C301 Normal Frequency Function

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Function subprograms FREQ and DFREQ compute the normal frequency function

$freq (x)$ ${1 2π}∫$ _-&inf;^xe^-{12}t² dt,

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

$freq (x) =$

${1 2}+ {1 2} erf (x/ 2)$ $(x≥0),$

${1 2} erfc (|x|/ 2)$ $(x<0).$

$.$

Accuracy:

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

References:

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

•

Janne Saarela
Mon Apr 3 15:06:23 METDST 1995

${1 2}+ {1 2} erf (x/ 2)$	$(x≥0),$
${1 2} erfc (\|x\|/ 2)$	$(x<0).$