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17
MPFR: A multipleprecision binary floatingpoint library with correct rounding
 ACM Trans. Math. Softw
, 2007
"... This paper presents a multipleprecision binary floatingpoint library, written in the ISO C language, and based on the GNU MP library. Its particularity is to extend to arbitraryprecision ideas from the IEEE 754 standard, by providing correct rounding and exceptions. We demonstrate how these stron ..."
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Cited by 70 (14 self)
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This paper presents a multipleprecision binary floatingpoint library, written in the ISO C language, and based on the GNU MP library. Its particularity is to extend to arbitraryprecision ideas from the IEEE 754 standard, by providing correct rounding and exceptions. We demonstrate how these strong semantics are achieved — with no significant slowdown with respect to other arbitraryprecision tools — and discuss a few applications where such a library can be useful. Categories and Subject Descriptors: D.3.0 [Programming Languages]: General—Standards; G.1.0 [Numerical Analysis]: General—computer arithmetic, multiple precision arithmetic; G.1.2 [Numerical Analysis]: Approximation—elementary and special function approximation; G 4 [Mathematics of Computing]: Mathematical Software—algorithm design, efficiency, portability
The pitfalls of verifying floatingpoint computations
 ACM Transactions on programming languages and systems
"... Current critical systems often use a lot of floatingpoint computations, and thus the testing or static analysis of programs containing floatingpoint operators has become a priority. However, correctly defining the semantics of common implementations of floatingpoint is tricky, because semantics ma ..."
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Cited by 34 (2 self)
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Current critical systems often use a lot of floatingpoint computations, and thus the testing or static analysis of programs containing floatingpoint operators has become a priority. However, correctly defining the semantics of common implementations of floatingpoint is tricky, because semantics may change according to many factors beyond sourcecode level, such as choices made by compilers. We here give concrete examples of problems that can appear and solutions for implementing in analysis software. 1
25 years of TEX and METAFONT: Looking back and looking forward: TUG 2003 keynote address
 TUGBOAT
, 2004
"... TEX has lasted longer than many other computer software technologies. This article reviews some of the history of TEX and METAFONT, how they have come to be used in practice, and what their impact has been on document markup, the Internet, and publishing. TEX has several design deficiencies that lim ..."
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Cited by 5 (4 self)
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TEX has lasted longer than many other computer software technologies. This article reviews some of the history of TEX and METAFONT, how they have come to be used in practice, and what their impact has been on document markup, the Internet, and publishing. TEX has several design deficiencies that limit its use and its audience. We look at what TEX did right, and with 25 years of hindsight, what it did wrong. We close with some observations about the challenges ahead for electronic representation of documents.
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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Cited by 2 (0 self)
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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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Cited by 2 (0 self)
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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
Real inferno
 In [Boisvert
, 1997
"... Inferno is an operating system well suited to applications that need to be portable, graphical, and networked. This paper describes the fundamental �oating point facilities of the system, including: tight rules on expression evaluation, binary�decimal conversion, exceptions and rounding, and the ele ..."
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Cited by 1 (0 self)
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Inferno is an operating system well suited to applications that need to be portable, graphical, and networked. This paper describes the fundamental �oating point facilities of the system, including: tight rules on expression evaluation, binary�decimal conversion, exceptions and rounding, and the elementary function library. Although the focus of Inferno is interactive media, its portability across hardware and operating platforms, its relative simplicity, and its strength in distributed computing make itattractive for advanced scienti�c computing as well. Since the appearance of a new operating system is a relatively uncommon event, this is a special opportunity for numerical analysts to voice their opinion about what fundamental facilities they need. The purpose of this short paper is to describe numerical aspects of the initial release of Inferno, and to invite comment before the tyranny of backward compatibility makes changes impossible. Overviews can be found at
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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Cited by 1 (0 self)
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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...
Cleaning up the tower: Numbers in Scheme
 Indiana University
, 2004
"... The R 5 RS specification of numerical operations leads to unportable and intransparent behavior of programs. Specifically, the notion of “exact/inexact numbers ” and the misleading distinction between “real ” and “rational ” numbers are two primary sources of confusion. Consequently, the way R 5 RS ..."
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Cited by 1 (1 self)
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The R 5 RS specification of numerical operations leads to unportable and intransparent behavior of programs. Specifically, the notion of “exact/inexact numbers ” and the misleading distinction between “real ” and “rational ” numbers are two primary sources of confusion. Consequently, the way R 5 RS organizes numbers is significantly less useful than it could be. Based on this diagnosis, we propose to abandon the concept of exact/inexact numbers from Scheme altogether. In this paper, we examine designs in which exact and inexact rounding operations are explicitly separated, while there is no distinction between exact and inexact numbers. Through examining alternatives and practical ramifications, we arrive at an alternative proposal for the design of the numerical operations in Scheme. 1
Type System Support for FloatingPoint Computation
, 2001
"... Floatingpoint arithmetic is often seen as untrustworthy. We show how manipulating precisions according to the following rules of thumb enhances the reliability of and removes surprises from calculations: • Store data narrowly, • compute intermediates widely, and • derive properties widely. Further, ..."
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Floatingpoint arithmetic is often seen as untrustworthy. We show how manipulating precisions according to the following rules of thumb enhances the reliability of and removes surprises from calculations: • Store data narrowly, • compute intermediates widely, and • derive properties widely. Further, we describe a typing system for floating point that both supports and is supported by these rules. A single type is established for all intermediate computations. The type describes a precision at least as wide as all inputs to and results from the computation. Picking a single type provides benefits to users, compilers, and interpreters. The type system also extends cleanly to encompass intervals and higher precisions. 1