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NESC0601 ERF/ERFC

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

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1. NAME OR DESIGNATION OF PROGRAM:  ERF/ERFC
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2. COMPUTERS
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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
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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.
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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).
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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.
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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.
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7. UNUSUAL FEATURES OF THE PROGRAM:
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8. RELATED AND AUXILIARY PROGRAMS

This package is a modification of
ALO-00241 transferred from the ALO-COSMIC collection.
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9. STATUS
Package ID Status date Status
NESC0601/01 18-OCT-1983 Tested at NEADB
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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.
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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.
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12. PROGRAMMING LANGUAGE(S) USED
Package ID Computer language
NESC0601/01 FORTRAN-IV
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13. OPERATING SYSTEM UNDER WHICH PROGRAM IS EXECUTED:   SCOPE.
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14. OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS:
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15. NAME AND ESTABLISHMENT OF AUTHOR

                 J. E. Vogel
                 Sandia Laboratories
                 P. O. Box 5800
                 Albuquerque, New Mexico  87115
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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
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17. CATEGORIES
  • P. General Mathematical and Computing System Routines

Keywords: data processing, error function, probability.