feat(v4.0.0): Q./ under D-11, with (UQ/), D2*C and the (Q/) variable

D-11 (ruled 2026-10-02): Q./ rounds toward zero, saturates to Q max /
Q min on overflow, and on division by zero returns Q max / Q min by the
dividend's sign (0 for 0/0) and sets the new NODE-ERROR register (7),
which VM-ERROR? reads.

- (UQ/): unsigned floor(a * 2^16 / b) for b != 0 and no overflow.
  Restoring division, 2N+16 steps, on one shifting register (quotient
  above remainder). Quotient register and divisor live in a 5-cell
  variable (Q/), like BASE and the hold buffer, so the stacks carry only
  the remainder, the quotient bit and the loop count. A first version
  kept the divisor on the return stack and overflowed it when called
  from Q./ (it never returned).
- D2*C: double shift left with carry in and out.
- Q./: zero-divisor handling, signs (kept in (Q/)), an overflow test
  that needs no division (|a| * 2^16 >= |b| * 2^(2N-1), possible only
  for |b| < 2^17), then (UQ/) and the sign.

Checked at 32- and 64-bit cells, optimised and ASan+UBSan, against an
independent limb-by-limb long division (including NODE-ERROR): every
pair of 18 edge Q values, 13 width-native edge values (true Q max/min at
either width), the overflow boundary, divisors in [2^(2N-2), 2^(2N-1)),
and pseudo-random cases; and against v3's q48_div for non-negative
a < 2^48. Q.* now also runs on the width-native edge values.
Mutations of the compare paths, the take path, the error flag and the
overflow mask are all caught (the mask matters only for Q min / -1.0).

Headroom (data under args / return): Q./ 3/2.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

This commit is contained in:

rajames

2026-10-03 00:17:11 -04:00

co-authored by

Claude Opus 5.5

parent 8f37e15f8a

commit 9e03bdab19

2 changed files with 475 additions and 5 deletions

v4/tests/test_foundation.c

+467 -2

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