Appendix a of hennessy and pattersons computer

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Unformatted text preview: t. When one of the arguments is a special value such as ¼, ½ or Æ Æ , the standard specifies conventions that attempt to be reasonable. For example ½ ¼ is defined to yield ½, while ½ · ¼ is defined to yield ·½. One strength of the IEEE standard’s method of specifying the behavior of floating-point operations is that it is independent of any particular hardware or software realization. Thus, we can examine its abstract mathematical properties without considering how it is actually implemented. We saw earlier that integer addition, both unsigned and two’s complement, forms an Abelian group. Addition over real numbers also forms an Abelian group, but we must consider what effect rounding has on these properties. Let us define Ü +f Ý to be ÊÓÙÒ ´Ü · Ý µ. This operation is defined for all values of Ü and Ý , although it may yield infinity even when both Ü and Ý are real numbers due to overflow. The operation is commutative, with Ü +f Ý Ý +f Ü for all values of Ü and Ý. On the other hand, the operation is not associative. For example, with single-precision floating point the expression (3.14+1e10)-1e10 would evalu...
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