core Tutorial

Generic analytic helper

fn hypot2[T : Add + Mul + Sqrt](x : T, y : T) -> T {
  (x * x + y * y).sqrt()
}

This expresses exactly which capability the algorithm needs, without tying it to one concrete numeric type.

Checked division

fn safe_ratio[T : DivChecked](x : T, y : T) -> Result[T, ArithmeticError] {
  x.div_checked(y, ArithmeticContext::new(32))
}

Use the checked layer when zero-division, domain validity, or precision sensitivity should be surfaced explicitly.

Checked comparison

fn ordering_or_error[T : CompareChecked](lhs : T, rhs : T) -> Result[Int, ArithmeticError] {
  lhs.compare_checked(rhs)
}

This is the right path when unordered values such as NaN must not be silently coerced into a total order.

Practical guidance

• Use unchecked traits only when direct backend semantics are acceptable.
• Use checked traits at API boundaries.
• Keep algebraic structure in luna-generic; use arithmetic for analytic capabilities.