What is the test for cross-examination in a criminal case?

"The Confrontation Clause of the Sixth Amendment guarantees the right of an accused in a criminal prosecution 'to be confronted with the witnesses against him.' " (Delaware v. Van Arsdall (1986) 475 U.S. 673, 678 [89 L.Ed.2d 674, 682-683].) " ' "[T]he main and essential purpose of confrontation is to secure for the opponent the opportunity of cross-examination." ' [Citation.] . . . '[T]he exposure of a witness' motivation in testifying is a proper and important function of the constitutionally protected right of cross-examination.' [Citation.]" (Id. at pp. 678-679, italics omitted.) Cross-examination is permitted not only to test the witness' perceptions and memory but also to discredit the witness by, for example, revealing possible biases, prejudices or ulterior motives. (Davis v. Alaska (1974) 415 U.S. 308, 316 [39 L.Ed.2d 347, 353-354].)