Algorithm 715: SPECFUN–a portable FORTRAN package of special function routines and test drivers

ABSTRACT

SPECFUN is a package containing transportable FORTRAN special function programs for real arguments and accompanying test drivers. Components include Bessel functions, exponential integrals, error functions and related functions, and gamma functions and related functions.

REFERENCES

• 1: RussoN, A. E., AND BLAIR, J.M. Rational function minimax approximations for the modifed Bessel functions Ko(x) and Kl(x). Atomic Energy of Canada Limited Rep. AECL-3461, Chalk River Nuclear Lab., Chalk River, Ontario, Oct. 1969.
• 2: BLAIR, J. M., AND EDWARDS, C.A. Stable rational minimax approximations to the modified Bessel functions In(x) and Ii(x). Atomic Energy of Canada Limited Rep. AECL-4928, Chalk River Nuc}{ear Lab., Chalk River, Ontario, Oct. 1974.
• 3: CAMPBELL, J.B. Bessel functions J,(x) and Y,,(x) of real order and real argument. Comput. Phys. Commun. 18 (1979), 133-142.
• 4: CAMPBELL, J.B. A FORTRAN IV subroutine fbr the modified Bessel functions of Lhe third kind of real order and real argument. Rep. NRC/ERB-925, Natmnal Research Council, Canada, 1980.
• 5: J. B. Campbell, On Temme's Algorithm for the Modified Bessel Function of the Third Kind, ACM Transactions on Mathematical Software (TOMS), v.6 n.4, p.581-586, Dec. 1980 [doi>10.1145/355921.355928]
• 6: ConY, W.J. Rational Chebyshev approximations for the error function. Math. Comput. 23 (1969), 631-637.
• 7: W. J. Cody, The FUNPACK Package of Special Function Subroutines, ACM Transactions on Mathematical Software (TOMS), v.1 n.1, p.13-25, March 1975 [doi>10.1145/355626.355631]
• 8: ConY, W.J. All overview of software development for special functions. In Lecture Notes tn Mathematics, 506, Numerical Analysts. G. A. Watson, Ed., Springer-Verlag, Berli{n, 1976, 38 48.
• 9: W. J. Cody, Algorithm 597: sequence of modified Bessel functions of the first kind, ACM Transactions on Mathematical Software (TOMS), v.9 n.2, p.242-245, June 1983 [doi>10.1145/357456.357462]
• 10: ConY, W. ~{. FUNPACK--A package of special function routines. In Sources and Development of Mathematical Software, W. R. Cowell, Ed., Prentice-Hall, Engtewood Cliffs, N.J., 1984, 49-67.
• 11: ConY, W.J. SPECFUN--A portable special function package. In New Computing Environments: Mwrocomputers in Large-Scale Scientific Computing, A. Wouk, Ed., SIAM, Philadelphia, 1987, 1-12.
• 12: W. J. Cody, Algorithm 665: Machar: a subroutine to dynamically determined machine parameters, ACM Transactions on Mathematical Software (TOMS), v.14 n.4, p.303-311, Dec. 1988 [doi>10.1145/50063.51907]
• 13: W. J. Cody, Performance evaluation of programs related to the real gamma function, ACM Transactions on Mathematical Software (TOMS), v.17 n.1, p.46-54, March 1991 [doi>10.1145/103147.103153]
• 14: W. J. Cody, Performance evaluation of programs for the error and complementary error functions, ACM Transactions on Mathematical Software (TOMS), v.16 n.1, p.29-37, March 1990 [doi>10.1145/77626.77628]
• 15: ConY, W. J., AND HILLSTROM, K.E. Chebyshev approximations for the natural logarithm of the gamma function. Math. Comput. 21 (1967), 198-203.
• 16: ConY, W. J., PACIOREK, K. A., AND THACHER, H. C., JR. Chebyshev approximations for Dawson's integral. Math. Comput. 24, i (1970), 171-178.
• 17: W. J. Cody , L. Stoltz, Performance evaluation of programs for certain Bessel functions, ACM Transactions on Mathematical Software (TOMS), v.15 n.1, p.41-48, March 1989 [doi>10.1145/62038.62039]
• 18: W. J. Cody , L. Stoltz, The use of Taylor series to test accuracy of function programs, ACM Transactions on Mathematical Software (TOMS), v.17 n.1, p.55-63, March 1991 [doi>10.1145/103147.103154]
• 19: ConY, W. J., STRECOK, A. J., ANn THACHER, H. C., JR. Chebyshev approximations for the psi function. Math. Comput. 27, i (1973), 123-127.
• 20: ConY, W. J., AND THACHER, H. C., JR. Rational Chebyshev approximations for the exponential integral El(x). Math. Cornput. 22 (1968), 641 649.
• 21: ConY, W. J., AND THACH~R, H. C., JR. Chebyshev approximations for the exponential integral Ei (x). Math. Comput. 23, 2 (1969), 289 303.
• 22: Walter Gautschi , Bruce J. Klein, Recursive computation of certain derivatives&a study of error propagation, Communications of the ACM, v.13 n.1, p.7-9, Jan. 1970 [doi>10.1145/361953.361959]
• 23: GAUTS('HI, W., AND KLEIN, B.J. Remark on Algorithm 282. Commun. ACM 13, i {1970), 53-54.
• 24: HART, J. F., ET AL. Coniput~r Approxtmatlons. Wiley, New York, 1979.
• 25: SOOKNE, D.J. Bessel functions of real argument and integer order. NBS J. Res. B 77B (1973), 125 132.
• 26: TEMME, N.M. On the numer:cal evaluation of the ordinary Bessel function of the second kind. J. Comput. Phys. 21, 3 (1976), 343-350.

INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.4 MATHEMATICAL SOFTWARE
      Subjects: Certification and testing

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

General Terms:
Algorithms

Keywords:
Bessel functions, error function, exponential integrals, gamma function