API reference

FloatByte{K,P,S<:Signedness,D<:DomainKind} <: AbstractFloat

One-byte floating-point value per IEEE P3109 draft 1: bitwidth K ∈ 3:8, precision P, signedness marker S, domain marker D. Users normally use the 120 exported aliases (Binary8p4se, …) rather than the raw parameters. Canonical-byte invariant: bits above K are zero for every native value.

SignedFormat: signedness marker Σ = Signed in FloatByte{K,P,S,D} (sign bit present; −Inf representable in extended domains).

UnsignedFormat: signedness marker Σ = Unsigned (no sign bit; no negative values).

FiniteDomain: domain marker Δ = Finite — no infinities in the datum set.

ExtendedDomain: domain marker Δ = Extended — +Inf (and −Inf when signed) are code points.

FORMAT_ALIASES

All 120 format aliases in canonical lattice order (format_id order): K ascending; Signed before Unsigned; P ascending; Finite before Extended.

quantize(F, x, ρ = DEFAULT_PROJECTION; entropy = nothing, index = 0) -> F

Mathematical construction: project real x into format F under ρ. This is the visible projecting constructor; fromcode is the raw one.

fromcode(T, code::Integer) -> T

The only safe code-identity constructor. Range-checked; reinterpret into a FloatByte is documented unsafe and confined to this file and the dense execution lowering.

codepoint(x::FloatByte) -> UInt8

The raw code point of x (the canonical byte; bits above K are zero).

isvalidcode(T, code::Integer) -> Bool

Whether code is in 0:2^K - 1 for format T.

decode(x::FloatByte) -> Float64

Exact decoded value (NaN, ±Inf for specials). One const-Memory load plus a bounds-elided indexed read; the offset folds per alias.

Projection{R<:RoundingMode, S<:SaturationMode}

A projection specification ρ = (rounding mode, saturation mode).

DEFAULT_PROJECTION

The immutable package default ρ: (NearestTiesToEven, SatNone). Used by the projecting constructors and the Base operator surface unless overridden with with_projection.

with_projection(f, ρ)

Run f() with the Base-operator projection scope set to ρ. Outside the performance interface: explicit apply(op, Fr, ρ, ...) is the fast path; only the Base-operator adapters read this scope. No mutable global numerical policy exists anywhere.

NearestTiesToEven(): round to nearest; ties to the even code (draft §4.7.4; for P == 1 formats evenness is defined on the code point). The package default.

NearestTiesToAway(): round to nearest; ties away from zero.

TowardPositive(): directed rounding toward +∞.

TowardNegative(): directed rounding toward −∞.

TowardZero(): directed rounding toward zero (truncation).

ToOdd(): round-to-odd — truncate, then force the kept code odd when inexact.

StochasticA(N): stochastic rounding, variant A of draft §4.7.4 — round away iff ⌊ν·2^N⌋ + R ≥ 2^N for the supplied N-bit entropy value R. N ∈ 1:63; this build implements N ≤ 32.

StochasticB(N): stochastic rounding, variant B — ⌊ν·2^(N+1)⌋ + 2R + 1 ≥ 2^(N+1).

StochasticC(N): stochastic rounding, variant C — RNITE(ν·2^N) + R ≥ 2^N.

SatFinite(): out-of-range results (including infinities) clamp to the extremal finite values.

SatPropagate(): representable infinities propagate; finite overflow clamps to the extremal finite values.

SatNone(): draft §4.7.5 default behavior — overflow goes to ±Inf where representable (NaN in finite domains and for negative results in unsigned formats), except that a rounding direction pointing inward forces the extremal finite value.

apply(op, Fr, ρ, xs...; entropy = nothing, index = 0) -> Fr

Public operation entry point. Fr is the result format, ρ the projection specification. Operands are FloatByte values (heterogeneous formats allowed). entropy is required for stochastic ρ: either a raw UInt64 word (top N bits are consumed) or an IndexedEntropy keyed by index. An unsupported operand is a MethodError, never a silent fall-through to host arithmetic.

defined_code(op, Fr, ρ, entropy::UInt64, xs::FloatByte...) -> UInt8

The internal seam: one semantic pipeline — code-point special rows in the draft's order, exact auxiliary computation over the closed extended reals, one final projection. A table entry is a call to this function.

Entropy contract: deterministic modes ignore the word; stochastic modes consume exactly the word passed (its top N bits), including for exact and special results. entropy = 0 under a stochastic mode is legal input, not a sentinel.

Abs: operation singleton — draft §4.10.1, absolute value. Apply with apply(Abs, Fr, ρ, x).

