UM* as first written in DECOMPOSITION.md section 4 was exact only while
u1 <= 2^(n-2): plain +* loses the carry out of T and its shift keeps T's
sign bit, so the loop is exact only while S and T stay in
[-2^(n-2), 2^(n-2)).
The rewrite multiplies by s = u1 2/, which always lies in that range,
starting T at t0 = u2 2/ when u1 is odd, so the loop yields
hi:lo = t0 + s*u2 exactly. Then
u1*u2 = 2*(hi:lo) + c_lo + c_hi*2^n
c_lo = u1 & u2 & 1
c_hi = (u1<0 ? u2 : 0) + (u1 odd and u2<0 ? 1 : 0)
restores the halved-away bits and the unsigned reading of both top bits.
test_foundation.c runs the new definition against v4_umul over every
pair of the edge vectors plus 20000 pseudo-random pairs, at 32- and
64-bit cells, optimised and under ASan+UBSan. The two pinned failing
cases are now ordinary exactness checks. Two hand mutations of the
correction step each fail more than 10000 checks at both widths.
DECOMPOSITION.md: section 4 UM* replaced, D-3 ruling text updated.
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
First code for StarForth v4 (JUSTIFICATION.md section 10, step 1): one node
of the 32-instruction core as a C99 model, with cell width as a build
parameter.
- Node: P, A, B, F18 circular stacks (10 and 9 deep, D-2), word-addressed
memory (D-1), 5% guard bands on every bounded list.
- Instruction word: six 5-bit slots in 32 bits at every cell width.
- Executor: all 32 opcodes of DECOMPOSITION.md 1.3. Cell arithmetic wraps
explicitly; no signed overflow or implementation-defined shift.
- Heat: per-opcode and per-call-target counters and the anti-clock, driven
by instruction retirement (1.4, D-6 interim).
- Slot packer and runner for tests, and a reference unsigned multiply in
plain C99 with no 128-bit type.
Tests run at 32- and 64-bit cells, and under ASan and UBSan. They cover
every opcode and execute the first section 4 definitions (NIP SWAP OR
NEGATE ROT 0< 0= 2DUP - U<) against the C operation each stands for.
UM* as written in section 4 is exact only while u1 <= 2^(n-2). Two known
failing cases are pinned in test_foundation.c until it is rewritten.
DECOMPOSITION.md: record D-9, the instruction word is 32 bits at every
cell width (ruled 2026-10-02).
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
