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finished bonus

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Tommaso Rodolfo Masera 2018-12-17 15:12:03 +01:00
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Homework 11/bonus.tex
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@ -275,6 +275,14 @@ $11110000000000000.0 = 2^16 + 2^15 + 2^14 + 2^13 = 65536 + 32768 + 16384 +
\section{Bonus Question 2}
Loss of significance can occur via subtraction of values that are close to each other so
that most of the significant digits get cancelled.
For example let x $= 1.5 \times 2^0$
and y $=\ 1.0 \times 2^{26}$ such that the sequence of operations $r =(x+y) - y $ results in r = 0.0 which is incorrect as the actual value should be 1.5.
This is due to catastrophic cancellation which occurred during the subtraction.
This kind of occurrences can't be identified unless data is further examined leaving no
way of checking that 0.0 is the wrong result.
\end{document}