Unformatted text preview: se to this was almost always
the same: replace the result by zero. In IEEE arithmetic, the result may
be a subnormal positive number instead of zero. This allows results much
smaller than the smallest normalized number to be stored, closing the gap
between the normalized numbers and zero as illustrated earlier. However,
it also allows the possibility of loss of accuracy, as subnormal numbers have
fewer bits of precision than normalized numbers.
Exercise 22 Work out the sensible rounding conventions for under ow. For example, using round to nearest, what values are rounded down to zero and
what values are rounded up to the smallest subnormal number? 1 following division by zero
indicates a programming problem. Given two numbers a and b, consider
setting
c = p 2a 2 d = p 2b 2
a +b
a +b
Is it possible that c or d (or both) is set to the value 1, even if a and b are
Exercise 23 More often than not the result of 25 Table 4: IEEE Standard Response to Exceptions
Invalid Operation
Set result to NaN
Division by Zero
Set result to 1
Over ow
Set result to 1 or largest f.p. number
Under ow
Set result...
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 Spring '09
 LIE
 oating point

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