R(8). Reserve public F/O/M/A/B, private I/J/K/T and lines 3000–3520. Keep private loop variables away from the caller’s active FOR variables. Combine routines.bas with the caller using build.py, with END, STOP or a jump before the helper. C64/BBC use GOSUB; Spectrum uses GO SUB. Call 3000 to clear the public fields and cache.
A/B are distinct integral object IDs zero through seven. Each array row is an integral byte. For a pair, the lower ID chooses row R(lower+1), and the higher ID chooses its bit. This canonical ordering means 0,3 and 3,0 address the same remembered pair.
Test, remember or clear
Set M=1 to test and remember, or M=2 to test without changing storage, then call 3100. O=1 means a valid query. F=1 means the pair was absent; F=0 means it was already present. A read-only query reporting F=1 does not reserve the pair.
Reusable numbered routines
3000 LET F=0: LET O=0: LET M=0: LET A=0: LET B=0
3010 GO SUB 3500: RETURN
3100 LET F=0: LET O=0
3110 IF M<>0 AND M<>1 AND M<>2 THEN RETURN
3120 IF M=0 THEN GO SUB 3500: LET O=1: RETURN
3130 IF A<0 OR A>7 OR A<>INT (A) THEN RETURN
3140 IF B<0 OR B>7 OR B<>INT (B) THEN RETURN
3150 IF A=B THEN RETURN
3160 FOR I=1 TO 8
3170 IF R(I)<0 OR R(I)>255 OR R(I)<>INT (R(I)) THEN RETURN
3180 NEXT I: LET J=A: LET K=B
3190 IF J>K THEN LET T=J: LET J=K: LET K=T
3200 LET T=2^K: LET I=INT (R(J+1)/T): LET O=1
3210 IF I-2*INT (I/2)<>0 THEN RETURN
3220 LET F=1
3230 IF M=1 THEN LET R(J+1)=R(J+1)+T
3240 RETURN
3500 FOR I=1 TO 8: LET R(I)=0: NEXT I: RETURNM=0 clears all eight rows and returns F=0/O=1 without validating old rows or IDs. It preserves A/B and can repair corrupt cache values. Other invalid calls return F/O=0, preserve IDs and leave every row unchanged. Self-pairs are invalid, as are out-of-range IDs, unsupported modes and non-byte row values.
Only the upper triangle of the conceptual eight-by-eight table is used. Lower-triangle and diagonal bits are left alone by ordinary queries. Clear removes them too. The arithmetic bit test avoids relying on a portable bitwise AND across the three dialects.
Keep the cache for a whole traversal
The normal caller remembers 0,3, presents its reverse, queries it again, then remembers 1,7. Only the first and fourth queries are new. The custom caller first queries an absent pair without remembering it, then remembers it and checks both orientations. It also reports two new results.
Example calls from the maintained caller
90 GO SUB 3000: LET AA=0: LET BB=0
100 LET NN=0
110 LET M=1: LET A=0: LET B=3: GO SUB 3100: GO SUB 2000: LET NN=NN+F
120 LET M=1: LET A=3: LET B=0: GO SUB 3100: GO SUB 2000: LET NN=NN+F
130 IF F=0 THEN LET AA=1
140 LET M=2: LET A=0: LET B=3: GO SUB 3100: GO SUB 2000: LET NN=NN+F
150 LET M=1: LET A=1: LET B=7: GO SUB 3100: GO SUB 2000: LET NN=NN+F
160 IF NN=2 THEN LET BB=1
170 LET M=0: GO SUB 3100: GO SUB 2000
180 LET M=2: LET A=0: LET B=3: GO SUB 3100: GO SUB 2000
190 PRINT "CACH RESULTS";AA;BB
200 POKE MB+995,AA: POKE MB+996,BB: POKE MB+997,GD: POKE MB+998,WC-256*INT (WC/256): POKE MB+999,INT (WC/256): POKE MB+1000,239: STOPA later clear begins a new traversal: a previously seen pair is new again. The saved early checks distinguish correct retention even though clearing can eventually bring different traces back to the same state. AA/BB/NN and JJ/KK (Z/Q on Spectrum), line 2000 and the mailbox belong to that diagnostic.
