Exact real arithmetic for interval number systems

Exact real arithmetic for interval number systems

An interval number system is given by an initial interval cover of the extended real line and by a finite system of nonnegative Möbius transformations. Each sequence of transformations applied to an initial interval determines a sequence of nested intervals whose intersection contains a unique real number. We adapt in this setting exact real algorithms which compute arithmetical operations to a...

Exact Real Arithmetic Systems: Results of Competition

Exact real arithmetic for Tcl

Once in a great while, the programmer has need for floating point arithmetic in greater precision than the hardware provides. This capability is usually not performance critical, since most performance critical code deals with measured quantities in the physical world, where it is hard to imagine a measurement precision that exceeds the sixteen or so decimal digits provided by standard IEEE-754...

Exact Real Arithmetic ?

One possible approach to exact real arithmetic is to use linear fractional transformations to represent real numbers and computations on real numbers. We show how to determine the digits that can be emitted from a transformation, and present a criterion which ensures that it is possible to emit a digit. Using these results, we prove that the obvious algorithm to compute n digits from the applic...

Lazy Algorithms for Exact Real Arithmetic

In this article we propose a new representation for the real numbers. This representation can be conveniently used to implement exact real number computation with a lazy programming languages. In fact the new representation permits the exploitation of hardware implementation of arithmetic functions without generating the granularity problem. Moreover we present a variation of the Karatsuba algo...