According to Calvinism, is a man justified by his faith or by a "limited atonement" by Christ?

According to Calvinism, is a man justified by his faith or by a "limited atonement" by Christ? Isn't "limited atonement" another gospel? If justification is all of grace, through faith, how is a "limited atonement" relevant at all? > **The covenant of life is not preached equally to all, and among those to whom it is preached, does not always meet with the same reception.** This diversity displays the unsearchable depth of the divine judgment, and is without doubt subordinate to God’s purpose of **eternal election**. (BOOK THIRD. THE MODE OF OBTAINING THE GRACE OF CHRIST. THE BENEFITS IT CONFERS, AND THE EFFECTS RESULTING FROM IT. Chapter 21, sentence 1 and 2) >The predestination by which God adopts some to the hope of life, and adjudges others to eternal death, no man who would be thought pious ventures simply to deny; but it is greatly caviled at, especially by those who make prescience its cause. We, indeed, ascribe both prescience and predestination to God; but we say, that it is absurd to make the latter subordinate to the former (see chap. 22 sec. 1). (Ibid, chapter 21, subchapter 5) There is much to be found within the texts , those are limited examples.