Decide what first means
Clear once before enumerating a step’s candidates. If M=1 returns F=1, process that candidate; later presentations can be skipped. Decide deliberately whether to mark a pair before geometry testing or only after some other rule. This cache records consideration, not physical overlap, collision response or an enter/leave event.
IDs must retain their meaning throughout the traversal. Recycling an ID halfway through can make a new object inherit an old object’s remembered pair. Stable slots or an explicit generation/epoch policy solve a different part of that problem. Contact history across frames needs retained previous/current contact sets, rather than simply skipping this clear.
Mistake and repair
The wrong caller clears row one before every query. Reversed pairs involving ID zero are repeatedly reported as new, so the saved duplicate and total-first checks both fail. Keep the cache until the traversal ends, then clear deliberately. Repaired source and loaded program match normal exactly.
Cost and Maths for Games
Every query validates eight numeric rows, then computes a bounded bit position and tests one row. A clear visits eight entries. Eight IDs admit twenty-eight distinct non-self unordered pairs; expanding the ID range needs a new storage layout and corresponding bounds, rather than merely accepting larger IDs.
Maths for Games connects unordered sets, canonical ordering and triangular tables. The Craft connects collision bookkeeping to effects that should happen once per intended contact decision.
Global names and line numbers
BASIC numeric names, arrays and numbered lines are global. To combine helpers, rename public and private fields and renumber the helper together with every GO SUB/GO TO reference. Keep each state block under one owner. The maintained build.py rejects duplicate line numbers; it does not automatically namespace or renumber routines.
Machine and measured size
Spectrum FOR variables must be single letters: this diagnostic uses Z/Q instead of the other callers’ JJ/KK. Numeric arrays start at one. AND/OR in these listings join comparisons; neither is being used as a bitwise operator. The diagnostic reserves its mailbox above CLEAR 59999.
The numbered helper occupies 565 tokenised program bytes on this interpreter, including line headers. This excludes the caller, test tables, numeric scalar/array storage, interpreter stacks and ROM. Tokenised size is not machine-code size or a hardware-cycle count. No real-time or whole-game performance budget is inferred from the diagnostic. The caller’s AA/BB/NN, Z/Q and RAM mailbox are observation machinery, not required game state.
Execution evidence
Working, custom, deliberately wrong and exact repaired callers executed through Spectrum’s stock BASIC interpreter under Emu198x 0.44.2. Build198x 0.2.9 tokenises C64 PRG and Spectrum TAP programs. C64 enters stock RUN, Spectrum uses ROM tape loading, and BBC enters every numbered source line through MOS/BASIC. Actual loaded program bytes, complete state packets, positive completion/count/guards and visible result pixels are checked. After the positive completion marker, the observer advances two complete display frames before capturing, so a partially scanned final character cannot masquerade as a finished picture. Firmware is not distributed.
An independent mathematical/order model checks the trace and rejects altered source, configuration, loaded program, state, completion and image evidence. Host exhaustive checks complement the native boundary/sequential examples; those host ranges are not claimed as natively exhaustive. The supplied diagnostic callers deliberately end with STOP; the interpreter report is expected. The wrong caller prints 0,0 and the normal/custom/repaired callers print 1,1.
Public CI checks retained evidence; it does not execute restricted firmware. Refresh with python3 scripts/verify-basic-contacts.py contact-pair-cache sinclair-zx-spectrum --tools /path/to/extracted/releases and inspect with python3 scripts/check-basic-contacts.py contact-pair-cache.
Explore further
Compare the assembly technique. The BASIC game-flow routine makes session boundaries explicit. Complete source and native evidence.