NAG CL Interface
s15aec (erf_​real)

1 Purpose

s15aec returns the value of the error function erfx.

2 Specification

#include <nag.h>
double  s15aec (double x)
The function may be called by the names: s15aec, nag_specfun_erf_real or nag_erf.

3 Description

s15aec calculates an approximate value for the error function
erfx = 2π 0x e-t2 dt = 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:
erfx xR,m x2 ,  
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
erfcx ex2 R,m x ;  
and for x>4 it is based on the expansion
erfcx ex2 x 1π + 1x2 R,m 1/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 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, s15aec returns erfx=1; for x-xhi it returns erfx=-1.

4 References

NIST Digital Library of Mathematical Functions
Cody W J (1969) Rational Chebyshev approximations for the error function Math.Comp. 23 631–637

5 Arguments

1: x double Input
On entry: the argument x of the function.

6 Error Indicators and Warnings


7 Accuracy

See Section 7 in s15adc.

8 Parallelism and Performance

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)