tally/.kiro/specs/calculator/design.md

# Design: Tally - Cross-Platform Calculator

## References

- #[[file:.kiro/specs/calculator/requirements.md]]

---

## 1. System Architecture

```
+-------------------------------------------------------------+
|                        Frontends                            |
+-------------+------------------+----------------------------+
|   CLI       |      TUI         |        Android             |
|  (Zig)      |  (Zig+libvaxis)  |   (Kotlin/Compose)         |
+------+------+--------+---------+------------+---------------+
       |               |                      |
       |  Zig import   |  Zig import          |  JNI (C ABI, not built yet)
       |               |                      |
+------v---------------v----------------------v---------------+
|                     Engine (Zig library)                    |
+-------------------------------------------------------------+
|  Parser.zig  |  evaluator.zig  |  programmer.zig  units.zig |
|  tokenizer   |  financial.zig  |  bitwise.zig   float_interp|
|  ast.zig     |  number/Rational/Integer         grouping.zig|
|  struct_layout.zig  CStructParser.zig                       |
+-------------------------------------------------------------+
```

The engine is a pure Zig library with no I/O. Frontends depend on the engine; the
engine depends on nothing outside `std`. The CLI and TUI ship today; the Android
column is a plan, and `c_api.zig` is the seam it will use (section 6).

### Build Graph

One `build.zig` at the workspace root. The per-frontend build files this section
used to describe (`engine/build.zig`, `cli/build.zig`, `tui/build.zig`) were never
written: the engine is one import the two frontends share, and splitting the build
would buy nothing.

```
build.zig
|- import "engine"     <- engine/src/engine.zig, shared by both frontends
|- exe "tally"         <- src/main.zig (CLI + TUI in one binary)
|- lib "tally"         <- static and shared libraries from engine/src/engine.zig
|- step "test"         <- three test binaries: engine, CLI, TUI
|- step "coverage"     <- kcov over the same three, one report each
                          (build/Coverage.zig, kcov downloaded on first use)
|- step "run"          <- runs the binary
```

**Build system philosophy:**
- `zig build` is the single entry point for all compilation. No Makefile, no CMake, no shell scripts.
- `zig build` (no args) -> builds the engine libraries and the `tally` binary for the host.
- `zig build test` -> runs every test in the three trees.
- `zig build coverage -Dcoverage-threshold=N` -> the same tests under kcov, failing below the threshold.
- Android cross-compilation (`-Dtarget=aarch64-linux-android`) is not wired up yet. When it is, the `android/` Gradle project will handle only APK packaging and Compose UI compilation; it will not invoke Zig.

**Toolchain management (mise):**
- `.mise.toml` at project root declares: Zig version, any other needed tools.
- `mise install` provisions the full dev environment. No other manual setup required.
- CI uses the same `.mise.toml` for reproducibility.

**Toolchain management (mise):**
- `.mise.toml` at project root declares: Zig version, any other needed tools.
- `mise install` provisions the full dev environment. No other manual setup required.
- CI uses the same `.mise.toml` for reproducibility.

---

## 2. Engine Design

### 2.1 File Breakdown

| File | Responsibility |
|--------|---------------|
| `grouping.zig` | The thousands rule, shared by both display paths |
| `Integer.zig` | A fixed-width integer (file-as-struct): `raw`, `width`, `signedness`, the interpretations, and the notations it renders in |
| `Rational.zig` | Exact rationals over big integers (file-as-struct) |
| `number.zig` | The exact/inexact numeric model (section 2.7), including how a value renders itself at a budget the caller supplies. Lowercase: `Number` is a tagged union, which a file-as-struct cannot express |
| `tokenizer.zig` | Lexer, and `Base` for literals |
| `ast.zig` | AST node definitions |
| `Parser.zig` | Pratt parser -> AST (file-as-struct) |
| `evaluator.zig` | Walk AST, produce results |
| `bitwise.zig` | The fixed-width operators (`& \| xor ~ << >> >>> rol ror`), shared by both modes |
| `programmer.zig` | Programmer-mode evaluation, its `Config`, wrapping arithmetic |
| `float_interp.zig` | IEEE 754 bit-level interpretation |
| `units.zig` | Unit conversion tables and resolver |
| `financial.zig` | CAGR, TVM, compound interest, amortization, and money display (cents are a property of money, not of a screen) |
| `struct_layout.zig` | Struct layout (section 3): the ABI profiles as data, a language-neutral `Definition`, and `compute`. Knows no syntax |
| `CStructParser.zig` | Reads a C struct definition into a `struct_layout.Definition` (file-as-struct, like `Parser.zig`), with its own lexer and positioned diagnostics |
| `message.zig` | Gone: the wording lives in `engine.zig` beside the `Error` union it words |
| `engine.zig` | Public API surface (Zig-native): the nine files a frontend imports, nine name aliases, the derived `Error` union, and `phrase` |
| `c_api.zig` | `extern "C"` seam for JNI/FFI consumers. Two of its three exports are stubs; see section 6 |

Every file declares its own error set; there is no shared one (section 10).

There is deliberately no `types.zig` and no `errors.zig`. `types.zig` existed, and
being named after a language feature rather than a concept, it accumulated four
unrelated groups: the error vocabulary, the fixed-width integer model, `Base` (used
only by the lexer and the AST), and `Mode` (which the engine stored and never read).
`errors.zig` was where the error vocabulary landed, until the same question showed that
what needed splitting was the type inside it. Each piece has gone to the file that
owns it.

A file is named TitleCase when the file *is* the type, with its fields at container
level: `Integer.zig`, `Rational.zig` and `Parser.zig`. `number.zig` stays lowercase
because `Number` is a tagged union and a Zig file is always a struct, so the file
cannot be that type without wrapping the union in a field, which would add a hop at
every use of the tag that is the type's whole identity. `tokenizer.zig` stays
lowercase for a different reason: `Base`, `TokenKind` and `Token` are the lexer's
vocabulary rather than parts of `Tokenizer`, and `Base` in particular is used by the
AST and both evaluators without a tokenizer anywhere in sight.

### 2.2 Core Data Types

The result of every calculation is a `Number`: two tiers, one type (section 2.7).

```zig
/// number.zig
pub const Number = union(enum) {
    exact: Rational,
    inexact: f64,
};

/// Integer.zig, the fixed-width value programmer mode computes on. The file IS the
/// type, so these are container-level fields.
raw: u128,                      // two's complement bit pattern, may carry bits above the width
width: BitWidth = .bits64,
signedness: Signedness = .signed,

pub const BitWidth = enum(u8) { bits8 = 8, bits16 = 16, bits32 = 32, bits64 = 64, bits128 = 128 };
pub const Signedness = enum { signed, unsigned };
```

An earlier version of this section described a `Value` union with `integer`, `float`,
`boolean`, `struct_layout` and `multi_base` members, and a `MultiBaseResult` carrying
five preformatted strings and a `[64]u1` bit array. None of it was built, and the
reasons are worth keeping:

- **`Value` was never the result type.** The exact tier needs one type that can be
  either exact or inexact and can move between the two, which is what `Number` is. A
  union with a `boolean` member also promised comparisons the language does not have.
- **`MultiBaseResult` was a frontend's job.** A result does not need to carry five
  renderings of itself: `Integer.fmt(.hex, .{})` renders on demand, at the width and
  byte order the caller asks for, and the bit grid reads the bits it needs from `raw`.
  Precomputing all five meant deciding separator style and grouping inside the engine,
  which is exactly the decision NFR-9.9 puts in the frontend.
- **`raw` is a `u128`, not a `u64`.** 128-bit width is supported, so the pattern needs
  the width to match; `bit_width` is spelled `width` because the file is already
  `Integer`.

### 2.3 AST Nodes

The shape as implemented (`engine/src/ast.zig`); the earlier sketch here omitted
the `text` field, which the whole exact tier depends on.

```zig
pub const Expr = union(enum) {
    number: Number,
    string_literal: []const u8,   // ASCII bytes to pack, quotes stripped
    unary: Unary,
    binary: Binary,
    call: Call,
    variable: []const u8,
    assignment: Assignment,
};

pub const Number = struct {
    base: Base,
    /// The literal exactly as written, pointing into the source. The only
    /// representation kept, because it is the only lossless one: each reader parses
    /// it at the precision it works in (`Number.parse` for the exact tier,
    /// `Base.parseDigits` for a fixed-width pattern). This node used to carry an
    /// `f64` and a `?u64` computed up front, which capped a literal at 128
    /// characters and 64 bits; see Task 5.18.
    text: []const u8,
};

pub const Base = enum {
    decimal,
    hex,
    octal,
    binary,
    /// The literal's digits as a value, separators skipped, `Overflow` past u128.
    pub fn parseDigits(self: Base, text: []const u8) error{Overflow}!u128 { ... }
};

pub const Binary = struct {
    op: BinaryOp,
    left: *Expr,
    right: *Expr,
};

pub const BinaryOp = enum {
    add, sub, mul, div, mod, pow,
    bit_and, bit_or, bit_xor, shift_left,
    shift_right, shift_right_logical,
    rotate_left, rotate_right,
};
```

Ownership: nodes are allocated individually and the caller releases the tree with
`parser.freeExpr`. Passing an arena and skipping the walk is allowed, but nothing
assumes it (see `ast.zig` for why that distinction matters).

**Size limits.** `Parser.max_nodes` (1000) and `Parser.max_nest_depth` (128) bound
the tree, because every walk over it recurses. A flat chain like `1+1+1+...` builds
a left-deep tree whose depth is the operator count, and 4000 terms segfaulted
`evalExact` before the limit existed. Exceeding either reports
`ExpressionTooLarge` or `NestingTooDeep`, so the message says which.

### 2.4 Parser Design

**Approach: Pratt parser (top-down operator precedence)**

Precedence table (low -> high):

| Level | Operators |
|-------|-----------|
| 1 | `\|` (OR), `or` |
| 2 | `xor` (XOR keyword) |
| 3 | `&` (AND), `and` |
| 4 | `<<`, `>>`, `>>>`, `rol`, `ror` |
| 5 | `+`, `-` |
| 6 | `*`, `/`, `%` |
| 7 | `^`, `**` (exponentiation, always) |
| 8 | Unary `-`, `~` (NOT), `not` |
| 9 | Function calls, parentheses |

**`^` is always exponentiation.** There is no mode-dependent operator
overloading. XOR is a keyword (`xor`), consistent with the existing
`rol`/`ror` keyword operators. Bitwise ops have both symbolic and
keyword forms: `&`/`and`, `|`/`or`, `~`/`not`. XOR is keyword-only
(`xor`) since `^` is reserved for power. Every operator means the same
thing in standard and programmer modes.

**The table above is one declaration in the code.** `parser.infix_table` lists each
infix operator once as `{ trigger, op, prec, assoc }`, where the trigger is either a
token kind or a keyword's text. It replaced four switches that had to agree pairwise
plus an inline special case for right-associativity; see Task 5.19. Both spellings of
power associate to the right (`2^3^2` is `2^(3^2)`), everything else to the left.

**Assignment is a statement, not an operator.** `name = expr` is recognised at the top
of an input, not in prefix position, so it cannot appear where an operand can. It has
a precedence level in the table above for documentation only: nothing returns it.

**One implementation of the fixed-width operators.** `bitwise.zig` implements the
eight fixed-width binary operators plus `~` and two's complement negation, over
`Integer` values that carry their own width and signedness. There is no separate
domain parameter: an operand is a pattern and the type to read it as, together, so an
operation cannot be handed a pattern from one width and a type from another. Standard
mode uses the `Integer` default, 64-bit signed and not configurable (FR-2.3);
programmer mode uses its configured width and signedness. `apply` asserts both
operands are the same type and returns a value of the left operand's type.

The operators this tier owns are named by `bitwise.Op`, a narrower enum than
`ast.BinaryOp`, with `fromBinaryOp` mapping between them and returning null for the
arithmetic operators, which are rational in standard mode and wrapping in programmer
mode and so have nothing to share. Both callers dispatch through an `inline else`
prong that resolves the operator at comptime, so an operator added to `BinaryOp` that
belongs in this tier fails to compile rather than falling through to the rational
tier. FR-2.13 covers the distance rules: shifts run to completion, rotations are
cyclic, negative distances are domain errors.

**No implicit multiplication**: adjacency (e.g. `2pi`) is an error;
use explicit `*`. Spaces within hex/oct/bin literals are separators
(e.g. `0xFF FF`).

**Parsing does not depend on the mode.** `Tokenizer.init(source)` and
`Parser.init(allocator, source)` take no `Mode`: the same text produces the same
tree in standard and programmer mode, and only evaluation differs. Both used to
accept and store a `Mode` that no code read, which implied a mode-dependent grammar
that does not exist.

### 2.5 Evaluation

The evaluator maintains an `Environment`:

```zig
pub const Environment = struct {
    allocator: Allocator,
    /// Variables hold `Number`, so an assignment keeps whatever exactness its
    /// expression had: `X = 0.1` stores exactly one tenth.
    variables: std.StringHashMap(Number),
    ans: Number,
};
```

It holds no mode and no programmer configuration. It used to hold both and read
neither: the caller picks `evalString` or `evalProgrammerString`, so which evaluator
runs is decided at the call rather than by state. The TUI was writing a mode into
that field on every mode change and nothing ever consulted it. `Mode` has left the
engine entirely; each frontend has its own, and they differ (the CLI has two, the TUI
has four including Convert, and the engine had a `financial` member it could never
act on because financial calculations are ordinary functions in expressions).

Programmer mode's configuration belongs to programmer mode:

```zig
// programmer.zig
pub const Config = struct {
    width: BitWidth = .bits64,
    signedness: Signedness = .signed,
    /// Big-endian by default so the HEX row reads as the number itself; see FR-2.8.
    display_endian: std.builtin.Endian = .big,
};

// Integer.zig: the file is the type
raw: u128,
width: BitWidth = .bits64,
signedness: Signedness = .signed,
```

`Integer.zig` is TitleCase because the file is the type. Width and signedness were
briefly a nested `IntType` struct, which existed only because `bitwise.zig` operated
on bare `u128` patterns and needed the pair passed alongside. Now that the operators
take values (`apply(op, left: Integer, right: Integer)`), nothing carries the pair
without bits to go with it, so the fields sit directly on the value and `Config` holds
them flat. That also removed a class of mistake: a pattern can no longer be operated on
at a width it did not come from.

Byte order is `std.builtin.Endian` rather than an engine enum of the same two members.

Standard mode evaluates to `Number`, the exact/inexact union of section 2.7. Programmer mode evaluates to `Integer`, which is a `u128` pattern plus the width and signedness that interpret it (the nested `IntType` this used to name is gone; the fields sit on `Integer` itself).

### 2.6 Number Display Formatting

The engine provides values that can render themselves at a budget the caller supplies;
frontends decide the budget (NFR-9.9) and the sink. There is no separate formatter:
`Number.render` and `Integer.fmt` are methods on the values, and both go through
`grouping.zig` for the thousands rule so every surface groups digits identically
(NFR-7). A `formatter.zig` held this once and was dismantled, because it had become a
second place where display decisions lived.

#### Decimal Formatting

| Context | Display | Clipboard |
|---------|---------|-----------|
| Standard result | `4,294,967,295` | `4294967295` |
| Fractional result | `231,677.04` | `231677.04` |
| Financial result | `$1,234,567.89` | `1234567.89` |
| Large decimals | `4,294,967,295` (never scientific unless > 15 digits of precision) | `4294967295` |

**Grouping applies to the integer part regardless of a fractional part.** Commas
group the digits left of the decimal point and never appear to the right of it,
so `231677.04` displays as `231,677.04` rather than ungrouped. Grouping only
whole numbers would make the same magnitude read two different ways depending on
whether cents happened to be present, which showed up immediately in financial
output. Because FR-1.8 accepts commas as input digit separators, the grouped
display remains valid input. Text already in scientific notation is left alone.

**Scientific notation threshold**: Only use scientific notation when the number exceeds what can be meaningfully displayed in decimal (> 15 significant digits, or absolute value > 10^15 or < 10^-15). Otherwise, always show full decimal with commas. This is a deliberate departure from calculators that jump to scientific notation at 10+ digits.

#### Programmer Mode Formatting

Values are displayed with visual grouping separators to aid readability, but clipboard copies the raw value without separators.

| Base | Display (value view) | Display (memory view) | Clipboard |
|------|---------------------|----------------------|-----------|
| Hex | `FF FF FF FF` | `FF FF FF FF` | `0xFFFFFFFF` |
| Bin | `1111 1111 1111 1111 1111 1111 1111 1111` | same | `0b11111111111111111111111111111111` |
| Oct | `0o37_777_777_777` | - | `0o37777777777` |
| Dec | `4,294,967,295` | - | `4294967295` |

Rationale for hex grouping:
- **Display uses space per byte** (`FF FF FF FF`): matches hex editors, debuggers, `xxd` output. Consistent with binary's nibble-space grouping. Universally readable.
- These are two different views of the same data: the *value* (what you'd write in source code) vs. the *memory* (how it sits in RAM). For this calculator, both use the same space-separated format.

Binary always groups by nibble (4 bits) with spaces - universally expected by programmers.

#### Formatting Data Structure

```zig
pub const FormattedValue = struct {
    /// Human-readable display string (with commas, underscores, spaces)
    display: []const u8,
    /// Machine/clipboard string (raw, no separators, includes prefix)
    raw: []const u8,
};
```

All frontends:
- Show `display` in the UI
- Copy `raw` to clipboard on long-press (Android) or yank (TUI)

---

### 2.7 Numeric Model: Exact and Inexact

#### 2.7.1 The problem

Standard mode currently evaluates everything as `f64`. That produces four
distinct classes of wrong answer, all reproducible today:

```
0.1 + 0.2            -> 0.30000000000000004    binary cannot represent 0.1
1.1 + 2.2            -> 3.3000000000000003     same
9007199254740993     -> 9.007199254740992e15   SILENTLY A DIFFERENT INTEGER
2^53 + 1             -> 9.007199254740992e15   same, past f64's integer limit
12 in in ft          -> 0.9999999999999998     conversion factors are decimal
factorial(171)       -> error: unknown function  f64 overflow, wrong error too
```

The third case is the serious one. The user typed an exact integer and got a
different integer back. Meanwhile programmer mode, one Tab away, is exact to 128
bits. That is an internal inconsistency, not a rounding preference.