Add: operation singleton — draft §4.10.3, addition. Apply with apply(Add, Fr, ρ, x, y).

ArcCos: operation singleton — draft §4.10.10, arccosine (|x| > 1 → NaN). Apply with apply(ArcCos, Fr, ρ, x).

ArcCosPi: operation singleton — draft §4.10.12, arccos(x)/π. Apply with apply(ArcCosPi, Fr, ρ, x).

ArcCosh: operation singleton — draft §4.10.11, inverse hyperbolic cosine (x < 1 → NaN). Apply with apply(ArcCosh, Fr, ρ, x).

ArcSin: operation singleton — draft §4.10.10, arcsine (|x| > 1 → NaN). Apply with apply(ArcSin, Fr, ρ, x).

ArcSinPi: operation singleton — draft §4.10.12, arcsin(x)/π. Apply with apply(ArcSinPi, Fr, ρ, x).

ArcSinh: operation singleton — draft §4.10.11, inverse hyperbolic sine. Apply with apply(ArcSinh, Fr, ρ, x).

ArcTan: operation singleton — draft §4.10.10, arctangent (ArcTan(±Inf) = ±π/2). Apply with apply(ArcTan, Fr, ρ, x).

ArcTan2: operation singleton — draft §4.10.15, two-argument arctangent (y, x) (ArcTan2(0,0) = NaN). Apply with apply(ArcTan2, Fr, ρ, x, y).

ArcTan2Pi: operation singleton — draft §4.10.16, two-argument arctangent divided by π. Apply with apply(ArcTan2Pi, Fr, ρ, x, y).

ArcTanPi: operation singleton — draft §4.10.12, arctan(x)/π (±Inf → ±1/2). Apply with apply(ArcTanPi, Fr, ρ, x).

ArcTanh: operation singleton — draft §4.10.11, inverse hyperbolic tangent (ArcTanh(±1) = ±∞). Apply with apply(ArcTanh, Fr, ρ, x).

Clamp: operation singleton — draft §4.11.4, clamp x to [lo, hi] (lo > hi → NaN). Apply with apply(Clamp, Fr, ρ, x, y, z).

Convert: operation singleton — draft §4.9.1, format conversion (the only cross-format tier-1 operation). Apply with apply(Convert, Fr, ρ, x).

CopySign: operation singleton — draft §4.10.2, magnitude of x with the sign of y. Apply with apply(CopySign, Fr, ρ, x, y).

Cos: operation singleton — draft §4.10.10, cosine (±Inf → NaN). Apply with apply(Cos, Fr, ρ, x).

CosPi: operation singleton — draft §4.10.12, cos(πx), exact at half-integers. Apply with apply(CosPi, Fr, ρ, x).

Cosh: operation singleton — draft §4.10.11, hyperbolic cosine. Apply with apply(Cosh, Fr, ρ, x).

Divide: operation singleton — draft §4.10.5, division (x/0 = NaN, x/±Inf = 0). Apply with apply(Divide, Fr, ρ, x, y).

Exp: operation singleton — draft §4.10.9, e^x. Apply with apply(Exp, Fr, ρ, x).

Exp2: operation singleton — draft §4.10.9, 2^x. Apply with apply(Exp2, Fr, ρ, x).

ExpMinusOne: operation singleton — draft §4.10.9, e^x − 1. Apply with apply(ExpMinusOne, Fr, ρ, x).

FAA: operation singleton — draft §4.10.7, fused add–add x + y + z, exactly associative, one projection. Apply with apply(FAA, Fr, ρ, x, y, z).

FMA: operation singleton — draft §4.10.6, fused multiply–add x*y + z, one projection. Apply with apply(FMA, Fr, ρ, x, y, z).

Hypot: operation singleton — draft §4.10.14, √(x² + y²) — algebraic, exact-window evaluated. Apply with apply(Hypot, Fr, ρ, x, y).

Log: operation singleton — draft §4.10.9, natural logarithm (Log(0) = −∞, negative → NaN). Apply with apply(Log, Fr, ρ, x).

Log2: operation singleton — draft §4.10.9, base-2 logarithm. Apply with apply(Log2, Fr, ρ, x).

LogOnePlus: operation singleton — draft §4.10.9, log(1 + x). Apply with apply(LogOnePlus, Fr, ρ, x).

Maximum: operation singleton — draft §4.11.1, maximum, NaN-propagating. Apply with apply(Maximum, Fr, ρ, x, y).

MaximumFinite: operation singleton — draft §4.11.3, maximum preferring finite operands. Apply with apply(MaximumFinite, Fr, ρ, x, y).

