core API

Purpose

arithmetic extends luna-generic with analytic capabilities. It models callable traits such as square root, logarithm, and trigonometric functions, plus checked/contextual arithmetic boundaries.

Unchecked capability traits

• Sqrt, Cbrt, Radical
• Exponential
• Logarithmic
• Power
• Trigonometric, InverseTrigonometric
• Hyperbolic, InverseHyperbolic
• Constants

These are defined in src/elementary.mbt.

Checked and contextual surface

Shared types

• FpClass
• RoundingMode
• ArithmeticContext
• ArithmeticErrorKind
• ArithmeticError

Checked traits

• SqrtChecked
• DivChecked
• CompareChecked
• PowNatChecked
• PowIntChecked
• ParseChecked

Enclosure relations

• Contains
• Overlaps
• DefinitelyLt
• DefinitelyLe
• MaybeEq

These are defined in src/checked.mbt.

Shipped instances

• Float and Double implement the broad elementary surface through Kaida-Amethyst/math.
• Float and Double also implement sqrt_checked, div_checked, compare_checked, pow_nat_checked, and pow_int_checked.
• BigInt and the integer family implement the narrower exact subset, most notably integer Power.

Semantic notes

• Unchecked traits leave domain restrictions and branch semantics to the concrete instance.
• On signed integers and BigInt, Power requires a non-negative exponent; negative exponents abort at runtime.
• ArithmeticContext::new clamps precision to at least 1.
• PowNatChecked treats x^0 as the multiplicative identity, including 0^0.
• Enclosure traits are relations, not a fake total order.