This preview shows page 1. Sign up to view the full content.
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, ﬂoatingpoint 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. Floatingpoint 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 singleprecision ﬂoating point, the expression (1e20*1e20)*1e20 will evaluate to ·½,...
View
Full
Document
This note was uploaded on 09/02/2010 for the course ELECTRICAL 360 taught by Professor Schultz during the Spring '10 term at BYU.
 Spring '10
 Schultz
 The American, Gulliver's Travels, 2.2.5 2.2.6 2.2.7 2.3 2.3.1 2.3.2 2.3.3 2.3.4 2.3.5

Click to edit the document details