MaximumMagnitude: operation singleton — draft §4.11.2, maximum by magnitude, signed tie-break. Apply with apply(MaximumMagnitude, Fr, ρ, x, y).

MaximumMagnitudeNumber: operation singleton — draft §4.11.2, NaN-replacing maximum by magnitude. Apply with apply(MaximumMagnitudeNumber, Fr, ρ, x, y).

MaximumNumber: operation singleton — draft §4.11.1, maximum; a NaN operand is replaced by the other operand. Apply with apply(MaximumNumber, Fr, ρ, x, y).

Minimum: operation singleton — draft §4.11.1, minimum, NaN-propagating. Apply with apply(Minimum, Fr, ρ, x, y).

MinimumFinite: operation singleton — draft §4.11.3, minimum preferring finite operands. Apply with apply(MinimumFinite, Fr, ρ, x, y).

MinimumMagnitude: operation singleton — draft §4.11.2, minimum by magnitude, signed tie-break. Apply with apply(MinimumMagnitude, Fr, ρ, x, y).

MinimumMagnitudeNumber: operation singleton — draft §4.11.2, NaN-replacing minimum by magnitude. Apply with apply(MinimumMagnitudeNumber, Fr, ρ, x, y).

MinimumNumber: operation singleton — draft §4.11.1, minimum; a NaN operand is replaced by the other operand. Apply with apply(MinimumNumber, Fr, ρ, x, y).

Multiply: operation singleton — draft §4.10.4, multiplication. Apply with apply(Multiply, Fr, ρ, x, y).

Negate: operation singleton — draft §4.10.1, negation (in unsigned formats nonzero results follow the saturation rows). Apply with apply(Negate, Fr, ρ, x).

RSqrt: operation singleton — draft §4.10.8, reciprocal square root (x ≤ 0 → NaN). Apply with apply(RSqrt, Fr, ρ, x).

Recip: operation singleton — draft §4.10.8, reciprocal (Recip(0) = NaN, Recip(±Inf) = 0). Apply with apply(Recip, Fr, ρ, x).

Sin: operation singleton — draft §4.10.10, sine (±Inf → NaN). Apply with apply(Sin, Fr, ρ, x).

SinPi: operation singleton — draft §4.10.12, sin(πx), exact at half-integers. Apply with apply(SinPi, Fr, ρ, x).

Sinh: operation singleton — draft §4.10.11, hyperbolic sine. Apply with apply(Sinh, Fr, ρ, x).

Softplus: operation singleton — draft §4.10.13, log(1 + e^x). Apply with apply(Softplus, Fr, ρ, x).

Sqrt: operation singleton — draft §4.10.8, square root (negative → NaN). Apply with apply(Sqrt, Fr, ρ, x).

Subtract: operation singleton — draft §4.10.3, subtraction. Apply with apply(Subtract, Fr, ρ, x, y).

Tan: operation singleton — draft §4.10.10, tangent (±Inf → NaN). Apply with apply(Tan, Fr, ρ, x).

TanPi: operation singleton — draft §4.10.12, tan(πx); poles at half-odd integers give ±∞. Apply with apply(TanPi, Fr, ρ, x).

Tanh: operation singleton — draft §4.10.11, hyperbolic tangent (Tanh(±Inf) = ±1 exactly). Apply with apply(Tanh, Fr, ρ, x).

bitwidth(F): BitwidthOf.

signedness(F): SignednessOf — SignedFormat or UnsignedFormat.

domain(F): DomainOf — FiniteDomain or ExtendedDomain.

exponent_bitwidth(F): ExponentBitwidthOf.

trailingsignificandbits(F): TrailingSignificandBitwidthOf.

exponent_bias(F): ExponentBiasOf.

maxfinite(F): MaxFiniteOf — maximum finite value of the format.

minfinite(F): MinFiniteOf — -maxfinite for signed formats, zero for unsigned.

minpositive(F): MinPositiveOf — least strictly positive value.

maxsubnormal(F): MaxSubnormalOf, or NaN when the format has no subnormals.

minnormal(F): MinNormalOf — least positive normal value.

compare_less(x, y): draft CompareLess — false whenever either operand is NaN; operands may differ in format.

compare_less_equal(x, y): draft CompareLessEqual — false on NaN operands.

compare_equal(x, y): draft CompareEqual — NaN compares unequal to everything, including itself.

compare_greater_equal(x, y): draft CompareGreaterEqual — false on NaN operands.

compare_greater(x, y): draft CompareGreater — false on NaN operands.

total_order(x, y) -> Bool

P3109 total order (§4.12.1): the single NaN compares as the most negative value — NaN first, the opposite end from Float64 sorting.

floatclass(x::FloatByte) -> FloatByteClass

The classifier operation Class (draft Table 2): every code point falls into exactly one of the eight classes.

