NAG Library Function Document

nag_erf (s15aec)

 Contents

    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
erfx=2π0xe-t2dt=1-erfcx.  
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:
erfxxR,mx2,  
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
erfcxex2R,mx;  
and for x>4 it is based on the expansion
erfcxex2x1π+1x2R,m1/x2.  
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

None.

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

None.

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)

© The Numerical Algorithms Group Ltd, Oxford, UK. 2017