#### 2.7.2 The representation

A tagged number with an exact tier and an inexact tier:

```zig
/// Exact rational: p/q with arbitrary-size integers, always reduced, q > 0.
pub const Rational = struct {
    num: std.math.big.int.Managed,
    den: std.math.big.int.Managed,
};

pub const Number = union(enum) {
    /// Exact value. Closed under + - * / and integer powers.
    exact: Rational,
    /// Inexact value, produced once a computation escapes the rationals.
    inexact: f64,
};
```

**Contagion rule:** any operation with an `inexact` operand yields `inexact`.
A value never silently becomes exact again. This is what keeps the guarantee
honest: `exact` means "no rounding has occurred anywhere in this value's
history", not "happens to look clean right now".

#### 2.7.3 Why rational and not decimal128

Both fix `0.1 + 0.2`. They are not otherwise equivalent:

| | decimal128 | arbitrary rational |
|---|---|---|
| Form | +/- 34-digit significand x 10^exp, 128 bits fixed | p/q, arbitrary-size integers |
| `0.1`, `0.0254` | exact | exact (`1/10`, `127/5000`) |
| `1/3` | 34-digit approximation | **exact** |
| `(1/3)*3` | `0.999...9` | **exactly 1** |
| `9007199254740993` | exact | exact |
| `sqrt(2)`, `pi` | approximation | **cannot represent** |
| Rounds | every operation | never |
| Memory | fixed 16 bytes | grows with denominators |
| Trailing zeros (`2.50`) | **preserved** (scale is part of the value) | lost |

Two conclusions:

1. **Every decimal128 value is a rational.** Rationals strictly subsume them.
   What decimal128 adds is fixed cost, standard rounding modes, and scale
   semantics, not additional expressiveness.
2. **decimal128 does not deliver correctness, it delivers familiarity.**
   `1/3 * 3` is still not 1. Since we are prioritizing correctness, rational
   wins outright.

Decimal's genuine advantage is scale preservation, which matters for money
(`2.50`, not `2.5`). We recover that in financial mode with an explicit display
scale plus banker's rounding at the commit boundary, rather than a second
numeric type. See section 5.

#### 2.7.4 The exact/inexact boundary

The trigger is **whether the operation escapes the rationals**, evaluated per
call rather than per function. Notably it is *not* the input base: `0xdeadbeef`
is exactly 3735928559, and base is a lexical and display property only.

| Stays exact | Becomes inexact |
|---|---|
| `+ - * /` on exact operands | `sin cos tan asin acos atan` |
| `^` with integer exponent | `^` with non-integer exponent |
| `sqrt` of a perfect square | `sqrt` of a non-square |
| `%`, `abs`, `ceil`, `floor`, `round` | `log ln log2 log10 exp cbrt` |
| `factorial` (unbounded) | constants `pi`, `e`, `tau` |
| integer and decimal literals | any operand already inexact |

`sqrt(4)` is 2 exactly; `sqrt(2)` is not. We deliberately stop short of a CAS:
Qalculate simplifies `sqrt(8)` to `2*sqrt(2)` symbolically, we will not.

#### 2.7.5 Denominator growth and the demotion policy

Rationals grow. Chained division with coprime denominators multiplies them, so a
pathological input can consume unbounded memory. This must be designed in from
the start, not discovered later:

- Cap the denominator at a bit-width budget (starting proposal: 4096 bits).
- On exceeding it, **demote to `inexact`** rather than erroring or growing.
- Demotion is silent in the result value but visible in the tag, so a frontend
  can indicate that exactness was lost.

Interactive single calculations will not approach this. The cap exists so the
failure mode is graceful degradation to today's behavior.

#### 2.7.6 Display

Exact values still have to be rendered at finite width, so display precision
remains a separate decision from compute precision:

- An exact value with a **terminating** decimal expansion prints exactly:
  `1/10` -> `0.1`, and `12 in in ft` -> `1`.
- An exact value with a **non-terminating** expansion is rendered by long
  division to a digit budget with correct rounding, and marked as approximate:
  `100 km in mi` is exactly `781250/12573`, displayed as `62.137119224`.
- Because the exact form is retained, we can additionally offer the fraction
  (`781250/12573`) as a display option. This is a feature, not a workaround.

This supersedes the unimplemented "exceeds 15 significant digits" clause of
NFR-7, which was never a precision decision and, read literally, would have
rendered `0.9999999999999998` as `9.999999999999998e-1`. NFR-7 needs a real
answer to a better-posed question: how many digits to show for a non-terminating
exact value.

#### 2.7.7 What is unaffected

- **Programmer mode** stays fixed-width `u128`. Wrapping and masking at a chosen
  bit width is the entire point of that mode; exact arithmetic would break it.
- **The IEEE 754 float view** stays binary `f32`/`f64`. It exists to show binary
  encodings.
- **The f64 rendering paths** remain, since the inexact tier still needs them.

#### 2.7.8 Fallback precision: why f64 and not f128

The obvious objection to `f64` for the inexact tier is that the usual
justification (hardware instructions) does not apply to a calculator, which
evaluates one expression per human action. That objection is correct, and
performance is *not* the reason. The reason is that Zig 0.16's f128 support is
partial and, worse, silently inconsistent. Probed directly:

| Operation | f128 status |
|---|---|
| `@sqrt` | compiles, accurate to full f128 (34 digits verified) |
| `@sin`, `@cos` | compiles, accurate to full f128 |
| `@log`, `@log10`, `@exp` | compiles, but **only f64-accurate** |
| `std.math.pow` | **does not compile** ("pow not implemented for f128") |
| `std.math.cbrt` | **does not compile** |
| `std.math.atan`, `asin` | compiles |
| `parseFloat` / formatting | works, 112 mantissa bits (~34 decimal digits) |

The middle row is the disqualifying one. `@log(2.0)` as f128 returns
`0.6931471805599452862267639829951804`, which is the *f64* value widened: it
diverges from the true value at the 17th significant digit. So f128 storage
would hand us 34 digits of which roughly 18 are noise, with nothing to
distinguish them. For a calculator that then displays those digits, this is
actively worse than knowingly using f64.

The general principle: **the precision of the inexact tier is bounded by the
accuracy of the underlying transcendental implementations, not by the width of
the storage type.** Widening storage without widening the algorithms buys
nothing but false confidence.

##### Upstream status (checked, not assumed)

The f64-accuracy above is not a misconfiguration or a version quirk. It is
visible in Zig's own source, with its own TODO markers. `lib/compiler_rt/log.zig`:

```zig
pub fn logq(a: f128) callconv(.c) f128 {
    // TODO: more correct implementation
    return log(@floatCast(a));
}
```

A systematic scan of `lib/compiler_rt/` in Zig 0.16.0 splits the f128 routines
cleanly in two:

- **Downcast to f64, all five marked TODO:** `expq`, `exp2q`, `logq`, `log2q`,
  `log10q`
- **Genuine f128 implementations:** `sinq`, `cosq`, `tanq`, `sqrtq`, `fabsq`,
  `floorq`, `ceilq`, `roundq`, `truncq`

That is an exact match for the probe results: `@sin`/`@cos`/`@sqrt` accurate,
`@log`/`@log10`/`@exp` only f64-accurate.

Tracker status, as of this writing. Note that Zig has moved to Codeberg and
GitHub is effectively frozen (GitHub last pushed 2025-11-27; Codeberg shows ~742
open issues against GitHub's ~2876, so most GitHub issues were **not** migrated):

| Gap | Tracked? |
|---|---|
| `std.math.pow` f128 | [GH #23602](https://github.com/ziglang/zig/issues/23602) open, labeled "contributor friendly". [PR #23631](https://github.com/ziglang/zig/pull/23631) implemented it but was **closed unmerged** 2026-01-05 ("no CI on GitHub anymore... reopen on Codeberg"). Nobody has. No Codeberg issue exists. |
| `std.math.cbrt` f128 | **No issue on either tracker.** Unreported. `cbrt.zig` is ported from musl, which only ships `cbrtf`/`cbrt`. |
| `logq`/`expq` etc. f64 accuracy | **No issue on either tracker.** Only the in-source TODOs. |

The nearest historical artifacts are [GH #4026](https://github.com/ziglang/zig/issues/4026)
("implement all the math functions for all the floating point types", closed
2022-12-28 under milestone 0.11.0 with its f128 column still unchecked) and
[GH #15711](https://github.com/ziglang/zig/issues/15711) (a reference table
created and closed in the same second, which lists the f128 symbols as
*existing* - existence, not accuracy).

Adjacent open work suggesting f128 remains a soft spot generally:
[GH #23865](https://github.com/ziglang/zig/pull/23865) "Better @sqrt for f32, f64
and f128", [GH #23173](https://github.com/ziglang/zig/issues/23173) "introduce new
float types", and Codeberg #36093 "compiler_rt: min(f128) / max(f128) causes
integer overflow".

**Conclusion: "wait for Zig to fix f128" is not a plan.** Two of the three gaps
are not even reported, and the one with a working patch lost it to a tracker
migration. Obtaining true f128 accuracy would mean writing or porting the
routines ourselves, which is the same category and scale of work as going
arbitrary-precision - so it should be justified on its own terms, not smuggled in
as "just use a wider type".

(Optional, off the critical path: reviving the `pow` PR on Codeberg is a
well-scoped upstream contribution, and the issue is explicitly labeled
contributor friendly.)

So `f64` is chosen because ~15-16 digits is the precision we can actually
justify, and we display no more than that. The upgrade path is therefore *not*
"switch the storage type to f128"; it is "implement or bind correctly-rounded
arbitrary-precision transcendentals" (the problem MPFR exists to solve), which is
a separate project with its own justification.

Incidentally, the probe also confirms that width alone never fixes the decimal
problem: in f128, `0.1 + 0.2` is
`0.30000000000000000000000000000000004`. Only exactness fixes it.

#### 2.7.9 Implementation sequencing

The change must not land as one diff mixing structural churn (signature changes
rippling through hundreds of test assertions) with behavioral change (results
becoming correct). Reviewing that combination is impractical: the interesting
lines are buried in mechanical ones.

Two orderings were considered.

**Rejected: structure first.** Introduce `Number`, rewrite every test and the
display path to consume it, review, then change behavior. This fails because the
structural rewrite is not behavior-neutral: rewriting a test to consume `Number`
requires asserting whether each result is `exact` or `inexact`, and that
classification *is* the behavioral design. Every such assertion would be written
against the old f64 behavior and then flipped in the later step. Double churn,
and the intermediate commit is a large diff that improves nothing.

**Chosen: behavior first, behind the existing signature.**

1. **Add `rational.zig` and `number.zig`, wired to nothing.** Pure addition with
   their own tests. Reviewable in isolation, zero risk to existing behavior.
2. **Switch the evaluator's internals to the exact tier, keeping `evalString`
   returning `f64`.** All existing tests must still pass. Review and commit.
3. **Change `evalString` and the display path to return and consume `Number`**,
   with the resulting mechanical churn in test signatures. Review and commit.
4. **Add the exactness tests** that only the `Number` API can express.

What makes step 2 worthwhile rather than invisible is that converting an exact
value to `f64` *once, at the boundary* already fixes most of the payoff. Today's
errors are accumulated: `0.1` and `0.2` are each rounded before being added. An
exact `3/10` rounded a single time to the nearest f64 prints as `0.3`.

Bug-by-bug, where the fix lands:

| Bug | Fixed by step 2 (f64 boundary) | Needs step 3 (`Number`) |
|---|---|---|
| `0.1 + 0.2` -> `0.3` | yes | - |
| `1.1 + 2.2` -> `3.3` | yes | - |
| `0.1 * 3` -> `0.3` | yes | - |
| `1e20 + 1 - 1e20` -> `1` | yes | - |
| `factorial(171)` | partly (becomes `inf`, not an error) | yes, for the exact value |
| `9007199254740993` | **no** (f64 cannot hold it) | yes |
| `2^53 + 1` | **no** | yes |
| `1/3` retained exactly | no (only observable as exact) | yes |
| `12 in in ft` -> `1` | **no** - see below | needs exact unit factors |

**Unit conversion is a separate problem from the evaluator.** An earlier draft of
this table claimed the exact evaluator would fix `12 in in ft`. It does not, and
the reason is worth recording: `UnitDef.to_base_factor` is an `f64`, so `0.0254`
is *already* the binary approximation before any arithmetic happens, and
`convertUnits` does its own f64 multiply and divide without ever touching the
evaluator. Making conversions exact requires the factors themselves to be exact
(declared as decimal text and parsed into rationals), which is a mechanical change
across ~100 table entries and belongs in its own commit. Tracked as Task 2.0e.

So step 2 is independently verifiable through the current API, and the
large-integer cases become the motivating tests for step 3 rather than
speculative ones.

#### 2.7.10 Migration and test impact

The dominant risk is **compile-time** breakage, not behavioral. An audit of the
402-test suite found **no test that asserts the broken behavior** - nothing
pins `0.30000000000000004`, the 2^53 cliff, or the `factorial` limit. So the
target is "no test changes its expected value", not "no test file is touched".

Unaffected by construction: `programmer.zig` (47), `float_interp.zig` (21),
`formatter.zig` (40), `types.zig` and `tui.zig` (16).

Kept passing by making the change additive:

- `tokenizer.zig` (39): `NumberValue` **gains** an exact field, does not replace
  `float`/`int_value`.
- `parser.zig` (32, 10 of which read `number.float_value`): the AST number node
  likewise gains a field.
- `evaluator.zig` (62, 40 asserting `@as(f64, ...)`): keep `evalString`
  returning `f64` as a wrapper over the exact core. Every one of those
  assertions involves small values where exact-to-f64 is bit-identical.
- `units.zig` (106, 95 routed through the `expectConvert` helper): change the
  helper once, leave the call sites alone.

Three existing items must change because we are invalidating their premise:

1. `tokenizer.zig` test `"parseNumber huge decimal falls back to float"` -
   `99999999999999999999999999` becomes exactly representable, so the test still
   passes but its intent is now false. Rewrite it.
2. `Number.renderInexact`'s 2^53 bound (then `formatter.zig`'s `is_integer`) - that guard is the display
   half of the `9007199254740993` bug.
3. `evaluator.zig` `factorial`'s `x > 170` rejection, which is also the source of
   the misleading `unknown function` error.

**Compatibility wrappers are scaffolding with a deadline, not an end state.** If
the CLI and TUI keep calling the `f64` API, the exactness never reaches the user
and the work is invisible. The display path must move to `Number` (step 3 of
2.7.9), and that is where `main.zig`'s ~20 output assertions get reviewed.
Literal zero test churn across the whole sequence would be evidence we had not
delivered anything.

Windows Calculator draws the same exact/inexact line we are drawing: its
arbitrary-precision rational engine covers basic arithmetic only, not
transcendentals.

New tests required: rational arithmetic and reduction, exact/inexact contagion,
the demotion policy at the denominator cap, rational-to-decimal rendering and
rounding, and a regression test per bug in 2.7.1 - including one asserting
`9007199254740993` round-trips, which nothing currently guards.

##### Allocation-failure testing

`errdefer` cleanup paths are not reachable by ordinary tests, and covering them
is worthless on its own: the line exists to *prevent a leak*, so executing it
proves nothing unless the test also asserts that nothing leaked.

`std.testing.FailingAllocator` fails after exactly N allocations. Sweeping N
across an operation's whole allocation sequence, with `testing.allocator`
underneath to detect leaks at test end, turns those paths into real assertions.
(`std.mem.Allocator.failing` fails on the *first* allocation, which only covers
entry-point OOM, not the interesting mid-construction failures.)

This is not a coverage exercise; the sweep immediately found three genuine bugs
in `rational.zig` that ordinary tests could never reach:

1. **A double free.** `initOwned` took its numerator and denominator *by value*
   and freed them via `errdefer` on its own failure, while every caller ALSO had
   an `errdefer` for the same values. Any allocation failure inside normalization
   freed them twice, which segfaulted.
2. **A dangling copy.** Because the parts were passed by value, and normalization
   can reallocate limbs, a caller's `errdefer` could free a stale pointer even
   without the double free.
   Fixed by renaming to `finish` and taking both parts **by pointer**, with the
   contract that ownership transfers only on success: on failure the caller's
   `errdefer` sees live, current values and frees them exactly once.
3. **Two struct-literal leaks.** `initInt`, `initZero` and `initRatio` built
   `.{ .num = try initSet(...), .den = try initSet(...) }` in a single literal.
   An `errdefer` cannot cover a value that does not exist yet, so a failure on
   the second allocation orphaned the first. Fixed by building the parts as
   separate statements, each with its own `errdefer`. `floor` and `factorial`
   were also missing an `errdefer` on their denominator.

The remaining uncovered lines in these files are `unreachable` arms guarded
upstream, and diagnostic paths inside the tests themselves.

---

## 3. Struct Layout Engine

Built as two engine files and a CLI subcommand (FR-3, FR-6.5). The TUI sub-view (8.3) and
the Android screen (9.4) are not, and the C ABI has no export for it yet. An earlier
version of this section was a proposal: a DSL of its own, an ABI interface of function
pointers, and a precomputed byte map. Each of those went a different way once built, and
3.6 says why.

The split is between syntax and layout:

- `CStructParser.zig` reads text into a `struct_layout.Definition`. It is the only part
  that knows C.
- `struct_layout.zig` lays a `Definition` out under an `Abi` and knows no syntax at all.
  A Rust `#[repr(C)]` or Zig `extern struct` front end would be a second parser
  producing the same `Definition` (FR-3.13).

