324_Book

# 324_Book

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Unformatted text preview: the user is willing to make between efﬁciency and faithfulness to the exact behavior of the original program. As a result, they tend to be very conservative, avoiding any optimizations that could have even the slightest effect on functionality. On the other hand, ﬂoating-point addition satisﬁes the following monotonicity property: if then Ü· Ü · for any values of , , and Ü other than Æ Æ . This property of real (and integer) addition is not obeyed by unsigned or two’s complement addition. Floating-point multiplication also obeys many of the properties one normally associates with multiplication, namely those of a ring. Let us deﬁne Ü *f Ý to be ÊÓÙÒ ´Ü ¢ Ý µ. This operation is closed under multiplication (although possibly yielding inﬁnity or Æ Æ ), it is commutative, and it has 1.0 as a multiplicative identity. On the other hand, it is not associative due to the possibility of overﬂow or the loss of precision due to rounding. For example, with single-precision ﬂoating point, the expression (1e20*1e20)*1e-20 will evaluate to ·½,...
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## This note was uploaded on 09/02/2010 for the course ELECTRICAL 360 taught by Professor Schultz during the Spring '10 term at BYU.

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