Algorithm 786: multiple-precision complex arithmetic and functions

ABSTRACT

This article describes a collection of Fortran routines for multiple-precision complex arithmetic and elementary functions. The package provides good exception handling, flexible input and output, trace features, and results that are almost always correctly rounded. For best efficiency on different machines, the user can change the arithmetic type used to represent the multiple-precision numbers.

REFERENCES

• 1: Milton Abramowitz, Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,, Dover Publications, Incorporated, 1974
• 2: David H. Bailey, Algorithm 719; Multiprecision translation and execution of FORTRAN programs, ACM Transactions on Mathematical Software (TOMS), v.19 n.3, p.288-319, Sept. 1993 [doi>10.1145/155743.155767]
• 3: David H. Bailey, A Fortran 90-based multiprecision system, ACM Transactions on Mathematical Software (TOMS), v.21 n.4, p.379-387, Dec. 1995 [doi>10.1145/212066.212075]
• 4: 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]
• 5: Paul Friedland, Algorithm 312: Absolute value and square root of a complex number, Communications of the ACM, v.10 n.10, p.665, Oct. 1967 [doi>10.1145/363717.363780]
• 6: T. E. Hull , Thomas F. Fairgrieve , Ping-Tak Peter Tang, Implementing complex elementary functions using exception handling, ACM Transactions on Mathematical Software (TOMS), v.20 n.2, p.215-244, June 1994 [doi>10.1145/178365.178404]
• 7: David M. Smith, Algorithm 693; a FORTRAN package for floating-point multiple-precision arithmetic, ACM Transactions on Mathematical Software (TOMS), v.17 n.2, p.273-283, June 1991 [doi>10.1145/108556.108585]
• 8: David M. Smith, A multiple-precision division algorithm, Mathematics of Computation, v.65 n.213, p.157-163, Jan. 1996 [doi>10.1090/S0025-5718-96-00688-6]
• 9: Robert L. Smith, Algorithm 116: Complex division, Communications of the ACM, v.5 n.8, p.435, Aug. 1962 [doi>10.1145/368637.368661]
• 10: Stephen Wolfram, Mathematica: a system for doing mathematics by computer (2nd ed.), Addison Wesley Longman Publishing Co., Inc., Redwood City, CA, 1991
• 11: WYNN, P. 1962. An arsenal of Algol procedures for complex arithmetic. Bit 2, 232-255.

INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.0 General
          Subjects: Computer arithmetic

Additional Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.2 Approximation
          Subjects: Elementary function approximation
  G.4 MATHEMATICAL SOFTWARE
      Subjects: Algorithm design and analysis; Efficiency

General Terms:
Algorithms, Performance, Reliability

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