C301: Normal Frequency Function

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

Function subprograms FREQ and DFREQ compute the normal frequency function

defined for all values of the real argument x.

On CDC and Cray computers, the double-precision version DFREQ is not available.

Structure:

FUNCTION subprograms
User Entry Names: FREQ, DFREQ

Usage:

In any arithmetic expression,

FREQ(X) or DFREQ(X) has the value freq(X),

where FREQ is of type REAL, DFREQ is of type DOUBLE PRECISION, and X has the same type as the function name.

Method:

Computation by rational Chebyshev approximation for the error function, using the formula

Accuracy:

FREQ has full single-precision accuracy (slightly less on CDC and Cray computers). DFREQ has an accuracy of 15 significant digits.

References:

1. W.J. Cody, Rational Chebyshev approximations for the error function, Math. Comp. 22 (1969) 631-637.