When the parties do not consent, the court may, upon the application of either, or of its own motion, direct a reference in either of the following cases: Where the trial of an issue of fact shall require the examination of mutual accounts, or when the account is on one side only, and it shall be made to appear to the court that it is necessary that the party on the other side should be examined as a witness to prove the account; in which case the referees may be directed to hear and report upon the whole issue, or upon any specific question of fact involved therein; or where the taking of an account shall be necessary for the information of the court before judgment, in cases which may be determined by the court, or for carrying a judgment into effect, or where a question of fact other than upon the pleadings, shall arise, upon motion or otherwise, in any stage of an action.