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Handling FloatingPoint Exceptions in Numeric Programs
 ACM Transactions on Programming Languages and Systems
, 1996
"... Language Constructs Termination exception mechanisms like in Ada and C++ are supposed to terminate an unsuccessful computation as soon as possible after an exception occurs. However, none of the examples of numeric exception handling presented earlier depends ACM Transactions on Programming Languag ..."
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Language Constructs Termination exception mechanisms like in Ada and C++ are supposed to terminate an unsuccessful computation as soon as possible after an exception occurs. However, none of the examples of numeric exception handling presented earlier depends ACM Transactions on Programming Languages and Systems, Vol. 18, No. 2, March 1996. Handling FloatingPoint Exceptions 167 on the immediate termination of a calculation signaling an exception. The IEEE exception flags scheme actually takes advantage of the fact that an immediate jump is not necessary; by raising a flag, making a substitution, and continuing, the IEEE Standard supports both an attempted/alternate form and a default substitution with a single, simple reponse to exceptions. A detraction of the IEEE flag solution, though, is its obvious lack of structure. Instead of being forced to set and reset flags, one would ideally have available a language construct that more directly reflected the attempted/alternate algorit...
Reasoning About the Elementary Functions of Complex Analysis
, 2001
"... There are many problems with the simplification of elementary functions, particularly over the complex plane. Systems tend to make "howlers" or not to simplify enough. In this paper we outline the "unwinding number" approach to such problems, and show how it can be used to preven ..."
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There are many problems with the simplification of elementary functions, particularly over the complex plane. Systems tend to make "howlers" or not to simplify enough. In this paper we outline the "unwinding number" approach to such problems, and show how it can be used to prevent errors and to systematise such simplification, even though we have not yet reduced the simplifiation process to a complete algorithm. The unsolved problems are probably more amenable to the techniques of artificial intelligence and theorem proving than the original problem of complexvariable analysis.
Implementing Complex Elementary Functions Using Exception Handling
 ACM Trans. Math. Softw
, 1994
"... this paper; it is difficult to develop an algorithm that does much better than simply evaluating cexp(w clog(z)) to approximate z w: We hope to consider this problem in a separate paper. ..."
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this paper; it is difficult to develop an algorithm that does much better than simply evaluating cexp(w clog(z)) to approximate z w: We hope to consider this problem in a separate paper.
Complex Square Root with Operand Prescaling
, 2004
"... We propose a radixr digitrecurrence algorithm for complex squareroot. The operand is prescaled to allow the selection of squareroot digits by rounding of the residual. This leads to a simple hardware implementation. Moreover, the use of digit recurrence approach allows correct rounding of the re ..."
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We propose a radixr digitrecurrence algorithm for complex squareroot. The operand is prescaled to allow the selection of squareroot digits by rounding of the residual. This leads to a simple hardware implementation. Moreover, the use of digit recurrence approach allows correct rounding of the result. The algorithm, compatible with the complex division, and its design are described at a highlevel. We also give rough comparisons of its latency and cost with respect to implementation based on standard floatingpoint instructions as used in software routines for complex square root.
Function Evaluation on Branch Cuts
 SIGSAM Bulletin
, 1996
"... Introduction Once it is decided that a CAS will evaluate multivalued functions on their principal branches, questions arise concerning the branch definitions. The first questions concern the standardization of the positions of the branch cuts. These questions have largely been resolved between the ..."
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Introduction Once it is decided that a CAS will evaluate multivalued functions on their principal branches, questions arise concerning the branch definitions. The first questions concern the standardization of the positions of the branch cuts. These questions have largely been resolved between the various algebra systems and the numerical libraries, although not completely. In contrast to the computer systems, many mathematical textbooks are much further behind: for example, many popular textbooks still specify that the argument of a complex number lies between 0 and 2ß. We do not intend to discuss these first questions here, however. Once the positions of the branch cuts have been fixed, a second set of questions arises concerning the evaluation of functions on their branch cuts. In [2], Kahan considered the closure problem from several points of view and discussed different possible solutions. One of his proposals was a principle called counter clockwise cont