Function nthRoot

src/compute-engine/interval/elementary.ts:296–309

(
  base: Interval | IntervalResult,
  n: number
)

 * negative base has no real value (`empty`/`partial`), as with `sqrt`.
 */
export function nthRoot(
  base: Interval | IntervalResult,
  n: number
): IntervalResult {
  const unwrapped = unwrapOrPropagate(base);
  if (!Array.isArray(unwrapped)) return unwrapped;
  const [b] = unwrapped;
  if (!Number.isInteger(n) || n === 0) return pow(ok(b), 1 / n);
  if (n % 2 === 0) return pow(ok(b), 1 / n);
  // Odd degree: real everywhere, monotone increasing.
  const root = (x: number): number =>
    Math.sign(x) * Math.pow(Math.abs(x), 1 / n);
  return ok({ lo: root(b.lo), hi: root(b.hi) });
}

/**
 * Exponential function (e^x).