FloatingPointRepresentation

Historically the response to this was almost always

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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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