farley_search.js

function approximateFraction(x) {
  // shourtcuts
  if (Math.floor(x) === x) {
    return [x, 1];
  }
  var xinv = 1 / x;
  if (Math.floor(xinv) === xinv) {
    return [1, xinv];
  }
  
  var x_ = x > 1 ? xinv : x;
  // a/b and c/d are neighbours in Farley sequence.
  var a = 0, b = 1, c = 1, d = 1;
  // Limiting search to order 8.
  var limit = 8;
  while (true) {
    // Generating next term in sequence (order of q).
    var p = a + c, q = b + d;
    if (q > limit) {
      break;
    }
    if (x_ <= p / q) {
      c = p; d = q;
    } else {
      a = p; b = q;
    }
  }
  // select closest of the neighbours to x
  if (x_ - a / b < c / d - x_) {
    return x_ === x ? [a, b] : [b, a];
  } else {
    return x_ === x ? [c, d] : [d, c];
  }
}