Algorithm 737: INTLIB—a portable Fortran 77 interval standard-function library
ACM Transactions on Mathematical Software (TOMS)
Pascal-XSC: Language Reference with Examples
Pascal-XSC: Language Reference with Examples
Computer Arithmetic in Theory and Practice
Computer Arithmetic in Theory and Practice
C-XSC: A C++ Class Library for Extended Scientific Computing
C-XSC: A C++ Class Library for Extended Scientific Computing
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
A Modified Staggered Correction Arithmetic with Enhanced Accuracy and Very Wide Exponent Range
Numerical Validation in Current Hardware Architectures
C-XSC and Closely Related Software Packages
Numerical Validation in Current Hardware Architectures
Complex inclusion functions in the CoStLy C++ class library
ICMS'10 Proceedings of the Third international congress conference on Mathematical software
Arbitrary precision complex interval computations in C-XSC
PPAM'11 Proceedings of the 9th international conference on Parallel Processing and Applied Mathematics - Volume Part II
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The practical calculation of range bounds for some complex standard functions is addressed in this article. The functions under consideration are root and power functions, the exponential, trigonometric and hyperbolic functions, and their inverse functions. For such a function f and a given rectangular complex interval z, some interval w is computed that contains all function values of f in z. This is done by expressing the real and the imaginary part of f as compositions of real standard functions and then estimating the ranges of these compositions. In many cases, the inclusions are optimal, such that w is the smallest rectangular interval containing the range of f. The algorithms presented in this article have been implemented in a C++ class library called CoStLy (Complex Standard Functions License), which is distributed under the conditions of the GNU General Public License.