### 3.1 The input is C

The point is pasting a struct from real code, so the input is C rather than a language
invented for the calculator: a struct copied out of a header should be accepted as it
stands, or rejected with a reason and a position. FR-3.1 and FR-3.12 list what the
subset accepts and refuses.

```
input       := directive* definition directive*
definition  := "typedef"? "struct" attrs? tag? attrs? "{" declaration* "}" attrs? name? ";"?
declaration := specifiers declarator ("," declarator)* ";"
declarator  := attrs? ("*" qualifier*)* (identifier | "(" "*"+ identifier dims ")" suffix)
               dims attrs?
dims        := ("[" integer? "]")*          // only the first may be empty
suffix      := "(" balanced ")" | dims       // a function pointer, or a pointer to an array
directive   := "#pragma pack(" (N | "push" ("," N)? | "pop" | "") ")"
```

Decisions worth recording:

- **Its own lexer.** The expression tokenizer was the obvious thing to reuse and is wrong
  for C in three places that would each give a wrong answer rather than an error: `1,000`
  is a grouped number there, `010` is ten (C says eight), and a hex literal continues
  across a space. It also has no braces or brackets.
- **Type words are counted, then resolved,** C's way: `unsigned` is `unsigned int`,
  `int long long unsigned` is `unsigned long long`, and `short char` is an error. A name
  that is none of the words and no known typedef is `UnknownType`, pointing at the name.
- **Unknown is an error, never a skip.** `#if 0` is refused rather than ignored, because
  ignoring it would count the members inside it. An unknown attribute is refused because
  `mode(DI)` and `vector_size` change a type. Harmless ones (`unused`, `deprecated`,
  `may_alias`) are accepted.
- **Every error carries a span** (`Diagnostic`), and `locate` turns it into a line and
  column, so the CLI can say `line 3, column 5: uint33_t`. Layout errors carry the
  member's index instead, and the member carries the span of its name.
- **`Parsed` owns an arena** with every name copied in, so a definition outlives its
  source. Input is capped at 64 KiB before anything is read (NFR-8).

### 3.2 An ABI is a table

```zig
pub const Abi = struct {
    id: []const u8,          // "sysv64", what --abi takes
    label: []const u8,       // "64-bit Linux and macOS (x86-64 SysV, AArch64)"
    shapes: std.EnumArray(Primitive, ?Shape),   // size and alignment, null where absent
    rules: Rules,            // .gnu or .microsoft (3.3)
};

pub const Primitive = enum {
    char, bool, short, int, long, long_long, int128,
    float, double, pointer, wchar, enumeration,
};
```

`Primitive` lists C's kinds rather than its spellings: `uint32_t`, `u32` and `unsigned int`
all arrive as `.int`, and `size_t` and every pointer as `.pointer`, because on every
profile here `size_t` is pointer-sized. A profile is a value in a table, not an
implementation of an interface: `EnumArray.init` requires a shape for every kind, so a
profile cannot forget one, and the proposal's function pointers would have bought
nothing a table cannot say.

| Profile | `long` | pointer | 8-byte types align to | `wchar_t` | `__int128` | Rules |
|---|---|---|---|---|---|---|
| `sysv64` (default) | 8 | 8 | 8 | 4 | 16, aligned 16 | GNU |
| `win64` | 4 | 8 | 8 | 2 | 16, aligned 16 | Microsoft |
| `i386` | 4 | 4 | 4 | 4 | absent | GNU |
| `arm32` | 4 | 4 | 8 | 4 | absent | GNU |

AArch64 is not its own profile: for every type here it matches x86-64 SysV, on Linux and
macOS alike (they differ in `long double`, which is not modelled). The clang check
(3.5) holds `sysv64` to all three targets, which is the evidence for folding them.

### 3.3 The algorithm

```
for each member:
    alignment = scalar alignment
    if packed (member or struct): alignment = 1
    gnu:       alignment = max(alignment, aligned);  alignment = min(alignment, pack)
    microsoft: alignment = min(alignment, pack);     alignment = max(alignment, aligned)
    offset = round_up(offset, alignment)        # padding_before = the difference
    place the member; offset += element size * product(dims)   # 0 for a flexible array
    struct_alignment = max(struct_alignment, alignment)
struct_alignment = max(struct_alignment, aligned on the struct)
size = round_up(offset, struct_alignment)       # tail padding = the difference
```

**The order of `aligned` and `pack` is the one rule that differs by compiler, and the
clang check found it.** The first version used the GNU order everywhere, and the
`windows-msvc` targets refused two of the test structs: under `#pragma pack(2)`,
`char c; alignas(8) int i;` puts `i` at 2 under GCC's rules and at 8 under MSVC's, where
an explicit alignment is applied after the cap and wins. That is now `Abi.rules`, a
property of the profile, since clang chooses it by target too. Bitfields are where the
two families differ most, which is one reason they are out of scope (FR-3.12).

Every size is checked arithmetic, and a struct larger than the ABI can address
(`PTRDIFF_MAX`: 2^31 - 1 on the 32-bit profiles) is `StructTooLarge`, because a C
compiler refuses it and a layout that no program could have is not an answer.

### 3.4 The result

```zig
pub const Layout = struct {
    abi: *const Abi,
    members: []const Member,     // borrowed from the definition
    placements: []Placement,     // owned: offset, size, alignment, padding_before
    size: u64,
    alignment: u32,
    tail_padding: u64,
    packed_size: u64,            // sum of member sizes: FR-3.10's comparison
    pub fn padding(self) u64;
    pub fn segments(self) SegmentIterator;   // member / padding / tail runs, in order
};
```

The proposal's `bytes: []const ByteInfo` is `segments()` instead: the same information,
derived on demand. A struct holding `char buf[1 << 20]` is three segments, not a million
entries, and the CLI's memory map draws a 2 GiB struct as quickly as a small one because
it finds its rows from the segments.

### 3.5 Checked against clang

NFR-3 says a layout must match what a C compiler produces, and this is how that is held
rather than hoped for. `engine/test/struct_oracle.zig` runs on the build machine and
writes one C file per profile:

- a probe per scalar kind: `sizeof`, and the offset of the scalar after a `char` (its
  in-struct alignment, which on i386 is not `_Alignof`'s answer for `double`);
- `__int128`'s presence or absence, as an `#error` when the target disagrees;
- for each of 29 test structs: `sizeof`, `_Alignof`, and every member's offset and size.

Each test struct is C read by the engine's own parser, so the compiler and the engine see
the same text. `build.zig` compiles each file, freestanding with `-Werror`, for every
clang target its profile claims:

| Profile | Targets |
|---|---|
| `sysv64` | `x86_64-linux-gnu`, `aarch64-linux-gnu`, `aarch64-macos` |
| `win64` | `x86_64-windows-msvc`, `aarch64-windows-msvc` |
| `i386` | `x86-linux-gnu` |
| `arm32` | `arm-linux-gnueabihf` |

Compiling is the test, inside `zig build test`, and nothing beyond Zig is needed: the
clang is the one Zig ships. A wrong table entry fails with the profile, the struct and the
claim in the message; changing i386's `double` to align 8 failed twenty assertions. The
generator refuses to run unless every profile in the engine has a target listed, so a
profile cannot be added without a compiler to answer to.

### 3.6 What changed from the proposal, and why

- **A DSL of our own became C.** The DSL's only user would have been someone retyping a
  struct they already had in C.
- **The function-pointer interface became a table.** Sizes and alignments are data;
  the one behavioural difference found so far (3.3) is an enum.
- **`packed` stopped being a profile.** It is a property of a struct, and applies under
  any ABI; a "packed profile" could not have said what a pointer's size is.
- **The byte map became an iterator** (3.4).
- **Endianness was deferred** (FR-3.8): without values it only relabels bytes.

---

## 4. Unit Conversion Engine

### 4.1 Architecture

Units are organized by category. Each category has a canonical base unit. All conversions go through the base unit (from -> base -> to), except temperature which uses formula-based conversion.

```zig
pub const UnitCategory = enum {
    length, mass, temperature, time, digital_storage,
    speed, area, volume, energy, pressure, data_rate, angle,
};

pub const UnitDef = struct {
    name: []const u8,            // canonical name (e.g., "km")
    aliases: []const []const u8, // alternatives (e.g., "kilometer", "kilometers")
    category: UnitCategory,
    /// base = value * to_base_factor + to_base_offset
    /// DERIVED at comptime from the exact text below; never written by hand.
    to_base_factor: f64,
    to_base_offset: f64 = 0,
    /// The factor as exact text (decimal or `p/q`), or null when the factor is
    /// irrational and no exact form exists.
    factor_text: ?[]const u8 = null,
    offset_text: ?[]const u8 = null,

    pub fn toBase(self: UnitDef, value: f64) f64 {
        return value * self.to_base_factor + self.to_base_offset;
    }

    /// The reverse direction is DERIVED, not stored.
    pub fn fromBase(self: UnitDef, base: f64) f64 {
        return (base - self.to_base_offset) / self.to_base_factor;
    }
};
```

**Factors are declared as exact text; the f64 is derived.** Tables are written
with `define(.length, &.{ .{ .name = "in", .factor = "0.0254" }, ... })`, and
`define` computes the f64 fields at comptime. This is the same single-source-of-
truth argument as `fromBase` below, applied one level up: an inch is exactly
127/5000 m, and if the exact and approximate forms were both hand-written they
could disagree.

Some factors need the `p/q` form because they have no terminating decimal
expansion: Fahrenheit scales by exactly 5/9, a knot is exactly 1852/3600 m/s, a
torr exactly 101325/760 Pa. A few units are defined in terms of pi (the angle
units, and the parsec at 648000/pi au) and so have NO exact rational factor;
those declare `approx_factor` instead and their conversions fall back to the
inexact tier.

**Only the to-base mapping is stored; the reverse is derived.** An earlier draft
of this design gave each unit four fields (`to_base_factor`/`to_base_offset`
plus `from_base_factor`/`from_base_offset`). That was changed because it lets a
table entry describe a conversion that disagrees with its own inverse: nothing
stops a typo in `from_base_factor` from making `km -> m -> km` lossy. Deriving
`fromBase` by inverting `toBase` gives one source of truth per unit, halves the
numbers a contributor has to get right, and makes round-trip correctness
structural rather than something tests have to police. A unit test still
round-trips every unit and every within-category unit pair as a guard against
bad factors.

### 4.2 Conversion Resolution

Unit names resolve through `findUnit(name)`, which searches every category's
table by canonical name and alias:

1. An **exact, case-sensitive** match is tried first. This is what keeps
   case-distinguished units meaningful: `K` is Kelvin (not a "kilo" something),
   `B` is byte and `b` is bit, `Mb` is megabit and `MB` is megabyte, and `kB`
   (1000) never silently becomes `KiB` (1024).
2. Only if nothing matches exactly does a **case-insensitive** pass run, which
   is what makes forgiving input like `KM` or `Celsius` work. That pass must find
   **exactly one** unit. Where a fold reaches two units that the tables
   deliberately distinguish by case, the name is `AmbiguousUnit` rather than a
   guess: `Mbps` is megabits per second and `MBps` is megabytes per second, so
   `MBPS` is a factor of eight away from one of the two readings with no way to
   tell which was meant. Returning the first fold match is how `MBPS` silently
   became `Mbps`, and how `mB` became `MB`.

Bits sit alongside bytes in `digital_storage` (`b`, `kb`, `Mb`, `Gb`, `Tb`, `Pb`),
because the category's whole convention is that lowercase `b` is a bit and
uppercase `B` a byte. Before they existed, `Mb` matched nothing exactly, fell
through to the fold, and `100 Mb to MB` answered `100 MB`: a megabit-to-megabyte
question returning an identity. A bit is an eighth of a byte, so every factor in
the category is still exact.

Conversion goes through the category base unit: `to.fromBase(from.toBase(value))`.
Both units must be in the same category, or the result is `IncompatibleUnits`.
An unrecognized name is `UnknownUnit`.

A single multiplicative factor is reported alongside the result only when both
units are linear (zero offset). Temperature conversions are affine, so no single
factor describes them and the factor is reported as null.

**Free-form conversion requests** (`units.parseRequest`) let conversion be plain
expression input rather than a special subcommand, so `tally 32F in C` and typing
`100 km to mi` in the TUI both work:

- A standalone, whitespace-delimited, case-insensitive `to` or `in` is the
  trigger. This needs no unit-aware tokenizer, because neither word is otherwise
  an identifier in the grammar.
- No separator means `parseRequest` returns null and the caller falls through
  to ordinary expression evaluation, so existing behavior is untouched.
- **`in` is both a separator and the name for inches.** Candidate separators are
  therefore tried last-to-first, keeping the first reading that yields a valid
  conversion. In `5 in in cm` the later `in` is the separator; in `100 mm in in`
  the earlier one is, because only that reading resolves. `1 in in in` is a valid
  identity. `min` is untouched because a separator must be whitespace-delimited.
- Backtracking also improves errors: if a candidate reading fails, the reason is
  remembered, so a committed-but-invalid request reports
  `UnknownUnit`/`IncompatibleUnits` instead of a confusing parse error.
- The trailing unit is split off by trying the **longest** suffix first, so
  `100 km` yields `("100", km)` and not `("100 k", m)`, and no space is required
  (`32F`). A candidate must start at a **token boundary** (the preceding
  character may not be a letter), which is what stops the trailing `s` of
  `100 smoots` from being read as seconds.
- The value portion is returned **unevaluated** as text, so `parseRequest` needs
  no dependency on the evaluator and callers can evaluate it in whatever
  environment they already have. This is why `2*3 kg to lb` works.

NOT YET IMPLEMENTED: unit-qualified arithmetic (`5 kg + 3 lb`), which genuinely
does need unit-aware tokenizing and evaluation. The planned approach:

For expressions like `5 kg + 3 lb`, the parser would:
1. Identify `5 kg` as a unit-qualified value
2. See `+ 3 lb` and convert `3 lb` to `kg` (left-hand unit wins)
3. Evaluate as `5 + 1.36078 = 6.36078 kg`

### 4.3 Adding New Units

New units require only a table entry - no parser changes:

```zig
// In units.zig
const length_units = [_]UnitDef{
    .{ .name = "m",  .aliases = &.{"meter", "meters"},  .category = .length, .to_base_factor = 1.0 },
    .{ .name = "km", .aliases = &.{"kilometer", "kilometers"}, .category = .length, .to_base_factor = 1000.0 },
    .{ .name = "mi", .aliases = &.{"mile", "miles"},    .category = .length, .to_base_factor = 1609.344 },
    // ... add new entries here
};
```

Invariants enforced by tests rather than convention: every category's base unit
must have `to_base_factor == 1` and no offset, no unit may have a zero factor,
canonical names must be unique across all categories, every unit must be listed
in the table matching its own `category` field, and every unit and unit pair must
round-trip. A bad table entry fails the suite instead of silently producing wrong
answers.

---

## 5. Financial Module

### 5.1 CAGR

```
CAGR = (end_value / start_value) ^ (1 / periods) - 1
```

### 5.2 Compound Interest

```
FV = PV * (1 + rate/100/m)^(m * years)
```

Solvable for any of its four variables, all in closed form:

```
PV    = FV / (1 + rate/100/m)^(m*years)
rate  = m * ((FV/PV)^(1/(m*years)) - 1) * 100
years = ln(FV/PV) / (m * ln(1 + rate/100/m))
```

`m` (compounds per year) is deliberately NOT solvable. As `m` rises, FV climbs
from the annual case toward the continuous limit `PV * e^(rate*years/100)`, so a
solution exists only inside that band: for 10,000 at 6% over 10 years, only for
future values between about 17,908 and 18,221. Nearly every real input has no
answer, and a fractional answer ("compound 7.3 times a year") would be
meaningless, so it stays an input with a prefilled default of 1.

**Nominal versus effective.** `compoundRate` returns a NOMINAL annual rate: at
`m = 12` it is the APR a lender quotes, not what the money earned.
`effectiveAnnualRate` converts (18% nominal monthly is 19.56% effective), and the
TUI shows both whenever `m > 1`. This only matters when solving, because a rate
that was typed in is one the user already understands; a rate the calculator
produces is one they are about to compare against something else.

Solving for the rate at `m = 1` is exactly CAGR. Both entry points are kept: CAGR
is a named thing people look for, and it takes periods rather than years so it
works for quarters or months without a frequency argument. A test asserts the two
agree, so they cannot drift.

### 5.3 TVM (Time Value of Money)

The five TVM variables: N (periods), I/Y (interest rate per period), PV (present value), PMT (payment), FV (future value).

Relationship:
```
PV * (1 + r)^N + PMT * [((1 + r)^N - 1) / r] + FV = 0
```
where `r = I/Y / 100`.

Solving for the unknown variable:
- **FV, PV, PMT**: algebraic (closed-form)
- **N**: logarithmic solution
- **I/Y**: Newton-Raphson iterative solver (no closed form)

Sign convention is the cash-flow one used by financial calculators: money
received is positive, money paid out is negative. A borrower taking a 200,000
loan has `pv = 200000` and a negative `pmt`. The solver never flips signs on the
caller's behalf, because a silent flip is harder to debug than a wrong-looking
answer.

The rate solver takes its derivative by central difference rather than
analytically: the annuity-due form of the derivative is unwieldy and the
numerical version is not the accuracy bottleneck. Two details make it reliable:

1. **Scale-relative acceptance.** The residual of the TVM equation is
   proportional to the size of the cash flows, so it is compared against
   `tolerance * max(|pv|, |fv|, |pmt| * n, 1)`. With an absolute tolerance a
   200,000 mortgage cannot converge at all, because floating-point noise in the
   residual exceeds any fixed epsilon.
2. **Multiple seeds.** The residual can be flat or badly sloped near a poor
   initial guess, so the solver retries from a small set of starting rates
   (5%, 1%, 10%, 0.5%, 25%, -5%, 50%). A single seed fails on well-posed inputs.

### 5.4 Amortization

An amortization schedule is generated period by period from the balance rather
than from a closed form, because that is the only way the rounding matches what a
lender's table shows. Each period:

```
interest  = round(balance * r)
principal = payment - interest
balance   = balance - principal
```

Rows are read from the borrower's side, so every figure is positive: `payment` is
an amount paid, `balance` an amount owed. Mixing in the TVM sign convention only
makes a table harder to read.

