NESC0601 ERF/ERFC

ERF/ERFC, Calculation of Error Function, Complementary Error Function, Probability Integrals

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, REFERENCE, MACHINE REQUIREMENTS, LANGUAGE, OPERATING SYSTEM UNDER WHICH PROGRAM IS EXECUTED, OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS, NAME AND ESTABLISHMENT OF AUTHOR, MATERIAL, CATEGORIES

[ top ]

1. NAME OR DESIGNATION OF PROGRAM: ERF/ERFC

[ 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
ERF/ERFC	NESC0601/01	Tested	18-OCT-1983

Machines used:

Package ID	Orig. computer	Test computer
NESC0601/01	CDC CYBER 740	CDC CYBER 740

[ top ]

3. DESCRIPTION OF PROBLEM OR FUNCTION

ERF  and  ERFC  are  used  to
compute  values of  the  error  function and  complementary  error
function for any  real number.  They may be used  to compute other
related functions such as the normal probability integrals.

[ top ]

4. METHOD OF SOLUTION

The  error function  and complementary  error
function  are  approximated  by rational  functions.   Three  such
rational approximations are used depending on whether -
   ^x^.LT.0.46875,
   0.46875.LE.^x^.LT.4.0, or
   ^x^.GE.4.0.
In the  first region the error  function is computed  directly and
the  complementary error  function is  computed  via the  identity
erfc(x)=1.0-erf(x).  In  the other  two regions  the complementary
error  function is  computed directly  and the  error function  is
computed from the identity erf(x)=1.0-erfc(x).  The error function
and complementary error function are  real-valued functions of any
real argument.   The range of the  error function is  (-1,1).  The
range of the complementary error functon is (0,2).

[ top ]

5. RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM

The    user     is
cautioned against  using ERF  to compute  the complementary  error
function   by  using   the   identity  erfc(x)=1.0-erf(x).    This
subtraction may  cause partial or  total loss of  significance for
certain values of x.

[ top ]

6. TYPICAL RUNNING TIME

Running time depends on the argument value
and will vary between 70 and 110 microseconds.
NEA-DB executed the test cases included in the package (NESC0601/01) on CDC CYBER 740 in 108 seconds of CPU time.

[ top ]

7. UNUSUAL FEATURES OF THE PROGRAM:

[ top ]

8. RELATED AND AUXILIARY PROGRAMS

This package is a modification of
ALO-00241 transferred from the ALO-COSMIC collection.

[ top ]

9. STATUS

Package ID	Status date	Status
NESC0601/01	18-OCT-1983	Tested at NEADB

[ top ]

10. REFERENCE

J. E. Vogel, ERF and ERFC: Mathematical Routines for
Computing the Error Function and Complementary Error Function, SC-
M-70-275, May 1970.

[ top ]

11. MACHINE REQUIREMENTS

ERF and ERFC each require about 260 (octal)
locations.
NEA-DB ran the test case on CDC CYBER 740 in 26,100 octal words of main storage.

[ top ]

12. PROGRAMMING LANGUAGE(S) USED

Package ID	Computer language
NESC0601/01	FORTRAN-IV

[ top ]

13. OPERATING SYSTEM UNDER WHICH PROGRAM IS EXECUTED: SCOPE.

[ top ]

14. OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS:

[ top ]

15. NAME AND ESTABLISHMENT OF AUTHOR

                 J. E. Vogel
                 Sandia Laboratories
                 P. O. Box 5800
                 Albuquerque, New Mexico  87115

[ top ]

16. MATERIAL AVAILABLE

NESC0601/01

File name	File description	Records
NESC0601_01.003	ERF/ERFC INFORMATION FILE	42
NESC0601_01.004	ERF/ERFC SOURCE + DATA	177
NESC0601_01.005	ERF/ERFC JCL	13
NESC0601_01.006	ERF/ERFC OUTPUT	16

[ top ]

17. CATEGORIES

P. General Mathematical and Computing System Routines

Keywords: data processing, error function, probability.