NESC0610 FUNPACK RELEASE 2
FUNPACK-2, Subroutine Library, Bessel Function, Elliptical Integrals, Minimax Approximation
NAME OR DESIGNATION OF PROGRAM, COMPUTER, DESCRIPTION OF PROBLEM OR FUNCTION, METHOD OF SOLUTION, RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM, TYPICAL RUNNING TIME, UNUSUAL FEATURES OF THE PROGRAM, RELATED AND AUXILIARY PROGRAMS, STATUS, REFERENCES, MACHINE REQUIREMENTS, LANGUAGE, OPERATING SYSTEM UNDER WHICH PROGRAM IS EXECUTED, OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS, NAME AND ESTABLISHMENT OF AUTHOR, MATERIAL, CATEGORIES
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| 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 |
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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
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
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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.
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.
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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.
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.
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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.
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.
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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
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
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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
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
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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 |
Keywords: Bessel functions, errors, gamma function, integrals, special functions.