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For example, the hardware provides storage formats corresponding to the IEEE data formats, operations on data in such formats, control over the rounding of results produced by these operations, status flags indicating the occurrence of IEEE numeric exceptions, and the IEEE-prescribed result when such an exception occurs in the absence of a user-defined handler for it. System software supports IEEE exception handling. The software libraries, including the math libraries, libm and libsunmath, implement functions such as exp(x) and sin(x) in a way that follows the spirit of IEEE Standard 754 with respect to the raising of exceptions. (When a floating-point arithmetic operation has no well-defined result, the system communicates this fact to the user by raising an exception.) The math libraries also provide function calls that handle special IEEE values like Inf (infinity) or NaN (Not a Number).
The three constituents of the floating-point environment interact in subtle ways, and those interactions are generally invisible to the applications programmer. The programmer sees only the computational mechanisms prescribed or recommended by the IEEE standard. In general, this manual guides programmers to make full and efficient use of the IEEE mechanisms so that they can write application software effectively.
Many questions about floating-point arithmetic concern elementary operations on numbers. For example,
The IEEE Standard 754 ensures that operations yield the mathematically expected results with the expected properties. It also ensures that exceptional cases yield specified results, unless the user specifically makes other choices.
In this manual, there are references to terms like NaN or subnormal number. The "Glossary" on page 243, defines terms related to floating-point arithmetic.