Function sin

src/compute-engine/interval/trigonometric.ts:25–50

(x: Interval | IntervalResult)

const THREE_HALF_PI = (3 * Math.PI) / 2;

/**
 * Sine of an interval.
 *
 * Sin is bounded [-1, 1] and periodic with extrema at pi/2 + n*pi.
 */
export function sin(x: Interval | IntervalResult): IntervalResult {
  const unwrapped = unwrapOrPropagate(x);
  if (!Array.isArray(unwrapped)) return unwrapped;
  const [xVal] = unwrapped;
  // Wide interval spans full range
  if (xVal.hi - xVal.lo >= TWO_PI) {
    return ok({ lo: -1, hi: 1 });
  }

  // Endpoint values
  const sinLo = Math.sin(xVal.lo);
  const sinHi = Math.sin(xVal.hi);
  let lo = Math.min(sinLo, sinHi);
  let hi = Math.max(sinLo, sinHi);

  // Check for maximum at pi/2 + 2n*pi
  if (containsExtremum(xVal, HALF_PI, TWO_PI)) {
    hi = 1;
  }
  // Check for minimum at 3*pi/2 + 2n*pi
  if (containsExtremum(xVal, THREE_HALF_PI, TWO_PI)) {
    lo = -1;
  }