Q.* is floor(a*b / 2^16), signed (D-8), cut to two cells. Cells 0..2 of
the product come from the unsigned cell products a0*b0, a0*b1, a1*b0 and
the low cell of a1*b1; reading a1 and b1 as signed takes
(a1<0 ? b0 : 0) + (b1<0 ? a0 : 0) off cell 2. The result is cells 0..2
shifted right 16 with Q.TO-INT twice. Clobbers A.
Checked at 32- and 64-bit cells, optimised and ASan+UBSan, on every pair
of 17 edge Q values plus 20000 pseudo-random pairs:
- against an independent reference (16-bit limbs, magnitudes multiplied
schoolbook, negated, shifted), and
- against v3's q48_mul for non-negative operands.
The first draft applied only a1's sign correction; the reference caught
the missing b1 term (9860 failures at 32-bit cells).
v3 bug found, not fixed: q48_mul's portable branch (used where there is
no __int128) returns (result_hi << 16) | (result_lo >> 16); the high
part must move up 48, so it is wrong whenever the product passes bit
64, e.g. 0.5 * Q max gives 0000ffffffffffff instead of 3fffffffffffffff.
The parity reference here is that branch with the shift corrected,
which matches v3's __int128 branch.
Stack use is tight: Q.* leaves its caller 2 data cells and 1 return
entry, because UM* parks three values on the return stack. Recorded in
5.26; to be improved next.
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
