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2 there is also a decimal version of the standard but

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Unformatted text preview: rs.2 (There is also a decimal version of the standard but we shall not discuss this.) The IEEE standard has three very important requirements: ANSI/IEEE Std 754-1985. Thanks to Jim Demmel for introducing the author to the standard. 2 4 consistent representation of oating point numbers across all machines adopting the standard correctly rounded arithmetic (to be explained in the next section) consistent and sensible treatment of exceptional situations such as division by zero (to be discussed in the following section). We will not describe the standard in detail, but we will cover the main points. We start with the following observation. In the last section, we chose to normalize a nonzero number x so that x = m 2E , where 1 m < 2, i.e. m = (b0:b1b2b3 : : :)2 with b0 = 1. In the simple oating point model discussed in the previous section, we stored the leading nonzero bit b0 in the rst position of the eld provided for m. Note, however, that since we know this bit has the value one, it is not necessary to store...
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