Function mul

src/compute-engine/numerics/rationals.ts:117–161

(lhs: Rational, rhs: Rational)

  // `a/b < 2^(la - lb + 1)`, so the value can be subnormal only when
  // `la - lb + 1 <= -1022`.
  if (la - lb <= -1023) {
    const num = a << 1074n;
    let k = num / b;
    const twiceRemainder = 2n * (num - k * b);
    if (twiceRemainder > b || (twiceRemainder === b && (k & 1n) === 1n))
      k += 1n;
    if (k <= 2n ** 52n) {
      const result = Number(k) * Number.MIN_VALUE;
      return negative ? -result : result;
    }
  }
  const e = la - lb - 64;
  const num = e < 0 ? a << BigInt(-e) : a;
  const den = e > 0 ? b << BigInt(e) : b;
  let q = num / den;
  if (q * den !== num) q |= 1n;
  const half = Math.trunc(e / 2);
  const result = Number(q) * 2 ** half * 2 ** (e - half);
  return negative ? -result : result;
}

export function isNeg(x: Rational): boolean {
  return x[0] < 0;
}

export function div(lhs: Rational, rhs: Rational): Rational {
  return mul(lhs, inverse(rhs));
}

/**
 * Add a literal numeric value to a rational.
 * If the rational is a bigint, this is a hint to do the calculation in bigint
 * (no need to check `bignumPreferred()`).
 * @param lhs
 * @param rhs
 * @returns
 */
export function add(lhs: Rational, rhs: Rational): Rational {
  if (typeof lhs[0] === 'number' && !Number.isFinite(lhs[0])) return lhs;

  const rhsNum = rhs;

  if (rhsNum === null) return lhs;

  if (isBigRational(rhsNum)) {
    lhs = [BigInt(lhs[0]), BigInt(lhs[1])];
    return [rhsNum[1] * lhs[0] + rhsNum[0] * lhs[1], rhsNum[1] * lhs[1]];
  }