Brummel
19dc42f5ca
The first formal-links milestone shipped clause-5 + 8 links across the
existing file layout. Browsing surfaced that file-only granularity is
only as precise as the file boundaries — three files mixed two or
three navigation targets under one address, so the 8 links could not
multiply without ambiguity. This commit fixes the substrate, then
applies the sweep the original milestone deferred.
Splits (each extracts an already-self-contained section into its own
file so links land on the topic, not the parent doc's TOC):
contracts/typeclasses.md
→ +contracts/prelude-classes.md (Eq/Ord/Show ships, polymorphic `print`)
→ +contracts/method-dispatch.md (5-step dispatch rule, candidate index)
contracts/memory-model.md
→ +contracts/language-constraints.md (the 4 binding constraints
making RC sound without a
cycle collector)
models/authoring-surface.md
→ +models/prose-projection.md (Form-B / `ail prose` / merge-prose)
Each new file enters design/INDEX.md as its own row (three contracts
share show_no_instance_e2e.rs / uniqueness.rs as ratifying tests;
prose-projection is a model). Two pre-existing links rebind to the
new topic-files (memory-model.md → method-dispatch.md;
float-semantics.md → prelude-classes.md).
Link sweep: 8 → 88 formal Markdown links over 23 files. Every file
in design/contracts/ + design/models/ now has at least one outgoing
link; the tree is fully connected. Links are file-relative
`[label](path)` per the established convention, fenced code blocks
are skipped (a `](` inside ```jsonc``` is literal text), the durable
tier (design/ + crates/ + runtime/) is enforced by clause-5.
Tests:
- design_index_pin.rs (5/5 clauses): clean-cut, INDEX resolution,
ratifying-test resolution, no decision-record prose in contracts/,
body links durable + resolving.
- docs_honesty_pin.rs (5/5): one assertion rebinds from typeclasses.md
to prelude-classes.md (where the gated sentence now lives);
design_corpus widens to include the 4 new files so the Wunschdenken
/ doc-archaeology sweeps continue to cover everything that used to
live in the parents.
No spec/plan/journal for this batch — interactive collaboration after
the milestone closed; the user gated the splits explicitly before the
sweep.
110 lines
5.3 KiB
Markdown
110 lines
5.3 KiB
Markdown
# Float semantics
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## Float semantics
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`Float` is IEEE-754 binary64 (LLVM `double`). One float type ships;
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no `f32` variant. The runtime / codegen contract:
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**Guaranteed:**
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- Every individual builtin (`+`/`-`/`*`/`/`/`neg`/`<`/`==`/...) lowers
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to a single LLVM IR instruction on the Float arm:
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`fadd/fsub/fmul/fdiv double`, `fneg double`, `fcmp olt/ole/ogt/oge
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double`, `fcmp oeq double`, `fcmp une double` (for `!=`). On a
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fixed `(target triple, LLVM version)` pair, the bit pattern of
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the result of any single op is reproducible.
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- NaN and ±Inf propagate per IEEE 754 — no silent collapse to zero,
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no trap. Arithmetic on a NaN operand produces NaN; division by
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zero produces ±Inf; `0.0 / 0.0` produces NaN.
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- `-0.0` and `+0.0` are distinct bit patterns at the canonical-JSON
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hash level (`{"bits":"0000000000000000",...}` vs
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`{"bits":"8000000000000000",...}` — distinct `def_hash`s) but
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compare equal via `==` per IEEE (`fcmp oeq double` returns true
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for `+0 == -0`). This asymmetry is the correct IEEE behaviour;
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it does mean `def_hash`-equality is finer than `==`-equality on
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Float.
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- `==` returns `false` whenever either operand is NaN
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(`fcmp oeq` is the ordered-equal predicate; ordered = both
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operands non-NaN).
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- `!=` returns `true` whenever either operand is NaN (`fcmp une`
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is the unordered-or-not-equal predicate). This matches Rust
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`f64::ne` and IEEE-`!=` exactly.
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- `is_nan` (`fcmp uno double %x, %x`) returns `true` iff `x` is
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NaN. Bit-pattern-based NaN detection without dependence on the
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payload bits.
