Numerical Computation with Rational Number Arithmetic
نویسنده
چکیده
where a, b, c, d are multi-digit integers. Since the product of two n-digit integers becomes 2n-digit, every multiplication operation doubles number of digits of the numerator and the denominator. Rational number computation divides them by their GCD to get irreducible form after every operation. We develop a computing environment in which multi-digit integer such as a, b, c, d in above expressions can be defined by data type longint,
منابع مشابه
Computation with the Extended Rational Numbers and an Application to Interval Arithmetic
Programming languages such as Common Lisp and virtu ally every computer algebra system CAS support exact arbitrary precision integer arithmetic as well as exact ra tional number computation Several CAS include interval arithmetic directly but not in the extended form indicated here We explain why changes to the usual rational number system to include in nity and not a number may be use ful espe...
متن کاملSymbolic-Numeric Integration of Rational Functions
We consider the problem of symbolic-numeric integration of symbolic functions, focusing on rational functions. Using a hybrid method allows the stable yet efficient computation of symbolic antiderivatives while avoiding issues of ill-conditioning to which numerical methods are susceptible. We propose two alternative methods for exact input that compute the rational part of the integral using He...
متن کاملAn Exact Arithmetic Package for Ml
We present the design and implementation of an exact rational arithmetic package for the programming language Caml, an ML dialect close to the original LCF-ML. Our arithmetic, written almost entirely in Caml, combines eeciency, power and exibility. For eeciency reasons, the package provides several diier-ent basic types to represent numbers, and to reinforce exibility, it implements many functi...
متن کاملRational Arithmetic for Minicomputers
A representation for numbers using two computer words is discussed, where the value represented is the ratio of the corresponding integers. This allows for better dynamic range and relative accuracy than single-precision fixed point, yet is less costly than floating point arithmetic. The scheme is easy to implement and particularly well suited for minicomputer applications that call for a great...
متن کاملLCF: A Lexicagraphic Binary representation of the Rationals
A binary representation of the rationals derived from their continued fraction expansions is described and analysed. The concepts \adjacency", \mediant" and \convergent" from the literature on Farey fractions and continued fractions are suitably extended to provide a foundation for this new binary representation system. Worst case representation-induced precision loss for any real number by a x...
متن کامل