NESC9641 SPECFUN2.5.

1. NAME OR DESIGNATION OF PROGRAM:  SPECFUN2.5.

3. DESCRIPTION OF PROGRAM OR FUNCTION

SPECFUN is a collection of transportable FORTRAN subroutines and test drivers to evaluate certain special functions. The individual subroutines are -
   NAME    DESCRIPTION
   ALGAMA  Log gamma function
   DAW     Dawson's integral
   EI      Exponential integrals
   ERF     Error function
   ERFC    Complementary error function
   GAMMA   Gamma function
   I0      Bessel function I-sub-0
   I1      Bessel function I-sub-1
   J0Y0    Bessel functions J-sub-0 and Y-sub-0
   J1Y1    Bessel functions J-sub-1 and Y-sub-1
   K0      Bessel function K-sub-0
   K1      Bessel function K-sub-1
   PSI     Logarithmic derivative of the gamma function
   REN     Random number generator
   RIBESL  Bessel function I-sub-(N,ALPHA)
   RJBESL  Bessel function J-sub-(N,ALPHA)
   RKBESL  Bessel function K-sub-(N,ALPHA)
   RYBESL  Bessel function Y-sub-(N,ALPHA)
   MACHAR  Machine-dependent constants

4. METHOD OF SOLUTION

SPECFUN generally uses rational minimax approximations for functions of one variable and recurrence relations for functions of two or more variables.

5. RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM

Accuracy is targeted at between 18 and 20 significant decimal digits.

6. TYPICAL RUNNING TIME:

7. UNUSUAL FEATURES OF THE PROGRAM

Predetermined parameters for a selection of popular machines are included in COMMENTs at the top of SPECFUN programs. Conversion of a program for a particular machine is then a simple matter of determining the proper parameter values,  either from the given values or through computations based upon the  definitions supplied, and inserting them in DATA statements in the routine. The MACHAR program computes machine parameters from a built-in model of the arithmetic system.

8. RELATED AND AUXILIARY PROGRAMS

Ultimately SPECFUN will contain counterparts for all of the special function programs in FUNPACK2 (NESC 610) as well as programs for additional functions.

10. REFERENCES

- W.J. Cody
  FUNPACK - A Package of Special Function Routines,
  W.R. Cowell, Eds, Sources and Development of Mathematical
  Software, Prentice-Hall, Englewood Cliffs, New Jersey, pp. 49-67,
  1984.
- W.J. Cody
  Implementation and Testing of Function Software,
  P.C. Messina and A. Murli, Ed., Problems and methodologies in
  Mathematical Software Production, Springer-Verlag, New York, pp.
  24-47, 1982.

- W.J. Cody:
  SPECFUN - A Portable Special Function Package
  ANL-MCSD Memorandum, Received (October 1989).
- W.J. Cody and L. Stoltz:
  The Use of Taylor Series to Test Accuracy of Function Programs
  ANL-MCSD Memorandum (July 19, 1989).
- W.J. Cody:
  Performance Evaluation of Programs for the Error and Complementary
  Error Functions
  Preprint MCS-P13-0988 (September 1988).
- W.J. Cody:
  ALGORITHM 665 MACHAR - A Subroutine to Dynamically Determine
  Machine Parameters
  Reprint ACM Vol.14, No.4, PP. 303-311 (December 1988).
- W.J. Cody and L. Stoltz:
  Performance Evaluation of Program for Certain Bessel Functions
  Reprint ACM Vol.15, No.1, pp. 41-48 (March 1989).
- L. Eyberger:
  SPECFUN2.5 Tape Description and Implementation Note
  NESC Note 91-61 (March 14, 1991).

11. MACHINE REQUIREMENTS:

13. OPERATING SYSTEM UNDER WHICH PROGRAM IS EXECUTED:  designed to be operating system independent.

14. OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS

All precision-dependent source statements are duplicated. Statements peculiar to single-precision contain 'CS' in the first two characters, while their immediately following double-precision counterparts contain 'CD'. A precision-specific source is produced by global editing changes of the characters 'CS' or 'CD' to blanks in the first two characters of the appropriate source statements.

15. NAME AND ESTABLISHMENT OF AUTHORS

          W.J. Cody
          Mathematics and Computer Science Division
          Argonne National Laboratory

File name	File description	Records
NESC9641_02.001	Information file	98
NESC9641_02.002	JCL to run the test programs	285
NESC9641_02.003	Preprocessor FORTRAN source program	13
NESC9641_02.004	ALGAMA	283
NESC9641_02.005	DAW	261
NESC9641_02.006	EI	509
NESC9641_02.007	ERF	339
NESC9641_02.008	GAMMA	253
NESC9641_02.009	I0	270
NESC9641_02.010	I1	273
NESC9641_02.011	J0Y0	439
NESC9641_02.012	J1Y1	413
NESC9641_02.013	K0	282
NESC9641_02.014	K1	275
NESC9641_02.015	MACHAR	249
NESC9641_02.016	PSI	261
NESC9641_02.017	REN	38
NESC9641_02.018	RIBESL	440
NESC9641_02.019	RJBESL	506
NESC9641_02.020	RKBESL	493
NESC9641_02.021	RYBESL	442
NESC9641_02.022	ALGTST Test program for ALGAMA	277
NESC9641_02.023	DAWTST Test program for DAW	239
NESC9641_02.024	EITEST Test program for EI	387
NESC9641_02.025	ERFTST Test program for ERF	371
NESC9641_02.026	GAMTST Test program for GAMMA	250
NESC9641_02.027	I0TEST Test program for IO	383
NESC9641_02.028	I1TEST Test program for I1	382
NESC9641_02.029	J0TEST Test program for J0	303
NESC9641_02.030	J1TEST Test program for J1	325
NESC9641_02.031	K0TEST Test program for K0	267
NESC9641_02.032	K1TEST Test program for K1	288
NESC9641_02.033	PSITST Test program for PSI	234
NESC9641_02.034	RITEST Test program for RIBESL	503
NESC9641_02.035	RJTEST Test program for RJBELS	466
NESC9641_02.036	RKTEST Test program for RKBELS	331
NESC9641_02.037	RYTEST Test program for RYBELS	495
NESC9641_02.038	Y0TEST Test program for Y0	288
NESC9641_02.039	Y1TEST Test program for Y1	299
NESC9641_02.040	Output of test ALGTST	135
NESC9641_02.041	Output of test DAWTST	138
NESC9641_02.042	Output of test EITEST	251
NESC9641_02.043	Output of test ERFTST	201
NESC9641_02.044	Output of test GAMTST	153
NESC9641_02.045	Output of test I0TEST	115
NESC9641_02.046	Output of test I1TEST	115
NESC9641_02.047	Output of test J0TEST	94
NESC9641_02.048	Output of test J1TEST	117
NESC9641_02.049	Output of test K0TEST	89
NESC9641_02.050	Output of test K1TEST	91
NESC9641_02.051	Output of test PSITST	137
NESC9641_02.052	Output of test RITEST	167
NESC9641_02.053	Output of test RJTEST	138
NESC9641_02.054	Output of test RKTEST	115
NESC9641_02.055	Output of test RYTEST	144
NESC9641_02.056	Output of test Y0TEST	129
NESC9641_02.057	Output of test Y1TEST	106