High-accuracy arithmetic software—some tests of the ACRITH problem-solving routines

ABSTRACT

The program package ACRITH (High-Accuracy Arithmetic Subroutine Library) provides FORTRAN subroutines for the solution of several standard mathematical problems. The routines use floating point operations with extended precision and interval arithmetic and are designated especially for the solution of ill-conditioned problems. Test results for most of the routines are presented with emphasis on the practical usability of the package. It turns out that not all routines are of equal high quality and reliability; in the documentation, hints to the implemented numerical algorithms are completely missing, and the error messages are not always concise. Some possible alternatives like symbolic algebra systems or multiple precision packages are mentioned.

REFERENCES

• 1: ACRITH. High-Accuracy Arithmetic Subroutine Library Program Description and User's Guide, IBM, SC33-6164-1.
• 2: Richard P. Brent, A Fortran Multiple-Precision Arithmetic Package, ACM Transactions on Mathematical Software (TOMS), v.4 n.1, p.57-70, March 1978 [doi>10.1145/355769.355775]
• 3: CLINE, A. K. AND REW, R.K. A set of counter-examples to three condition number estimators. SIAM J. Sci. Stat. Comput. 4, 4 (Dec. 83), 602-611.
• 4: GREGORY, R. T. AND KARNEY, D. L. A Collection of Matrices for Testing Computational Algorithms. Robert E. Krieger, N.Y. 1978.
• 5: IMSL Library Reference Manual (9th ed.). IMSL, Houston, Texas 1982.
• 6: Rand REDUCE User's Manual, Version 3.1. Anthony C. Hearn Ed. Rand Publication CP78, Santa Monica, CA, 1984.
• 7: James H. Wilkinson, Rounding Errors in Algebraic Processes, Dover Publications, Incorporated, 1994
• 8: J. M. Yohe, Software for Interval Arithmetic: A Reasonably Portable Package, ACM Transactions on Mathematical Software (TOMS), v.5 n.1, p.50-63, March 1979 [doi>10.1145/355815.355819]

INDEX TERMS

Classification:
  D. Software
  D.3 PROGRAMMING LANGUAGES
      D.3.2 Language Classifications

          Nouns: FORTRAN

  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.0 General
          Subjects: Numerical algorithms
  G.4 MATHEMATICAL SOFTWARE
      Subjects: Reliability and robustness
      Nouns: ACRITH

  I. Computing Methodologies
  I.1 SYMBOLIC AND ALGEBRAIC MANIPULATION
      I.1.3 Languages and Systems

          Nouns: REDUCE

General Terms:
Algorithms