Formats

A format is a tuple (K, P, Σ, Δ): bitwidth K ∈ 3:8, precision P, signedness Σ ∈ {Signed, Unsigned}, domain Δ ∈ {Finite, Extended}. The value type is the one-byte primitive FloatByte{K,P,S,D}; users normally write the 120 exported aliases, named per the draft:

Binary{K}p{P}{s|u}{e|f} — e.g. Binary8p4se is 8 bits, precision 4, signed, extended; Binary5p2uf is 5 bits, precision 2, unsigned, finite.

Signed formats allow 1 ≤ P ≤ K−1; unsigned allow 1 ≤ P ≤ K. Extended formats have +Inf (and −Inf when signed) as code points; finite formats have neither. Every format has exactly one NaN and one zero.

julia> using FloatBytes

julia> bitwidth(Binary8p4se), precision(Binary8p4se), exponent_bias(Binary8p4se)
(8, 4, 8)

julia> signedness(Binary8p4se), domain(Binary8p4se)
(SignedFormat, ExtendedDomain)

julia> Float64.((maxfinite(Binary8p4se), minpositive(Binary8p4se)))
(224.0, 0.0009765625)

Code identity vs. mathematical value

Two constructors, visibly different:

• fromcode(F, code) — raw code identity, range-checked. The only safe way to name a specific bit pattern.
• F(value::Real) / quantize — mathematical construction: projects a real value into the format (F(value) uses the package default projection; quantize takes an explicit ρ).

julia> FloatBytes.fromcode(Binary8p4se, 0x44)
Binary8p4se(0x44 ↦ 1.5)

julia> FloatBytes.codepoint(Binary8p4se(1.5))
0x44

julia> quantize(Binary8p4se, 2/3, Projection(TowardNegative(), SatNone()))
Binary8p4se(0x3a ↦ 0.625)

reinterpret into a FloatByte is documented unsafe: it can fabricate nonzero bits above K, violating the canonical-byte invariant. show masks and flags such bytes instead of throwing.

Exact decoding

Every datum of every covered format is exactly representable in both Float32 and Float64; FloatBytes.decode is a table lookup into a precomputed atlas and is exact, never rounded (Float64(x) and Float32(x) expose it). This is asserted exhaustively by the test suite, not assumed.

julia> Float64(FloatBytes.fromcode(Binary8p1uf, 0x01))   # 2^-127, exact
5.877471754111438e-39

Format-level queries

Draft §4.14 queries, all folding to constants at compile time: bitwidth, Base.precision, signedness, domain, exponent_bitwidth, trailing_significand_bits, exponent_bias; value queries maxfinite, minfinite, minpositive, maxsubnormal (NaN when P == 1 — no subnormals exist), minnormal.