Three behaviors are deliberate:

- **The final period settles the balance exactly.** Cent rounding leaves a
  residue over hundreds of periods, so the last payment differs slightly from the
  rest. This is what real schedules do, and it is why the total of the principal
  column equals the loan amount to the cent.
- **An overlarge payment retires the loan early**, and the schedule simply ends
  short of `periods`.
- **An underfunded term ends in a balloon.** A payment that covers the interest
  but not the full term leaves a large final payment, which is shown rather than
  smoothed away. A payment that does not cover even the first period's interest
  never amortizes at all, so it is a domain error rather than an infinite loop.

Single rows (`amortizationEntry`) and totals (`amortizationTotals`) walk the same
cursor as the full schedule, so a row fetched on its own can never disagree with
the same row inside a table. Only the full schedule allocates.

### 5.5 Reachability: expression functions, not just a mode

Financial calculations are exposed as ordinary expression functions in standard
mode, mirroring how unit conversion is reachable from a bare expression. That
keeps them composable (`cagr(10000, 25000, 5) * 100`) and usable from the CLI
without a subcommand per formula. See FR-5.7 for the function list.

This required the evaluator's function dispatch to grow beyond the 0/1/2-argument
cases it previously handled; financial functions take three or four arguments. An
unknown name at those arities still reports `UnknownFunction`, and a wrong arity
for a known financial function does too, rather than filling in defaults.

The one exception is the amortization table itself: a table is not a value, so it
lives behind the `tally amort` subcommand (FR-6.11). The per-period figures are
still reachable as functions (`amort_interest(...)` and friends).

### 5.6 Precision: f64 plus explicit rounding

This part of the engine is f64, not the exact `Number` tier used elsewhere (design 2.7).
Every formula here needs a non-integer power or a logarithm - CAGR raises to
`1/n`, the period solver takes `ln`, the rate solver iterates - and those escape
the rationals by definition, so there is nothing for the exact tier to preserve.

What money needs is not exactness but controlled rounding, which is a separate
concern: `roundToScale(value, decimals, mode)` and `roundToCents` are applied at
the point a figure becomes an amount. The default is half-even (banker's
rounding); half-up is available but is not the default because it biases totals
upward across many roundings.

---

## 6. C API (for Android/FFI)

**What exists today:** `engine/src/c_api.zig` is the root of the shared library and
implements the design below. Twelve exports, a hand-written `include/tally.h`, and two
test layers: Zig tests that build sessions with `std.testing.allocator` so the whole seam
is leak-checked, and `engine/test/c_abi_test.c`, which links against the real library
through the real header and is run by `zig build test`. `zig build android`
cross-compiles the library for arm64-v8a, x86_64 and armeabi-v7a, laid out for Gradle's
`jniLibs`, with the JNI layer (6.4) on top.

What is not built: the financial and float-view payloads. Standard mode, programmer
mode, unit conversion, preview (6.5), whole-category conversion (6.6), save and load
(6.7) and the units
catalogue are across.

```zig
pub const Status = enum(c_int) { ok = 0, eval_error = 1, out_of_memory = 2, invalid_argument = 3 };
pub const Mode = enum(c_int) { standard = 0, programmer = 1 };

/// Interpretation and display, set once on the session rather than per call. The
/// display fields are NFR-9.9: the engine holds no digit budget of its own.
pub const Config = extern struct {
    bits: u16 = 64,                        // 8, 16, 32, 64, 128
    is_signed: u8 = 1,
    big_endian: u8 = 1,
    separators: u8 = 1,
    never_abbreviate: u8 = 0,
    fraction_digits: u16 = 20,
    max_integer_digits: u16 = 40,
    significant_digits: u16 = 17,
    scientific_below_exponent: u16 = 15,
};

export fn tally_session_new() ?*Session;
export fn tally_session_free(?*Session) void;
export fn tally_session_configure(?*Session, ?*const Config) Status;
export fn tally_session_config(?*Session, ?*Config) Status;
export fn tally_eval(?*Session, ?[*]const u8, usize, c_int, ?*[*]const u8, ?*usize) Status;
export fn tally_preview(?*Session, ?[*]const u8, usize, c_int, ?*[*]const u8, ?*usize) Status;
export fn tally_convert(?*Session, ?[*]const u8, usize, ?[*]const u8, usize, ?*[*]const u8, ?*usize) Status;
export fn tally_session_save(?*Session, ?*[*]const u8, ?*usize) Status;
export fn tally_session_load(?*Session, ?[*]const u8, usize) Status;
export fn tally_unit_catalog(?*Session, ?*[*]const u8, ?*usize) Status;
export fn tally_version(?*usize) [*]const u8;
export fn tally_abi_version() u32;
```

Design notes:
- **No null-terminated strings.** All inputs take `(ptr, len)` pairs. This prevents buffer overread, allows binary data in expressions if ever needed, and is the idiomatic C pattern for length-known strings.
- **A session, not a function.** `Environment` outlives an evaluation, so the handle does too: `x = 5` then `x * 2` works, and `Ans` has a value. This is what the one-shot `tally_eval` in the original sketch could not do.
- **`tally_result_free` is gone.** Results are borrowed from the session (6.2), so there is nothing for a caller to free and no way to free it wrongly.
- **JSON payloads**, written by `std.json` rather than by hand, so escaping is not a local invention. A standard result is
  `{"ok":true,"display":"256","exact":true,"truncated":false,"bases":{"hex":"01 00",...}}`,
  with `bases` present only when the expression used a non-decimal literal (FR-1.9) and
  `conversion` present only when it was a unit conversion. Programmer mode returns every
  row the screen shows. An error is `{"ok":false,"error":"division by zero"}`, worded by
  `engine.phrase`, which is where the CLI and TUI get the same sentence.
- **Statuses distinguish three failures**: the expression was bad (`eval_error`, with the
  reason in the JSON), the machine is out of memory (`out_of_memory`, with no JSON,
  because there may be no memory to write it), or the call itself was malformed
  (`invalid_argument`, which touches nothing).
- **A units catalogue**, so a picker is filled from `units.unitsIn` and the aliases table
  rather than from a list retyped in Kotlin.

### 6.1 The decisions this design still owes

The boundary is designed with the Android app rather than ahead of it: the JNI layer is
the only caller, so its access pattern decides the shape. Each decision below is
additive - the Zig API the CLI and TUI use needs nothing new to support any of them.

1. **Session lifetime.** `Environment` holds the variables and the last answer, and
   both frontends keep one alive across evaluations. A one-shot `tally_eval` cannot:
   `x = 5` then `x * 2` would fail, and `Ans` would never have a value, on the surface
   least able to compensate because a phone has no scrollback to retype from. The C API
   needs an opaque handle (`tally_session_new` / `tally_session_free`, with every other
   entry point taking one). Decide this first: it changes every signature.
2. **Memory ownership.** See 6.2, which is the longest of these because it is the one
   that fails silently.
3. **Who chooses the display budget.** `Number.render` takes `FormatOptions`, and
   NFR-9.9 says the frontend supplies them; a phone screen is not an 80-column terminal
   and should not inherit one's digit counts. Either the options cross the ABI as
   fields on the session config, or the C layer invents a budget and Android lives with
   it. The CLI and TUI each declare their own, so there is a precedent to copy rather
   than a question to answer from scratch.
4. **What the JSON carries.** A result is more than a string in three places: the
   multi-base rows of programmer mode, the decomposition of the float view, and the
   amortization schedule. The unit tables and the financial forms also need
   enumerating, or Android has to hardcode lists the engine already owns. Rendering
   inside the library keeps one grouping rule (NFR-7) and one set of words for errors
   (`engine.phrase`), which argues for the JSON carrying rendered text alongside the
   raw values rather than values alone. Whatever shape this takes is also what a CLI
   `--json` would print, which is why the old FR-6.9 was removed rather than specified
   separately.

### 6.2 Memory ownership across the boundary

Every engine entry point takes an `Allocator`; nothing allocates behind a caller's
back. That is a good position to start from and it means the ABI gets to choose, so the
choice should be made explicitly rather than inherited from the first export written.

**What JNI actually does.** Kotlin declares an `external fun`, calls it, and reads the
returned bytes into a `ByteArray` or `String` before returning from the same JNI frame.
The copy is immediate and the app then owns a JVM object. Nothing on the Kotlin side
wants to hold a native pointer, and nothing can be trusted to free one on a predictable
schedule: a `ViewModel` is cleared whenever Android decides.

**Options considered.**

- *A library-owned global allocator*, with `tally_result_free` handing memory back to
  it. This is the shape the current stub implies. It puts a mutable global in the
  shipped library, which is the one property the engine does not have today (the only
  container-level `var` in the tree is inside a test). It is also where the
  cross-allocator free bug lives: any path that frees a result after its session is
  gone, or through the wrong allocator, is a corruption rather than an error. A global
  `DebugAllocator` never runs its leak check in a shared library either, so leaks go
  unreported.
- *A caller-provided buffer*, snprintf style: the app passes a buffer and a capacity,
  the library writes into it and reports the length it needed. No ownership question at
  all, no free, thread-safe by construction, and every byte is accounted for as JVM
  memory. The cost is the two-call pattern when a result does not fit, which for an
  amortization schedule is the common case rather than the rare one.
- *Caller-provided allocator callbacks.* The app passes malloc/free function pointers
  at session creation. Maximum control, and more machinery than a calculator needs.

**The recommendation.** The session owns all of it, and results are borrowed:

- `tally_session_new` allocates a session that holds the `Environment`, a scratch arena
  reset at the end of every call, and a reusable result buffer. No global state: two
  sessions share nothing, so a test and an app can hold one each.
- A result is a `(ptr, len)` into that session's result buffer, valid until the next
  call on the same session or until `tally_session_free`. The caller copies it
  immediately, which is what JNI was going to do anyway. `tally_result_free` disappears,
  and with it every way to free the wrong thing at the wrong time.
- One session is used from one thread at a time. That is what a `ViewModel` does
  naturally, and it keeps locks out of the library. Documented rather than enforced,
  because enforcing it means a mutex on every call for a constraint the only caller
  already satisfies.
- Out of memory is a status code on every export, never a crash. The engine already
  threads `error.OutOfMemory` through every path, so this costs nothing to honour.

#### Three lifetimes, three allocators

The split is not a preference; it is what the engine's own ownership rules already
imply. `Environment.setVar` and `setAns` clone into the environment's own allocator
(`evaluator.zig`), while `evalStringInfo(env, allocator, source)` builds the parse tree
and the returned value from the allocator it is handed. So:

| Lifetime | Holder | Allocator |
|---|---|---|
| Session: variables, `Ans`, the result buffer | `Environment`, `ArrayList(u8)` | the session's general-purpose allocator |
| One call: parse tree, intermediate rationals, rendered text | nothing; the arena owns it | `ArenaAllocator` over the session allocator, `reset(.retain_capacity)` at the end of each call |
| The bytes handed back | the session's result buffer | session allocator, `clearRetainingCapacity` per call |

- **The session allocator is `std.heap.page_allocator`** at the C boundary, and the
  loader chose it, not taste. The Android library declares no dynamic dependencies (6.3),
  so every symbol it references must be one it defines: `smp_allocator` keeps its
  per-thread state in a thread-local, which emits a TLS segment and an undefined
  `__tls_get_addr` that only Bionic's libc can satisfy. It links on a desktop and fails in
  `dlopen` on a device, before any code runs. `std.heap.DebugAllocator` over
  `page_allocator` is free of that symbol and is the upgrade if page granularity ever
  costs anything measurable; what rules out page granularity being a problem today is the
  arena below, which buys pages in chunks and hands out bytes. The allocations that do hit
  `page_allocator` one for one are `Environment` variable clones and the geometric growth
  of the result buffer, both bounded by what a person types.
- **The allocator is a parameter everywhere above the boundary.** The Zig-visible
  session type takes an `Allocator`, so tests pass `std.testing.allocator` and get leak
  detection; only the `export fn` picks a default. That is how the ABI gets leak-checked
  without the library carrying a debug allocator into production. It is also what made the
  fix above a one-line change to one function.
- **`retain_capacity` is what makes the steady state cheap.** The first evaluation buys
  the arena's pages and every later one reuses them, so a calculator being typed into
  stops calling the backing allocator almost entirely.

**One rule this imposes on the ABI code**, learned by writing the probe rather than by
thinking about it: values allocated from the arena must never be individually `deinit`'d.
The arena owns them and the reset frees them, and a `defer value.deinit()` in the same
scope as the reset runs *after* it - which segfaulted on the first attempt, freeing
big-integer limbs into memory the arena had already reclaimed. With an arena the teardown
is the reset, and nothing else.

A probe that ran `x = 2^100`, then `x + 1`, then `Ans / 2`, resetting the arena between
each, produced exactly `633,825,300,114,114,700,748,351,602,688.5` and leaked nothing
under the testing allocator. That is the shape the real `tally_eval` should have.

**What this trades away.** A borrowed pointer is a rule the caller has to follow: hold
it past the next call and it is stale. The alternative that removes the rule is the
caller-provided buffer, at the cost of a size-negotiation round trip. If the JNI layer
turns out to want a pointer it can keep, the caller-provided buffer is the fallback, and
the switch touches only the ABI: the session design above is unchanged either way.

**What was verified, and what is still assumed.** The cross-compile has now been run.
Building the engine for `aarch64-linux-android` and `x86_64-linux-android` produces a
shared object per ABI with **no dynamic dependencies at all** (zero `DT_NEEDED` entries),
containing the full exact tier: a probe that evaluated `2^100 + 1` and rendered it
through `Number.render` compiled and linked on both, at 230KB under `ReleaseSmall`. No
NDK was involved, and the three-lifetime design above compiles for both ABIs too. The
shipped libraries, with the panic machinery removed below, are 170KB to 186KB.

Asking for `-lc` on those targets fails outright: Zig 0.16 bundles glibc and musl and no
Bionic, so it reports `unable to provide libc for target 'aarch64-linux...android.29'`
and suggests the gnu and musl triples instead. Anyone wanting libc there needs an NDK
sysroot. That is what removed `std.heap.c_allocator` from this design - it was the
recommendation here until the build was actually attempted - and the upside is a library
that needs no NDK at all. The cost is that allocations do not pass through `malloc`, so
Android's malloc-based tooling cannot attribute them; for a calculator whose steady state
is an arena reset per keystroke, that is a fair trade.

**No longer assumed.** The library loads under `System.loadLibrary`, the JVM resolves the
symbols, and the engine computes correctly on a device: on an Android 15 x86_64 image with
16 KiB pages, `2+3*4` gave `14`, `100 km to mi` gave
`62.13711922373339696174 mi`, `x = 7` then `x * 6` gave `42` - which is the
`Environment`-survives-the-arena-reset rule holding across calls - and `1/0` reported
`division by zero` rather than crashing. The 10 instrumented tests pass on the same image.
What remains untested is a physical device, arm64-v8a in particular, and behaviour under
real memory pressure.

**What a library with no `DT_NEEDED` actually costs, found on a device.** The zero above
is a constraint, not just a property, and the first build that ran on an emulator did not
load at all:

```
java.lang.UnsatisfiedLinkError: dlopen failed: cannot locate symbol "__tls_get_addr"
  referenced by ".../lib/x86_64/libtally.so"
```

Nothing in the engine asked for a libc symbol on purpose. Three pieces of std did, all on
paths that had nothing to do with arithmetic:

| Symbol | Pulled in by | Removed by |
|---|---|---|
| `__tls_get_addr` | `smp_allocator`'s thread-local | `page_allocator` (6.2) |
| `__tls_get_addr`, `getauxval` | std's default panic handler: a thread-local recursion guard, and reading the library's own ELF headers to print a stack trace | a panic handler that writes the message to stderr and traps, letting Android's own crash handler produce the tombstone |
| `getauxval` (arm64-v8a only) | `std.heap.pageSize()`, a runtime auxv query wherever Zig's `page_size_min` and `page_size_max` differ - which is aarch64 alone, at 4 KiB to 64 KiB | `std.options.queryPageSize` returning 16 KiB, with only the *maximum* overridden |

Two things about that last row are worth keeping. It reproduced on **arm64-v8a only**,
so the x86_64 emulator that caught the first failure would have passed it while most real
phones failed - the symbol audit below is what catches that class, not testing. And
`page_size_min` was deliberately left alone: std documents it as the alignment a caller
may assume from a page allocation, and on a 4 KiB kernel `mmap` returns 4 KiB-aligned
memory, so raising it would promise an alignment the kernel does not give. Overriding the
ceiling and the query rounds lengths up, which is the safe direction.

The general lesson is that a freestanding shared library's dependencies are decided by
code that never runs. Two of the three came from a debugging aid on the panic path, and
with `BIND_NOW` set - it is, on all three ABIs - even an unreferenced PLT entry is
resolved at load, so "nothing calls it" is not a defence. The audit is therefore part of
the build rather than a one-time check: `zig build android` runs `build/audit_android.zig`
over each ABI's library before installing any of them, and requires zero `DT_NEEDED`, zero
undefined dynamic symbols, no TLS segment, `LOAD` aligned to 0x4000, the right ELF machine,
and the JNI entry points exported. `zig build test` holds the auditor itself to failing on
a fixture library that breaks every one of those rules (Task 5.32). Removing the
panic machinery also took the libraries from ~290KB to ~170-186KB.

### 6.4 How Kotlin reaches the C ABI

**Decided: a hand-written `engine/src/jni.zig`, compiled only for Android, with no NDK.**

A Kotlin `external fun` cannot call `tally_eval` directly; something has to translate
`jstring` and `JNIEnv*` into pointers and lengths (design 6.3). Three ways to get that
glue were considered:

1. **`engine/src/jni.zig`, compiled only for Android.** The glue stays in one language, is
   testable from Zig, and adds no dependency to the app. It needs the JNI type
   definitions, which means either the NDK's `jni.h` or hand-declaring what it uses.
2. **A small C shim compiled by Gradle** (`externalNativeBuild` with CMake). Standard
   Android practice, and it moves native compilation into Gradle, which this design has
   kept out.
3. **JNA**, which calls a plain C ABI with no per-project glue at all. Cheapest to start,
   and it costs a dependency and per-call marshalling.

The first, without `jni.h`, because the library already builds with no NDK and no libc
(6.2) and dragging in a sysroot for three functions would undo that.