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- `int_to_float` (`sitofp`) is exact for `|n| < 2^53`,
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round-to-nearest-even otherwise.
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- `float_to_int_truncate` (`@llvm.fptosi.sat.i64.f64`) is total:
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NaN → 0, +Inf → i64::MAX, -Inf → i64::MIN, finite-out-of-range
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saturates, finite-in-range truncates toward zero. Matches Rust
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`as i64` semantics (since 1.45).
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**Unspecified:**
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- FMA contraction. LLVM may fold `fadd (fmul a b) c` into
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`fma a b c`. Bit results may differ between an op-emitted-in-
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isolation pattern and an op-folded-into-FMA pattern.
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- Reassociation. The compiler may reorder a chain like
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`(a + b) + c` into `a + (b + c)`, producing a bit-different
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result on numerically sensitive inputs.
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- Subnormal flushing modes. If the target enables FTZ (flush-to-
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zero) or DAZ (denormals-are-zero), subnormal results round to
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zero; AILang does not enable these flags but does not forbid the
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target from doing so.
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- The exact NaN bit pattern produced by an op. Any quiet NaN bit
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pattern is conformant; `0.0 / 0.0` may produce
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`0x7ff8000000000000` on one target and a different qNaN on
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another.
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- The textual rendering of NaN through `float_to_str` (the runtime
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C helper that backs `instance Show Float` and, post-iter-rpe.1,
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every Float-typed `print` call). The libc `printf("%g", nan)`
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glue used by `float_to_str` is permitted to emit `nan` / `-nan`
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/ `NaN` etc. depending on libc version and the NaN's sign bit;
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AILang does not normalise this, since the prose / surface-print
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paths render NaN as the explicit `"NaN"` spelling and Float
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rendering is for human-readable output, not round-trip.
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The same libc-`%g` rendering applies to `show 1.5` / `show nan` /
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`show inf` via `instance Show Float` (which calls `float_to_str`
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internally — see [Prelude (built-in) classes](prelude-classes.md) for the Show ship).
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The NaN-spelling caveat above is observable via `do print x` for
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Float-typed `x`; the rendering is libc-version-dependent and
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target-libc-specific. AILang does NOT canonicalise Float textual
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representation; the LLM-author who needs deterministic Float
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rendering for cross-platform test fixtures should bypass `show` /
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`print` and emit a custom formatter.
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These are the Rust / Swift / standard-LLVM defaults — not
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research-grade reproducibility guarantees. The stronger guarantee
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(e.g. Pythonic `float.fromhex`-level bit reproducibility across
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ops) would require `-ffp-contract=off` plus per-op intrinsic
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selection — out of scope for the milestone; revisit only if a real
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use case appears.
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**Form-A serialisation:** Float literals carry the IEEE-754
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bit pattern as a 16-character lowercase hex string in the canonical
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JSON: `{"kind":"float","bits":"<16-hex>"}` (see
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[Data model](data-model.md) for the literal schema). Routing through the
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JSON *string* path (not `serde_json::Number`) preserves bit
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stability across `serde_json` versions and lets NaN / ±Inf
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round-trip through Form-A — JSON numbers cannot represent them.
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This bits-hex encoding is what keeps Floats inside the
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[Roundtrip Invariant](roundtrip-invariant.md).
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**Pattern matching:** `Pattern::Lit` on `Literal::Float` (see
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[Data model](data-model.md) for the pattern schema) is hard-
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rejected at typecheck (`CheckError::FloatPatternNotAllowed`). IEEE
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semantics make Float patterns semantically dubious — NaN never
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matches via IEEE-`==`, and bit-exact equality is rarely what an
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LLM-author wants. Use ordering operators (`<`, `>`, ...) and
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`is_nan` to discriminate Floats.
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`float_to_str` (Float → Str) and `int_to_str` (Int → Str) are
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fully wired through checker, codegen, and runtime. Both allocate
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a fresh heap-Str slab at the call site (see [Str ABI](str-abi.md)
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for the dual realisation) and carry `ret_mode: Own` so the let-binder
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for the call result is RC-tracked and the slab is freed at scope
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close.
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Ratified by: `crates/ail/tests/eq_float_noinstance.rs`.
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