feat(v4.0.0): Q.* from four UM* cell products
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>
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@@ -147,7 +147,7 @@ IF body1 ELSE body2 THEN → if L1 drop body1 jump L2
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times, as on the F18. `FOR ... UNEXT` is the same but the body must fit in one instruction word.
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**Register conventions.** `A` and `B` are caller-saved. A word that uses them says so. Words in this
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document that clobber `A`: `@ ! +! -! 2@ 2! C@ C! UM* * UM/MOD Q.FROM-INT Q.TO-INT SEND RECV`. Words that clobber `B`:
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document that clobber `A`: `@ ! +! -! 2@ 2! C@ C! UM* * UM/MOD Q.FROM-INT Q.TO-INT Q.* SEND RECV`. Words that clobber `B`:
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`SEND RECV`.
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**Return-stack words** (`>R R> R@ 2>R 2R> 2R@ I J UNLOOP` and the loop runtimes) are always IN.
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@@ -647,7 +647,7 @@ word. Per D-10 it occupies two cells on a 64-bit node too. Per D-8, v4 Q values
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| Word | Fate | Notes |
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| --- | --- | --- |
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| `Q.+` `Q.-` | CAP | `D+`, `D-` — executed on the golden model (2026-10-02) against v3's `q48_add`/`q48_sub` (`uint64_t` wrapping): bit-for-bit at 32-bit cells; at 64-bit cells the low cell is v3's, per D-10. |
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| `Q.*` | CAP | 64×64 product from four `UM*` partial products, shifted right 16. |
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| `Q.*` | CAP | `2OVER drop over 0< over and push over UM* pop - push push push over pop UM* drop pop pop push SWAP pop + push push over 0< over and pop pop push SWAP pop SWAP - push push over over UM* pop pop D+ push push push drop pop UM* 0 pop pop D+ push dup push Q.TO-INT pop pop Q.TO-INT` — `floor(a*b / 2^16)`, signed (D-8), cut to two cells. Cells 0–2 of the product come from the four unsigned cell products `a0*b0`, `a0*b1`, `a1*b0`, `a1*b1` (low cell only); 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. Executed on the golden model (2026-10-02) against an independent limb-by-limb reference, and against v3's `q48_mul` for non-negative operands. **Stack use is tight:** it leaves its caller 2 data cells under its arguments and 1 return entry, because `UM*` itself parks three values on the return stack; to be improved. Clobbers `A`. |
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| `Q./` | CAP | Shifted long division. **Division by zero sets an error** (v3 returned 0 silently). |
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| `Q.ABS` `Q.NEG` | CAP | `DABS`, `DNEGATE` — executed on the golden model (2026-10-02) against v3's `q48_abs` and `0 - q`: bit-for-bit at 32-bit cells, including v3's wrap of Q min to itself; at 64-bit cells the low cell is v3's and the high cell is the true sign, per D-10. |
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| `Q.LOG` `Q.EXP` `Q.SQRT` `Q.SIN` `Q.COS` | CAP | Algorithms ported from `q48_words.c`; the hosted C versions are the golden model. |
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