PASCAL-XSC New Concepts for Scientific Computation and Numerical Data Processing

Abstract

The new programming language PASCAL XSC is presented with an emphasis on the new concepts for scienti c computation and numerical data processing of the PASCAL XSC compiler. PASCAL XSC is a universal PASCAL extension with extensive standard modules for scienti c computation. It is available for personal computers, workstations, mainframes and supercomputers by means of an implementation in C. By using the mathematical modules of PASCAL XSC, numerical algorithms which deliver highly accurate and automatically veri ed results can be programmed easily. PASCAL XSC simpli es the design of programs in engineering scienti c computation by modular program structure, user-de ned operators, overloading of functions, procedures, and operators, functions and operators with arbitrary result type, dynamic arrays, arithmetic standard modules for additional numerical data types with operators of highest accuracy, standard functions of high accuracy and exact evaluation of expressions. The most important advantage of the new language is that programs written in PASCAL XSC are easily readable. This is due to the fact that all operations, even those in the higher mathematical spaces, have been realized as operators and can be used in conventional mathematical notation. In addition to PASCAL XSC a large number of numerical problem-solving routines with automatic result veri cation are available. The language supports the development of such routines.

Scalar fused multiply-add instructions produce floating-point matrix arithmetic provably accurate to the penultimate digit

“…(6.2)], which restricts their portability, and they can make computations impractically slow [Overton 2001, p. 93]. Multiple-precision facilities embedded in higher-level languages, for instance, C and C-XSC [Lawo 1993], FORTRAN and ACRITH-XSC [Walter 1993], or PASCAL and PASCAL-XSC [Hammer et al 1993], require special compilers or hardware that simulate or implement, respectively, a fixed-point adder and accumulator of length greater than |2E max − 2E min | + 2m [Bleher 2001, p. 100;Bohlender and Grüner 1983, p. 259;Kulisch and Miranker 1986, p. 26]. For Intel's Itanium 17-bit exponent range and 64-bit mantissa, the floating-point accumulator would have to accommodate more than |2E max − 2E min | + 2m = 131 066 + 128 = 131 194 binary bits!…”

Interval extensions of non-smooth functions for global optimization and nonlinear systems solvers

“…Linear problems, they are based on fitting a line y = ax + b to the data set {(x i, yy)} = { (0,1), (1,4), (2,5), (3,8)} (3) in the 12, l I and l~ sense, respectively, as follows.…”

“…Traditionally, such methods have been implemented with subroutine packages for interval extensions, ad-hoc packages, or special commercial languages, such as the "SC" family or the "XSC" family developed at Karlsruhe ( [2], [5], [18], etc.). Recent work, such as described in [4,Ch.…”

Mechanising the theory of intervals using OBJ3

“…The programming languages Pascal-XSC [4], ACRITH-XSC [9], and C-XSC [6] are extensions of the programming languages Pascal, FORTRAN, and C++, respectively. These extensions, beyond the usual primitive data types, have the type £ntervat and the arithmetic operations are defined by the horizontal method [5].…”