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Unformatted text preview: l real number x is positive, (and normalized
or subnormal), with x = (b0:b1b2 : : :b23b24b25 : : :)2 2E
we have x; = (b0:b1b2 : : :b23)2 2E : Thus, x; is obtained simply by truncating the binary expansion of m at the
23rd bit and discarding b24, b25, etc. This is clearly the closest oating point
number which is less than x. Writing a formula for x+ is more complicated
since, if b23 = 1, nding the closest oating point number bigger than x will
involve some bit \carries" and possibly, in rare cases, a change in E . If x is
negative, the situation is reversed: it is x+ which is obtained by dropping bits
b24, b25, etc., since discarding bits of a negative number makes the number
closer to zero, and therefore larger (further to the right on the real line).
12 The IEEE standard de nes the correctly rounded value of x, which we
shall denote round(x), as follows. If x happens to be a oating point number,
then round(x) = x. Otherwise, the correctly rounded value depends on which
of the following four rounding modes is in e ect:
round(x) = x; :
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This note was uploaded on 02/12/2014 for the course MATH 4800 taught by Professor Lie during the Spring '09 term at Rensselaer Polytechnic Institute.
- Spring '09