**What that costs, and how it is held down.** `JNIEnv*` is a pointer to a table of
function pointers at fixed indices, so reaching `NewStringUTF`, `GetStringUTFChars` and
`ReleaseStringUTFChars` without the header means four integers have to be right, and a
wrong one is a jump into the wrong function rather than a compile error. Three things
guard it:

- The table is declared at its full published length (233 entries since JNI 1.6, with
  `GetObjectRefType` last), and a comptime check rejects an index past the end. The
  arithmetic that arrives at exactly that length is written out in the file, because that
  count is what catches a dropped entry.
- `JNI_OnLoad` proves the indices against the JVM that is actually running, before
  anything else: it checks the version, then round-trips a string through `NewStringUTF`
  and `GetStringUTFChars` and compares the bytes. On failure it returns `JNI_ERR`, so
  `System.loadLibrary` throws at startup rather than the app crashing later inside an
  evaluation.
- The tests run every entry point against a synthetic function table, covering the
  marshalling, the handle arithmetic and the self-check in both directions (including a
  deliberately broken table). They cannot check the indices themselves, because they
  supply the table.
- **A real JVM can, and not only Android's.** JNI's function table is fixed by the
  specification rather than by the platform, so a desktop JVM resolves the same indices an
  Android runtime does. `zig build jvm-test` builds the library for the host, compiles
  `engine/test/java/dev/lerch/tally/TallyEngine.java`, and runs it: `System.loadLibrary`
  executes `JNI_OnLoad`, and the test then drives every entry point, including a catalogue
  string over 4KB. Moving one index by a single slot makes that step fail, which is how we
  know the check has teeth. It is a separate step rather than part of `zig build test`
  because it needs a JDK and nothing else in the suite does.

**The glue is also what makes borrowed results safe.** The bytes from `tally_eval` become
a Java string inside the same function that asked for them, so the app never holds a
native pointer and cannot outlive one. `c_api` leaves a NUL just past the reported length
for exactly this, so the copy the JVM makes is the only copy in the call.

The C ABI is unchanged by this choice: a Swift or C consumer links the same library and
calls it directly.

### 6.3 Who the ABI is for, and what is actually Android-specific

The shape in 6.2 was chosen from Android's access pattern, which invites a fair
question: should the exports be named for Android, or built differently per target? The
answer is no to the first and yes to the second, for reasons that are not symmetrical.

**The C ABI is not Android-specific, and its names should not pretend to be.** Take the
decisions one at a time and ask which consumer they came from:

- *A session handle* is what any caller wants. Variables and `Ans` outlive a single
  evaluation for a C program, a Swift app or a WASM page exactly as they do for Kotlin.
- *Borrowed results* suit every managed binding, because they all copy on receipt: JNI
  into a `ByteArray`, Swift into a `String` or `Data`, JS into a string. The rule only
  chafes for a raw C caller that wants to accumulate results without copying, and
  `sqlite3_column_text` has held that exact contract for two decades in the most widely
  embedded C library there is.
- *Status codes instead of crashes on OOM* is table stakes anywhere.
- *One session per thread at a time* is what a `ViewModel` does naturally and what a C
  caller can arrange trivially.

Only two choices are platform-flavoured, and neither is visible in a signature: using
`c_allocator` for the session's long-lived allocations (internal), and preferring JSON
for compound results (a preference Kotlin, Swift and JS all share).

So the exports keep names that say what they do: `tally_session_new`, `tally_eval`,
`tally_session_free`. Naming them `tally_android_eval` would encode the first consumer
into a contract that outlives it, and the second consumer would then either call
functions labelled for a platform it is not, or get a duplicate set to keep in step.
This project has already renamed one thing for that reason: `Coverage.addModule` became
`addReport` because the old name described the caller's mental model rather than the
thing itself. If a future consumer genuinely cannot live with a borrowed pointer, the
answer is one more function beside the existing ones (`tally_eval_into`, taking a
caller-provided buffer), not a rename and not a parallel set.

**There is an Android-specific layer, and it is not the C ABI.** A Kotlin `external fun`
does not call `tally_eval`. JNI resolves either a symbol named
`Java_<package>_<Class>_<method>` or whatever `JNI_OnLoad` registers with
`RegisterNatives`, and either way the function's signature is in JNI's terms: a
`JNIEnv*`, a `jobject`, and `jstring` arguments that have to be pinned with
`GetStringUTFChars` and released again. That translation is genuinely Android's:

- it names a Java package, so it cannot be shared with anything else,
- it needs `jni.h` types that do not exist on any other target,
- and it is thin: convert, call the C ABI, copy the result into a `jstring` or
  `ByteArray`, return.

That layer belongs in its own file (`engine/src/jni.zig`), compiled only for Android
behind a build option, with names that do say Android because JNI requires it. The C ABI
stays byte-identical on every target; Android gets an additional, thinner set of exports
on top of it. A Swift or C consumer links the same library and calls the C ABI directly,
with no shim at all, because Swift imports C headers natively.

**The shim is also what makes borrowed results safe here.** The copy into JVM memory
happens inside `jni.zig`, in the same function, before control returns to Kotlin. The
app never holds a native pointer and cannot outlive one, so the lifetime rule in 6.2 is
enforced by code in this repository that can be tested, rather than by an app developer
remembering a sentence in a document. That is a better position than the caller-buffer
alternative would leave us in, and it is the argument that settled 6.2 for me.

Two things to add while the boundary is being written, both cheap and both awkward to
retrofit:

- **A hand-written `include/tally.h`.** Zig no longer emits reliable C headers, and the
  header is what a Swift or C consumer actually compiles against. Writing it by hand is
  fine; leaving it to drift is not, so a test should compile it against the real exports
  (a `translate-c` of the header, or a C file that takes the address of every function,
  built as part of `zig build test`).
- **`tally_abi_version()` beside `tally_version()`.** Android ships a prebuilt `.so`
  that can fall out of step with the Kotlin calling it, and a struct layout or an
  argument order that changed silently is a crash in the field rather than an error. The
  product version and the ABI version are different facts and should be separately
  readable.

### 6.5 Preview: an evaluation that stores nothing

**Decided and built, for the live result on the standard screen (9.2).** A screen that
answers as you type calls the engine on every keystroke, and `tally_eval` is the wrong
call for that: typing `x = 7` would assign `x` at `x =` ... `7`, and every intermediate
answer would overwrite `Ans`, so `Ans` would mean "whatever was last on screen" rather
than "what I last committed". Both are silent - the numbers are plausible - which is
the kind of wrong a calculator cannot afford.

```zig
export fn tally_preview(?*Session, ?[*]const u8, usize, c_int, ?*[*]const u8, ?*usize) Status;
```

Same arguments, same JSON, same borrowing rule as `tally_eval`; the only difference is
that nothing in the session changes. An assignment previews as the value it would store,
and a built-in target (`pi = 3`) previews as the error committing it would give.

- **A separate function, not a flag.** A `bool` on `tally_eval` changes a signature that
  shipped; folding a bit into `mode` makes one integer mean two things. A new export is
  additive, and `abi_version` moves to 2 so a prebuilt library without it is refused at
  startup rather than failing on the first keystroke.
- **The guarantee is the type, not a branch.** Assignment is a statement (Task 5.19): the
  parser only produces it at the root, never inside an expression. So `evalStringInfo`
  now handles the root assignment itself, and the recursive evaluator below it takes a
  `*const Environment` - it *cannot* store anything. The preview path,
  `engine.previewStringInfo`, is the same walk without the two writes at the end, and it
  takes a `*const Environment` too, so "preview mutated the session" is a compile error
  rather than a test. The CLI and TUI get the same function; neither uses it yet.
- **Programmer mode is already pure** - it never touches the environment - so its preview
  is its evaluation.

### 6.6 Convert: one value, every unit

**Decided and built, for the converter screen (9.6).**

```zig
export fn tally_convert(?*Session, value: ?[*]const u8, usize, unit: ?[*]const u8, usize, ?*[*]const u8, ?*usize) Status;
```

`{"ok":true,"input":"100","from":"C","category":"temperature","results":[{"unit":"C",
"display":"100","exact":true,"truncated":false},{"unit":"F","display":"212",...},...]}`

- **The whole category in one call,** because the screen shows all of it. The
  alternative - one `tally_eval("100 C to F")` per row - is a dozen JNI round trips and
  a dozen parses per keystroke, and puts the list of units in Kotlin.
- **The value is an expression, previewed** (6.5): `6*12` in inches works, and nothing
  in the session changes.
- **A row that fails carries its own `error`** and leaves the rest of the table alone.
- **The rendering budget is the session's** (`Config`, 6.1 point 3), so the converter
  sets fewer digits on its own session than the calculator does. Over JNI that is
  `configureDisplay`, which reads the current config, changes the two digit counts and
  writes it back, so the other fields keep their values.
- `abi_version` 3.

---

### 6.7 Save and load: a session that survives the process

**Decided and built, for the calculator reopening as it was left (9.2).** The engine
holds the variables and `Ans`, so the app saving only what its screen shows would bring
back `x * 2` without `x`.

```zig
export fn tally_session_save(?*Session, ?*[*]const u8, ?*usize) Status;
export fn tally_session_load(?*Session, ?[*]const u8, usize) Status;
```

`{"format":1,"ans":{"exact":"1/7"},"variables":[{"name":"r","value":{"bits":"3ff6a09e667f3bcd"}}]}`

- **Exact, both tiers.** An exact value is saved as `toFractionString` writes it, every
  digit; it loads through `Rational.parseFraction`, which has no length cap, because
  `parse`'s 512-digit limit is right for typing and wrong for `factorial(1000)`. An
  inexact value is saved as its IEEE-754 bits, so it comes back as the same float and
  not a decimal near it. A reloaded session saves to the same bytes it was loaded from.
- **Not a replay.** Re-evaluating the history on launch was the alternative and is
  wrong twice: `Ans * 2` depends on every answer before it, so history cannot be trimmed
  without changing values, and clearing it would silently drop the variables.
- **All or nothing.** The text is read and checked completely - format, a name an
  assignment could have made, no duplicates, exactly one well-formed value form - and
  only then swapped in. A refused load leaves the session untouched. Unknown fields are
  ignored, so a later format can add to it.
- **Deterministic:** variables are listed by name.
- **Not included:** the configuration, which is the frontend's to set.
- Tested by round trips (2^100, 1/3, sqrt(2), factorial(500), `Ans`), a byte-identical
  re-save, a load that replaces rather than merges, fourteen malformed states each
  leaving the session as it was, and an allocation-failure sweep over save and load. ABI
  version 5.

### 6.8 Programmer mode from a frontend that holds the value

**Built, for the programmer screen (9.3), ABI version 6.** Two additions, both because
the screen keeps a register rather than a text answer:

- **`pattern` in the programmer result:** the value masked to the width, as lowercase
  hex with no prefix or grouping (`"pattern":"ff"`). The rows are for reading and their
  format is free to change; this is for holding. Unsigned at the width, so a negative
  8-bit result is `f0`, never sign-extended past it. Before it, the only way to learn
  the value was to parse the binary row.
- **`configureProgrammer(handle, bits, signed, bigEndian)` in JNI:** read the session's
  configuration, change the three programmer fields, configure. The display budget is
  untouched, as `configureDisplay` leaves the programmer fields untouched. The C ABI
  already had this through `tally_session_configure`; only JNI lacked it.

Tested in `c_api` (masking, a negative at 8 bits, zero, all 128 bits of -1), the C ABI
check through the header, JNI against the synthetic table (each of the three settings
visible in one result, a nonzero `jboolean` as true, refused widths changing nothing),
`jvm-test` (an int and two booleans through a real JVM), and an instrumented test.


## 7. CLI Design

```
tally [OPTIONS] <expression>
tally convert <value> <from-unit> [to] <to-unit>
tally amort <principal> <rate-per-period> <periods> [payment] [--monthly] [--summary] [--exact]
tally struct <definition | file | -> [--abi <name>] [--color <when>]

Options:
  -p, --programmer       Programmer mode
  --bits <N>             Bit width: 8, 16, 32, 64, 128 (default 64). Implies -p
  --signed / --unsigned  How to read programmer values (default signed). Imply -p
  --endian <big|little>  Byte order of the hex and ASCII rows (default big). Implies -p
  -h, --help             Show help
  --version              Show version

Each subcommand answers -h with its own usage.
```

The flags this section used to list (`-b`, `--base`, `--json`) were never built.
`--bits` is the spelling, there is no way to select a single output base (the
multi-base view appears when the expression used a non-decimal literal), and JSON
output belongs to the C API rather than the CLI. `--abi` exists, but on `tally struct`
rather than at the top level, since nothing else has an ABI.

### CLI Output Examples

Standard:
```
$ tally "2^32 - 1"
4,294,967,295
```

Programmer (actual output, verified against the binary):
```
$ tally -p "0xFF & 0x0F"
  dec(signed):   15
  dec(unsigned): 15
  hex: 00 00 00 00 00 00 00 0F
  oct: 0 000 000 000 000 000 000 017
  bin: 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 1111
```
Separators are spaces, not underscores, and the base prefix appears only in the
clipboard form. There is no `bits:` line.

Struct (actual output). Each member's letter in the table is its letter in the map,
`.` is padding, and the profile is named because the answer depends on it:
```
$ tally struct 'struct packet { uint8_t kind; uint32_t len; char name[24]; void *next; }'
struct packet
ABI sysv64: 64-bit Linux and macOS (x86-64 SysV, AArch64)

     Offset  Size  Align  Type      Name
  a       0     1      1  uint8_t   kind
          1     3                   (padding)
  b       4     4      4  uint32_t  len
  c       8    24      1  char[24]  name
  d      32     8      8  void *    next

  40 bytes, alignment 8, 3 bytes of padding (7.5%); 37 bytes packed

  0x00  a . . .  b b b b  c c c c  c c c c
  0x10  c c c c  c c c c  c c c c  c c c c
  0x20  d d d d  d d d d
```
The sketch this replaced used box-drawing rules and a middle dot, a `Padding` column, and
a map of one bracketed run per member. The output is ASCII, a padding run is a row of its
own so the table reads in address order, and the map is one letter per byte: sixteen
bytes a row is what a hex dump looks like, so the eye already knows how to read it. Rows
that repeat collapse to `*`, as in hexdump, and the map is found from the layout's
segments rather than walked byte by byte, so a 2 GiB array costs three lines.

On a terminal the same output is colored (FR-6.5.1): a member's key and name in the
table and its run of bytes in the map share one of the terminal's six hues, and padding
is faint, so the map reads as colored blocks with gaps between them. Color is layered on
rather than substituted: `format.Paint` is `plain` or `ansi`, the renderer writes the
same text either way plus escape codes in the second case, and a test strips the codes
and compares the result to the plain output byte for byte. `main` decides which, from
`--color`, whether stdout supports escape codes, `NO_COLOR` and `TERM`, through a pure
`ColorChoice.resolve` that is tested on its own. Three choices behind it:

- **The terminal's palette, not fixed RGB.** The TUI's Molokai triples (open item 17)
  ignore the user's theme; SGR 31-36 are whatever the theme says, and a theme is built
  so its own colors read on its own background.
- **No background, ever.** Forcing black was considered as insurance against an
  unreadable hue and rejected: it would undo the theme on every light terminal to fix a
  problem the theme already solves.
- **Faint for padding, not bright black.** Several themes (Solarized among them) draw
  bright black in nearly the background color, which would make padding vanish where it
  should recede. Every code begins with a reset, because faint persists until cleared.

An error names its place:
```
$ tally struct 'struct { int a; uint33_t b; }'
error: unknown type (typedefs and macros from elsewhere are not visible)
  line 1, column 17: uint33_t
```

Unit conversion (actual output):
```
$ tally convert 100 km mi
100 km = 62.13711922373339696174 mi

$ tally "72 F to C"
72 F = 22.22222222222222222222 C
```
Both operands are echoed, canonical short names are used rather than long or
symbol forms, and the full exact expansion is shown (20 fractional digits for a
non-terminating one). `tally "5 kg + 3 lb"` is FR-4.2 and is NOT implemented: it
reports `error: unexpected token`.

---

## 8. TUI Layout

The mockups in this section are sketches of intent, not records of output. Where one
disagrees with the program, the program is right: the frames in `src/tui.zig`'s render
tests are drawn by the real draw path and asserted character by character, which is
where to look for what a view actually produces. Sketches that are known to have
drifted are marked.

### 8.0.0 How the TUI is tested

Terminal code is usually left uncovered on the grounds that it needs a terminal.
Most of it does not. Two harnesses cover nearly all of it:

- **Rendered frames.** `src/tui/test_render.zig` draws a real frame through the
  real widget draw path into a real surface, then reads the cells back as rows of
  text. Assertions are made against what a user would see (`"= PMT  -1,199.10"`,
  `"rows 1-7 of 360"`), plus two structural checks bundled as
  `test_render.expectSound(rows, full_width_rows)`: `furniture(rows).intact()`, which
  checks that the separator, prompt and status rows are still where they belong, and
  `noTextClipped`, which checks that no row other than the ones drawn full width on
  purpose reaches the final column. The first catches content that overflowed its
  region downward; the second catches content too wide for the terminal, which
  `draw.writeStr` truncates in silence.

  This originally offered `wellFormed(rows, width)` instead, described here as a
  check that no column had been miscomputed. It compared each row's length against
  the width it had just been allocated with, so it could never fail. Two layout
  bugs (programmer rows drawn over the prompt at 100x16, financial chips drawn over
  it at 20x5) lived under a green suite because of it. `noTextClipped` was written at
  the same time and then left uncalled for as long, which hid two more: the 64-bit
  binary row needed 90 columns and lost its low bits on an 80-column terminal, and
  every mode's status line lost its last hint mid-word. Style is still not
  observable: `flatten` keeps graphemes and drops attributes, so focus highlighting
  and the cursor cannot be asserted, and tests that care assert a neighbouring
  glyph and say so.
- **Real event handlers.** `vxfw.EventContext` is constructible in a test, so key
  presses and mouse events go through `handleKey` and `handleMouse` rather than
  through a reimplementation of them. This is what catches a binding that was
  never routed, or one mode swallowing another mode's keys.

