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Arbitrary-Precision Floating Point
2017Floating-Point numbers using the IEEE standard have a fixed number of bits associated with them. This limits the precision with which they can represent actual real numbers. In this chapter we examine arbitrary precision, also called multiple precision, floating-point numbers. We look at how they are represented in memory and how basic arithmetic works.
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Arbitrary accuracy with variable precision arithmetic
1986For the calculation of interval-solutions Y including the true solution y of a given problem we need not only that y∈Y holds. Furthermore we are interested in the value of span(Y). So we should get that for an a priori and arbitrarily given bound ɛ>0 the calculation yields that the error remains below ɛ or that span(Y) 0 by using an interval ...
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Software Implementation of Numerical Algorithms in Arbitrary Precision
2013 15th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, 2013We introduce a Matlab mprec arbitrary precision library with applications to numerical analysis. For maximum efficiency arithmetic operators and algebraic functions are implemented in the mpreal class. The examples are chosen to reflect the diversity of types of problems for which multiple precision can play a useful role.
Zinovi L. Krougly +2 more
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Algorithms for arbitrary precision floating point arithmetic
[1991] Proceedings 10th IEEE Symposium on Computer Arithmetic, 2002The author presents techniques for performing computations of very high accuracy using only straightforward floating-point arithmetic operations of limited precision. The validity of these techniques is proved under very general hypotheses satisfied by most implementations of floating-point arithmetic. To illustrate the applications of these techniques,
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An arbitrary precision real arithmetic package in REDUCE
1979A REDUCE arbitrary precision real arithmetic package is described which will become a part of the kernel of an algebraic-numeric system being developed for REDUCE. The basic design principles of this package are first, it is as efficient as possible in both calculation speed and memory usage, second, even a casual user can use it, and third, it is ...
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Computing the Incomplete Gamma Function to Arbitrary Precision
2003I consider an arbitrary-precision computation of the incomplete Gamma function from the Legendre continued fraction. Using the method of generating functions, I compute the convergence rate of the continued fraction and find a direct estimate of the necessary number of terms.
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Experiments in Calculation with Arbitrary Numerical Precision
2023In programming language design projects, there is often a limitation on the maximum size allocated for certain variable types. This constraint poses challenges for applications that require more precise representation of numbers with a higher number of digits than the language’s capacity allows.
Machado dos Santos, Nathan +4 more
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On implementing arbitrary precision arithmetic in NIL
ACM SIGSAM Bulletin, 1980NIL, currently under development at MIT's Laboratory for Computer Science, is the "New Implementation of Lisp" intended for the latest generation of large address space computers. This system is being developed in Lisp itself (following the successful pattern of the Lisp Machine Project at MIT), and among other goals, eliminates a few internal ...
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Towards Semantic Category Verification with Arbitrary Precision
2011Many tasks related to or supporting information retrieval, such as query expansion, automated question answering, reasoning, or heterogeneous database integration, involve verification of a semantic category (e.g. "coffee" is a drink, "red" is a color, while "steak" is not a drink and "big" is not a color). We present a novel framework to automatically
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Arbitrary Precision Complex Interval Computations in C-XSC
2012Based on the libraries MPFR and MPFI for arbitrary precision real and arbitrary precision real interval computations and corresponding interfaces to the C++ class library C-XSC, the new data type MpfciClass (multiple precision floating-point complex intervals) and corresponding operations/functions for arbitrary precision complex intervals have been ...
Walter Krämer, Frithjof Blomquist
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