nag_erf (s15aec) (PDF version)
s Chapter Contents
s Chapter Introduction
NAG Library Manual

NAG Library Function Document

nag_erf (s15aec)


    1  Purpose
    7  Accuracy

1  Purpose

nag_erf (s15aec) returns the value of the error function erfx.

2  Specification

#include <nag.h>
#include <nags.h>
double  nag_erf (double x)

3  Description

nag_erf (s15aec) calculates an approximate value for the error function
Let x^ be the root of the equation erfcx-erfx=0 (then x^0.46875). For xx^ the value of erfx is based on the following rational Chebyshev expansion for erfx:
where R,m denotes a rational function of degree  in the numerator and m in the denominator.
For x>x^ the value of erfx is based on a rational Chebyshev expansion for erfcx: for x^<x4 the value is based on the expansion
and for x>4 it is based on the expansion
For each expansion, the specific values of  and m are selected to be minimal such that the maximum relative error in the expansion is of the order 10-d, where d is the maximum number of decimal digits that can be accurately represented for the particular implementation (see nag_decimal_digits (X02BEC)).
For xxhi there is a danger of setting underflow in erfcx (the value of xhi is given in the Users' Note for your implementation). For xxhi, nag_erf (s15aec) returns erfx=1; for x-xhi it returns erfx=-1.

4  References

Abramowitz M and Stegun I A (1972) Handbook of Mathematical Functions (3rd Edition) Dover Publications
Cody W J (1969) Rational Chebyshev approximations for the error function Math.Comp. 23 631–637

5  Arguments

1:     x doubleInput
On entry: the argument x of the function.

6  Error Indicators and Warnings


7  Accuracy

See Section 7 in nag_erfc (s15adc).

8  Parallelism and Performance

nag_erf (s15aec) is not threaded in any implementation.

9  Further Comments


10  Example

This example reads values of the argument x from a file, evaluates the function at each value of x and prints the results.

10.1  Program Text

Program Text (s15aece.c)

10.2  Program Data

Program Data (s15aece.d)

10.3  Program Results

Program Results (s15aece.r)

nag_erf (s15aec) (PDF version)
s Chapter Contents
s Chapter Introduction
NAG Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2016