The speed of digital Computers is ever increasing. While the emphasis in computing was traditionally on speed, more emphasis can now be put on accuracy and reliability of results. Numerical mathematics has devised algorithms which deliver highly accurate and automatically verified results by applying mathematical fixed-point theorems. This means that these computation carry their own accuracy control. However, their implementation requires suitable arithmetic support and powerful programming tools which are not generally available.
Different hardware solutions are available for Personal Computers, Workstations, Mainframes and Super Computers. In particular a vector arithmetic coprocessor for the PC has been developed in VLSI-technology. Language support is available on the basis of FORTRAN, PASCAL, and C (ACRITH-XSC, Fortran-XSC, PASCAL-XSC, and C- XSC). Problem-solving routines with automatic result verification have been developed for many standard problems of numerical analysis as for linear or nonlinear systems of equations, for differential and integral equations, etc. as well as for a large number of applications in the engineering and natural sciences.
Language eXtensions for Scientific Computation provide all features indispensable for modern numerical software development, such as
- Operator concept (user-defined operators)
- Overloading concept
- Module concept
- Dynamic arrays
- Controlled rounding
- Predefined arithmetic data types real, (extended real), complex, interval, complex interval, and corresponding vector and matrix types
- Predefined arithmetic operators of highest accuracy for the arithmetic data types
- Predefined elementary functions of highest accuracy for the arithmetic data types
- Data type dotprecision for the exact representation of dot products
- Library of mathematical problem-solving routines with automatic result verification and high accuracy