C300: Error Function and Complementary Error Function

Author(s): G.A. Erskine Library: MATHLIB or Fortran Compiler Library
Submitter: K.S. Kölbig Submitted: 20.04.1970
Language: Fortran Revised: 07.06.1992

Function subprograms ERF, ERFC and DERF, DERFC compute the error and complementary error functions

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defined for all values of the real argument x.

On CDC and Cray computers, the double-precision versions DERF and DERFC are not available.

Structure:

FUNCTION subprograms
User Entry Names: ERF, ERFC, DERF, DERFC

Usage:

In any arithmetic expression,

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where ERF, ERFC, are of type REAL, DERF, DERFC, are of type DOUBLE PRECISION, and X has the same type as the function name.

Method:

Computation by rational Chebyshev approximation.

Accuracy:

The system-supplied versions (see Notes) have full machine accuracy. The CERN-supplied versions of ERF and ERFC have full single-precision accuracy (slightly less on CDC and Cray computers). The CERN-supplied versions of DERF and DERFC have an accuracy of 15 significant digits.

Notes:

On some computers, one or both of these functions is available in the system-supplied Fortran mathematical library. In this case the system-supplied version will be loaded instead of the CERN version.

References:

  1. W.J. Cody, Rational Chebyshev approximations for the error function, Math. Comp. 22 (1969) 631-637.
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Michel Goossens Tue Jun 4 20:58:32 METDST 1996