last modified: 01-APR-1975 | catalog | categories | new | search |

NESC0610 FUNPACK RELEASE 2

FUNPACK-2, Subroutine Library, Bessel Function, Elliptical Integrals, Minimax Approximation

top ]
1. NAME OR DESIGNATION OF PROGRAM:  FUNPACK Release 2
top ]
2. COMPUTERS
To submit a request, click below on the link of the version you wish to order. Only liaison officers are authorised to submit online requests. Rules for requesters are available here.
Program name Package id Status Status date
FUNPACK-2 NESC0610/01 Tested 01-OCT-1977

Machines used:

Package ID Orig. computer Test computer
NESC0610/01 IBM 370 series IBM 370 series
top ]
3. DESCRIPTION OF PROBLEM OR FUNCTION

FUNPACK  is a  collection  of
FORTRAN subroutines  to evaluate  certain special  functions.  The
individual subroutines are -
IDENTIFICATION  DESCRIPTION
NATSI0    F2I0  Bessel function I-sub-0
NATSI1    F2I1  Bessel function I-sub-1
NATSJ0    F2J0  Bessel function J-sub-0
NATSJ1    F2J1  Bessel function J-sub-1
NATSK0    F2K0  Bessel function K-sub-0
NATSK1    F2K1  Bessel function K-sub-1
NATSBESY  F2BY  Bessel function Y-sub-nu
DAW       F1DW  Dawson's integral
DELIPK    F1EK  Complete elliptic integral of the first kind
DELIPE    F1EE  Complete elliptic integral of the second kind
DEI       F1EI  Exponential integrals
NATSPSI   F2PS  Psi (logarithmic derivative of gamma function)
MONERR    F1MO  Error monitoring package
top ]
4. METHOD OF SOLUTION

FUNPACK    uses   evaluation    of    minimax
approximations.
top ]
5. RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM:
top ]
6. TYPICAL RUNNING TIME:
top ]
7. UNUSUAL FEATURES OF THE PROGRAM

These    routines   have    been
certified under  the NATS project  for the machines  and operating
systems indicated  in item 13 and  for the compilers  indicated in
item  12.   Extensive  testing  on these  machines  has  shown  no
evidence of performance difficulties.  Exceptions follow -
   CDC versions  of these  subroutines are  tuned to  perform best
using the rounded arithmetic option on CDC compilers.
   The accuracy  of the subroutines  for the  elementary functions
(EXP, ALOG, etc.) can affect the accuracy of FUNPACK subroutines.
   The  IBM  version  of this  package  assumes  the  IBM-supplied
traceback subroutine ERRTRA is available.
   The NATS project fully supports certified routines in the sense
that reports  of poor  or incorrect  performance on  at least  the
machines  and  operating  systems  listed  will  be  examined  and
necessary  corrections made.   This assurance  of support  applies
only  when the  software is  obtained directly  from the  National
Energy Software Center and has not been modified.
top ]
8. RELATED AND AUXILIARY PROGRAMS

FUNPACK   Release    2   replaces
FUNPACK, an earlier package submitted in July 1973 and distributed
by the Center as NESC No.  610 prior to this release.  Subroutines
identified  as  F1xx in  item  3  above  are unmodified  from  the
previous release, with the possible exception of the test material
for the IBM machines.
top ]
9. STATUS
Package ID Status date Status
NESC0610/01 01-OCT-1977 Tested at NEADB
top ]
10. REFERENCES

J.  M.  Blair  and C.  A.  Edwards,  Stable  Rational
Minimax Approximations to the Modified  Bessel Functions I0(x) and
I1(x), AECL-4928, 1974.
             J.  M.  Blair  and A.  E.  Russon,  Rational  Minimax
Approximations  for   the  Bessel   Functions  K0(x)   and  K1(x),
AECL-3461, 1969.
             W. J. Cody, Chebyshev Approximations for the Complete
Elliptic Integrals K  and E, Mathematics of  Computation, Vol. 19,
pp. 105-112, 1965.
             W. J.  Cody, R. M. Motley,  and L. W.  Fullerton, The
Computation  of Real  Fractional  Order  Bessel Functions  of  the
Second Kind, Applied Mathematics Division Technical Memorandum No.
291, Argonne National Laboratory, 1976.
             W. J. Cody,  K. A. Paciorek, and H.  C. Thacher, Jr.,
Chebyshev  Approximations for  Dawson's  Integral, Mathematics  of
Computation, Vol. 24, pp. 171-178, 1970.
             W. J. Cody, A. J. Strecok, and Henry C. Thacher, Jr.,
Chebyshev  Approximations for  the  Psi  Function, Mathematics  of
Computation, Vol. 27, pp. 123-127, 1973.
             W.  J.  Cody  and Henry  C.  Thacher,  Jr.,  Rational
Chebyshev  Approximations  for  the  Exponential  Integral  E1(x),
Mathematics of Computation, Vol. 22, pp. 641-649, 1968.
             W.  J.  Cody  and Henry  C.  Thacher,  Jr.,  Rational
Chebyshev  Approximations  for  the  Exponential  Integral  Ei(x),
Mathematics of Computation, Vol. 23, pp. 289-303, 1969.
top ]
11. MACHINE REQUIREMENTS:
top ]
12. PROGRAMMING LANGUAGE(S) USED
Package ID Computer language
NESC0610/01 FORTRAN-IV
top ]
13. OPERATING SYSTEM UNDER WHICH PROGRAM IS EXECUTED

