IEEE oating-point arithmetic standards 754 and 854 re ect the present state of the art in designing and implementing oating-point arithmetic units. A formalism applied to a standard non-trapping mode oating-point system shows incorrectness of some numeric and non-numeric results. A software emulation of decimal oating-point computer arithmetic supporting an enhanced set of exception symbols is ...

The common approach to real arithmetic on computers is floating point arithmetic, which can produce erroneous results due to roundoff errors. An alternative is exact real arithmetic and in this project such arithmetic is implemented in the well-known computer system Mathematica by the use of constructive real numbers. All basic operations are implemented as well as the common elementary functio...

The strong connection between mathematics and informatics highlights the important role of scientific computing in many applications. Unfortunately, is traditionally taught without investigating possible connections abstract problem solving use algorithms capable being implemented on a computer. Since mathematical theory practice are separately, students fail to appreciate utility mathematics. ...

This is a short introduction to an implementation of interval arithmetic data structures and operations for the Maxima computer algebra system. We expect that further algorithms necessary to implement the forthcoming IEEE 1788 standard for interval arithmetic can be readily fit into this structure.

Decimal computer arithmetic is experiencing a revived popularity, and there is quest for highperformance decimal hardware units. Successful experiences on binary computer arithmetic may find grounds in decimal arithmetic. For example, the traditional fully redundant (i.e., the result and both of the operands are represented in a redundant format) and semi-redundant (i.e., the result and only on...

Being algebraic completion of the conventional interval arithmetic, the arithmetic on extended (proper and improper) intervals possesses group and other algebraic properties suitable for implementation in computer algebra systems. We give an overview of a Mathematica package directed.m supporting the completed set of intervals and discuss the bene ts, provided by this package, for doing numeric...

This is a short introduction to an implementation of interval arithmetic data structures and operations for the Maxima computer algebra system. We expect that further algorithms necessary to implement the forthcoming IEEE 1788 standard for interval arithmetic can be readily fit into this structure.