The handling of the exceptional cases (underflow, overflow, Not A Number, “inexact” flag...) requires even more caution with the elementary functions than with the basic operations +, -, ×, ÷, and the square root. This is due to the high nonlinearity of the elementary functions: when one obtains +∞ as the result1 of a calculation that only contains the four basic operations and the square root, this does not necessarily mean that the exact result is infinite or too large to be representable, but at least the exact result is likely to be fairly large. Similarly, when one obtains 0, the exact result is likely to be small.2. With the elementary functions, this is not always true. Consider the following examples.
KeywordsElementary Function Exact Result Newton Iteration Arctangent Function Machine Number
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