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

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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
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docs/v4.0.0/DECOMPOSITION.md
+8 -3
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@@ -147,8 +147,8 @@ IF body1 ELSE body2 THEN → if L1 drop body1 jump L2
times, as on the F18. `FOR ... UNEXT` is the same but the body must fit in one instruction word.
**Register conventions.** `A` and `B` are caller-saved. A word that uses them says so. Words in this
document that clobber `A`: `@ ! +! -! 2@ 2! C@ C! UM* * UM/MOD Q.FROM-INT Q.TO-INT Q.* SEND RECV`. Words that clobber `B`:
`SEND RECV`.
document that clobber `A`: `@ ! +! -! 2@ 2! C@ C! UM* * UM/MOD Q.FROM-INT Q.TO-INT Q.* Q./ SEND RECV`. Words that clobber `B`:
`Q./ SEND RECV`.
**Return-stack words** (`>R R> R@ 2>R 2R> 2R@ I J UNLOOP` and the loop runtimes) are always IN.
@@ -172,6 +172,7 @@ definition below depends on one, it says so.
| **D-8** | Q48.16 signedness. | **Signed.** v3's unsigned comparisons and `Q.FROM-INT` clamping are retired. |
| **D-9** | Instruction word width on a 64-bit-cell host (ruled 2026-10-02). | **32 bits at every cell width.** Six 5-bit slots plus 2 spare bits, as in §1.2. On a 64-bit host the instruction word is the low 32 bits of the cell and the high half is ignored, so compiled code is identical at both widths. Only data and `@p` literals are a full cell wide. |
| **D-10** | Q48.16 width on a 64-bit-cell node (ruled 2026-10-02). | **Two cells at every cell width.** A Q value is a signed double on 32- and 64-bit nodes alike, so every Q word is the same double word at both widths. At 32-bit cells this is bit-for-bit v3's 64-bit Q. At 64-bit cells the low cell is v3's value, and where v3 wraps on Q48.16 overflow (a sum past Q max, `ABS` or `NEG` of Q min) the high cell carries the true result instead. |
| **D-11** | `Q./` semantics: division by zero, rounding, overflow (ruled 2026-10-02). | **Saturate and flag; round toward zero; saturate on overflow.** The quotient of `a * 2^16 / b` is rounded toward zero, like `SM/REM`. When it does not fit a Q value it is clamped to Q max or Q min by its sign. Division by zero returns Q max or Q min by the sign of the dividend (`0 / 0` gives 0) and sets the node's `NODE-ERROR` register (§7), which `VM-ERROR?` reads. v3 returned 0 on division by zero and saturated whenever the dividend was 2^48 or more, even when the quotient would have fit. |
**Consequences of D-2 that every definition must respect.** The data stack holds 10 items and the
return stack 9, and every `call`, `FOR`, `DO` loop frame and `push` uses return-stack slots. Nesting
@@ -657,7 +658,10 @@ word. Per D-10 it occupies two cells on a 64-bit node too. Per D-8, v4 Q values
| --- | --- | --- |
| `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. |
| `Q.*` | CAP | `SWAP push over over UM* drop push push over pop -if L1 SWAP jump L2 L1: SWAP drop 0 L2: pop SWAP - push push over pop UM* pop + ROT pop dup push over -if L3 drop dup jump L4 L3: drop 0 L4: push UM* pop - D+ ROT pop UM* SWAP push 0 D+ pop push over pop SWAP Q.TO-INT push Q.TO-INT pop SWAP` (`SWAP` and `ROT` in line) — `floor(a*b / 2^16)`, signed (D-8), cut to two cells. Cells 0–2 of the product come from the unsigned cell products `a1*b1` (low cell), `a0*b1`, `a1*b0`, `a0*b0`, in that order, each input dropped after its last use and `b0` waiting on the return stack. Reading `a1` and `b1` as signed takes `(b1<0 ? a0 : 0)` and `(a1<0 ? b0 : 0)` off cell 2; each is folded in as soon as its operands are adjacent. 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. Leaves its caller 3 data cells under its arguments and 3 return entries. Clobbers `A`. |
