Function canonicalInteger

src/compute-engine/numerics/numeric.ts:117–164

(
  n: number,
  exponent: number
)

    return ri;

  return r;
}

/* @todo Consider https://cp-algorithms.com/algebra/factorization.html */

/** Return `[factor, root]` such that
 * pow(n, 1/exponent) = factor * pow(root, 1/exponent)
 *
 * canonicalInteger(75, 2) -> [5, 3] = 5^2 * 3
 *
 */
export function canonicalInteger(
  n: number,
  exponent: number
): readonly [factor: number, root: number] {
  if (n >= Number.MAX_SAFE_INTEGER) return [1, n];
  if (n === 0) return [0, 0];
  if (n === 1) return [1, 1];
  // @todo: handle negative n
  console.assert(Number.isInteger(n) && n > 0 && n < Number.MAX_SAFE_INTEGER);
  if (exponent === 2) {
    const result = (
      [
        [0, 0],
        [1, 1],
        [1, 2],
        [1, 3],
        [2, 1],
        [1, 5],
        [1, 6],
        [1, 7],
        [2, 2], // √8 = 2√2
        [3, 1],
        [1, 10],
        [1, 11],
        [2, 3],
        [1, 13],
        [1, 14],
        [1, 15],
        [4, 1],
        [1, 17],
        [3, 2],
        [1, 19],
        [2, 5], // √20 = 2√5
      ] as const
    )[n];
    if (result) return result;
  }
  const factors = primeFactors(n);
  let f = BigInt(1);
  let r = BigInt(1);