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By default, an IEEE 754 exception is resumable and is handled by substituting a predefined value for different exceptions, e.g. infinity for a divide by zero exception, and providing [[floating-point arithmetict#Dealing with exceptional cases|status flags]] for later checking of whether the exception occurred (see [[C99#IEEE 754 floating-point support|C99 programming language]] for a typical example of handling of IEEE 754 exceptions). An exception-handling style enabled by the use of status flags involves: first computing an expression using a fast, direct implementation; checking whether it failed by testing status flags; and then, if necessary, calling a slower, more numerically robust, implementation.<ref name="Xiaoye Li and James Demmel 1994 983–992">{{cite journal |author1=Xiaoye Li|author1-link=Sherry Li |author2=James Demmel | title=Faster Numerical Algorithms via Exception Handling, IEEE Transactions on Computers, 43(8) | year= 1994 | pages=983–992}}</ref>
The IEEE 754 standard uses the term "trapping" to refer to the calling of a user-supplied exception-handling routine on exceptional conditions, and is an optional feature of the standard. The standard recommends several usage scenarios for this, including the implementation of non-default pre-substitution of a value followed by resumption, to concisely handle [[Removable singularity|removable singularities]].<ref name="Xiaoye Li and James Demmel 1994 983–992"/><ref name=grail>{{cite web|url=http://www.cs.berkeley.edu/~wkahan/Grail.pdf|title=A Demonstration of Presubstitution for ∞/∞|author=W.Kahan|date=July 5, 2005|url-status=live|archive-url=https://web.archive.org/web/20120310130507/http://www.cs.berkeley.edu/~wkahan/Grail.pdf|archive-date=March 10, 2012}}</ref><ref>{{cite journal |last1=Hauser |first1=John R. |title=Handling floating-point exceptions in numeric programs |journal=ACM Transactions on Programming Languages and Systems |date=March 1996 |volume=18 |issue=2 |pages=139–174 |doi=10.1145/227699.227701|s2cid=9820157 |doi-access=free }}</ref>
The default IEEE 754 exception handling behaviour of resumption following pre-substitution of a default value avoids the risks inherent in changing flow of program control on numerical exceptions. For example, the 1996 [[Cluster (spacecraft)|Cluster spacecraft]] launch ended in a catastrophic explosion due in part to the [[Ada (programming language)|Ada]] exception handling policy of aborting computation on arithmetic error. [[William Kahan]] claims the default IEEE 754 exception handling behavior would have prevented this.<ref name=grail />
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