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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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Cited by 22 (3 self)
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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.
Experience with a Primal Presolve Algorithm
 IN LARGE SCALE OPTIMIZATION: STATE OF THE
, 1994
"... Sometimes an optimization problem can be simplified to a form that is faster to solve. Indeed, sometimes it is convenient to state a problem in a way that admits some obvious simplifications, such as eliminating fixed variables and removing constraints that become redundant after simple bounds on th ..."
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Cited by 13 (4 self)
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Sometimes an optimization problem can be simplified to a form that is faster to solve. Indeed, sometimes it is convenient to state a problem in a way that admits some obvious simplifications, such as eliminating fixed variables and removing constraints that become redundant after simple bounds on the variables have been updated appropriately. Because of this convenience, the AMPL modeling system includes a "presolver" that attempts to simplify a problem before passing it to a solver. The current AMPL presolver carries out all the primal simplifications described by Brearely et al. in 1975. This paper describes AMPL's presolver, discusses reconstruction of dual values for eliminated constraints, and presents some computational results.
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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Cited by 2 (0 self)
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This paper was written for the proceedings of a seminar on "Symbolicalgebraic
LowPower FloatingPoint Encoding For Signal Processing Applications
"... IEEE organization defined a standard for floatingpoint arithmetic, used by processing systems, in its directive 754 [1]. This directive encodes floatingpoint numbers using a maximum of 64 bits: 23 bit of fractional as single precision format and 52 bit of fractional as double precision format. The ..."
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IEEE organization defined a standard for floatingpoint arithmetic, used by processing systems, in its directive 754 [1]. This directive encodes floatingpoint numbers using a maximum of 64 bits: 23 bit of fractional as single precision format and 52 bit of fractional as double precision format. The new multimedia terminals require lowpower applications; the most important floatingpoint units (adders and multipliers) represent a significant part of total power wasted by a modern SystemOnChip. They might dissipate less power, using a reduced format representation. To verify this possibility, real systems simulate floating  point operations using different formats. In this conference paper, multimedia systems operate in different scenarios: wireless communication and image manipulation.
Numerical Issues and Influences in the Design of Algebraic Modeling Languages for Optimization
"... The idea of a modeling language is to describe mathematical problems symbolically in a way that is familiar to people but that allows for processing by computer systems. In particular the concept of an algebraic modeling language, based on objective and constraint expressions in terms of decision va ..."
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The idea of a modeling language is to describe mathematical problems symbolically in a way that is familiar to people but that allows for processing by computer systems. In particular the concept of an algebraic modeling language, based on objective and constraint expressions in terms of decision variables, has proved to be valuable for a broad range of optimization and related problems. One modeling language can work with numerous solvers, each of which implements one or more optimization algorithms. The separation of model specification from solver execution is thus a key tenet of modeling language design. Nevertheless, several issues in numerical analysis that are critical to solvers are also important in implementations of modeling languages. Socalled presolve procedures, which tighten bounds with the aim of eliminating some variables and constraints, are numerical algorithms that require carefully chosen tolerances and can benefit from directed roundings. Correctly rounded binarydecimal conversion is valuable in portably conveying problem instances and in debugging. Further rounding options offer tradeoffs between accuracy, convenience, and readability in displaying