linear-algebra/arithmetic

API baseline for Luna-Flow/linear-algebra/arithmetic in the current 0.4.7 repository state.

Purpose

arithmetic owns operation-level traits used by the linear-algebra package. An operation trait means “this operation is available”; it does not state algebraic laws. Algebraic law-bearing structure belongs in linear-algebra/algebra.

Project Setup

If you want to use the linear-algebra operation traits together with the shared upstream abstractions, start with:

moon add Luna-Flow/linear-algebra@0.4.7
moon add Luna-Flow/luna-generic@0.3.3
moon add Luna-Flow/arithmetic@0.2.2

Recommended moon.pkg imports:

import {
  "Luna-Flow/linear-algebra/arithmetic" @la_arithmetic,
  "Luna-Flow/luna-generic" @lf_alg,
  "Luna-Flow/arithmetic" @lf_arith,
}

Re-exported Types

From Luna-Flow/arithmetic:

• ArithmeticContext
• ArithmeticError
• ArithmeticErrorKind
• FpClass
• RoundingMode

These preserve their upstream behavior and are used by checked operations.

Re-exported Operation Traits

From Luna-Flow/luna-generic:

• Zero
• One
• Inverse
• Conjugate

From Luna-Flow/arithmetic:

• Sqrt
• Cbrt
• Power
• Constants
• Exponential
• Logarithmic
• SqrtChecked
• DivChecked
• CompareChecked

Abs

///|
test "Abs captures absolute-value support" {
  inspect(@la_arithmetic.Abs::abs(-3), content="3")
}

Absolute-value operation. Implemented for:

• Int
• Float
• Double

ApproxEq

///|
test "ApproxEq captures approximate comparison support" {
  inspect(
    @la_arithmetic.ApproxEq::approx_eq(1.0, 1.0 + 1.0e-13),
    content="true",
  )
}

Approximate equality operation. It is an operation-level capability, not an equivalence-law claim. Implemented for:

• Int
• Float
• Double

CheckedDiv

///|
test "CheckedDiv carries context-aware division" {
  let ctx : @lf_arith.ArithmeticContext = @lf_arith.ArithmeticContext::new(32)
  inspect(
    @la_arithmetic.CheckedDiv::checked_div(6.0, 2.0, ctx).unwrap(),
    content="3",
  )
}

Checked division operation using ArithmeticContext. Implemented for:

• Float
• Double

CheckedSqrt

///|
test "CheckedSqrt carries context-aware square root" {
  let ctx : @lf_arith.ArithmeticContext = @lf_arith.ArithmeticContext::new(32)
  inspect(
    @la_arithmetic.CheckedSqrt::checked_sqrt(9.0, ctx).unwrap(),
    content="3",
  )
}

Checked square-root operation using ArithmeticContext. Implemented for:

• Float
• Double

CheckedCompare

///|
test "CheckedCompare returns an explicit ordering result" {
  inspect(
    @la_arithmetic.CheckedCompare::checked_compare(2.0, 3.0).unwrap(),
    content="-1",
  )
}

Checked scalar comparison. Implemented for:

• Float
• Double

Boundary

This package must not import matrix, vector, or backend types. In the dependency graph, it sits below algebra and all backend packages.