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Correctly Rounded BinaryDecimal and DecimalBinary Conversions
 NUMERICAL ANALYSIS MANUSCRIPT 9010, AT&T BELL LABORATORIES
, 1990
"... This note discusses the main issues in performing correctly rounded decimaltobinary and binarytodecimal conversions. It reviews recent work by Clinger and by Steele and White on these conversions and describes some efficiency enhancements. Computational experience with several kinds of arithmeti ..."
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This note discusses the main issues in performing correctly rounded decimaltobinary and binarytodecimal conversions. It reviews recent work by Clinger and by Steele and White on these conversions and describes some efficiency enhancements. Computational experience with several kinds of arithmetic suggests that the average computational cost for correct rounding can be small for typical conversions. Source for conversion routines that support this claim is available from netlib.
A precision independent tool for testing floatingpoint arithmetic I: basic operations, square root and remainder
, 2000
"... ing with credit is permitted. To copy otherwise, to republish, to post on servers, to redistribute to lists, or to use any component of this work in other works, requires prior specific permission and/or a fee. Permissions may be requested from Publications Dept, ACM Inc., 1515 Broadway, New York, N ..."
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ing with credit is permitted. To copy otherwise, to republish, to post on servers, to redistribute to lists, or to use any component of this work in other works, requires prior specific permission and/or a fee. Permissions may be requested from Publications Dept, ACM Inc., 1515 Broadway, New York, NY 10036 USA, fax +1 (212) 8690481, or permissions@acm.org. 2 \Delta A. Cuyt, B. Verdonk and D. Verschaeren 1. INTRODUCTION AND MOTIVATION The IEEE standard [IEEE 1985] for floatingpoint arithmetic, which became official in 1985 and which we shall refer to as IEEE754, has been adopted by most major microprocessor manufacturers. Whereas guaranteeing 100% correctness of an IEEE floatingpoint implementation is hardly feasible, as the famous Intel Pentium bug clearly demonstrated, several good but unrelated tools exist to test different aspects of a floatingpoint implementation for compliance with the IEEE754 standard. Concurrent with the adoption of IEEE754 by the microprocessor ind...
A program for testing IEEE decimalbinary conversion
, 1991
"... Regardless of how accurately a computer performs floatingpoint operations, if the data to operate on must be initially converted from the decimalbased representation used by humans into the internal representation used by the machine, then errors in that conversion will irrevocably pollute the res ..."
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Regardless of how accurately a computer performs floatingpoint operations, if the data to operate on must be initially converted from the decimalbased representation used by humans into the internal representation used by the machine, then errors in that conversion will irrevocably pollute the results of subsequent
On intermediate precision required for correctlyrounding decimaltobinary floatingpoint conversion
 In Proceedings of 6th Conference Real Numbers and Computers (RNC’6). Schloss Dagstuhl
"... The algorithms developed ten years ago in preparation for IBM’s support of IEEE FloatingPoint on its mainframe S/390 processors use an overly conservative intermediate precision to guarantee correctlyrounded results across the entire exponent range. Here we study the minimal requirement for both b ..."
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The algorithms developed ten years ago in preparation for IBM’s support of IEEE FloatingPoint on its mainframe S/390 processors use an overly conservative intermediate precision to guarantee correctlyrounded results across the entire exponent range. Here we study the minimal requirement for both bounded and unbounded precision on the decimal side (converting to machine precision on the binary side). An interesting new theorem on Continued Fraction expansions is offered, as well as an open problem on the growth of partial quotients for ratios of powers of two and five. Key words: FloatingPoint conversion, Continued Fractions 1
A precision and range independent tool for testing floatingpoint arithmetic I: basic operations, square root and remainder
, 1999
"... This paper introduces a precision and range independent tool for testing the compliance of hardware or software implementations of (multiprecision) floatingpoint arithmetic with the principles of the IEEE standards 754 and 854. The tool consists of a driver program, o#ering many options to test onl ..."
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This paper introduces a precision and range independent tool for testing the compliance of hardware or software implementations of (multiprecision) floatingpoint arithmetic with the principles of the IEEE standards 754 and 854. The tool consists of a driver program, o#ering many options to test only specific aspects of the IEEE standards, and a large set of test vectors, encoded in a precision independent syntax to allow the testing of basic and extended hardware formats as well as multiprecision floatingpoint implementations.
Numerical Computation Guide
, 1996
"... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 Rounding Error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 Floati ..."
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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 Rounding Error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 Floatingpoint Formats . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152 Contents vii Relative Error and Ulps. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 Guard Digits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156 Cancellation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 Exactly Rounded Operations . . . . . . . . . . . . . . . . . . . . . . . . . 163 The IEEE Standard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 Formats and Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 Special Quantities . . . . . . . . . . . . . . . . . . . . . . ....
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...
Underflow Revisited
, 1999
"... Underflow is a floatingpoint phenomenon. Although the use of gradual underflow as defended in [2] and [5] is now widespread, most numerical analysts may not be aware of the fact that several implementations of the same principle are in existence, leading to different behaviour of code on different ..."
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Underflow is a floatingpoint phenomenon. Although the use of gradual underflow as defended in [2] and [5] is now widespread, most numerical analysts may not be aware of the fact that several implementations of the same principle are in existence, leading to different behaviour of code on different platforms, mainly with respect to exception signaling. We intend to thoroughly discuss the slight differences among these implementations. Examples will be taken from current hardware and from our own multiprecision software class library. Throughout the discussion the focus is on the analysis of the phenomenon and not on any implementation issues. Many programmers are also unaware of the fact that the IEEE 754 and 854 standards do not guarantee that a program will deliver identical results on all conforming systems. Of all the differences that can occur crossplatform, the underflow exception is just one. ? Research Director FWOVlaanderen ffl Supported by an NOIgrant from the Universi...
Sun Microsystems, Inc. 901 San Antonio Road Palo Alto, CA 94303 U.S.A. 6509601300
"... This product or document is distributed under licenses restricting its use, copying, distribution, and decompilation. No part of this product or document may be reproduced in any form by any means without prior written authorization of Sun and its licensors, if any. Thirdparty software, including f ..."
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This product or document is distributed under licenses restricting its use, copying, distribution, and decompilation. No part of this product or document may be reproduced in any form by any means without prior written authorization of Sun and its licensors, if any. Thirdparty software, including font technology, is copyrighted and licensed from Sun suppliers. Parts of the product may be derived from Berkeley BSD systems, licensed from the University of California. UNIX is a registered trademark in the U.S. and other countries, exclusively licensed through X/Open Company, Ltd. For Netscape™, Netscape Navigator™, and the Netscape