Pair-precision elementary functions
We discussed some of the limitations of pair-precision arithmetic in Chapter 13 on page 353. Although our pair precision routines for the basic operations of add, subtract, multiply, divide, square root, and cube root are on average correctly rounded in IEEE 754 arithmetic with the default round-to-nearest mode, we cannot guarantee correct rounding in general. Indeed, as the tables in Section 13.20 on page 379 show, worst-case errors of almost four ulps can be discovered by extensive testing with random arguments. In the non-default rounding modes of IEEE 754, errors of almost 10 ulps are found.
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