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31
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 prevent errors and to syst ..."
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Cited by 18 (9 self)
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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.
Complex Square Root with Operand Prescaling
 in "Journal of VLSI Signal Processing
, 2006
"... prescaling. 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 roundin ..."
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Cited by 8 (4 self)
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prescaling. 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. 1
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.
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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Cited by 3 (1 self)
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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
Borneo 1.0.2  Adding IEEE 754 floating point support to Java
, 1998
"... 1 2. INTRODUCTION 1 2.1. Portability and Purity 2 2.2. Goals of Borneo 3 2.3. Brief Description of an IEEE 754 Machine 3 2.4. Language Features for Floating Point Computation 6 3. FUTURE WORK 9 3.1. Incorporating Java 1.1 Features 9 3.2. Unicode Support 10 3.3. Flush to Zero 10 3.4. Variable Trappin ..."
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1 2. INTRODUCTION 1 2.1. Portability and Purity 2 2.2. Goals of Borneo 3 2.3. Brief Description of an IEEE 754 Machine 3 2.4. Language Features for Floating Point Computation 6 3. FUTURE WORK 9 3.1. Incorporating Java 1.1 Features 9 3.2. Unicode Support 10 3.3. Flush to Zero 10 3.4. Variable Trapping Status 10 3.5. Parametric Polymorphism 10 4. CONCLUSION 10 5. ACKNOWLEDGMENTS 11 6. BORNEO LANGUAGE SPECIFICATION 13 6.1. indigenous 13 6.2. Floating Point Literals 16 6.3. Float, Double, and Indigenous classes 17 6.4. New Numeric Types 18 6.5. Floating Point System Properties 20 + This material is based upon work supported under a National Science Foundation Graduate Fellowship. Any opinions, findings, conclusions or recommendations expressed in this publication are those of the author(s) and do not necessarily reflect the views of the National Science Foundation. ii 6.6. Fused mac 21 6.7. Rounding Modes 21 6.8. Floating Point Exception Handling 31 6.9. Operator Overloading 51 6.10...
Computation with the Extended Rational Numbers and an Application to Interval Arithmetic
, 1994
"... Programming languages such as Common Lisp, and virtually every computer algebra system (CAS), support exact arbitraryprecision integer arithmetic as well as exact rational number computation. Several CAS include interval arithmetic directly, but not in the extended form indicated here. We explain w ..."
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Programming languages such as Common Lisp, and virtually every computer algebra system (CAS), support exact arbitraryprecision integer arithmetic as well as exact rational number computation. Several CAS include interval arithmetic directly, but not in the extended form indicated here. We explain why changes to the usual rational number system to include infinity and "notanumber" may be useful, especially to support robust interval computation. We describe techniques for implementing these changes. 1 Introduction It is well known that any rational number can be represented as an ordered pair of integers, namely numerator and denominator. In order to make this representation canonical, we usually impose the additional constraints that the greatest common divisor of numerator and denominator be 1, and that the denominator be positive. The exact rational operations of addition, subtraction, multiplication, and division, plus a variety of other useful operations (comparison, reading, ...