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Unformatted text preview: matching 2.4. FLOATING POINT Mode Round-to-even Round-toward-zero Round-down Round-up \$1.40 \$1 \$1 \$1 \$2 \$1.60 \$2 \$1 \$1 \$2 \$1.50 \$2 \$1 \$1 \$2 \$2.50 \$2 \$2 \$2 \$3 \$–1.50 \$–2 \$–1 \$–2 \$–1 75 Figure 2.25: Illustration of Rounding Modes for Dollar Rounding. The ﬁrst rounds to a nearest value, while the other three bound the result above or below. value Ü¼ that can be represented in the desired ﬂoating-point format. This is the task of the rounding operation. The key problem is to deﬁne the direction to round a value that is halfway between two possibilities. For example, if I have \$1.50 and want to round it to the nearest dollar, should the result be \$1 or \$2? An alternative approach is to maintain a lower and an upper bound on the actual number. For example, we could determine representable values Ü and Ü· such that the value Ü is guaranteed to lie between them: Ü Ü Ü· . The IEEE ﬂoating-point format deﬁnes four different rounding modes. The default method ﬁnds a c...
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