| `Q./` | CAP | Shifted long division. **Division by zero sets an error** (v3 returned 0 silently). |
| `Q./` | CAP | `over over OR if ZERO drop push over pop SWAP over xor (Q/) 4 + b! !b -if L1 DNEGATE L1: push push -if L2 DNEGATE L2: pop pop dup if CHK drop jump DIV CHK: drop over -131072 and if CHK2 drop jump DIV CHK2: drop push push dup pop dup push N-18 FOR 2* UNEXT over over xor -if SAME drop drop -if NOOV jump OV SAME: drop push inv pop + inv -if OV NOOV: drop pop pop jump DIV OV: drop drop drop pop pop drop drop (Q/) 4 + b! @b -if OVP drop 0 MSB ; OVP: drop -1 MAXHI ; DIV: (UQ/) (Q/) 4 + b! @b -if L3 drop DNEGATE ; L3: drop ; ZERO: drop drop drop NODE-ERROR b! -1 !b over over OR if Z0 drop -if ZP drop drop 0 MSB ; ZP: drop drop -1 MAXHI ; Z0: drop ;` — D-11: `a * 2^16 / b`, rounded toward zero; saturated to Q max / Q min on overflow; on division by zero, Q max / Q min by the dividend's sign (0 for `0 / 0`) and `NODE-ERROR` set. The sign of the result waits in `(Q/)`. Overflow needs no division: the quotient reaches `2^(2N-1)` exactly when `|a| * 2^16 >= |b| * 2^(2N-1)`, possible only for `|b| < 2^17`, where it is `a1 >= b0 << (N-17)` unsigned. `MSB` and `MAXHI` are the high cells of Q min and Q max. Executed on the golden model (2026-10-02) against an independent limb-by-limb reference (including `NODE-ERROR`), on width-native edge values, and against v3's `q48_div` for non-negative `a < 2^48`. Leaves its caller 3 data cells under its arguments and 2 return entries. Clobbers `A` and `B`. |
| `(UQ/)` | CAP | Internal to `Q./`: unsigned `floor(a * 2^16 / b)` for `b != 0` and no overflow. Restoring division, `2N+16` steps, on one shifting register — quotient (starting as `a`) above remainder — with the quotient and divisor in `(Q/)` so the stacks carry only the remainder, the quotient bit and the loop count. Each step's quotient bit enters at the next step's shift; with no overflow the bits leaving the quotient in the last 16 steps are zeros. Trial subtraction by in-line sign tests (`x - y` with `y` on top is `push inv pop + inv`). Executed on the golden model (2026-10-02). Clobbers `A` and `B`. |
| `D2*C` | CAP | `( lo hi cin -- lo' hi' cout )`: the double shifted left one bit, `cin` entering at the bottom and `cout` the bit leaving the top (both 0 or 1). `ROT dup -if L1 drop 1 jump L2 L1: drop 0 L2: push 2* + SWAP dup -if L3 drop 1 jump L4 L3: drop 0 L4: push 2* pop pop ROT + SWAP`, `ROT` and `SWAP` in line. Executed on the golden model (2026-10-02). |
| `(Q/)` | CAP | Variable, 5 cells: `Q./`'s quotient register, divisor and result sign. Like `BASE` and the hold buffer, it lives in node memory. |
| `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. |
| `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. |
| `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`. |
@@ -765,3 +769,4 @@ Addresses are assigned in the node memory map (D-4). Names only here.
| `GOV-*` | R/W | Governor parameters and Jacquard selector state (`L8-*`, decay rate). |
| `REC-ENABLE` | R/W | DoE recorder on/off (`HB-ON` / `HB-OFF`). |
| `PORT-STATUS` | R | Per-port ready flags, for non-blocking polls. |
| `NODE-ERROR` | R/W | Arithmetic error flag: set to −1 by `Q./` on division by zero (D-11), cleared by writing 0. `VM-ERROR?` reads it. |