What is left uncovered is the terminal boundary itself: the event loop, `vaxis`
initialisation, and `main`. Coverage is reported per source tree (engine, CLI,
TUI) with disjoint include paths, so a file is never accounted for twice and a
query tool never has to guess which report answers for it.

### 8.0 Mouse Input Architecture

The TUI is mouse-driven as well as keyboard-driven (FR-7.11). Rather than each
view doing its own coordinate arithmetic against hardcoded layout constants, hit
targets are registered as a side effect of drawing:

```zig
pub const Action = union(enum) {
    mode: Mode,                                          // tab bar
    prog_field: struct { field: ProgField, bit: ?u7 },   // focus field, optional cursor
    toggle_bit: u7,                                       // flip one bit
    focus_input, close_help, toggle_float,
    cycle_width, toggle_endian, toggle_signedness, toggle_float_format,
    conv_category: UnitCategory, conv_from: usize, conv_to: usize, conv_swap,
    fin_form: Form, fin_field: usize,                     // financial chips and rows
};

pub const RegionSet = struct {
    items: [512]HitRegion,   // { row, col, len, action }
    count: usize,
    pub fn clear(self: *RegionSet) void;
    pub fn add(self: *RegionSet, row: u16, col: u16, len: u16, action: Action) void;
    pub fn at(self: *const RegionSet, row: u16, col: u16) ?Action;
};
```

Key properties:

- **Regions are rebuilt every frame.** `clearRegions()` runs at the top of the
  draw function, and each view calls `addRegion` right where it draws the thing.
  Hit targets therefore cannot drift out of sync with what is on screen, which is
  the usual failure mode for hand-maintained click maps.

  With one caveat that was found by review: registration is co-located with
  drawing, but drawing itself had no bounds check, so a row drawn off the bottom
  registered a region anyway and a click on the separator focused an invisible
  field. Co-location keeps the mapping honest only as far as the drawing is; the
  height guards added to the programmer and convert views are what make the
  property hold.
- **Newest region wins.** `at()` searches backwards, so a view can register a
  broad row-wide fallback first (click anywhere on the HEX row to focus it) and
  then finer targets on top (click a specific nibble to put the cursor there).
- **Draw-time registration means one source of truth.** The same loop that
  decides where a bit character goes also registers that cell, so the mapping
  from cell to bit index is written once. `registerDigitRegions` mirrors
  `drawFieldWithCursor`'s digit walk for the same reason.
- **Left press only.** Release, motion, and drag are ignored so one physical
  click produces exactly one action. The wheel is the one exception: in financial
  mode `wheel_up`/`wheel_down` scroll the amortization schedule, handled before
  the press filter because a wheel event is not a press. The wheel does not go
  through the region table at all, since it acts on the view rather than on a
  specific cell.
- **A fixed-size buffer, not an allocation.** Drawing happens on every keystroke
  and must not fail; an exhausted budget silently drops extra regions (a click
  does nothing) instead of erroring. 512 comfortably covers the worst case, the
  128-bit programmer view.

vxfw already puts the terminal in mouse mode and hit-tests surfaces, delivering
`.mouse` events to the root widget with local coordinates equal to screen
coordinates, so no terminal-level setup is needed here.

Click semantics are chosen per field to match what the data means: a bit grid
cell and a BIN digit each represent exactly one bit, so clicking flips it, while
a HEX nibble or OCT digit holds several bits with no single sensible "toggle", so
clicking places the cursor for typing instead.

### 8.1 Standard Mode
```
+- Tally ----------------- [Standard] [Programmer] [Financial] [Convert] -+
|                                                                        |
|  History:                                                              |
|    2^10 = 1024                                                         |
|    sqrt(144) = 12                                                      |
|    Ans * 2 = 24                                                        |
|                                                                        |
|  ---------------------------------------------------------------       |
|  > 3 * pi + 1_                                                         |
|                                                                        |
|  = 10.42477796...                                                      |
|                                                                        |
+- ?:help | Tab:mode | Enter:eval | Ctrl-L:clear | Ctrl-C:quit -----------+
```

The footer is the real status line. The `[d]ec [h]ex [o]ct [b]in` quick-switch it
used to show was FR-7.8, which has been removed: those letters are hex and binary
digits once the value fields became editable.

Two details the sketch simplifies: there is no "History:" heading, and the answer is
not repeated under the prompt. A result appears in the history list as `= value` on the
line under its expression, which is where the sketch's `= 10.42...` line comes from.

### 8.2 Programmer Mode

A real 80-column frame, 64-bit, value 0xDEADBEEFCAFEF00D:

```
| Tally                               Standard  Programmer  Financial  Convert   |
|                                                                                |
|  Bits: 64  Signed: yes  Endian: BE                            [float: Ctrl-F]  |
|                                                                                |
|  1101 1110 1010 1101 1011 1110 1110 1111                                       |
|  1100 1010 1111 1110 1111 0000 0000 1101                                       |
|                                                                                |
|  DEC(s):  -2,401,053,089,206,439,923                                           |
|  DEC(u):  16,045,690,984,503,111,693                                           |
|  HEX:     DE AD BE EF CA FE F0 0D                                              |
|  ASCII:    .  .  .  .  .  .  .  .                                              |
|  OCT:     1 572 555 756 771 277 570 015                                        |
|  BIN:     1101 1110 1010 1101 1011 1110 1110 1111                              |
|           1100 1010 1111 1110 1111 0000 0000 1101                              |
|                                                                                |
|  (history)                                                                     |
|--------------------------------------------------------------------------------|
| >                                                                              |
| Tab:mode | Arrows:nav | Space:toggle | Up/Down:field | Ctrl-W:width            |
```

The binary row wraps at 32 bits because 64 will not fit an 80-column terminal
(FR-7.3.2); a 90-column one shows it on one line. The status line drops whole hints
from the end rather than cutting one in half (FR-7.9.1), which is why `Ctrl-E:endian`
and `Ctrl-F:float` are absent here and the float affordance sits on the header row
instead.

An earlier wireframe in this section showed a bordered "Bit Pattern (63 -> 0)" box, a
`cursor: bit 3` indicator, `0x`-prefixed hex, and a footer of single-letter keys
(`w:width s:sign e:endian y:yank`). None of that was built: there are no borders, the
prefix appears only in the clipboard form, the width and sign keys are Ctrl-chords
because plain letters are hex digits in an editable field (FR-7.8), and there is no
yank command yet (open item 14).

#### 8.2.1 Programmer Mode - Editable Fields (REVISED DESIGN)

The programmer mode is an **editable multi-field form** where every
representation of the value is live-editable. A change in any field
instantly updates all others. Closer to integer.exposed than a
traditional calculator with a prompt.

Fields (navigable with Up/Down):
1. Bit grid - arrow keys move, Space toggles individual bits
2. DEC(s) - editable signed decimal
3. DEC(u) - editable unsigned decimal
4. HEX - editable hex (space-separated bytes: FF 00 AB CD)
5. ASCII - read-only (derived) view of the bytes, one glyph per byte,
   MSB first, aligned column-for-column under the HEX row directly above
   it. Printable bytes (0x20-0x7E) show as themselves; every other byte
   shows as `.`, matching the `xxd` hex-dump convention (e.g. `.ELF`,
   `...ascii`). Not part of the Up/Down focus cycle since it has nothing
   to edit.
6. OCT - editable octal
7. BIN - editable binary (nibble-separated: 1111 0000)
8. Expression - full expression evaluator (& | ^ ~ << >> etc.)

Field 8 was never built. `ProgField.expression` exists and Up/Down cycles through it,
but no row is drawn for it and no key does anything there, so it reads as a keystroke
that did nothing (open item 18). The expression language is reachable from the input
line instead, which is where it has always been.

Navigation:
- Up/Down moves focus between fields
- When a text field is focused, typing replaces its content;
  value updates on Enter (or live as you type - TBD)
- When bit grid is focused: left/right/up/down navigate, Space toggles
- Tab cycles between Standard/Programmer mode
- Ctrl-W cycles bit width (8/16/32/64/128)
- Ctrl-E toggles endianness display (LE/BE)

Bit width is a non-destructive display lens:
- The stored value keeps full precision (u128). Cycling the width never
  truncates it, so narrowing to a smaller width and then widening again
  restores the hidden upper bits.
- The DEC/HEX/OCT/BIN/ASCII rows and the bit grid show the value masked to
  the current width.
- While the stored value has bits set beyond the current width, a warning
  line is shown ("value exceeds N bits - showing low bits (widen to
  restore)"). It is a warning, not an error: the value is still usable.
- Explicit value edits (typing a decimal digit, toggling a bit, editing a
  hex/oct/bin digit) commit to the current width, clearing any hidden upper
  bits. Only width cycling is non-destructive; deliberately editing at a
  narrow width means you are now working at that width.

Endianness:
- Toggle with Ctrl-E; header shows current setting (`Endian: LE` / `Endian: BE`)
- Default: big-endian. The HEX row's primary job is to show the value in hex,
  so by default it reads MSB-first and matches DEC/OCT/BIN. Little-endian is
  the opt-in "how it sits in x86-64 memory" view.
- Affects: HEX byte display order and ASCII byte order only. In LE the display
  bytes are reversed (e.g. 0xDEADBEEF -> `EF BE AD DE`).
- Does NOT affect: the underlying value, DEC, OCT, or BIN display, nor the
  clipboard `raw` form of HEX (which stays the canonical MSB-first number).
- Rationale for BE default (revised from an earlier LE default): defaulting to
  LE would reverse the HEX row so it no longer matches the number shown in the
  DEC/BIN rows directly beside it, which is surprising in a calculator context.

Text/ASCII literals:
- Single-quoted strings in expressions: `'ELF'`, `'RIFF'`, `'a'`
- Each character becomes one byte packed into the integer
- Packing order follows endianness setting:
  - BE: first char -> most significant used byte (`'AB'` = 0x4142)
  - LE: first char -> least significant byte (`'AB'` = 0x4241)
- Max chars = bit_width / 8 (1 for 8-bit, 2 for 16, 4 for 32, 8 for 64)
- Non-ASCII characters are an error
- Useful for: magic numbers (`'ELF'`), protocol tags, inspecting
  how string bytes pack into integer registers

IEEE 754 float interpretation:
- A sub-view within programmer mode (toggle with a key, e.g. Ctrl-F)
- Reinterprets the current bit pattern as an IEEE 754 float
- Supported formats:
  - float32 (1 sign + 8 exponent + 23 significand, bias 127)
  - float64 (1 sign + 11 exponent + 52 significand, bias 1023)
- Bit grid color-codes the three fields:
  - Sign bit: one color (e.g. pink)
  - Exponent: another color (e.g. cyan)
  - Significand: another color (e.g. green)
- Display below the bit grid shows:
  - Decimal value (exact)
  - Value and ULP use scientific notation for very small/large
    magnitudes (e.g. a subnormal ULP shows as `1.4e-45`), fixed-point
    otherwise, so each row stays on one line
  - Formula: (-1)^s * 2^(e-bias) * 1.mantissa
  - Classification: normal, denormal, zero, infinity, NaN
  - ULP: delta to next representable value
  - Raw fields: sign=0, exp=127 (unbiased: 0), frac=0x000000
- Input: can type a decimal float value (e.g. `3.14`) and it
  shows the closest representable bit pattern, noting if rounding
  occurred
- Auto-entry: switching into programmer mode (Tab) with a non-integer
  value in `ans` opens this float view automatically on the exact f64
  bit pattern, since the integer bit views cannot represent a fraction.
  An integer `ans` uses the integer views as usual. Infinity/NaN also
  open the float view (the only place they are representable).
- Toggling bits in the grid updates the float interpretation live
- Does NOT change bit_width setting - float32 uses 32-bit view,
  float64 uses 64-bit view (auto-switches width when toggling
  float format)

### 8.3 Struct Visualizer (sub-view of Programmer Mode) - DESIGN ONLY, NOT BUILT

The engine behind this exists (section 3); the view does not, deliberately. It waits
until `tally struct` has been used enough to say what an interactive view should do:
whether people paste whole definitions or build them a member at a time, and whether
reordering to watch the padding move is worth a key. The sketch below predates the CLI,
and where they disagree the CLI's table and map (section 7) are the better starting
point, not least because the TUI draws one byte per cell and cannot show the box and
block glyphs this sketch uses.

```
┌─ Tally ────────────────── [Programmer > Struct Layout] ─────────────┐
│ ABI: x86-64 SysV  Endian: LE                                         │
│                                                                        │
│ Definition:                                                            │
│   struct { u32 x; u8 flags; u16 id; u64 ts; }                        │
│                                                                        │
│ ┌─ Memory Map ─────────────────────────────────────────────────────┐  │
│ │ 00 01 02 03 │ 04 │ 05 │ 06 07 │ 08 09 0A 0B 0C 0D 0E 0F │     │  │
│ │ ████████████ │ ▓▓ │ ░░ │ ▒▒▒▒▒ │ ░░░░░░░░░░░░░░░░░░░░░░░ │     │  │
│ │     x        │flag│pad │  id   │           ts              │     │  │
│ └───────────────────────────────────────────────────────────────────┘  │
│                                                                        │
│  Field        Type   Offset  Size  Align  Pad Before                   │
│  x            u32    0       4     4      0                            │
│  flags        u8     4       1     1      0                            │
│  id           u16    6       2     2      1                            │
│  ts           u64    8       8     8      0                            │
│                                                                        │
│  Total: 16 bytes | Alignment: 8 | Padding: 1 byte (6.25%)            │
│  Packed would be: 15 bytes                                             │
└──── a:abi  e:endian  Enter:edit struct  Esc:back ─────────────────────┘
```

### 8.4 Convert Mode

```
Tally                                  [Standard] [Programmer] [Convert]

  Category:
    Length  Mass  Temperature  Time  Digital Storage  Speed  Area
    Volume  Energy  Pressure  Data Rate  Angle

  100 km
  = 62.13711922373339 mi
  1 km = 0.621371192237334 mi

  From                      To
  > nm                        nm
    um                        um
    mm                        mm
    ...                     > mi

  ------------------------------------------------------------------
  > 100
  Arrows:select | Ctrl-S:swap | `:input | Tab:mode | ?:help
```

Structure:

- **Category chips** wrap to as many lines as the terminal width needs. The
  selected chip is highlighted; when the selection zone has focus on the category
  column it is highlighted differently again.
- **The value** comes from the shared input line at the bottom, keeping input
  consistent with the other modes. A bare number is used directly; anything else
  is evaluated as a standard expression first, so `2*3.5` or `sqrt(2)` work as
  input values.
- **The factor line** shows the single multiplicative factor between the two
  units. Temperature is affine, so instead of a misleading number it says so.
- **Two unit columns** (From and To) list every unit in the category with the
  selection marked. Both columns are clickable; the whole column slot is the
  click target, not just the name text, so a one-character unit like `m` is not a
  one-character target.
- If the terminal is too short to show every unit, a `... N more (resize to see
  all)` line is drawn rather than silently truncating the list.

Interaction:

- Backtick toggles between the input zone and the selection zone, matching the
  convention already used in programmer mode.
- In the selection zone, Left/Right move between the category, From, and To
  columns; Up/Down move the selection within the focused column, wrapping.
- Ctrl-S swaps the two units, and works from either zone.
- Selecting a new category resets the unit pair to that category's defaults (its
  base unit plus a distinct second unit), since the previous indices would refer
  to unrelated units in the new table.

---

### 8.5 Financial Mode

```
Tally                     [Standard] [Programmer] [Financial] [Convert]

  Calculation:
     CAGR   Compound   TVM   Amortization

  > Principal           200,000
    Rate per period     0.5 %
    Periods             360
    Payment             (derived)

  Payment 1,199.10 | total interest 231,677.04 | total paid 431,677.04

    Period      Payment     Interest    Principal      Balance
         1     1,199.10     1,000.00       199.10   199,800.90
         2     1,199.10       999.00       200.10   199,600.80
         3     1,199.10       998.00       201.10   199,399.70
         ...
    rows 1-7 of 360  (PgUp/PgDn)
  ------------------------------------------------------------------
  >
  Up/Dn:field | L/R:calc | Enter:eval | Space:END/BGN | Ctrl-U:clear
```

Four forms behind one set of chips: CAGR, Compound, TVM, Amortization. The TVM
form adds a sixth row, an END/BGN toggle for annuity due.

**Solving by omission.** TVM and compound interest solve for whichever field is
left blank, the way a financial calculator does and the way the engine's own
`TvmParams` is shaped. Blank is therefore a meaningful state rather than an error,
and a blank solve-for field renders as `[solve]` instead of looking like missing
input. When the form is not yet answerable it says what it is waiting for ("clear
one field to solve for it"), so an incomplete form is never a silent no-op.
Amortization treats a blank payment differently: it means "derive it", since a
schedule always has a payment.

**Defaults are prefilled, not placeheld.** Compounds/year starts at `1` rather
than showing an empty field that means "annual". That keeps "blank means solve for
this" true for every field the user sees, instead of blank meaning a default in one
place and a solve slot in another. The prefill is baked into the comptime initial
state rather than applied at draw time, because a draw-time default cannot tell
"never touched" from "deliberately cleared". Clearing a non-solvable field has
to report that it needs a value, not try to solve for it.

**A solved rate says which kind it is.** Above annual compounding the compound
form reports `= rate 18.00% nominal (19.56% effective)`. See design 5.2 for why:
the nominal figure alone invites a wrong comparison against a quoted APY, and this
is the only place the calculator produces a rate rather than consuming one.

**Two ways to enter a number, deliberately.** Typing in the form zone goes
straight into the focused field, which is what makes quick entry work. The shared
input line at the bottom evaluates an expression and drops the result into the
focused field, so a value can also be computed from outside the form.

**Fields hold expressions, and group as you type.** `12 * 30` is valid input for a
period count; it displays verbatim in orange with an `(Enter)` prompt, and Enter
evaluates it in place. A plain number is grouped for display as it is typed
(`200` then `0` shows `2,000`), while the buffer keeps the ungrouped text so it
still parses and still round-trips through Enter. Grouping the buffer instead
would mean stripping separators on every read and would make cursor arithmetic
depend on where the commas happen to fall. A typed comma is absorbed for the same
reason.

