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118 lines
5.8 KiB
Markdown
118 lines
5.8 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 arithmetic builtin (`+`/`-`/`*`/`/`/`neg`) lowers
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to a single LLVM IR instruction on the Float arm: `fadd / fsub /
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fmul / fdiv double`, `fneg double`. Float comparison goes through
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the named prelude fns `float_eq` / `float_ne` / `float_lt` /
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`float_le` / `float_gt` / `float_ge` (Float has no Eq/Ord instance
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— see [Prelude (built-in) classes](0017-prelude-classes.md)); each fn
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lowers to a single `fcmp` instruction (`oeq` / `une` / `olt` /
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`ole` / `ogt` / `oge` respectively) via the codegen intercept
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`try_emit_primitive_instance_body`, with the `alwaysinline`
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attribute on the generated `define` so the call folds to one
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instruction at every use site. On a fixed `(target triple, LLVM
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version)` pair, the bit pattern of the result of any single op is
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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 `float_eq` per IEEE (`fcmp oeq double` returns
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true for `+0 == -0`). This asymmetry is the correct IEEE
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behaviour; it does mean `def_hash`-equality is finer than
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`float_eq` on Float.
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- `float_eq` 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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- `float_ne` returns `true` whenever either operand is NaN
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(`fcmp une` is the unordered-or-not-equal predicate). This matches
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Rust `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 every Float-typed
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`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](0017-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](0002-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](0009-roundtrip-invariant.md).
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**Pattern matching:** `Pattern::Lit` on `Literal::Float` (see
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[Data model](0002-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 `float_eq` (its `fcmp oeq` lowering is `false` for
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NaN), and bit-exact equality is rarely what an LLM-author wants.
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Use the explicit comparison fns (`float_lt`, `float_gt`, ...) 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](0011-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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