feat(v4.0.0): the Q48.16 words and DUMP at the prompt

- capsule/qmath.v4: Q.FROM-INT Q.TO-INT Q.1 Q.0 Q.SCALE Q.+ Q.- Q.* Q./
  Q.ABS Q.NEG Q.= Q.< Q.> Q.0= Q.MAX Q.MIN Q.EXP Q.SQRT Q.LOG Q.SIN Q.COS
  Q.PRINT -- the definitions test_foundation.c executes on the mesh node,
  now in the host node's vocabulary.
- numout.v4: DUMP.
- Q./ by zero, and Q.SQRT and Q.LOG outside their domain, leave the
  result D-11 and D-12 give and then raise an error (D-18): "Division by
  zero", "Argument out of range".  v3 returns 0 silently.
- tests/test_host_quit.c: 122 results printed by Q.PRINT are transcripts
  of the v3 binary, the same at both cell widths; signed values, the
  errors and DUMP's layout besides.

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

docs/v4.0.0/DECOMPOSITION.md

@@ -179,7 +179,7 @@ definition below depends on one, it says so.
 | **D-15** | Division by zero in `/` `MOD` `/MOD` `*/` `*/MOD` `M/MOD` (ruled 2026-10-04). | **Guarded: the word reports it and the line ends.** Each of these words tests its divisor before anything else. If it is zero the word prints v3's message, its own name and `: Division by zero`, takes its operands off the stack as v3 does, ends any definition that was open, prints ` ERROR` and returns to the prompt, from however deep; its caller is not returned to. `M/MOD` says so too, where v3 printed ` ERROR` alone. Source in `v4/capsule/forth.v4`; executed on the golden model's host node (2026-10-04), including transcripts of the v3 binary. `Q./` keeps D-11 (saturate and flag). `UM/MOD` and `SM/REM` are internal and unguarded: their callers have checked. What a mesh node, with no console, does on a zero divisor comes with the mesh (step 2); §4's definitions, which the mesh-node tests execute, still leave it unspecified. |
 | **D-16** | Stack overflow and underflow; `DEPTH`, `PICK`, `ROLL` (ruled 2026-10-04; revises D-2). | **Guarded: a stack fault.** Each stack counts what it holds. Before every opcode the node checks that the stacks hold what the opcode takes — including a `T` or `S` it only reads — and have room for what it leaves. If not, the opcode does nothing and the node faults exactly as for a bad address (D-14), to that kind's handler: `Stack overflow`, `Stack underflow`, `Return stack overflow`, `Return stack underflow`, then ` ERROR` and the prompt. **Every fault, D-14's included, empties both stacks**: the handler does not return, and what a word stopped part-way has left on the data stack is of no use to its caller. (v3 keeps what the failing word had not taken, and names the word: `DROP: Stack underflow`.) The fault handler is a table of five words, one per kind, each a jump (`(FAULTS)` in `v4/capsule/quit.v4`). Two registers (§7) are all a programme sees of the stacks: `DSTACK-DEPTH` and `RSTACK-DEPTH` read as the depth, and a store to one empties that stack. There is still no stack pointer and no address for a stack cell, so `SP@` and `SP!` stay retired; `.S` waits for number output to reach the capsule. The sizes were unchanged by this ruling, 10 and 9 (D-17 then deepens the host node's): one more value, or one more level of call, is now an error message where it used to be silent corruption. Executed on the golden model (2026-10-04): `tests/test_exec.c` for every opcode at every depth of both stacks, `tests/test_host_quit.c` from the prompt. |
 | **D-17** | Stack sizes on the host node (2026-10-04, following D-16). | **32 values and 32 return entries on the host node; a mesh node keeps the F18's 10 and 9.** Once the stacks are counted (D-16) their size is a parameter of the node, like its memory, and the host node is the one that runs the interpreter and the compiler underneath the user's programme: at 10 and 9 the prompt left a programme about six values, and `/` could be used only four words deep. The mechanism is the same at both sizes — top registers over a ring — and so is every word's definition. v3's stacks are deeper still. In the golden model the sizes are `V4_DATA_RING` and `V4_RET_RING` (`stack.h`), set for the host-node tests in `v4/Makefile`. |
-| **D-18** | Every other error (ruled 2026-10-04: "guard all errors"). | **A word that finds an error raises it, and the line ends there.** The word takes its own arguments off the stack and stores an error code in `NODE-ERROR` (§7). On a node with a prompt that store is a trap, a sixth kind of fault beside D-14's and D-16's: nothing after it executes, the return stack is emptied, and the prompt prints the code's message, ends any definition that was open, prints ` ERROR` and waits for the next line. Unlike the other faults it leaves the data stack as the word left it. The codes: 1 `Negative count` (`CMOVE`, `TYPE`), 2 `Not a number` (`NUMBER`), 3 `Number too long` (`HOLD` into a full buffer), 4 `Not a character` (`HOLD`), 5 `Dictionary full` (`,` `C,` `ALLOT`, any defining word), 6 `Name missing` (a defining word with nothing after it), 7 `Control structure mismatch`, 8 `Control structures too deep`, 9 `Shift count out of range`, 10 `Protected word`; −1 means the word printed its own message (`UNKNOWN WORD: 'xxx'`, `xxx: compile-only`). Before this ruling these set the flag and the line ran on to its end. v3 stops at once too; its messages name the word (`LOOP: missing DO`) where v4's name the fault. With the trap not attached `NODE-ERROR` is plain memory and the word returns, which is how the words are tested below the prompt. D-11, D-12 and D-13 said "set `NODE-ERROR`"; on a node with a prompt that now means this. Executed on the golden model (2026-10-04): `tests/test_exec.c`, `tests/test_host_quit.c`. |
+| **D-18** | Every other error (ruled 2026-10-04: "guard all errors"). | **A word that finds an error raises it, and the line ends there.** The word takes its own arguments off the stack and stores an error code in `NODE-ERROR` (§7). On a node with a prompt that store is a trap, a sixth kind of fault beside D-14's and D-16's: nothing after it executes, the return stack is emptied, and the prompt prints the code's message, ends any definition that was open, prints ` ERROR` and waits for the next line. Unlike the other faults it leaves the data stack as the word left it. The codes: 1 `Negative count` (`CMOVE`, `TYPE`), 2 `Not a number` (`NUMBER`), 3 `Number too long` (`HOLD` into a full buffer), 4 `Not a character` (`HOLD`), 5 `Dictionary full` (`,` `C,` `ALLOT`, any defining word), 6 `Name missing` (a defining word with nothing after it), 7 `Control structure mismatch`, 8 `Control structures too deep`, 9 `Shift count out of range`, 10 `Protected word`, 11 `Division by zero` (`Q./`), 12 `Argument out of range`; −1 means the word printed its own message (`UNKNOWN WORD: 'xxx'`, `xxx: compile-only`). Before this ruling these set the flag and the line ran on to its end. v3 stops at once too; its messages name the word (`LOOP: missing DO`) where v4's name the fault. With the trap not attached `NODE-ERROR` is plain memory and the word returns, which is how the words are tested below the prompt. D-11, D-12 and D-13 said "set `NODE-ERROR`"; on a node with a prompt that now means this. Executed on the golden model (2026-10-04): `tests/test_exec.c`, `tests/test_host_quit.c`. |
 