A field holding an unevaluated expression is reported as such rather than being
treated as empty, since a blank field means "solve for this" in two of the four
forms and silently conflating the two would be a wrong answer rather than a
cosmetic problem.

**Rates say they are rates.** A percent field renders a trailing `%` after the
value and absorbs a typed one, so `6%` and `6` both mean six percent. The label
carries that information too, but not once the eye has moved to the value column,
which is where a bare `6` is ambiguous between a rate and a multiplier.

**Focus styling.** The focused field is a dark selection fill (Molokai's own
selection colour) with the value in its normal foreground, and a single yellow
block cursor. The earlier version reversed bright cyan into the background, which
read as a 1980s terminal and fought every other colour on screen; a neutral fill
keeps the number legible and leaves the cursor as the only bright cell on the row.
The row marker and focused label are yellow, matching the mode's own tab colour
rather than introducing a fourth accent.

**Results are live, not history.** Every keystroke recomputes, so there is
nothing to submit and nothing is appended to history. That is why financial mode
is the one mode whose input line does not produce a history entry.

**The schedule is the reason this mode exists.** Everything else here is
available as an expression function (FR-5.7), but a 360-row table is not a value.
It scrolls with PgUp/PgDn from either zone and with the mouse wheel, and shows
`rows X-Y of N` whenever it is showing a window rather than the whole thing. The
scroll offset is clamped at draw time rather than at scroll time, so a resize or a
changed period count cannot leave a stale offset showing an empty table.

**Formula breakdown.** Under the result, the relationship being solved is shown,
plus a substituted line for the forms where it fits (`= (25000 / 10000)^(1/5) -
1`). TVM and amortization show the general form only; substituting five variables
into the TVM identity produces a line too long to be useful.

Interaction, consistent with the other modes:

- Backtick toggles the input zone and the form zone.
- Up/Down move between fields, wrapping. Left/Right switch calculation, so every
  form is reachable from the keyboard alone (FR-7.7).
- Enter evaluates the focused field in place.
- Space toggles END/BGN on the payments row; Ctrl-U (or Delete) empties a field,
  which is also how a TVM variable is marked as the one to solve for.
- Clicking a chip selects a calculation; clicking a row focuses that field.
  Switching calculation resets the focused field and the scroll offset, but each
  form keeps its own entries, so moving between them does not discard typing.

### 8.6 Help Overlay

The overlay is a static line list (headers, bindings, free text) rendered through
one windowed loop, not a sequence of sections that each gate themselves on the
remaining height. The old shape had a specific failure: every section ended with
`if (row < height - 6)`, so as sections were added the later ones silently
disappeared on a 24-row terminal with no indication anything was missing. That was
found by a test asserting the Convert section was present, which failed once the
Financial section was added above it.

As a line list the content can be scrolled (Up/Down, PgUp/PgDn, wheel) and its
length is knowable without drawing, which is what lets the App clamp its own
scroll offset. Any non-scrolling key returns, preserving the "press a key to get
out" behaviour. The footer shows `lines X-Y of N` only when something is off
screen, so a tall terminal is not cluttered with a position indicator it does not
need.

---

## 9. Android UI Design

The shell (9.1), standard (9.2), programmer (9.3) and convert (9.6) are built; struct
layout, financial and tablet (9.4, 9.5, 9.7) are still DESIGN ONLY. 9.2 was rewritten
after the first build ran on a device, which is the input the rest of this section was
waiting for.

That first build was a text field, the system keyboard, an `=` button and a monospace
scrollback: the TUI's prompt moved onto glass, the exact paradigm the paragraph below
rules out. It proved the boundary and was nearly unusable, and the specific ways it
failed are what 9.2 is now built against. Read the struct layout screen (9.4) as doubly
speculative, since the engine feature behind it is also unbuilt.

The remaining designs are deliberately left unreconciled with what the TUI became during
the review, even where the two now disagree (9.5 has a Calculate button; the TUI dropped
it because results are live). Expect each to be rewritten the way 9.2 was: from a
running screen, not from what the TUI settled on.

**The principle the built screens converged on,** written down because it was learned by
having proposals rejected, and the unbuilt screens are where it will be tested next:

- **Nothing moves unless the user moves it.** No auto-scroll to a chosen item, no
  reordering under a finger, no list that jumps when a value changes. The value line
  already says what was chosen; motion the user did not cause costs them their place.
  (Rejected along the way: scrolling the result list to the chosen unit; recency order
  within a category.)
- **State is remembered, not guessed.** Each screen reopens exactly as it was left, and
  each part of it keeps its own memory - the converter's categories each keep their
  value, unit and scroll position. When something is unknown, the honest default (the
  top of a list, a blank field) beats a plausible reconstruction. (Rejected: carrying a
  number across categories, so 98.6 km became 98.6 kg.)
- **Stable layouts are an interface.** Fixed order, things highlighted in place rather
  than removed, so that where something is on screen is worth remembering.
- **Look before designing.** The first build was the TUI on glass; every good decision
  since came from reacting to something running, usually against a concrete reference
  (NCalc) with taps counted.

The Android app uses a fundamentally different interaction model from the TUI. Where the TUI is keyboard-driven with a prompt, Android is **touch-first with purpose-built input surfaces** for each mode. No text-cursor-in-a-prompt paradigm - instead, tappable buttons, interactive grids, and form fields.

### 9.1 Navigation & Shell

**Built: a hamburger drawer, as in NCalc.** Calculator, Programmer, Convert, and
Settings below a divider, under the app name and the engine version (which crossed JNI
to be there).
Opened by the hamburger only; an edge swipe would fight the system back gesture and the
keys nearest the edge. Each screen also has a one-tap link to the other in its top bar,
because the drawer is two taps and switching between calculating and converting is the
common move. The app reopens on whichever was last open; Settings is never reopened.

**Settings** holds one thing so far: the theme - follow the device (the default),
light, or dark. The choice is saved, and the system bar icons follow the app's choice
rather than the device's. The palettes are Material's baseline light and dark schemes,
not the system's dynamic colours: those were tried and, on the test device, gave the
keypad's accent bands light containers in dark mode.

The original plan, kept for the record: a bottom navigation bar with 4 destinations,
**Standard**, **Programmer**, **Financial**, **Convert**. Financial is not built, and
will be a drawer entry when it is. Programmer has no top-bar link: calculating and
converting are the common move between screens, and the drawer covers the rest.

```
┌─────────────────────────────────────────┐
│  ┌─────────────────────────────────┐    │
│  │                                 │    │
│  │        Mode Content Area        │    │
│  │                                 │    │
│  └─────────────────────────────────┘    │
│                                         │
│  ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━  │
│  🔢 Standard  💻 Programmer  💰 Finance  🔄 Convert │
└─────────────────────────────────────────┘
```

### 9.2 Standard Calculator Screen

**Decided after the first build, and built.** Touch-first: the keypad is the input, the
system keyboard is on request, and the answer is visible before `=` is pressed. The
layout follows NCalc (NCalcLibre on F-Droid), which is the reference for "what this
should feel like": a display card over a pad, a scientific block on an accent band above
the digits, and the rarer functions on a panel that slides up over the numbers.

```
+-----------------------------------------+
| Tally                          History  |  <- the only chrome
|                                         |
|                            x / 3 + 1|   |  <- expression, large, with a cursor;
|                     = 4.2255e29 (dim)   |     operators drawn as glyphs
|-----------------------------------------|
|  sin   cos   tan   ln    log   sqrt     |  <- scientific block, accent band
|  (     )     ^     x^2   n!    e        |
|  x     A     B     ,     mod   abc      |
|-----------------------------------------|
|  7     8     9     CLR   <x             |  <- NCalc's numeric block, key for key
|  4     5     6     *     /              |
|  1     2     3     +     -              |
|  0     .     pi    Ans   =              |
|-----------------------------------------|
|             more functions             |  <- slides a panel up over the digits:
+-----------------------------------------+     asin acos atan atan2 exp log2 log10
                                                cbrt abs floor ceil round min max tau C
```

- **No system keyboard by default.** Every key inserts plain engine syntax at the cursor
  (`*`, `sqrt(`, `pi`), and the field still takes a tap to move the cursor. `abc` hides
  the pad and raises the system keyboard for what a pad cannot offer - any other
  variable name, functions not on it; Enter or Done means `=`, and dismissing the
  keyboard brings the pad back. Both write the same text, so either can finish what the
  other started.
- **Variables without a keyboard.** `x`, `A`, `B` (and `C` on the panel) insert their
  name; a long-press stores into them - the expression if one is typed, `Ans` otherwise.
  A calculator's STO, written as the `A = ...` assignment the engine already has.
- **Live result.** Every edit asks the engine for a *preview* (6.5): the same evaluation,
  with nothing stored. Typing `x = 7` shows `= 7` without assigning `x`, and `Ans` stays
  the last committed answer until `=`. A preview that fails - usually an unfinished
  expression like `2 +` - shows nothing rather than an error, so the screen does not
  flash red on every other keystroke.
- **`=` commits.** The entry goes into history, the answer becomes the display at full
  size, and the expression that produced it sits above it, dimmed. A key that continues
  an expression (an operator, `^`, `x^2`, `mod`) starts from `Ans`, so `= 14`, then `* 2`,
  means `Ans * 2`. A digit starts fresh. Backspace brings the committed expression back
  for editing. An error on `=` is shown in place and the expression is kept.
- **The answer is the largest thing on screen,** right-aligned, and shrinks to keep a
  long exact answer on one line: `2^100` is 41 characters with its separators and fits.
  Long-press copies it.
- **Backspace** deletes before the cursor; **long-press** or `CLR` clears.
- **`,` inserts `, `.** The engine reads `1,234` as a grouped number, so an argument
  separator needs its space: `max(1,234)` is 1234, `max(1, 234)` is 234.
- **History is its own screen,** as in NCalc, so the calculator keeps its whole height
  for the display and the pad. Newest first; tap an entry to put its expression back,
  long-press to copy its answer. Results are not inserted as text: they carry separators
  and may be abbreviated, which is display rather than the value. The engine version -
  the first proof that a string crossed JNI - is on its empty state.
- **No unit conversion.** It is its own screen with pickers (9.6), not something typed
  here. The engine still converts a typed `100 km to mi` (FR-4.1), so it works through
  `abc`, but the screen offers it nowhere.
- **Evaluation is off the main thread.** A preview of `factorial(5000)` has to cost a
  frame, not an ANR, so every engine call runs on one dedicated thread. One, because a
  session takes no locks (6.1, rule 3): serialising the calls is the caller's job, and a
  single-threaded executor does it - including at teardown, where the session is freed
  by a task queued behind anything still running.
- **Colours are the system's** (Material You) on Android 12 and later, Material's
  defaults before that; light and dark follow the system.

- **It reopens as it was left.** The expression and its cursor, the answer on display,
  the history (newest 500), and - through the engine's own save (6.7) - every variable
  and `Ans`, exactly. Saved on every edit, so even a kill with the app in the
  foreground loses nothing. Clearing history keeps the variables: history is a record
  of what was typed, not where values live. Verified on the emulator: store 7 in A,
  `A x 6 =`, leave `2+` half typed, force-stop in the foreground, relaunch - `2+` is
  there, `2+Ans` previews 44, `A` is 7, and all four entries are in history.

Not yet: landscape (9.7), a `sqrt` drawn as a radical in the expression, and any check
on a physical device.

### 9.3 Programmer Mode Screen

**Built (first version), for reaction on a device.** Replaces a wireframe that predated
the TUI's programmer mode and disagreed with it on width, hex format, signedness and
editing. This one starts from what the TUI actually does (8.2, 8.2.1), the standard
screen's pad-and-preview model (9.2), and the principles at the top of section 9.

```
+-----------------------------------------+
| =  Programmer                           |
| [8][16][32][64][128]   signed     BE    |  <- settings strip, fixed positions
|-----------------------------------------|
|                     0xDEAD << 4 | 3|    |  <- expression, cursor, no keyboard
|                         = 0xDEAD3 (dim) |  <- live preview, in the input base
| DEC(s)  912,083                         |
| DEC(u)  912,083                         |  <- every row is the shown value
| [HEX]   00 00 00 00 00 0D EA D3         |  <- the input base, highlighted in place
| OCT     0 000 000 000 000 003 365 323   |
| ASCII    .  .  .  .  .  .  .  .         |
| BIN                  (warning, if any)  |
| 63  0000 0000 0000 0000                 |  <- bit grid: 16 per row, bit 0 always
| 47  0000 0000 0000 0000                 |     bottom right; tap toggles
| 31  0000 0000 0000 1101                 |
| 15  1110 1010 1101 0011                 |
|-----------------------------------------|
|  AND   OR   XOR   NOT   mod             |  <- operator band
|  <<    >>   >>>   ROL   ROR             |
|-----------------------------------------|
|  A   B   C   D   E   F                  |  <- dimmed where the base has no such digit
|  7   8   9   CLR  <x                    |
|  4   5   6   *    /                     |
|  1   2   3   +    -                     |
|  0       (   )    =                     |
+-----------------------------------------+
```

**Two things on screen: an expression and a value.** The value is a register - a
128-bit pattern, as the TUI's `prog_value` is - and every row and the grid show it.
The expression is engine syntax, written by the pad, exactly as on the standard screen.

- **Live, as on the standard screen.** While the expression is not empty, the rows and
  the grid show its preview. Programmer evaluation reads no environment, so a preview
  is the evaluation. When the expression stops evaluating mid-edit (`0xDEAD <<`), they
  keep the last value it had, dimmed, rather than flashing back to the register: the
  user is still typing and nothing they did changed the value. With nothing typed they
  show the register.
- **`=` puts the answer in the register.** The expression is kept above the answer,
  dimmed, until the next key, as on the standard screen. An error on `=` is shown in
  place and the expression is kept.
- **The expression line is never blank while the register holds a value.** With
  nothing typed it shows, dimmed, the expression `=` last put there or, failing that -
  after a bit tap, after CLR took a half-typed expression, or after a restart that only
  had the value - the register itself as a literal in the input base (`0x9CE6...`). It
  is blank only when the register is zero. The first build left it blank in those
  cases, and on the phone that read as the value not having been saved, though it had.
- **There is no `Ans`** in programmer evaluation (it takes no environment). The pad
  writes the register in instead: whenever that line is showing, an operator starts
  from the value as a literal in the input base (`0xF0 and `), NOT wraps it (`~0xF0`), a
  digit starts fresh, and backspace brings the line back for editing - the standard
  screen's rules after `=`, with a literal where that screen has `Ans`.
- **A tap on the grid edits what is shown.** With nothing typed it flips a bit of the
  register. With an expression showing its preview, the tap is `=` and then the flip,
  so the flip lands on the value the user was looking at; the line then shows the new
  value. While the grid is dimmed it does not answer taps: what it shows is not a value
  anything holds.
- **CLR** clears the expression; with the expression already empty, it zeroes the
  register (a calculator's CE then C). Long-press on backspace clears both.
- **Backspace removes an operator whole.** Operators are written with their spaces
  (` and `, ` << `) because the keyword forms need them; backspace after one deletes all
  of it rather than costing five taps.

**The input base is chosen by tapping a row's label** - HEX, DEC(s) or DEC(u) (both
mean decimal), OCT, or BIN above the grid - and is highlighted in place; nothing moves.
A digit that starts a number is written with the base's prefix (`0x`, `0o`, `0b`; none
for decimal), so typing `F F` in hex gives `0xFF`. A digit next to a number continues it,
whatever the base, so editing an existing literal works. Digits the base does not have
stay where they are and are dimmed. Everything typed is visible engine syntax, so a
shift distance typed in hex reads `<< 0x10`, not a silent 16.

**Width is a lens, as in the TUI.** Narrowing never masks the register: its rows and
grid show the low bits, a warning on the BIN line says bits are hidden, and widening
brings them back. Any edit - a bit, `=`, CLR - commits to the width on screen. The
engine renders every value: Kotlin sends the register as a masked hex literal and the
configuration (`configureProgrammer`, ABI 6), and reads the rows and the pattern back.
The pattern is a new `pattern` field in the programmer JSON - lowercase hex, unsigned,
masked, no grouping - so Kotlin never parses a display string to learn a value.

**Signedness and byte order** are toggles in the strip, as in the TUI: signedness
decides `>>` and how a decimal literal re-enters; byte order decides the HEX
and ASCII rows only. Both DEC rows are always shown (FR-2.5).

**BIN is the grid.** A 128-bit binary row is four lines on a phone and says exactly what
the grid says, so there is no BIN row; its label sits above the grid. The grid is 16 bits
a row, nibble-grouped, with each row's top bit index on the left. Its area is the same
height at every width: bit 0 is always bottom right, so bit N is in the same place at
every width that has it, and 128 bits fit by halving the row height.

**It reopens as it was left:** width, signedness, byte order, input base, register,
expression and cursor, and the committed expression on display.

**A long-press copies a row** - on its label or its value - as something you could type:
`0xBEEE`, `0o137356`, `0b1011...`, `48878`, `-18`. Prefixed, ungrouped, at the width on
screen, and for hex most significant first whatever the byte order, since the byte order
is a view and the clipboard is the value (the clipboard column of 2, "Programmer Mode
Formatting"). DEC(s) and DEC(u) each copy their own reading; BIN copies from its label
above the grid; ASCII has no typed form and copies nothing. Verified on the emulator by
pasting into the calculator: `0xBEEE` evaluated to 48,878, and an 8-bit DEC(s) copied
as `-18`.

**The rows are one line each, at a size chosen per width,** from the longest value that
width can produce (octal is the longest: 57 characters at 128 bits), so typing never
reflows them and nothing below moves. The size is measured with the monospace face
rather than assumed, which takes the device's font scale into account; the first
version guessed a glyph width and clipped the last octal digits, because the theme's
body style adds letter spacing the guess did not include. At 128 bits that size is
small (about 9 sp for octal); the grid uses the room the shorter rows leave.