FloatByteClass

Enumeration returned by floatclass (draft §4.13.1, Table 2): ClsNaN, ClsNegativeInfinity, ClsNegativeNormal, ClsNegativeSubnormal, ClsZero, ClsPositiveSubnormal, ClsPositiveNormal, ClsPositiveInfinity. Every code point falls into exactly one class.

nextgreaterthan(x) -> same format

NextGreaterThan: least value comparing greater, or NaN (NextGreaterThan(+Inf) = NaN, unlike IEEE-754 nextUp).

nextlessthan(x) -> same format

NextLessThan: greatest value comparing less, or NaN.

ClsNaN: FloatByteClass member (draft §4.13.1 Table 2).

ClsNegativeInfinity: FloatByteClass member (draft §4.13.1 Table 2).

ClsNegativeNormal: FloatByteClass member (draft §4.13.1 Table 2).

ClsNegativeSubnormal: FloatByteClass member (draft §4.13.1 Table 2).

ClsPositiveInfinity: FloatByteClass member (draft §4.13.1 Table 2).

ClsPositiveNormal: FloatByteClass member (draft §4.13.1 Table 2).

ClsPositiveSubnormal: FloatByteClass member (draft §4.13.1 Table 2).

ClsZero: FloatByteClass member (draft §4.13.1 Table 2).

IndexedEntropy(seed, stream, invocation)

Reproducible entropy source for stochastic rounding. entropy_word derives one word per (logical index, projection slot) key.

entropy_word(ie, index, slot, ::Val{N}) -> UInt64

The top-N-bit entropy value R < 2^N for one logical output. N is a Val so 64 - N folds to a constant shift.

InconclusiveProjectionError

The rigorous enclosure loop hit its precision ceiling undecided. The destination is never mutated and no guess is written.

EntropyRequiredError

A stochastic ρ was requested without an entropy source; thrown at preparation, never mid-loop.

WorkspaceError

A caller-owned workspace is too small; thrown before any mutation of the destination (required and provided sizes carried).

AliasingError

Overlapping array views where the operation's semantics would differ.

Binary3p1se: FloatByte{3,1,SignedFormat,ExtendedDomain} — bitwidth 3, precision 1, signed, extended (has infinities); exponent bias 2.

Binary3p1sf: FloatByte{3,1,SignedFormat,FiniteDomain} — bitwidth 3, precision 1, signed, finite; exponent bias 2.

Binary3p1ue: FloatByte{3,1,UnsignedFormat,ExtendedDomain} — bitwidth 3, precision 1, unsigned, extended (has infinities); exponent bias 4.

Binary3p1uf: FloatByte{3,1,UnsignedFormat,FiniteDomain} — bitwidth 3, precision 1, unsigned, finite; exponent bias 4.

Binary3p2se: FloatByte{3,2,SignedFormat,ExtendedDomain} — bitwidth 3, precision 2, signed, extended (has infinities); exponent bias 1.

Binary3p2sf: FloatByte{3,2,SignedFormat,FiniteDomain} — bitwidth 3, precision 2, signed, finite; exponent bias 1.

Binary3p2ue: FloatByte{3,2,UnsignedFormat,ExtendedDomain} — bitwidth 3, precision 2, unsigned, extended (has infinities); exponent bias 2.

Binary3p2uf: FloatByte{3,2,UnsignedFormat,FiniteDomain} — bitwidth 3, precision 2, unsigned, finite; exponent bias 2.

Binary3p3ue: FloatByte{3,3,UnsignedFormat,ExtendedDomain} — bitwidth 3, precision 3, unsigned, extended (has infinities); exponent bias 1.

Binary3p3uf: FloatByte{3,3,UnsignedFormat,FiniteDomain} — bitwidth 3, precision 3, unsigned, finite; exponent bias 1.

Binary4p1se: FloatByte{4,1,SignedFormat,ExtendedDomain} — bitwidth 4, precision 1, signed, extended (has infinities); exponent bias 4.

Binary4p1sf: FloatByte{4,1,SignedFormat,FiniteDomain} — bitwidth 4, precision 1, signed, finite; exponent bias 4.

Binary4p1ue: FloatByte{4,1,UnsignedFormat,ExtendedDomain} — bitwidth 4, precision 1, unsigned, extended (has infinities); exponent bias 8.

