Elementary functions whose argument range is large can often be related to similar functions with diminished arguments, where those functions are more easily, and more accurately, computed. The ultimate accuracy of elementary functions depends critically on how well that argument reduction is carried out, and historically, that has been the weak point in many vendor libraries. Although the argument-reduction problem is usually easy to state, it is not easy to solve, because it often requires access to arithmetic of higher precision than is available.
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