packages/qiskit-devs-js/lib/factor.js
function findPeriod() {
    let bestSoFar = 1;

    for (let attempts = 0; attempts < 2 * numOutBits; attempts += 1) {
      // NOTE: Here we take advantage of the fact that, for Shor's algorithm,
      // we know that f(x) = f(x+i) ONLY when i is an integer multiple of the rank r.
      if (f(bestSoFar) === f0) {
        dbg(`The period of ${a}^x mod ${n} is ${bestSoFar}`);
        return bestSoFar;
      }

      dbg('Starting quantum computation ...');
      const sample = determineFrequency(f);
      dbg('Done quantum computation, result', { sample });

      // Each "sample" has a high probability of being approximately equal to some
      // integer multiple of (inputRange/r) rounded to the nearest integer.
      // So we use a continued fraction function to find r (or a divisor of r).
      const continuedFraction = qubitsMath.continuedFraction(
        sample / inputRange,
        accuracyRequiredForContinuedFraction,
      );
      // The denominator is a "candidate" for being r or a divisor of r (hence we need to find
      // the least common multiple of several of these).
      const candidateDivisor = continuedFraction.denominator;
      dbg('Candidate divisor of r: ', { candidateDivisor });

      // Reduce the chances of getting the wrong answer by ignoring obviously wrong results!
      if (candidateDivisor > 1 && candidateDivisor <= outputRange) {
        if (f(candidateDivisor) === f0) {
          dbg('This is a multiple of the rank');
          bestSoFar = candidateDivisor;
        } else {
          const lcm = qubitsMath.lcm(candidateDivisor, bestSoFar);
          if (lcm <= outputRange) {
            dbg('This is a good candidate');
            bestSoFar = lcm;
          }
        }
      }
      dbg('Least common multiple so far: ', { bestSoFar, attempts });
    }
    dbg(`Giving up trying to find rank of ${a}`);
    return 'failed';
  }
function findPeriod() {
    let bestSoFar = 1;

    for (let attempts = 0; attempts < 2 * numOutBits; attempts += 1) {
      // NOTE: Here we take advantage of the fact that, for Shor's algorithm,
      // we know that f(x) = f(x+i) ONLY when i is an integer multiple of the rank r.
      if (f(bestSoFar) === f0) {
        dbg(`The period of ${a}^x mod ${n} is ${bestSoFar}`);
        return bestSoFar;
      }

      dbg('Starting quantum computation ...');
      const sample = determineFrequency(f);
      dbg('Done quantum computation, result', { sample });

      // Each "sample" has a high probability of being approximately equal to some
      // integer multiple of (inputRange/r) rounded to the nearest integer.
      // So we use a continued fraction function to find r (or a divisor of r).
      const continuedFraction = qubitsMath.continuedFraction(
        sample / inputRange,
        accuracyRequiredForContinuedFraction,
      );
      // The denominator is a "candidate" for being r or a divisor of r (hence we need to find
      // the least common multiple of several of these).
      const candidateDivisor = continuedFraction.denominator;
      dbg('Candidate divisor of r: ', { candidateDivisor });

      // Reduce the chances of getting the wrong answer by ignoring obviously wrong results!
      if (candidateDivisor > 1 && candidateDivisor <= outputRange) {
        if (f(candidateDivisor) === f0) {
          dbg('This is a multiple of the rank');
          bestSoFar = candidateDivisor;
        } else {
          const lcm = qubitsMath.lcm(candidateDivisor, bestSoFar);
          if (lcm <= outputRange) {
            dbg('This is a good candidate');
            bestSoFar = lcm;
          }
        }
      }
      dbg('Least common multiple so far: ', { bestSoFar, attempts });
    }
    dbg(`Giving up trying to find rank of ${a}`);
    return 'failed';
  }
Determine the period of f (i.e. find r such that f(x) = f(x+r).