Function asin

src/compute-engine/interval/trigonometric.ts:230–253

(x: Interval | IntervalResult)

}

/**
 * Arc sine (inverse sine).
 *
 * Domain: [-1, 1], Range: [-pi/2, pi/2]
 */
export function asin(x: Interval | IntervalResult): IntervalResult {
  const unwrapped = unwrapOrPropagate(x);
  if (!Array.isArray(unwrapped)) return unwrapped;
  const [xVal] = unwrapped;
  // Entirely outside domain
  if (xVal.lo > 1 || xVal.hi < -1) {
    return { kind: 'empty' };
  }

  // Clip to domain if needed
  if (xVal.lo < -1 || xVal.hi > 1) {
    const clippedLo = Math.max(xVal.lo, -1);
    const clippedHi = Math.min(xVal.hi, 1);
    return {
      kind: 'partial',
      value: { lo: Math.asin(clippedLo), hi: Math.asin(clippedHi) },
      domainClipped:
        xVal.lo < -1 && xVal.hi > 1 ? 'both' : xVal.lo < -1 ? 'lo' : 'hi',
    };
  }

  // Within domain - asin is monotonically increasing