module.exports = fromMat3

/**
 * Creates a quaternion from the given 3x3 rotation matrix.
 *
 * NOTE: The resultant quaternion is not normalized, so you should be sure
 * to renormalize the quaternion yourself where necessary.
 *
 * @param {quat} out the receiving quaternion
 * @param {mat3} m rotation matrix
 * @returns {quat} out
 * @function
 */
function fromMat3 (out, m) {
  // Algorithm in Ken Shoemake's article in 1987 SIGGRAPH course notes
  // article "Quaternion Calculus and Fast Animation".
  var fTrace = m[0] + m[4] + m[8]
  var fRoot

  if (fTrace > 0.0) {
    // |w| > 1/2, may as well choose w > 1/2
    fRoot = Math.sqrt(fTrace + 1.0)  // 2w
    out[3] = 0.5 * fRoot
    fRoot = 0.5 / fRoot  // 1/(4w)
    out[0] = (m[5] - m[7]) * fRoot
    out[1] = (m[6] - m[2]) * fRoot
    out[2] = (m[1] - m[3]) * fRoot
  } else {
    // |w| <= 1/2
    var i = 0
    if (m[4] > m[0]) {
      i = 1
    }
    if (m[8] > m[i * 3 + i]) {
      i = 2
    }
    var j = (i + 1) % 3
    var k = (i + 2) % 3

    fRoot = Math.sqrt(m[i * 3 + i] - m[j * 3 + j] - m[k * 3 + k] + 1.0)
    out[i] = 0.5 * fRoot
    fRoot = 0.5 / fRoot
    out[3] = (m[j * 3 + k] - m[k * 3 + j]) * fRoot
    out[j] = (m[j * 3 + i] + m[i * 3 + j]) * fRoot
    out[k] = (m[k * 3 + i] + m[i * 3 + k]) * fRoot
  }

  return out
}