Binary4p1uf: FloatByte{4,1,UnsignedFormat,FiniteDomain} — bitwidth 4, precision 1, unsigned, finite; exponent bias 8.

Binary4p2se: FloatByte{4,2,SignedFormat,ExtendedDomain} — bitwidth 4, precision 2, signed, extended (has infinities); exponent bias 2.

Binary4p2sf: FloatByte{4,2,SignedFormat,FiniteDomain} — bitwidth 4, precision 2, signed, finite; exponent bias 2.

Binary4p2ue: FloatByte{4,2,UnsignedFormat,ExtendedDomain} — bitwidth 4, precision 2, unsigned, extended (has infinities); exponent bias 4.

Binary4p2uf: FloatByte{4,2,UnsignedFormat,FiniteDomain} — bitwidth 4, precision 2, unsigned, finite; exponent bias 4.

Binary4p3se: FloatByte{4,3,SignedFormat,ExtendedDomain} — bitwidth 4, precision 3, signed, extended (has infinities); exponent bias 1.

Binary4p3sf: FloatByte{4,3,SignedFormat,FiniteDomain} — bitwidth 4, precision 3, signed, finite; exponent bias 1.

Binary4p3ue: FloatByte{4,3,UnsignedFormat,ExtendedDomain} — bitwidth 4, precision 3, unsigned, extended (has infinities); exponent bias 2.

Binary4p3uf: FloatByte{4,3,UnsignedFormat,FiniteDomain} — bitwidth 4, precision 3, unsigned, finite; exponent bias 2.

Binary4p4ue: FloatByte{4,4,UnsignedFormat,ExtendedDomain} — bitwidth 4, precision 4, unsigned, extended (has infinities); exponent bias 1.

Binary4p4uf: FloatByte{4,4,UnsignedFormat,FiniteDomain} — bitwidth 4, precision 4, unsigned, finite; exponent bias 1.

Binary5p1se: FloatByte{5,1,SignedFormat,ExtendedDomain} — bitwidth 5, precision 1, signed, extended (has infinities); exponent bias 8.

Binary5p1sf: FloatByte{5,1,SignedFormat,FiniteDomain} — bitwidth 5, precision 1, signed, finite; exponent bias 8.

Binary5p1ue: FloatByte{5,1,UnsignedFormat,ExtendedDomain} — bitwidth 5, precision 1, unsigned, extended (has infinities); exponent bias 16.

Binary5p1uf: FloatByte{5,1,UnsignedFormat,FiniteDomain} — bitwidth 5, precision 1, unsigned, finite; exponent bias 16.

Binary5p2se: FloatByte{5,2,SignedFormat,ExtendedDomain} — bitwidth 5, precision 2, signed, extended (has infinities); exponent bias 4.

Binary5p2sf: FloatByte{5,2,SignedFormat,FiniteDomain} — bitwidth 5, precision 2, signed, finite; exponent bias 4.

Binary5p2ue: FloatByte{5,2,UnsignedFormat,ExtendedDomain} — bitwidth 5, precision 2, unsigned, extended (has infinities); exponent bias 8.

Binary5p2uf: FloatByte{5,2,UnsignedFormat,FiniteDomain} — bitwidth 5, precision 2, unsigned, finite; exponent bias 8.

Binary5p3se: FloatByte{5,3,SignedFormat,ExtendedDomain} — bitwidth 5, precision 3, signed, extended (has infinities); exponent bias 2.

Binary5p3sf: FloatByte{5,3,SignedFormat,FiniteDomain} — bitwidth 5, precision 3, signed, finite; exponent bias 2.

Binary5p3ue: FloatByte{5,3,UnsignedFormat,ExtendedDomain} — bitwidth 5, precision 3, unsigned, extended (has infinities); exponent bias 4.

Binary5p3uf: FloatByte{5,3,UnsignedFormat,FiniteDomain} — bitwidth 5, precision 3, unsigned, finite; exponent bias 4.

Binary5p4se: FloatByte{5,4,SignedFormat,ExtendedDomain} — bitwidth 5, precision 4, signed, extended (has infinities); exponent bias 1.

Binary5p4sf: FloatByte{5,4,SignedFormat,FiniteDomain} — bitwidth 5, precision 4, signed, finite; exponent bias 1.

Binary5p4ue: FloatByte{5,4,UnsignedFormat,ExtendedDomain} — bitwidth 5, precision 4, unsigned, extended (has infinities); exponent bias 2.

Binary5p4uf: FloatByte{5,4,UnsignedFormat,FiniteDomain} — bitwidth 5, precision 4, unsigned, finite; exponent bias 2.

