@ball_float.BallFloat

This page tracks the current repository implementation and is written as the 0.2.0 API baseline.

Semantics

BallFloat represents the enclosure:

center +/- radius

The implementation stores that enclosure as lower and upper BinFloat bounds and prefers correctness of containment over returning the narrowest possible interval.

Construction

• BallFloat::new
• BallFloat::exact
• BallFloat::from_int
• BallFloat::from_bigint
• BallFloat::from_float
• BallFloat::from_double

Constraints:

• The center must be finite.
• The radius must be finite and non-negative.
• exact, from_float, and from_double abort on non-finite source values.

Notes:

• Center retuning widens the stored radius by the induced center displacement so the enclosure never shrinks.
• Radius quantization always rounds outward.

Accessors and Interval Shape

• lower_bound
• upper_bound
• center
• radius
• precision
• classify
• sign
• is_bounded
• is_entire
• contains_zero
• normalized
• with_precision

Notes:

• center() and radius() abort on unbounded intervals.
• If the enclosure spans both negative and positive values, sign() returns Sign::Zero.
• classify() reports Infinity for unbounded intervals.

Relations and Comparison

• contains
• overlaps
• separated_from
• definitely_lt
• definitely_le
• definitely_gt
• maybe_eq

Notes:

• Relations are enclosure-oriented and intentionally do not pretend to be a scalar total order.

Arithmetic and Checked Capability Behavior

• add
• sub
• mul
• div

Supported operators:

• +
• -
• *
• /
• unary -

Checked-behavior notes:

• Checked division may widen to the whole-real enclosure when the divisor contains zero.
• Checked integer power preserves enclosure correctness and uses the same whole-real fallback for zero-containing inverse cases.
• BallFloat does not implement scalar CompareChecked.
• This pass does not expose non-integer power, transcendental functions, calculus, matrices, complex balls, or special functions.

Trait Surface

BallFloat currently implements:

• @def.Floating
• @arithmetic.Contains
• @arithmetic.Overlaps
• @arithmetic.DefinitelyLt
• @arithmetic.DefinitelyLe
• @arithmetic.MaybeEq
• @arithmetic.DivChecked
• @arithmetic.PowNatChecked
• @arithmetic.PowIntChecked
• Eq, Add, Sub, Mul, Div, Neg, Show