SM/REM as written in section 4 never returned correctly for a negative
dividend. It holds three entries on the return stack and then calls
DABS -> DNEGATE -> D+ -> U> -> SWAP/U<, which overflows the 9-deep
circular return stack (D-2). DABS itself could not run: DNEGATE as
written (inv SWAP inv SWAP 1 0 D+) left its caller no return entries.
- DNEGATE: inv over if L1 drop push inv 1 + pop ; L1: drop 1 + ;
i.e. ~d + 1, carrying into the high cell exactly when lo = 0.
- SM/REM: sign tests are native -if (as in 0<) and NEGATE is in line;
the only calls are DNEGATE and UM/MOD, both call-free inside.
Executed on the golden model at 32- and 64-bit cells, optimised and
under ASan+UBSan:
- SM/REM on dividends built as q*n + r with |r| < |n| and r signed as
d: every edge-vector q, n with r = 0 and r = +-(|n|-1), plus 20000
pseudo-random cases.
- /MOD, U>, ABS, S>D, D+ and DABS as written in section 5, against C
(D+ over all 50625 edge-vector quadruples).
Mutations of DNEGATE's carry and of each SM/REM sign branch are caught.
Headroom (data cells under args / return entries under return address):
SM/REM 5/3, /MOD 5/2, DNEGATE 7/7, DABS 7/6, ABS 8/7, U> 6/5.
D+ as written is exact but leaves only 1 return entry; recorded in
DECOMPOSITION.md 5.7 as not yet revised.
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