Binary5p5ue: FloatByte{5,5,UnsignedFormat,ExtendedDomain} — bitwidth 5, precision 5, unsigned, extended (has infinities); exponent bias 1.

Binary5p5uf: FloatByte{5,5,UnsignedFormat,FiniteDomain} — bitwidth 5, precision 5, unsigned, finite; exponent bias 1.

Binary6p1se: FloatByte{6,1,SignedFormat,ExtendedDomain} — bitwidth 6, precision 1, signed, extended (has infinities); exponent bias 16.

Binary6p1sf: FloatByte{6,1,SignedFormat,FiniteDomain} — bitwidth 6, precision 1, signed, finite; exponent bias 16.

Binary6p1ue: FloatByte{6,1,UnsignedFormat,ExtendedDomain} — bitwidth 6, precision 1, unsigned, extended (has infinities); exponent bias 32.

Binary6p1uf: FloatByte{6,1,UnsignedFormat,FiniteDomain} — bitwidth 6, precision 1, unsigned, finite; exponent bias 32.

Binary6p2se: FloatByte{6,2,SignedFormat,ExtendedDomain} — bitwidth 6, precision 2, signed, extended (has infinities); exponent bias 8.

Binary6p2sf: FloatByte{6,2,SignedFormat,FiniteDomain} — bitwidth 6, precision 2, signed, finite; exponent bias 8.

Binary6p2ue: FloatByte{6,2,UnsignedFormat,ExtendedDomain} — bitwidth 6, precision 2, unsigned, extended (has infinities); exponent bias 16.

Binary6p2uf: FloatByte{6,2,UnsignedFormat,FiniteDomain} — bitwidth 6, precision 2, unsigned, finite; exponent bias 16.

Binary6p3se: FloatByte{6,3,SignedFormat,ExtendedDomain} — bitwidth 6, precision 3, signed, extended (has infinities); exponent bias 4.

Binary6p3sf: FloatByte{6,3,SignedFormat,FiniteDomain} — bitwidth 6, precision 3, signed, finite; exponent bias 4.

Binary6p3ue: FloatByte{6,3,UnsignedFormat,ExtendedDomain} — bitwidth 6, precision 3, unsigned, extended (has infinities); exponent bias 8.

Binary6p3uf: FloatByte{6,3,UnsignedFormat,FiniteDomain} — bitwidth 6, precision 3, unsigned, finite; exponent bias 8.

Binary6p4se: FloatByte{6,4,SignedFormat,ExtendedDomain} — bitwidth 6, precision 4, signed, extended (has infinities); exponent bias 2.

Binary6p4sf: FloatByte{6,4,SignedFormat,FiniteDomain} — bitwidth 6, precision 4, signed, finite; exponent bias 2.

Binary6p4ue: FloatByte{6,4,UnsignedFormat,ExtendedDomain} — bitwidth 6, precision 4, unsigned, extended (has infinities); exponent bias 4.

Binary6p4uf: FloatByte{6,4,UnsignedFormat,FiniteDomain} — bitwidth 6, precision 4, unsigned, finite; exponent bias 4.

Binary6p5se: FloatByte{6,5,SignedFormat,ExtendedDomain} — bitwidth 6, precision 5, signed, extended (has infinities); exponent bias 1.

Binary6p5sf: FloatByte{6,5,SignedFormat,FiniteDomain} — bitwidth 6, precision 5, signed, finite; exponent bias 1.

Binary6p5ue: FloatByte{6,5,UnsignedFormat,ExtendedDomain} — bitwidth 6, precision 5, unsigned, extended (has infinities); exponent bias 2.

Binary6p5uf: FloatByte{6,5,UnsignedFormat,FiniteDomain} — bitwidth 6, precision 5, unsigned, finite; exponent bias 2.

Binary6p6ue: FloatByte{6,6,UnsignedFormat,ExtendedDomain} — bitwidth 6, precision 6, unsigned, extended (has infinities); exponent bias 1.

Binary6p6uf: FloatByte{6,6,UnsignedFormat,FiniteDomain} — bitwidth 6, precision 6, unsigned, finite; exponent bias 1.

Binary7p1se: FloatByte{7,1,SignedFormat,ExtendedDomain} — bitwidth 7, precision 1, signed, extended (has infinities); exponent bias 32.

Binary7p1sf: FloatByte{7,1,SignedFormat,FiniteDomain} — bitwidth 7, precision 1, signed, finite; exponent bias 32.

Binary7p1ue: FloatByte{7,1,UnsignedFormat,ExtendedDomain} — bitwidth 7, precision 1, unsigned, extended (has infinities); exponent bias 64.