 **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
@@ -758,7 +758,7 @@ call would bury what it works on. A **compile-only** word may not be executed by
 `v4/capsule/forth.v4` holds the first words of the vocabulary flagged this way (`DUP`, `+`, `>R`, `I`,
 `LEAVE`, `@`, the in-line variables and so on).
 
-**The vocabulary at the prompt.** The host node's capsule is `v4/capsule/`, loaded in this order: `core.v4` (bytes, console, strings the rest rest on), `input.v4`, `dict.v4`, `codegen.v4`, `compile.v4`, `quit.v4` (the prompt, faults and errors), `forth.v4` (stack, arithmetic, division, `DEPTH` `PICK` `ROLL`), `numout.v4` (number output, `.S`), `system.v4` (`WORDS`, `FORGET`) and `words.v4` (the stack, comparison, shift, double, mixed and string words of §5.1–5.9: `2SWAP 2OVER 2ROT 2>R 2R> 2R@ 2@ 2! -! 0<> 0> <> <= >= U< U> ABS MAX MIN WITHIN LSHIFT RSHIFT D- DABS D0= D0< D= D2* D2/ D< DMAX DMIN M+ M- CMOVE> MOVE FILL ERASE BLANK -TRAILING COMPARE SEARCH SCAN SKIP ?TERMINAL TRUE FALSE INVERT NOP`). Each is the definition this document gives; `tests/test_host_quit.c` runs them from the prompt against transcripts of the v3 binary. As v3, `LSHIFT` and `RSHIFT` with a count that is negative or as large as the cell is wide are an error (D-18, code 9, `Shift count out of range`). `M+`, like `M-` and `M/MOD`, takes its double in the standard order, low cell first; v3 takes it low cell on top.
+**The vocabulary at the prompt.** The host node's capsule is `v4/capsule/`, loaded in this order: `core.v4` (bytes, console, strings the rest rest on), `input.v4`, `dict.v4`, `codegen.v4`, `compile.v4`, `quit.v4` (the prompt, faults and errors), `forth.v4` (stack, arithmetic, division, `DEPTH` `PICK` `ROLL`), `numout.v4` (number output, `.S`), `system.v4` (`WORDS`, `FORGET`), `qmath.v4` (the Q48.16 words of §5.26: `Q.FROM-INT Q.TO-INT Q.1 Q.0 Q.SCALE Q.+ Q.- Q.* Q./ Q.ABS Q.NEG Q.= Q.< Q.> Q.0= Q.MAX Q.MIN Q.EXP Q.SQRT Q.LOG Q.SIN Q.COS Q.PRINT`; `DUMP` is in `numout.v4`) and `words.v4` (the stack, comparison, shift, double, mixed and string words of §5.1–5.9: `2SWAP 2OVER 2ROT 2>R 2R> 2R@ 2@ 2! -! 0<> 0> <> <= >= U< U> ABS MAX MIN WITHIN LSHIFT RSHIFT D- DABS D0= D0< D= D2* D2/ D< DMAX DMIN M+ M- CMOVE> MOVE FILL ERASE BLANK -TRAILING COMPARE SEARCH SCAN SKIP ?TERMINAL TRUE FALSE INVERT NOP`). Each is the definition this document gives; `tests/test_host_quit.c` runs them from the prompt against transcripts of the v3 binary. From the prompt, 122 results of the Q words printed by `Q.PRINT` — which shows all sixteen bits of a fraction — are digit for digit v3's, at both cell widths. Under D-18, `Q./` by zero and `Q.SQRT` and `Q.LOG` outside their domain leave the result D-11 and D-12 give and then raise an error (codes 11 `Division by zero` and 12 `Argument out of range`); v3 returns 0 and says nothing. As v3, `LSHIFT` and `RSHIFT` with a count that is negative or as large as the cell is wide are an error (D-18, code 9, `Shift count out of range`). `M+`, like `M-` and `M/MOD`, takes its double in the standard order, low cell first; v3 takes it low cell on top.
 
 **The stacks and the compiler.** The interpreter and compiler run on the same stacks as the user's
 words, with the user's values beneath them. The capsule was written for stacks of ten cells and nine