Function mod

src/compute-engine/interval/elementary.ts:589–651

(
  a: Interval | IntervalResult,
  b: Interval | IntervalResult
)

 * Domain: positive reals (x > 0)
 * - Entirely non-positive: empty
 * - Entirely positive: straightforward monotonic
 * - Contains/touches zero: partial with -Infinity lower bound
 */
function lnRaw(x: Interval | IntervalResult): IntervalResult {
  const unwrapped = unwrapOrPropagate(x);
  if (!Array.isArray(unwrapped)) return unwrapped;
  const [xVal] = unwrapped;
  // Case 1: Entirely non-positive - no valid values
  if (xVal.hi <= 0) {
    return { kind: 'empty' };
  }

  // Case 2: Entirely positive - straightforward
  if (xVal.lo > 0) {
    return ok({ lo: Math.log(xVal.lo), hi: Math.log(xVal.hi) });
  }

  // Case 3: Includes zero or negative values
  // ln(x) -> -Infinity as x -> 0+
  return {
    kind: 'partial',
    value: { lo: -Infinity, hi: Math.log(xVal.hi) },
    domainClipped: 'lo',
  };
}

/**
 * Base-10 logarithm.
 */
function log10Raw(x: Interval | IntervalResult): IntervalResult {
  const unwrapped = unwrapOrPropagate(x);
  if (!Array.isArray(unwrapped)) return unwrapped;
  const [xVal] = unwrapped;
  if (xVal.hi <= 0) {
    return { kind: 'empty' };
  }

  if (xVal.lo > 0) {
    return ok({ lo: Math.log10(xVal.lo), hi: Math.log10(xVal.hi) });
  }

  return {
    kind: 'partial',
    value: { lo: -Infinity, hi: Math.log10(xVal.hi) },
    domainClipped: 'lo',
  };
}

/**
 * Base-2 logarithm.
 */
function log2Raw(x: Interval | IntervalResult): IntervalResult {
  const unwrapped = unwrapOrPropagate(x);
  if (!Array.isArray(unwrapped)) return unwrapped;
  const [xVal] = unwrapped;
  if (xVal.hi <= 0) {
    return { kind: 'empty' };
  }