Binary7p1uf: FloatByte{7,1,UnsignedFormat,FiniteDomain} — bitwidth 7, precision 1, unsigned, finite; exponent bias 64.

Binary7p2se: FloatByte{7,2,SignedFormat,ExtendedDomain} — bitwidth 7, precision 2, signed, extended (has infinities); exponent bias 16.

Binary7p2sf: FloatByte{7,2,SignedFormat,FiniteDomain} — bitwidth 7, precision 2, signed, finite; exponent bias 16.

Binary7p2ue: FloatByte{7,2,UnsignedFormat,ExtendedDomain} — bitwidth 7, precision 2, unsigned, extended (has infinities); exponent bias 32.

Binary7p2uf: FloatByte{7,2,UnsignedFormat,FiniteDomain} — bitwidth 7, precision 2, unsigned, finite; exponent bias 32.

Binary7p3se: FloatByte{7,3,SignedFormat,ExtendedDomain} — bitwidth 7, precision 3, signed, extended (has infinities); exponent bias 8.

Binary7p3sf: FloatByte{7,3,SignedFormat,FiniteDomain} — bitwidth 7, precision 3, signed, finite; exponent bias 8.

Binary7p3ue: FloatByte{7,3,UnsignedFormat,ExtendedDomain} — bitwidth 7, precision 3, unsigned, extended (has infinities); exponent bias 16.

Binary7p3uf: FloatByte{7,3,UnsignedFormat,FiniteDomain} — bitwidth 7, precision 3, unsigned, finite; exponent bias 16.

Binary7p4se: FloatByte{7,4,SignedFormat,ExtendedDomain} — bitwidth 7, precision 4, signed, extended (has infinities); exponent bias 4.

Binary7p4sf: FloatByte{7,4,SignedFormat,FiniteDomain} — bitwidth 7, precision 4, signed, finite; exponent bias 4.

Binary7p4ue: FloatByte{7,4,UnsignedFormat,ExtendedDomain} — bitwidth 7, precision 4, unsigned, extended (has infinities); exponent bias 8.

Binary7p4uf: FloatByte{7,4,UnsignedFormat,FiniteDomain} — bitwidth 7, precision 4, unsigned, finite; exponent bias 8.

Binary7p5se: FloatByte{7,5,SignedFormat,ExtendedDomain} — bitwidth 7, precision 5, signed, extended (has infinities); exponent bias 2.

Binary7p5sf: FloatByte{7,5,SignedFormat,FiniteDomain} — bitwidth 7, precision 5, signed, finite; exponent bias 2.

Binary7p5ue: FloatByte{7,5,UnsignedFormat,ExtendedDomain} — bitwidth 7, precision 5, unsigned, extended (has infinities); exponent bias 4.

Binary7p5uf: FloatByte{7,5,UnsignedFormat,FiniteDomain} — bitwidth 7, precision 5, unsigned, finite; exponent bias 4.

Binary7p6se: FloatByte{7,6,SignedFormat,ExtendedDomain} — bitwidth 7, precision 6, signed, extended (has infinities); exponent bias 1.

Binary7p6sf: FloatByte{7,6,SignedFormat,FiniteDomain} — bitwidth 7, precision 6, signed, finite; exponent bias 1.

Binary7p6ue: FloatByte{7,6,UnsignedFormat,ExtendedDomain} — bitwidth 7, precision 6, unsigned, extended (has infinities); exponent bias 2.

Binary7p6uf: FloatByte{7,6,UnsignedFormat,FiniteDomain} — bitwidth 7, precision 6, unsigned, finite; exponent bias 2.

Binary7p7ue: FloatByte{7,7,UnsignedFormat,ExtendedDomain} — bitwidth 7, precision 7, unsigned, extended (has infinities); exponent bias 1.

Binary7p7uf: FloatByte{7,7,UnsignedFormat,FiniteDomain} — bitwidth 7, precision 7, unsigned, finite; exponent bias 1.

Binary8p1se: FloatByte{8,1,SignedFormat,ExtendedDomain} — bitwidth 8, precision 1, signed, extended (has infinities); exponent bias 64.

Binary8p1sf: FloatByte{8,1,SignedFormat,FiniteDomain} — bitwidth 8, precision 1, signed, finite; exponent bias 64.

Binary8p1ue: FloatByte{8,1,UnsignedFormat,ExtendedDomain} — bitwidth 8, precision 1, unsigned, extended (has infinities); exponent bias 128.

