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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
Hooking Your Solver to AMPL
, 1997
"... This report tells how to make solvers work with AMPL's solve command. It describes an interface library, amplsolver.a, whose source is available from netlib. Examples include programs for listing LPs, automatic conversion to the LP dual (shellscript as solver), solvers for various nonlinear probl ..."
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Cited by 28 (5 self)
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This report tells how to make solvers work with AMPL's solve command. It describes an interface library, amplsolver.a, whose source is available from netlib. Examples include programs for listing LPs, automatic conversion to the LP dual (shellscript as solver), solvers for various nonlinear problems (with first and sometimes second derivatives computed by automatic differentiation), and getting C or Fortran 77 for nonlinear constraints, objectives and their first derivatives. Drivers for various well known linear, mixedinteger, and nonlinear solvers provide more examples.
How to read floating point numbers accurately
 Proceedings of PLDI ’90
, 1990
"... Converting decimal scientific notation into binary floating point is nontrivial, but this conversion can be performed with the best possible accuracy without sacrificing efficiency. 1. ..."
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Cited by 25 (0 self)
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Converting decimal scientific notation into binary floating point is nontrivial, but this conversion can be performed with the best possible accuracy without sacrificing efficiency. 1.
Printing FloatingPoint Numbers Quickly and Accurately
 In Proc. of the ACM SIGPLAN ’96 Conference on Programming Language Design and Implementation
"... This paper presents a fast and accurate algorithm for printing floatingpoint numbers in both free and fixedformat modes. In freeformat mode, the algorithm generates the shortest, correctly rounded output string that converts to the same number when read back in, accommodating whatever rounding m ..."
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Cited by 15 (2 self)
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This paper presents a fast and accurate algorithm for printing floatingpoint numbers in both free and fixedformat modes. In freeformat mode, the algorithm generates the shortest, correctly rounded output string that converts to the same number when read back in, accommodating whatever rounding mode the reader uses. In fixedformat mode, the algorithm generates a correctly rounded output string using special # marks to denote insignificant trailing digits. For both modes, the algorithm employs a fast estimator to scale floatingpoint numbers efficiently. Keywords: floatingpoint printing, runtime systems 1 Introduction In this paper we present an efficient floatingpoint printing algorithm, which solves the output problem of converting floatingpoint numbers from an input base (usually a power of two) to an output base (usually ten). The algorithm supports two types of output, free format and fixed format. For freeformat output the goal is to produce the shortest, correctly ro...
Adding Interval Support to the GNU Fortran Compiler
 Proceedings of the International Symposium on Scientific Computing, Computer Arithmetic, and Validated Numerics
, 1997
"... Compiler support for intervals as an intrinsic data type is essential for promoting widespread use of interval arithmetic. This document gives an overview of modifications being made to the GNU Fortran Compiler to provide support for interval arithmetic. It also describes the design of interval run ..."
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Cited by 3 (2 self)
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Compiler support for intervals as an intrinsic data type is essential for promoting widespread use of interval arithmetic. This document gives an overview of modifications being made to the GNU Fortran Compiler to provide support for interval arithmetic. It also describes the design of interval runtime libraries that will be used by the modified compiler, and discusses the methodology used to test the compiler and runtime libraries. The modifications being made to the compiler are based on the Interval Arithmetic Specification being prepared by Chiriaev and Walster [1]. Their specification builds upon the work of Kearfott [2] and Priest [3] to provide a standard for supporting interval arithmetic in Fortran. Contents 1 Introduction 3 1.1 Interval arithmetic . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Interval applications . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Interval software and standardization . . . . . . . . . . . . . . . . . . 4 1.4 Com...
The IntervalEnhanced GNU Fortran Compiler
 Reliable Computing, Submitted
, 1998
"... . Compiler support for intervals as intrinsic data types is essential for promoting the development and widespread use of interval software. It also plays an important role in encouraging the development of hardware support for interval arithmetic. This paper describes modifications made to the GNU ..."
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Cited by 2 (0 self)
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. Compiler support for intervals as intrinsic data types is essential for promoting the development and widespread use of interval software. It also plays an important role in encouraging the development of hardware support for interval arithmetic. This paper describes modifications made to the GNU Fortran Compiler to provide support for interval arithmetic. These modifications are based on a recently proposed Fortran 77 Interval Arithmetic Specification, which provides a standard for supporting interval arithmetic in Fortran. This paper also describes the design of the compiler's interval runtime libraries and the methodology used to test the compiler. The compiler and runtime libraries are designed to be portable to platforms that support the IEEE 754 floating point standard. Keywords: Fortran, interval arithmetic, compiler, runtime libraries, validate, containment. 1. Introduction Interval arithmetic provides an efficient method for performing operations on intervals of real num...
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
SymbolicAlgebraic Computations in a Modeling Language for Mathematical Programming
, 2000
"... This paper was written for the proceedings of a seminar on "Symbolicalgebraic ..."
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This paper was written for the proceedings of a seminar on "Symbolicalgebraic
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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Cited by 2 (0 self)
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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.