Verified on the emulator by driving it by label: `D E A D` in hex gives `0xDEAD`; ` << `
then `4` writes `0xDEAD << 0x4` and previews 912,080 in both DEC rows; a trailing operator dims
the rows and grid without moving them; backspace takes ` << ` whole; `=`, then AND,
writes `0xDEAD0 and `; bit taps on the register, and on a preview (`=` then flip); at
8 bits the warning appears and 64 brings 32,977 back; DEC(s) dims A-F and `200 =` reads
-56 with `200` above it; little-endian `0xDEADBEEF and 0xFF` reads `EF 00 00 00`; a
force-stop restores width, byte order and the half-typed expression; light and dark.
Not verified: a physical device (until the install at the end), TalkBack, landscape.

Rejected or deferred, and why:
- **Editing each row in place** (the TUI's positional editing). The TUI does it with a
  cursor and a keyboard; on glass it means a small target per digit. The input base plus
  a pad does the same job with large keys, and the grid covers per-bit edits.
- **A separate primary-base display** (the old wireframe's "tap to make primary").
  Folded into the rows: the label is the switch, and the highlight is the state.
- **History** is not on this screen yet; the committed expression above the answer is
  the only record. The TUI shares one history between modes, which this app's two
  screens do not.
- **The float view (Ctrl-F), ASCII literals (`'ELF'`) and the system keyboard** are not
  built: none needs the engine to change, and each is easier to place once the screen
  has been used.
- **Struct layout** (9.4) waits for a C ABI export of the engine's layout (section 3),
  and for the TUI view to settle what an interactive one should do.

### 9.4 Struct Layout Screen (Programmer sub-screen)

Accessed via a button within Programmer mode. Uses a **form-based struct builder** rather than raw text DSL (though raw text input is available via a toggle).

```
┌─────────────────────────────────────────┐
│  ← Back to Programmer                  │
│                                         │
│  ┌─── ABI / Settings ──────────────┐   │
│  │ ABI: [x86-64 SysV ▾]  Endian: [LE ▾]│
│  └──────────────────────────────────┘   │
│                                         │
│  ┌─── Fields ───────────────────────┐   │
│  │ ┌────────┬──────────┬─────────┐  │   │
│  │ │ Type ▾ │ Name     │    ⊖    │  │   │  ← each row is a field
│  │ ├────────┼──────────┼─────────┤  │   │
│  │ │ u32    │ x        │    ⊖    │  │   │
│  │ │ u8     │ flags    │    ⊖    │  │   │
│  │ │ u16    │ id       │    ⊖    │  │   │
│  │ │ u64    │ ts       │    ⊖    │  │   │
│  │ └────────┴──────────┴─────────┘  │   │
│  │          [ + Add Field ]          │   │
│  │     [ ✏️ Raw DSL input toggle ]    │   │
│  └──────────────────────────────────┘   │
│                                         │
│  ┌─── Memory Map ───────────────────┐   │
│  │ ██████████ ▓▓ ░░ ▒▒▒▒ ░░░░░░░░░ │   │  ← color-coded byte bar
│  │ x(4)      fl p  id   ts(8)      │   │  ← labels below
│  └──────────────────────────────────┘   │
│                                         │
│  ┌─── Summary ──────────────────────┐   │
│  │ Total: 16 bytes  Align: 8        │   │
│  │ Padding: 1 byte (6.25%)          │   │
│  │ Packed: 15 bytes                  │   │
│  └──────────────────────────────────┘   │
└─────────────────────────────────────────┘
```

**Key interactions:**
- Type dropdown for each field (Material exposed dropdown menu)
- Swipe-to-delete or tap ⊖ to remove a field
- Drag handles to reorder fields (see padding change in real-time)
- Memory map is a custom Canvas composable with tappable segments (tap a segment -> highlights field info)
- Toggle for raw DSL text input (for copy-paste from code)
- Share button: export struct layout as text or image

### 9.5 Financial Mode Screen

Card-based interface with function selector at top.

```
┌─────────────────────────────────────────┐
│  ┌─── Function ────────────────────┐    │
│  │ [●CAGR] [TVM] [Compound] [PV]  │    │  ← scrollable chip row
│  └─────────────────────────────────┘    │
│                                         │
│  ┌─── CAGR Inputs ────────────────┐     │
│  │                                 │     │
│  │  Start Value                    │     │
│  │  ┌─────────────────────────┐    │     │
│  │  │ 10,000                  │    │     │  ← text field
│  │  └─────────────────────────┘    │     │
│  │                                 │     │
│  │  End Value                      │     │
│  │  ┌─────────────────────────┐    │     │
│  │  │ 25,000                  │    │     │
│  │  └─────────────────────────┘    │     │
│  │                                 │     │
│  │  Periods (years)                │     │
│  │  ┌─────────────────────────┐    │     │
│  │  │ 5                       │    │     │
│  │  └─────────────────────────┘    │     │
│  │                                 │     │
│  │       [ Calculate ]             │     │
│  └─────────────────────────────────┘     │
│                                         │
│  ┌─── Result ─────────────────────┐     │
│  │  CAGR = 20.11%                 │     │
│  │                                 │     │
│  │  Formula:                       │     │
│  │  (25000/10000)^(1/5) - 1       │     │
│  │  = 2.5^0.2 - 1                 │     │
│  │  = 0.2011...                    │     │
│  └─────────────────────────────────┘     │
└─────────────────────────────────────────┘
```

**Key interactions:**
- Chip row selects function type, input form adapts
- For TVM: 5 input fields, user leaves one blank -> that's the solve target
- Compute triggers engine call, result animates in
- Result card shows formula breakdown (expandable)
- Long-press result to copy

### 9.6 Convert Screen

**Decided and built, against NCalc's.** NCalc makes a temperature conversion cost four
steps before a digit: Unit Converter, Temperature, the input unit, then the number - and
it starts at the converter list every time it opens. The goal here is the opposite: the
common case costs no navigation at all.

```
+-----------------------------------------+
| =  Convert                   Calculator |
| [Search] [Temperature] [Length] [Mass]..|  <- search tile that never moves, then
|          [   37 C    ] [180 mi]         |     EVERY category, most recent first
|                          [37]  [C v]    |  <- the value (highlighted = the next
|-----------------------------------------|     digit replaces it); the unit picker
| C   Celsius                        37   |  <- highlighted in place
| F   Fahrenheit                   98.6   |  <- every unit of the category, in a
| K   Kelvin                     310.15   |     FIXED order: tap a row to view from
| R   Rankine                    558.27   |     it, long-press to copy
|-----------------------------------------|
|  7    8    9    <x                      |  <- digits only
|  4    5    6    CLR                     |
|  1    2    3    +/-                     |
|  0         .                          |
+-----------------------------------------+
```

- **It reopens where it was left,** on the category, value and unit, with the value
  highlighted so the next digit starts a new number.
- **Each category remembers its own value and unit.** Leave Temperature at `98.6 F` and
  Length at `180 mi` (Seattle to Portland, for telling foreigners), and a tap on either
  lands exactly there. A category never visited starts at 1 of its base unit.
- **The top row is every category, most recently used first,** scrollable. A tap moves
  that category to the front and the row scrolls back to show it there. A chip shows the
  category and, once visited, the value it will land on - `Temperature` over `37 C` -
  because a value reads as where you left off, where a bare unit would read as the only
  unit on offer.
- **A search tile leads the row and never moves,** which is what keeps the LRU order
  from feeling like a shuffle: search, or pick from what you used. It searches every unit
  by name, alias or category, focused at once because it was asked for. Before anything
  is typed it lists every category in the row's order: history for a returning user,
  the first-run order (Temperature, Length, Mass, Volume, Speed, then the rest) as
  suggestions for a new one. Picking a unit goes to its category in that unit.
- **Within a category the order is fixed** - the engine's table order - because with 4 to
  15 units, knowing where a unit sits beats any reordering. The unit on display is
  highlighted where it is, not removed, so a tap moves only the highlight. A recency
  sort here was considered and set aside; it is a small change if fixed order turns out
  to mean hunting.
- **Direction is one tap.** Tap the C row after typing 98.6 F and the screen views from
  Celsius. Nothing is recomputed - the rows are already the typed value in every unit -
  so viewing from mi and back to km is exact. Typing then edits the number on screen,
  in the unit on screen.
- **The list moves only when you scroll it.** Each category keeps its own scroll
  position, saved with its value and units and restored without animation, so coming
  back to Length - after another category, or a relaunch - puts the list exactly where
  it was. Choosing a unit, from a row, the dropdown or search, never scrolls: the value
  line already says what was chosen, and someone reading down the column comparing
  values would lose their place. The position is the unit in the top row plus the pixels
  of it scrolled off, anchored by name rather than row number, so a unit the engine adds
  above it does not shift the list onto a different unit; an anchor the engine has
  dropped means the top. Saved when the category is left, the screen goes, or the app
  goes to the background - not on every scroll.
- **The unit button is a dropdown** of the category's units, opening in place with the
  value still visible: the list is 4 to 15 long, too short to earn a screen of its own,
  which is what the first version gave it. Picking one is a result-row tap. Search stays
  a full screen, because it needs the keyboard and spans every category.
- **Names come from the engine.** Every unit in `units.zig` carries a required display
  `label` - US spelling, singular, "Meter per second" - and a unit without one does not
  compile. It reaches the app through the catalogue (ABI 4), and the CLI and TUI can
  list the same names. It replaced a Kotlin guess from the aliases, which gave
  "Meterpersecond".
- **Inexact rows say so** with a leading approx sign: degrees to radians goes through pi.
- **Fewer digits than the calculator:** ten decimals and twelve significant digits, set
  on the converter's own session.
- **The rules are plain Kotlin** (`Converter.kt`), unit tested on the JVM; the view model
  only connects them to the engine, the disk and the screen.

Tap costs against the previous design: a used category is one tap and lands on its own
value (it used to be one tap that carried the wrong number across); a specific unit in
another category is two (category, then row); a never-used category is a scroll and a
tap, or search.

Not yet: currency (needs a network; the app has no permissions), compound units beyond
the tables, and expressions in the value - the calculator's `abc` route still converts
`100 km to mi` for that.

### 9.7 Tablet Layout (landscape / large screen)

On tablets, modes use a two-pane layout:

```
┌─────────────────────┬──────────────────────────────┐
│                     │                              │
│   Input / Controls  │    Results / Visualization   │
│                     │                              │
│  (button grid,      │   (history, bit grid,        │
│   form fields,      │    memory map, formula        │
│   struct editor)    │    breakdown)                 │
│                     │                              │
└─────────────────────┴──────────────────────────────┘
│  🔢 Standard  💻 Programmer  💰 Finance  🔄 Convert │
└─────────────────────────────────────────────────────┘
```

### 9.8 Android Architecture (Technical)

```
┌──────────────────────────────────────┐
│  Compose UI Layer                    │
│  ├── StandardScreen                  │
│  ├── ProgrammerScreen                │
│  │   ├── BitGridComposable           │
│  │   └── StructVisualizerScreen      │
│  ├── FinancialScreen                 │
│  └── ConvertScreen                   │
├──────────────────────────────────────┤
│  ViewModel Layer                     │
│  ├── CalculatorViewModel             │
│  ├── ProgrammerViewModel             │
│  ├── FinancialViewModel              │
│  ├── ConvertViewModel                │
│  └── manages state, calls engine     │
├──────────────────────────────────────┤
│  JNI Bridge (TallyEngine.kt)         │
│  ├── external fun evaluate(...)      │
│  ├── external fun structLayout(...)  │
│  ├── external fun convert(...)       │
│  └── JSON serialization/deser        │
├──────────────────────────────────────┤
│  Native .so (libtally.so)            │
│  └── C ABI from engine/c_api.zig    │
└──────────────────────────────────────┘
```

The JNI bridge sends expression strings down and receives JSON results back. This keeps the boundary thin and debuggable.

---

## 10. Error Handling Strategy

Each file declares what it can fail with, and the sets compose:

```zig
// Parser.zig
pub const Error = error{
    UnexpectedToken, UnmatchedParen, UnexpectedEnd,
    ExpressionTooLarge, NestingTooDeep, InvalidNumber, UnterminatedString, OutOfMemory,
};

// Rational.zig, inherited by number.zig
pub const Error = error{
    OutOfMemory, DivisionByZero, InvalidNumber,
    ExponentTooLarge, NegativeRoot,
};

// bitwise.zig
pub const Error = error{DomainError};

// units.zig: its own three, plus whatever the exact path raises
pub const Error = error{ UnknownUnit, AmbiguousUnit, IncompatibleUnits, OutOfMemory } || number.Error;

// financial.zig
pub const Error = error{
    InsufficientParameters, ConvergenceFailure,
    DomainError, DivisionByZero, OutOfMemory,
};

// struct_layout.zig: what a definition can fail to lay out with
pub const Error = error{
    EmptyStruct, TooManyMembers, DuplicateMember, TypeUnavailable,
    InvalidArrayLength, MisplacedFlexibleArray, InvalidAlignment, StructTooLarge, OutOfMemory,
};

// CStructParser.zig: what reading C can fail with, sharing the expression parser's
// names (and so its wording) for the three they have in common
pub const Error = error{
    UnexpectedToken, UnexpectedEnd, InvalidNumber, UnterminatedComment,
    UnknownType, UnsupportedType, IncompleteType, UnsupportedAttribute,
    BitfieldNotSupported, NestedTypeNotSupported, PreprocessorNotSupported,
    DefinitionTooLong, InvalidArrayLength, InvalidAlignment, TooManyMembers, OutOfMemory,
};

// evaluator.zig: its own, plus every dependency's
pub const Error = error{
    UnknownFunction, WrongArgumentCount, UnknownVariable,
    AssignmentToConstant, DomainError, Overflow,
} || Parser.Error || number.Error || bitwise.Error || financial.Error;

// engine.zig: what any entry point can return, for frontends to switch over
pub const Error = evaluator.Error || programmer.Error || units.Error || financial.Error ||
    struct_layout.Error || CStructParser.Error;
```

This replaced one hand-written `CalcError` with 20 members that every engine function
claimed to return. That signature was false in both directions: `parser.parse` said it
might return `ConvergenceFailure` and `UnknownUnit`, so no caller could switch on what
a parse can actually produce, and four members (`InvalidType`, `InvalidFieldName`,
`DuplicateFieldName`, `StructTooLarge`) belonged to a struct layout feature that did not
exist yet, so nothing could return them while `errorPhrase` still gave them wording.
When the feature was built its errors arrived with it, from the module that raises them,
and only `StructTooLarge` kept its old name.

Error members unify by name in Zig, so the per-file sets compose with no
coordination: `parser.Error.OutOfMemory` and `units.Error.OutOfMemory` are the same
value. The unions are written with `||` rather than enumerated, so the compiler
maintains them.

Deleting the single set also deleted the translation between tiers. `number.toCalcError`
existed to map the numeric model's errors into the engine-wide set, and what it mapped
away were the more useful names: `ExponentTooLarge` became `Overflow` and `NegativeRoot`
became `DomainError`. Now `sqrt(-1)` reports "square root of a negative number" and
`2^3000000` reports "the exponent is too large to compute".

Errors carry no position or context. An `ErrorInfo` with a source position was
specified here and declared in the code, but nothing ever constructed one, and the
parser fields that would have fed it were written on every error path and never read.
Adding position reporting means threading it through the returns, which is worth doing
deliberately rather than leaving a half-built shape in place.

The wording lives in exactly one place, `engine.phrase`, in the engine rather than a
frontend because every frontend needs the same words, including the Android app across
the C ABI. Its switch has no `else`, so an error added to any of those sets fails to
compile until it is given a phrase, and a comptime block checks the other direction, so
it cannot carry wording for an error the engine is incapable of producing. Frontends
decorate at comptime (`switch (err) { inline else => ... }`): the CLI adds `error: ` and
a newline, the TUI adds `error: `, and a view with better context can override
individual cases, as the financial form does for `DomainError`. Each frontend used to
carry its own copy of the whole table, and the TUI's had drifted three errors behind.

---

## 11. Key Design Decisions

| # | Decision | Rationale |
|---|----------|-----------|
| 1 | Pratt parser over recursive descent | Easier to extend precedence levels; cleaner for infix with mixed prefix operators |
| 2 | `u128` storage for all programmer integers | One representation for every width; `width` masks and interprets rather than deciding storage, which is what makes the width a non-destructive display lens (8.2.1). This said `u64` until 128-bit support landed |
| 3 | JSON over C ABI boundary | Avoids complex struct marshaling; Kotlin/Swift handle JSON natively; small perf cost acceptable for calculator. Still the plan; not built (section 6) |
| 4 | A separate parser, for C rather than a DSL | Struct definitions are pasted from C, and the expression tokenizer reads C's numbers wrongly (`010`, `1,000`). Section 3.1 |
| 5 | ABI as interface/vtable | Adding Windows x64 or ARM is implementing one struct; no changes to layout algorithm. Not built (section 3) |
| 6 | libvaxis for TUI | Most mature Zig TUI; supports Windows/Mac/Linux; active development; used by Ghostty |
| 7 | `^` always means power; XOR is the `xor` keyword | Avoids mode-dependent operator overloading; every operator means the same thing in both modes; consistent with existing `rol`/`ror` keyword operators |
| 8 | Statically-linked desktop binaries | Zero dependencies for end user; Zig makes this trivial |
| 9 | Unit conversion via base-unit normalization | Simple to implement, easy to extend; only temperature needs special case (offset) |
| 10 | Android: button grids, not text prompts | Touch-first UX; no keyboard needed for basic use; purpose-built surfaces per mode beat a generic expression prompt. Not built (section 9) |
| 11 | Android: form-based struct builder + raw toggle | Most users won't want to type DSL syntax on a phone; visual builder is more natural; power users can toggle to raw text. Not built |
| 12 | Android: live conversion without "Calculate" button | Conversions are instant; eliminating a tap makes the UX feel responsive and direct. Not built |
| 13 | Display budgets belong to the frontend, not the engine | A terminal, a clipboard and a phone screen want different digit counts, so `Number.render` takes `FormatOptions` and each frontend declares its own (NFR-9.9). The engine held these constants once and the CLI inherited a budget chosen for the TUI |
| 14 | One list per shared vocabulary, derived where possible | The financial function list, the general function list, the error wording and the mode tab order each exist once and are rendered by whoever needs them. Every one of these was a duplicated list first, and every duplicate had drifted by the time it was found |