Binary8p1uf: FloatByte{8,1,UnsignedFormat,FiniteDomain} — bitwidth 8, precision 1, unsigned, finite; exponent bias 128.

Binary8p2se: FloatByte{8,2,SignedFormat,ExtendedDomain} — bitwidth 8, precision 2, signed, extended (has infinities); exponent bias 32.

Binary8p2sf: FloatByte{8,2,SignedFormat,FiniteDomain} — bitwidth 8, precision 2, signed, finite; exponent bias 32.

Binary8p2ue: FloatByte{8,2,UnsignedFormat,ExtendedDomain} — bitwidth 8, precision 2, unsigned, extended (has infinities); exponent bias 64.

Binary8p2uf: FloatByte{8,2,UnsignedFormat,FiniteDomain} — bitwidth 8, precision 2, unsigned, finite; exponent bias 64.

Binary8p3se: FloatByte{8,3,SignedFormat,ExtendedDomain} — bitwidth 8, precision 3, signed, extended (has infinities); exponent bias 16.

Binary8p3sf: FloatByte{8,3,SignedFormat,FiniteDomain} — bitwidth 8, precision 3, signed, finite; exponent bias 16.

Binary8p3ue: FloatByte{8,3,UnsignedFormat,ExtendedDomain} — bitwidth 8, precision 3, unsigned, extended (has infinities); exponent bias 32.

Binary8p3uf: FloatByte{8,3,UnsignedFormat,FiniteDomain} — bitwidth 8, precision 3, unsigned, finite; exponent bias 32.

Binary8p4se: FloatByte{8,4,SignedFormat,ExtendedDomain} — bitwidth 8, precision 4, signed, extended (has infinities); exponent bias 8.

Binary8p4sf: FloatByte{8,4,SignedFormat,FiniteDomain} — bitwidth 8, precision 4, signed, finite; exponent bias 8.

Binary8p4ue: FloatByte{8,4,UnsignedFormat,ExtendedDomain} — bitwidth 8, precision 4, unsigned, extended (has infinities); exponent bias 16.

Binary8p4uf: FloatByte{8,4,UnsignedFormat,FiniteDomain} — bitwidth 8, precision 4, unsigned, finite; exponent bias 16.

Binary8p5se: FloatByte{8,5,SignedFormat,ExtendedDomain} — bitwidth 8, precision 5, signed, extended (has infinities); exponent bias 4.

Binary8p5sf: FloatByte{8,5,SignedFormat,FiniteDomain} — bitwidth 8, precision 5, signed, finite; exponent bias 4.

Binary8p5ue: FloatByte{8,5,UnsignedFormat,ExtendedDomain} — bitwidth 8, precision 5, unsigned, extended (has infinities); exponent bias 8.

Binary8p5uf: FloatByte{8,5,UnsignedFormat,FiniteDomain} — bitwidth 8, precision 5, unsigned, finite; exponent bias 8.

Binary8p6se: FloatByte{8,6,SignedFormat,ExtendedDomain} — bitwidth 8, precision 6, signed, extended (has infinities); exponent bias 2.

Binary8p6sf: FloatByte{8,6,SignedFormat,FiniteDomain} — bitwidth 8, precision 6, signed, finite; exponent bias 2.

Binary8p6ue: FloatByte{8,6,UnsignedFormat,ExtendedDomain} — bitwidth 8, precision 6, unsigned, extended (has infinities); exponent bias 4.

Binary8p6uf: FloatByte{8,6,UnsignedFormat,FiniteDomain} — bitwidth 8, precision 6, unsigned, finite; exponent bias 4.

Binary8p7se: FloatByte{8,7,SignedFormat,ExtendedDomain} — bitwidth 8, precision 7, signed, extended (has infinities); exponent bias 1.

Binary8p7sf: FloatByte{8,7,SignedFormat,FiniteDomain} — bitwidth 8, precision 7, signed, finite; exponent bias 1.

Binary8p7ue: FloatByte{8,7,UnsignedFormat,ExtendedDomain} — bitwidth 8, precision 7, unsigned, extended (has infinities); exponent bias 2.

Binary8p7uf: FloatByte{8,7,UnsignedFormat,FiniteDomain} — bitwidth 8, precision 7, unsigned, finite; exponent bias 2.

Binary8p8ue: FloatByte{8,8,UnsignedFormat,ExtendedDomain} — bitwidth 8, precision 8, unsigned, extended (has infinities); exponent bias 1.

Binary8p8uf: FloatByte{8,8,UnsignedFormat,FiniteDomain} — bitwidth 8, precision 8, unsigned, finite; exponent bias 1.