   OS/360                          IBM360/67
   OS/360(19.6)                    IBM360/65
   OS/360(20.1)                    IBM370/165
   OS/360(20.7)                    IBM360/75,195
   OS/360(21.0)                    IBM360/75,91
   OS/360(21.7)                    IBM360/75,370/195
   OS/360(21.8)                    IBM360/75
   OS/MVT(21.7)                    IBM370/165-II
   OS/MVT(21.8)                    IBM360/65,91,IBM370/158
   OS/VS2(1.6)                     IBM370/168
   MTS                             IBM360/67,AMDAHL470V/6
   Stanford University             IBM360/67
   Purdue University               CDC6500,6400-6500
   Lawrence Berkeley Laboratory    CDC6600,7600
   Lawrence Livermore Laboratory   CDC6600,7600
   NCAR                            CDC6600,7600
   SCOPE(3.3)                      CDC6400
   SCOPE(3.4)                      CDC6600
   UT2D                            CDC6600-6400
   EXEC 8                          UNIVAC1108
   EXEC 31.244E                    UNIVAC1108
   EXEC MACC 31.66                 UNIVAC1110
top ]
14. OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS

   Locations and machines used for FUNPACK testing were -
            Machine                    Test Site
       IBM360/65,IBM370/158   Ames Laboratory, Iowa State
       IBM360/75,195,370/195  Argonne National Laboratory
       IBM360/75,91           Oak Ridge National Laboratory
       IBM360/67,91,370/168   Stanford University
       IBM360/75              Stockholm Data Center
       IBM360/65              The University of Chicago
       IBM360/75              University of Illinois at
       IBM360/67,AMDAHL470V/6 The University of Michigan
       IBM360/67              The University of New Mexico
       IBM370/165,165-II      University of Toronto
       CDC6600                Kirtland Air Force Base/AFWL
       CY173,175              ICASE/NASA Langley Research Center
       CDC6600,7600           Lawrence Berkeley Laboratory
       CDC6600,7600           Lawrence Livermore Laboratory
       CDC6600,7600           National Center for Atmospheric
       CDC6400                Northwestern University
       CDC6400-6500           Purdue University
       CDC6600-6400           The University of Texas at Austin
       UNIVAC1108             Illinois Institute of Technology
       UNIVAC1108             Jet Propulsion Laboratory
       UNIVAC1108,1110        University of Wisconsin
top ]
15. NAME AND ESTABLISHMENT OF AUTHOR

   Author        W. J. Cody
   Contact       Burton S. Garbow
                 Applied Mathematics Division
                 Argonne National Laboratory
                 9700 South Cass Avenue
                 Argonne, Illinois  60439
top ]
16. MATERIAL AVAILABLE
NESC0610/01
File name File description Records
NESC0610_01.001 INFORMATION 29
NESC0610_01.002 FUNPACK-2 SOURCE - F4 EBCDIC 3902
NESC0610_01.003 DEMONSTRATION PROGRAM 2083
NESC0610_01.004 DOCUMENTATION 4532
NESC0610_01.005 JOB CONTROL CARDS 17
NESC0610_01.006 SAMPLE PROBLEM PRINTED OUTPUT (BESI0) 208
NESC0610_01.007 SAMPLE PROBLEM PRINTED OUTPUT (BESI1) 222
NESC0610_01.008 SAMPLE PROBLEM PRINTED OUTPUT (BESJ0) 163
NESC0610_01.009 SAMPLE PROBLEM PRINTED OUTPUT (BESJ1) 175
NESC0610_01.010 SAMPLE PROBLEM PRINTED OUTPUT (BESK0) 225
NESC0610_01.011 SAMPLE PROBLEM PRINTED OUTPUT (BESK1) 232
NESC0610_01.012 SAMPLE PROBLEM PRINTED OUTPUT (BESYN) 391
NESC0610_01.013 SAMPLE PROBLEM PRINTED OUTPUT (DAW) 56
NESC0610_01.014 SAMPLE PROBLEM PRINTED OUTPUT (ELIPE) 193
NESC0610_01.015 SAMPLE PROBLEM PRINTED OUTPUT (ELIPK) 196
NESC0610_01.016 SAMPLE PROBLEM PRINTED OUTPUT (EXPEI) 313
NESC0610_01.017 SAMPLE PROBLEM PRINTED OUTPUT (PSI) 134
top ]
17. CATEGORIES
  • P. General Mathematical and Computing System Routines

Keywords: Bessel functions, errors, gamma function, integrals, special functions.