feat(v4.0.0): Q.FROM-INT and Q.TO-INT as +* double shifts
DECOMPOSITION.md 5.26 described both words in prose only. They are now
written out, call-free, on one observation: +* with S = 0 never adds, so
each step is an exact arithmetic right shift of the double T:A.
: Q.FROM-INT ( n -- q ) push 0 a! 0 pop 15 FOR +* UNEXT push drop a pop ;
T:A = n:0 is n * 2^N; N-16 shifts leave n * 2^16 (count 15 at
32-bit cells, 47 at 64).
: Q.TO-INT ( q -- n ) push a! 0 pop 15 FOR +* UNEXT drop drop a ;
16 shifts at every width; the low cell is left in A. Rounds toward
minus infinity, as v3's arithmetic shift does.
Both clobber A; added to the section 2 list.
Checked at 32- and 64-bit cells, optimised and ASan+UBSan:
- Q.FROM-INT against n * 2^16 for edge values and 20000 pseudo-random n,
and against v3's q48_from_u64 for n >= 0 (low cell at 64-bit, D-10).
- Q.TO-INT against v3's (int64_t)q >> 16 on the edge Q values and 20000
pseudo-random Q values, and against a C double shift on 20000
arbitrary doubles.
- Round trip Q.TO-INT(Q.FROM-INT(n)) = n.
Mutating either shift count or the S = 0 setup fails 40000+ checks.
Note: make sanitize prints UBSan reports but does not fail on them. One
was found here, in the test's own random shift amount (fixed); a grep of
the full sanitize output now shows no runtime errors.
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
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co-authored by
Claude Opus 5.5
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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 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 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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@@ -650,8 +650,8 @@ word. Per D-10 it occupies two cells on a 64-bit node too. Per D-8, v4 Q values
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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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| `Q.FROM-INT` | CAP | `S>D` shifted left 16. Negative values are no longer clamped to 0. |
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| `Q.TO-INT` | CAP | Shift right 16, take the low cell. |
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| `Q.FROM-INT` | CAP | `push 0 a! 0 pop 15 FOR +* UNEXT push drop a pop` — `n * 2^16` as a signed double. `+*` with `S = 0` never adds, so each step is an exact arithmetic right shift of `T:A`; starting from `T:A = n:0` (that is, `n * 2^N`) and shifting `N-16` bits leaves `n * 2^16`. The count is `N-17`: 15 at 32-bit cells, 47 at 64. Negative values are no longer clamped to 0. Executed on the golden model (2026-10-02): matches v3's `q48_from_u64` for `n >= 0` (at 64-bit cells in the low cell, where v3 wraps for `n >= 2^47`, per D-10). Clobbers `A`. |
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| `Q.TO-INT` | CAP | `push a! 0 pop 15 FOR +* UNEXT drop drop a` — the same `+*` shift, 16 bits at every cell width, leaving the low cell in `A`. Rounds toward minus infinity, as v3's arithmetic shift does (−1.5 gives −2). Executed on the golden model (2026-10-02): v3's `q48_to_u64` exactly at 64-bit cells, its low cell at 32. Clobbers `A`. |
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| `Q.1` `Q.0` `Q.SCALE` | IN | Double-cell constants. |
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| `Q.=` `Q.<` `Q.>` `Q.0=` `Q.MAX` `Q.MIN` | CAP | `D=`, `D<`, `SWAP D<` (for `Q.>`), `D0=`, `DMAX`, `DMIN`. Signed. |
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| `Q.PRINT` | CAP | Pictured output, five fractional digits. |
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