Algorithm 737: INTLIB—a portable Fortran 77 interval standard-function library

ABSTRACT

INTLIB is meant to be a readily available, portable, exhaustively documented interval arithmetic library, written in standard Fortran 77. Its underlying philosophy is to provide a standard for interval operations to aid in efficiently transporting programs involving interval arithmetic. The model is the BLAS package, for basic linear algebra operations. The library is composed of elementary interval arithmetic routines, standard function routines for interval data and values, and utility routines. The library can be used with INTBIS (Algorithm 681), and a Fortran 90 module to use the library to define an interval data type is available from the first author.

REFERENCES

• 1: ALEFELD, G. AND HERZBERGER, J. 1983. Introduction to Interval Computations. Academic Press, New York.
• 2: B~AUNE, K. D. 1987. Hochgenaue standardfunktionen fdr reele und komplexe punkte und intervalle in beliebigen gleitpunktrastern. Ph.D. dissertation, Universit~t Karlsruhe.
• 3: CONNELL, A. AND CORLESS, R. M. 1993. An experimental interval arithmetic package in Maple. Interval Comput. 2, 120-134.
• 4: CORLISS, G. F. 1993. Comparing software packages for interval arithmetic. Preprint, Dept. of Mathematics, Marquette Univ., Milwaukee, Wisc.
• 5: CORLmS, G. F. 1991. Proposal for a Basic Interval Arithmetic Subroutines Library (BIAS). Preprint, Dept. of Mathematics, Marquette Univ., Milwaukee, Wisc.
• 6: CRARY, F. 1976. The AUGMENT precompiler. Tech. Report 1470, Mathematics Research Center, The Univ. of Wisconsin, Madison.
• 7: H^MMER, R., N~AGA, M., AND RATZ, D. 1993. PASCAL-XSC, New concepts for scientific computation and numerical data processing. In Sc~enti~c Computing' with Automatic Result Ver~fzcation. Academic Press, New York, 15-44.
• 8: HANSEN, E. R. 1992. Global Optimization using' Interval Analysis. Marcel Dekker, New York. Hu, C. AND KEARFOTT, R. B. 1993. On bounding the range of some elementary functions in FORTRAN 77. Interval Comput. 3, 29 39.
• 9: KAUCHER~ E. W. AND MmANK~R, W. L. 1984. Self-Validating Numerics for Function Space Problems. Academic Press, Orlando, Fla.
• 10: R. Baker Kearfott, A Fortran 90 environment for research and prototyping of enclosure algorithms for nonlinear equations and global optimization, ACM Transactions on Mathematical Software (TOMS), v.21 n.1, p.63-78, March 1995 [doi>10.1145/200979.200991]
• 11: R. Baker Kearfott , Manuel Novoa, III, Algorithm 681: INTBIS, a portable interval Newton/bisection package, ACM Transactions on Mathematical Software (TOMS), v.16 n.2, p.152-157, June 1990 [doi>10.1145/78928.78931]
• 12: KEARFOTT, R. B., DAWANDE, M., DU, K.-S., AND HU, C.-Y. 1992. INTLIB: A portable FORTRAN 77 elementary function library. Interval Comput. 3, 5, 96-105.
• 13: KEIPER, J. B. 1993. Interval arithmetic in mathematica. Interval Comput. 3, 76-87.
• 14: KNUPPEL, O. 1993. BIAS--Basic interval arithmetic subroutines. In the abstracts for the IMACS /GAMM International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics.
• 15: KORN, C. F. AND ULLRICH, C. 1993. Extending LINPACK by verification routines for linear systems. In the abstracts for the IMACS/GAMM International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics.
• 16: KR'~ER, W. 1987. Inverse standardfunktionen ~dr reelle und komplexe intervallargumente mit a priori fehlerabsch~itzungen. Ph.D. dissertation, Universit~t Karlsruhe.
• 17: KULISCH, U. W. AND MIRANKER, W. L. 1983. A New Approach to Scientific Computation. Academic Press, New York.
• 18: LAWO, C. 1993. C-XSC A programming environment for verified scientific computing and numerical data processing. In Scientific Computing with Automatic Result Verification. Academic Press, New York, 71-86.
• 19: C. L. Lawson , R. J. Hanson , D. R. Kincaid , F. T. Krogh, Basic Linear Algebra Subprograms for Fortran Usage, ACM Transactions on Mathematical Software (TOMS), v.5 n.3, p.308-323, Sept. 1979 [doi>10.1145/355841.355847]
• 20: LUTHER, W. AND OTTEN, W. 1993. Computation of standard interval functions in multipte~ precision interval arithmetic. Tech. Rep. SM-DU-233, Universit~t Duisburg.
• 21: Ramon E. Moore , Fritz Bierbaum, Methods and Applications of Interval Analysis (SIAM Studies in Applied and Numerical Mathematics) (Siam Studies in Applied Mathematics, 2.), Soc for Industrial & Applied Math, 1979
• 22: NEUMAmR, A. 1990. Interval Methods for Systems of Equations. Cambridge University Press, Cambridge, England.
• 23: WALTER, W. V. 1993a. FORTRAN-XSC: A portable Fortran 90 module library for accurate and reliable scientific computing. Computing Supplementum 9,265-286. Supplement.
• 24: WALTER, W. V. 1993b. ACRITH-XSC: A Fortran-like language for verified scientific computing. In Scientific Computing with Automatic Result Verification. Academic Press, New York, 45-70.

INDEX TERMS

Primary Classification:
  D. Software
  D.2 SOFTWARE ENGINEERING
      D.2.2 Design Tools and Techniques
          Subjects: Software libraries

Additional Classification:
  D. Software
  D.2 SOFTWARE ENGINEERING
      D.2.7 Distribution, Maintenance, and Enhancement
          Subjects: Portability; Documentation
  D.3 PROGRAMMING LANGUAGES
      D.3.2 Language Classifications

          Nouns: FORTRAN 77

  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.0 General
          Subjects: Computer arithmetic
      G.1.2 Approximation
          Subjects: Elementary function approximation

General Terms:
Algorithms

Keywords:
BLAS, Fortran 77, Fortran 90, interval arithmetic, operator overloading, standard functions