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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 134 (18 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 ..."
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Cited by 35 (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 28 (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 18 (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...
Fast Decimal FloatingPoint Division
"... Abstract—A new implementation for decimal floatingpoint (DFP) division is introduced. The algorithm is based on highradix SRT division1 with the recurrence in a new decimal signeddigit format. Quotient digits are selected using comparison multiples, where the magnitude of the quotient digit is ca ..."
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Abstract—A new implementation for decimal floatingpoint (DFP) division is introduced. The algorithm is based on highradix SRT division1 with the recurrence in a new decimal signeddigit format. Quotient digits are selected using comparison multiples, where the magnitude of the quotient digit is calculated by comparing the truncated partial remainder with limited precision multiples of the divisor. The sign is determined concurrently by investigating the polarity of the truncated partial remainder. A timing evaluation using a logic synthesis shows a significant decrease in the division execution time in contrast with one of the fastest DFP dividers reported in the open literature. Index Terms—Binarycoded decimal (BCD), decimal floatingpoint (DFP) arithmetic, digit recurrence division. I.
LPFML: A W3C XML Schema for Linear and Integer Programming
"... There are numerous modeling systems for generating linear programs and numerous solvers for optimizing them. However, it is often not possible for modelers to combine their preferred modeling system with their preferred solver. Current modeling systems use their own proprietary model instance forma ..."
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Cited by 3 (2 self)
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There are numerous modeling systems for generating linear programs and numerous solvers for optimizing them. However, it is often not possible for modelers to combine their preferred modeling system with their preferred solver. Current modeling systems use their own proprietary model instance formats that various solvers have been adapted to recognize. The existence of all of these formats suggests that one way to encourage modeling system and solver compatibility is to use a standard representation of a problem instance. Such a standard must: be simple to manipulate and validate; be able to express instancespecific and vendorspecific information; and promote the integration of optimization software with other software. In this paper we present LPFML, an XML Schema for representing linear programming (LP) instances. In addition, we provide open source C++ libraries that simplify the exchange of problem instance and solution information between modeling systems and solvers. We show how our system is used to enable previously unavailable languagesolver connections and how our design improves on the state of the art under three different scenarios relevant to communication between solvers and modeling systems.
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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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...
SymbolicAlgebraic Computations in a Modeling Language for Mathematical Programming
 In Symbolic Algebraic Methods and Verification
, 2001
"... AMPL is a language and environment for expressing and manipulating mathematical programming problems, i.e., minimizing or maximizing an algebraic objective function subject to algebraic constraints. The AMPL processor simplifies problems, as discussed in more detail below, but calls on separate solv ..."
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Cited by 3 (0 self)
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AMPL is a language and environment for expressing and manipulating mathematical programming problems, i.e., minimizing or maximizing an algebraic objective function subject to algebraic constraints. The AMPL processor simplifies problems, as discussed in more detail below, but calls on separate solvers to actually
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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. 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...