9. Consider IEEE double precision floating point arithmetic, using round to nearest. Let a, b, and e be normalized double precision floating point numbers, and let , e, 8, and Ø denote correctly rounded floating point addition, subtraction, multiplication, and division. (a) Is it necessarily true that a e b=b@a? Explain why or give an example where this does not hold.

Computer Networking: A Top-Down Approach (7th Edition)
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9. Consider IEEE double precision floating point arithmetic, using round to nearest. Let a, b,
and e be normalized double precision floating point numbers, and let , e, ®, and Ø denote
correctly rounded floating point addition, subtraction, multiplication, and division.
(a) Is it necessarily true that aeb = bea? Explain why or give an example where this does
not hold.
(b) Is it necessarily true that (a e b) e c = a& (b€ c)? Explain why or give an example
where this does not hold.
Transcribed Image Text:9. Consider IEEE double precision floating point arithmetic, using round to nearest. Let a, b, and e be normalized double precision floating point numbers, and let , e, ®, and Ø denote correctly rounded floating point addition, subtraction, multiplication, and division. (a) Is it necessarily true that aeb = bea? Explain why or give an example where this does not hold. (b) Is it necessarily true that (a e b) e c = a& (b€ c)? Explain why or give an example where this does not hold.
(c) Determine the maximum possible relative error in the computation (a ®b) Oc, assuming
that c + 0. [You may omit terms of order O(e?) and higher.] Suppose e = 0. What are
the possible values that (a 8 b) O c could be assigned?
Transcribed Image Text:(c) Determine the maximum possible relative error in the computation (a ®b) Oc, assuming that c + 0. [You may omit terms of order O(e?) and higher.] Suppose e = 0. What are the possible values that (a 8 b) O c could be assigned?
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