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|
+-------------------------------------------------------------+

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)
message.zig	Gone: the wording lives in engine.zig beside the Error union it words
engine.zig	Public API surface (Zig-native): the seven 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. struct_layout.zig does not exist; section 3 is a design, not a description.

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).

/// 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.

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:

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:

// 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

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:

/// 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:

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 open, labeled "contributor friendly". PR #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 ("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 (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 "Better @sqrt for f32, f64 and f128", GH #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 (DESIGN ONLY, NOT BUILT)

Nothing in this section exists. There is no struct_layout.zig, no ABI profile interface, no tally struct subcommand and no struct sub-view in the TUI, and the four errors this design needs (InvalidType, InvalidFieldName, DuplicateFieldName, StructTooLarge) were deleted from the engine because nothing could produce them.

The feature is wanted (FR-3) and is sequenced after the Android app. The design is kept because it is the one part of the plan with a grammar and an algorithm worked out in advance, and because the shape below is still what we would build.

Read what follows as a proposal.

3.1 Mini-DSL Grammar

struct_def    := "struct" "{" field_list "}"
field_list    := (field ";")*
field         := type_name identifier
type_name     := "u8" | "u16" | "u32" | "u64"
                | "i8" | "i16" | "i32" | "i64"
                | "f32" | "f64" | "bool" | "ptr"
                | "[" number "]" type_name        // arrays
identifier    := [a-zA-Z_][a-zA-Z0-9_]*

3.2 ABI Profile Interface

pub const AbiProfile = struct {
    name: []const u8,
    pointer_size: u8,       // bytes
    max_alignment: u8,      // maximum alignment enforced

    /// Given a field type, return its (size, alignment) in bytes
    field_layout: *const fn (field_type: FieldType) -> struct { size: u8, alignment: u8 },

    /// Struct-level alignment (usually max of all field alignments)
    struct_alignment: *const fn (fields: []const FieldInfo) -> u8,

    /// Whether tail padding is added to round up to struct alignment
    tail_padding: bool,
};

// Built-in profiles
pub const x86_64_sysv = AbiProfile{ ... };    // default
pub const x86_64_win64 = AbiProfile{ ... };   // future
pub const packed = AbiProfile{ ... };          // no padding

3.3 Layout Computation Algorithm

function compute_layout(fields, abi):
    offset = 0
    struct_align = 1
    result_fields = []

    for each field in fields:
        (size, align) = abi.field_layout(field.type)
        struct_align = max(struct_align, align)

        # Insert padding for alignment
        padding = (align - (offset % align)) % align
        if padding > 0:
            emit_padding(offset, padding)
        offset += padding

        # Place field
        emit_field(field.name, field.type, offset, size)
        offset += size

    # Tail padding
    if abi.tail_padding:
        tail = (struct_align - (offset % struct_align)) % struct_align
        if tail > 0:
            emit_padding(offset, tail)
        offset += tail

    return StructLayout {
        total_size: offset,
        alignment: struct_align,
        fields: result_fields,
    }

3.4 Layout Result Structure

pub const StructLayoutResult = struct {
    total_size: usize,
    alignment: u8,
    fields: []const LayoutField,
    bytes: []const ByteInfo,     // byte-by-byte map for visualization
    abi_name: []const u8,
};

pub const LayoutField = struct {
    name: []const u8,
    type_name: []const u8,
    offset: usize,
    size: usize,
    alignment: u8,
    padding_before: usize,
};

pub const ByteInfo = union(enum) {
    field: struct { field_index: usize, byte_within_field: usize },
    padding: struct { before_field_index: usize },
    tail_padding: void,
};

---

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.

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:

// 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.

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's evidence rather than a one-time check: for each ABI, zero DT_NEEDED, zero undefined dynamic symbols, no TLS segment, and LOAD aligned to 0x4000. 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.

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).

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.

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]

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, --abi) 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. tally struct goes with section 3.

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 (SKETCH, section 3 is not built):

$ tally struct "struct { u32 x; u8 flags; u16 id; u64 ts; }"
ABI: x86-64 System V | Endian: little

  Offset  Size  Field       Type   Align  Padding
  ──────  ────  ──────────  ─────  ─────  ───────
  0       4     x           u32    4
  4       1     flags       u8     1
  5       1     (padding)                  1 byte
  6       2     id          u16    2
  8       8     ts          u64    8

  Total: 16 bytes (alignment: 8, padding: 1 byte, tail: 0)

  Memory map:
  00: [xxxx xxxx xxxx xxxx xxxx xxxx xxxx xxxx] x
  04: [ffff ffff] [········] [iiii iiii iiii iiii] flags, pad, id
  08: [tttt tttt tttt tttt tttt tttt tttt tttt  ts
  0C:  tttt tttt tttt tttt tttt tttt tttt tttt]

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:

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

┌─ 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 FR-3.

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:

// 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,
};

// 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;

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 does not exist, so nothing could return them while errorPhrase still gave them wording.

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	Separate parser for struct DSL	Struct grammar is different enough from expressions; keeps both parsers simple. Not built (section 3)
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