Algorithm 693: a FORTRAN package for floating-point multiple-precision arithmetic

ABSTRACT

FM is a collection of FORTRAN-77 routines which performs floating-point multiple-precision arithmetic and elementary functions. Results are almost always correctly rounded, and due to improved algorithms used for elementary functions, reasonable efficiency is obtained.

REFERENCES

• 1: Jon Bentley, Programming pearls, ACM Press, New York, NY, 1986
• 2: Jon Louis Bentley, Writing Efficient Programs, Prentice Hall PTR, Upper Saddle River, NJ, 1982
• 3: Cheryl M. Black , Robert Burton and Thomas H. Miller, The Need for an Industry Standard of Accuracy for Elementary-Function Programs, ACM Transactions on Mathematical Software (TOMS), v.10 n.4, p.361-366, Dec. 1984 [doi>10.1145/2701.356101]
• 4: BRENT, R. P. The complexity of multiple-precision arithmetic. In Complexity of Computational Problem Solwng, R. S. Anderssen and R. P. Brent, Eds., University of Queensland Press, Brisbane, 1976, 126-165.
• 5: Richard P. Brent, Fast Multiple-Precision Evaluation of Elementary Functions, Journal of the ACM (JACM), v.23 n.2, p.242-251, April 1976 [doi>10.1145/321941.321944]
• 6: 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]
• 7: Fred D. Crary, A Versatile Precompiler for Nonstandard Arithmetics, ACM Transactions on Mathematical Software (TOMS), v.5 n.2, p.204-217, June 1979 [doi>10.1145/355826.355834]
• 8: KAHAN, W. M. And now for something completely different: The TI SR-52. Univ. of California, Berkeley Electronics Research Lab Rep. UCB/ERL M77/23, Apr. 1977.
• 9: KAHAN, W.M. Can you count on your calculator? Univ. of California, Berkeley Electronics Research Lab. Rep. UCB/ERL M77/21, Apr. 1977.
• 10: KAHAN, W. M. Implementation of algorithms. Univ. of California, Berkeley Computer Science Tech. Rep. 20, 1973. Also distributed by National Technical Information Service under DDC AD-769 124.
• 11: Donald E. Knuth, The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms, Addison-Wesley Longman Publishing Co., Inc., Boston, MA, 1997
• 12: RAMANUJAN, S. Modular equations and approximations to ~r. Q. J. Math. 45 (1914), 350-372. Also in Collected Papers ofSrtnivasa Ramanujan, G. H. Hardy, P. V. Seshu Aiyar, and B. M. Wilson, Eds., Cambridge University Press, 1927, 23-39.
• 13: SHANKS, D., AND WRENC~t, J.W. Calculation of ~r to 100,000 places. Math. Comput. 16 (1962), 76-99.
• 14: SMITH, D.M. Efficient multiple-precision evaluation of elementary functions. Math. Comput. 52 (1989), 131-134.

INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.0 General
          Subjects: Numerical algorithms

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

          Nouns: FORTRAN 77

General Terms:
Algorithms

Keywords:
FORTRAN, accuracy, arithmetic elementary function evaluation, floating point, mathematical library, multiple precision portable software