Floating-point arithmetic: Difference between revisions

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Only one copy of the canonical Goldberg citation is needed.
History: clarification: it must be clear that the rounding is to the destination precision and that there is a single rounding (i.e. there are no intermediate results, these are the exact results that are directly rounded to the destination precision); also warn about the possible wider exponent range (which is explicitly allowed by IEEE 754-1985).
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* The ability of [[IEEE 754#Exception handling|exceptional conditions]] (overflow, [[Division by zero|divide by zero]], etc.) to propagate through a computation in a benign manner and then be handled by the software in a controlled fashion.
 
These features would be inherited into IEEE 754-1985 (with the exception of the encoding of special values and exceptions), though the extended internal precision of x87 means it requires explicit rounding of intermediateexact results directly to the destination precision in order to match standard IEEE 754 results.<ref name="Goldberg_1991"/> However, the behavior may not be the same as a rounding to the destination format due to a possible wider exponent range of the extended format.
 
== Range of floating-point numbers ==