Function pow

src/compute-engine/interval/elementary.ts:113–168

(
  base: Interval | IntervalResult,
  exp: number
)

  if (isNaNInterval(xVal)) return ok(NAN_INTERVAL);
  if (xVal.lo >= 0) {
    // Entirely non-negative: monotonically increasing
    return ok({ lo: xVal.lo * xVal.lo, hi: xVal.hi * xVal.hi });
  } else if (xVal.hi <= 0) {
    // Entirely non-positive: monotonically decreasing, flip bounds
    return ok({ lo: xVal.hi * xVal.hi, hi: xVal.lo * xVal.lo });
  } else {
    // Interval contains 0 - minimum is 0
    return ok({ lo: 0, hi: Math.max(xVal.lo * xVal.lo, xVal.hi * xVal.hi) });
  }
}

/**
 * Integer power helper for non-negative integer exponents.
 */
function intPow(base: Interval, n: number): Interval {
  if (n === 0) return { lo: 1, hi: 1 };
  if (n === 1) return base;

  // For even powers, the function has a minimum at 0
  if (n % 2 === 0) {
    if (base.lo >= 0) {
      return { lo: Math.pow(base.lo, n), hi: Math.pow(base.hi, n) };
    } else if (base.hi <= 0) {
      return { lo: Math.pow(base.hi, n), hi: Math.pow(base.lo, n) };
    } else {
      // Contains zero - minimum is 0
      return {
        lo: 0,
        hi: Math.max(Math.pow(base.lo, n), Math.pow(base.hi, n)),
      };
    }
  }

  // For odd powers, the function is monotonically increasing
  return { lo: Math.pow(base.lo, n), hi: Math.pow(base.hi, n) };
}

/**
 * Power function for intervals.
 *
 * Handles integer and fractional exponents differently:
 * - Integer exponents: consider sign and parity
 * - Negative integer: x^(-n) = 1/x^n, singular if base contains 0
 * - Fractional: requires non-negative base for real result
 */
function powRaw(base: Interval | IntervalResult, exp: number): IntervalResult {
  const unwrapped = unwrapOrPropagate(base);
  if (!Array.isArray(unwrapped)) return unwrapped;
  const [baseVal] = unwrapped;
  if (Number.isInteger(exp)) {
    if (exp >= 0) {
      return ok(intPow(baseVal, exp));
    } else {
      // Negative integer: x^(-n) = 1/x^n - singularity if base contains 0
      if (containsZero(baseVal)) {
        return { kind: 'singular' };
      }
      const denom = intPow(baseVal, -exp);