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Unformatted text preview: ¾ ¿¾ ) down ¿ ½ to ½¼ ¼¼¾ (¾), and ½¼ ¼¼½½¼¾ (¾ ½ ) up to ½¼ ¼½¾ (¾ ), because these values are not halfway between two possible values. We would round ½¼ ½½½¼¼¾ (¾ ) up to ½½ ¼¼¾ (¿) and ½¼ ½¼½¼¼¾ down to ½¼ ½¼¾ (¾ ½ ), ¾ since these values are halfway between two possible results, and we prefer to have the least signiﬁcant bit equal to zero. 2.4.5 Floating-Point Operations
The IEEE standard speciﬁes a simple rule for determining the result of an arithmetic operation such as addition or multiplication. Viewing ﬂoating-point values Ü and Ý as real numbers, and some operation ¬ deﬁned over real numbers, the computation should yield ÊÓÙÒ ´Ü ¬ Ý µ, the result of applying rounding to the exact result of the real operation. In practice, there are clever tricks ﬂoating-point unit designers use to avoid performing this exact computation, since the computation need only be sufﬁciently precise to guarantee a correctly rounded resul...
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